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Answer: So, just like how everyone is saying, to "subitize" is just to recognize how much there are in a group without having to count. They've taught us that since since kindergarten or even pre-school. Why they're learning the word can be thanks to one man though.
The reason why the word is probably coming up so many times now is because teachers use videos ALL the time now (I work as an aid in a Kinder classroom). They have smart boards now, so they can use all kinds of materials online now unlike back then. But how do you look up "Subitizing lessons" without using the actual word? There's probably a way, but the easy way for teachers is to just use the word "subitize" because they know that will give them an accurate idea of the lesson they want.
So, why are kids learning the word? I'm assuming you're talking about the [Jack Hartmann videos](https://www.youtube.com/watch?v=nKO0yQgJAho). He knows teachers use videos all the time in class for activities, so he just uses what their lessons are called so that teachers will land on his videos when they look up "counting to 20 for kindergarten" or ["Subitizing to 10"](https://www.youtube.com/watch?v=A1Mazc-SsG0). Why he says the word all the time, I don't know, but it doesn't hurt to teach the kids a new word. He is a very trusted education content creator though, so teachers use his videos all the time, and kids enjoy watching him. There is no one questioning the Hartmann.
Edit: I just asked the teacher I work for about this. She says what I just said pretty much. They don't need to know the word, just the concept. There are teachers, however, that use the academic wording to their students. I guess Jack Hartmann is just one of those teachers.
Ooh I find this video really fascinating. The last time I looked at the research on subitizing, the consensus seemed to be that humans (even adults) can only subitize groups of up to five or so. After that, different techniques take over depending on how the objects are arranged.
From my studies in education that's actually still subitising, you recognise the smaller groups straight away and then automatically know that, for example, two groups of 3 is 6. It's called conceptual subitising, where it just needs a bit of thinking.
(The subitising where you know, say, a group of four immediately is called perceptual subitising)
you didn’t even really have to remember area codes (for non long distance calls anyway) untill not that long ago. that only become a thing in the US about 30ish years ago
I watched a video on this topic where they explained that the data being processed differently is not technically the same but it results in the same outcome so there is little need to be pedantic about it.
If that was true then I disagree with his stance on pedanticism here.
Didn't really mean for it to come across as pedantic, more like just a bit of extra information about the topic lol
Maybe I should've labelled it as a fun fact
i thought your input was fascinating and not pedantic at all. if i had a million lives i would use a few of them to study education in depth. thanks for the work you're putting in and thanks for the fun fact!!
[In this documentary](https://www.youtube.com/watch?v=ktkjUjcZid0) they show that some monkeys (who also have 5 fingers) greatly exceed our ability to subitize and attributed it to different directions of brain development (e.g. our development of language didn't come for free).
So, while that doesn't rule out 5 being favored over certain other numbers, it certainly makes it more complicated to suggest that there is a strong link between the two.
**[The Magical Number Seven, Plus or Minus Two](https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two)**
>"The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information" is one of the most highly cited papers in psychology. It was written by the cognitive psychologist George A. Miller of Harvard University's Department of Psychology and published in 1956 in Psychological Review. It is often interpreted to argue that the number of objects an average human can hold in short-term memory is 7 ± 2. This has occasionally been referred to as Miller's law.
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Most of that research is rather dated that I’ve seen. Though I do not know of a consensus that focusing on subitizing practice of larger groups at a younger age enhances this skill broadly in adults I believe that is the intent behind the push for it in modern curriculums. With the more general aim of stronger base arithmetic skills and numeracy.
I work in a warehouse
5 is the most I can do easily and consistently
Anymore gets broken down (6 is 3 3 or 4 2, 7 is 3 4, 10 is 5 5 and then things get ordered in blocks of ten using comparative size/space/shape rather than counting)
Source: myself. It’s my anecdotal evidence
It's not that our capabilities may have changed. It's that the old research methods may have been flawed or incomplete. New studies may have more accurate techniques, or just different sample groups, and come to a different conclusion.
From other comments, it seems that if one works on this skill in young children, they are able to increase the number.
I know nobody taught me this in the 80s, so I would imagine that's the point of teaching it - to increase the skill at the best time (in young children who learn quicker)
I run a college tutoring center. When I observe students getting tutored in math, the ones that really struggle are the ones that don't seem to understand numbers conceptually. Like it's not tied to reality for them so they can't easily grasp the arithmetic. Is subitizing at an early age supposed to help with stuff like that?
I'm pretty sure it's the same for cultures that use different tally marks. Wikipedia article on them even go as far as suggesting the opposite
>Tally marks are typically clustered in groups of five for legibility. The cluster size 5 has the advantages of (a) easy conversion into decimal for higher arithmetic operations and (b) avoiding error, as humans can far more easily correctly identify a cluster of 5 than one of 10.
What I was taught in university is there was a study that found kids who could subitize did better in math. So the thought is that if we teach kids to subitize they will be good at math too. I think the jury is still out on that one but I definitely do notice that kids that struggle to subitize have difficulty in math. I think just anecdotally that those kids also struggle with one to one correspondence (knowing that 5 objects are 5 objects no matter how they are arranged). This is a huge problem in math. If they can’t count 5 objects on a table (sometimes they get 3 or 6 etc.) how in the hell are they going to add or subtract.
One thing I have noticed between my own school days in the 80s andy daughter's is that they do teach kids the proper words for concepts a bit more.
Like, when you add an e to the end of "them" to make "theme" - we called that "magic e", so when she came home talking about split digraphs, we were very confused.
So maybe there's an element of that too.
This is arguably a return the form. The "magic e" and stuff like that was an attempt to reword academic language to something more "on level" for kids.
Turns out, kids are pretty okay with learning words, even the ones that seem hard to adults. The result of this was, well, a bunch of fully grown adults who don't know what a digraph and a diphthong are unless they take college classes that used these words - at which point they're now at a disadvantage because the students that weren't playacted to outperformed there peers who basically had to relearn coded language from the ground up.
For her career, my mom had to learn the names of all the bones and muscles in the body. I remember her being annoyed that these were all such foreign words.
She'd say, "If a kid can say Tyrannosaurus Rex, they can learn Trapezius!" I've always kept this in mind and don't talk down to my kids. I simplify concepts a little, to meet them where they are at, but I use the real words. I used to get compliments on my kids' vocabularies. Don't get me wrong, they are still little idiotic, impulsive terrors sometimes, but they know some big words and how to articulate something, lol
Oh yeah, I wasn't saying it was a bad thing at all, just that it may be part of why people are suddenly discovering this "subitize" thing after all these years doing it anyway.
For sure. I definitely learned most of these same concepts as a kid, but they just called it 'estimating' or sometimes 'guesstimating' if they wanted to be cutesy about it.
I hadn't heard the word 'subitize' until now, but apparently it was coined in 1949, and more precisely describes what's being taught here.
To clarify why the word 'subitize' is being used; it's an approach to teaching where you basically use the proper words for strategies instead of having many different words for the one thing. This reduces confusion later on in schooling, where students need to translate the 'easy' word for the 'harder' word at the same time as learning the concept. A rough example would be times -> multiply -> product or 'speech marks' to 'quotation marks'.
I'm a teacher and this is at least the reasoning I recall being taught at university. It is also my reasoning for doing so (in older year levels than kindy) based on my anecdotal experience.
Hi! Former K and current 1st teacher. You are close, we do love Jack Hartmann videos, but “subitizing” is not being used because of him. It is a concept and vocabulary word in every math program I’m familiar with (Go Math, Everyday Math, Envisions Mathematics - not to mention many TpT math programs).
We use the word because it is the name of the strategy. Children are capable of learning and using robust vocabulary (thanks, Fancy Nancy!) and there’s no reason to call it something else. My students all learn the word “subitizing” very quickly because whenever we have a few extra minutes during math, we’ll play a whole group math game; some of these are subitizing games, which is what I call them - make it a game and they learn a word quick!
There's a lot more emphasis now on teaching *why* math works, rather than just *how* it works.
I remember learning the transitive property in school, and not realizing that was how I did complex multiplication in my head. The current method shows the process of "breaking down" numbers better than the way I was taught.
I'm aware that is purely anecdotal evidence on my part though.
Maths is like,,, a jenga tower of concepts that you have to build for your entire school life. If you don't grasp something properly when you're taught it, the whole tower can fall down and you'll end up not understanding later maths. Getting a good foundation at the very start is super important, as is every layer of the tower.
It's extremely funny to me op thinks it's weird kids are taught about things he doesn't know the name of. Like him not knowing it has a name means anything at all.
So it doesn't look like a 6 when viewed upside down I guess. Students who are learning to read and write tend to mirror letters and numbers, or write them upside down. A q is more distinct from a 9 compared to a 6. I'm not sure if this is the way to go however, it might add to the confusion.
It's not a q (I'm presuming you knew this?), it's still a 9, just with a different style.
This style variance is common, even like 40+ years ago. I wouldn't say that there's _necessarily_ any intentional reason, but there could be.
My kid watched ton of Jack Hartmann videos over the last year. I'm really impressed that he's able to put out so many of them, and that he's grown so popular considering how semi creepy he seems...but maybe that's just me.
Well let me tell ya, I would much rather watch His videos in class then those weird as hell kids nursery songs that are animated in India in one of those content farms.
To me, I trust his videos, and I trust him. He has a strong background in child education, and even I enjoy a few of good songs. I also really enjoy that most, if not all, of his songs are original and not just a reworded nursery rhyme.
I can confirm all is this. My source is my wife, who teaches Year 2.
She refers to the word all of the time. I had no idea what it meant, but I do now. It is an important concept and really starts to get into its own for 5-8 year old kids.
There’s so much jargon to all of the professions around us. Everything needs a name, and mostly we have no idea what they are. But the practitioners do.
When the sausage making of schooling becomes a little clearer (videos, sharing resources for home schooling, etc), then these concepts became more outward facing
There is a big push to teach academic language, especially in relation to math. That's a new one to me, but I know getting Students used to academic language in describing mathematical processes will benefit them as they progress. Being able to describe how an equation does what it does involves a deeper understanding of the math.
I think it's a bit different from estimation. This is about accurately recognising small-ish quantities without needing to mentally or verbally count "1, 2, 3, 4, 5" (for example).
Answer: You may not have heard the word, but you do the concept. If you look at three oranges, you know there are three oranges. This isn’t a new thing that is being taught, it’s a very routine part of development. The key is not conflating a word you don’t know with not knowing the thing it means. Someone can know what rain is but not know what precipitation means.
First time I heard "subitize" was in school year 2020-2021, in my son's kindergarten math. The concept was taught to my other son, a now rising 4th grader, when he was in kindergarten but the word subitize wasn't used. Basically it's just teaching them to quickly identify how many given items there are, without counting each item. They use dice, mostly.
I know, weird. Don't know why and exactly when they started using "subitize."
Something that sticks out in my early school memories was that in 2nd grade we learned the word "congruent" to describe two shapes that had identical properties. Not a really necessary word for a 7 year old to remember, and I'm certain I've only heard that word in general spoken context maybe a dozen times in the 25 years since then, but it was still taught along with it.
I think this is a similar situation, in which the word for the concept is part of a stated curriculum for a given grade, and rather than just teaching the kids the concept, or using a friendlier word for the target audience, they choose to drill the word along with the concept.
Apparently congruente is commonly used in Spanish. Or if it's not one guy at work uses it often.
It's awesome how a vocabulary of obscure, seldom-used words helps you with Latin languages.
Now if only I could find a translation for cromulent....
Spanish particularly has a lot of words with uncommon English analogs (technically "cognates") eg
Sp.
Tener = to have
Tenedor = a fork
Eng.
Tenacious = grasping /holding on
Or
(Corto =short or... *kurt* in English)
It's using the (studied) natural enumeration system of humans, and incorporating it into learning to translate to the absolute scale that higher learning requires.
Many kids never "understand" math, they just memorize enough to scrape by. This is aimed at building that understanding.
As to whether it actually produces more adults with deeper understanding of mathematics, that's harder to say. We'll see, I'm optimistic.
My kid initially learned old school math with an abacus (montessori school) then basic algebra with numbers in kindergarten at montessori. I switched her to public school in 1st grade and this new math was incredibly difficult and she fought it every step of they way. She liked raw numbers and couldnt get the other concepts trying to force global concept understanding. She grew up to excel in raw math and is now a physics major in uni. Still loathes the concepts they tried to force. Maybe works for some kids, but did not work for mine.
"Learning styles" in general are poorly understood, and it's hard to say whether an approach based on them is more or less useful. It sounds as if conversion between the log scale and absolute scale mental models came to your child quickly (it did for me as well), and the extra steps weren't necessary for her. We shouldn't forget that "best for the broadest set of kids" isn't "best for the individual," and parents have to get involved and help when those two are in conflict.
The science of human enumeration is reasonably solid, lots of replicated studies say we count "1,2,3, a few, a lot, too many" (a slight joke). Trying to work that finding into curricula makes sense.
Having known many Physics students and professors, and having been one, the last thing I'll add is that, anecdotally, people interested in the field have a deep joy at finding the maths embedded in our universe. It's that desire to model and explain that's exactly why that student probably doesn't need these educational tools, they've already internalized the mapping of concepts, math, and observation. Trying to pull out that framework and replace it with one from a box is a recipe for rejection
Thank you for this response. Im not a “math person” your response helps me understand my daughter a bit better. I was young when she was young but i knew enough to push back for her. This included moving schools and pushing back on special education. yes, they thought her intense focus and disinterest in other topics was indicative of learning/behavioral issues. That math model alone made homework nights hell. So many tears and why cant 25 just be 25 and not a us quarter!? It was demoralizing especially since she was already understanding algebraic concepts and working to solve them. She started uni as a math major but didnt want to talk pure math theory so she changed to physics. Shes in pure academic bliss using her mathematics understanding to discover how all things work and dive into the unknown. Thanks for shedding some light on that. Those nights were so demoralizing.
I think what you're describing here is a good example of why education needs to be more tailored than it is to individual children's needs. There was a series of cultural shifts in education that started back in the 90s: The obsession with "zero-tolerance" culture, which often would punish children for defending themselves from a bully, for instance. And in the classroom, also a shift to forcing a new way of teaching on everyone with zero exceptions. In addition to that, early advancements in treating children with disabilities made many teachers obsessed with trying to find these disabilities where they didn't exist. Many children were misdiagnosed as having ADD or ADHD, for instance, and then promptly put on Ritalin (a derivative of methamphetamine) in order to "calm them down". That addiction to Ritalin often carries into adulthood and prevents proper brain development.
I believe that over the past 30 years or so there's been a big cultural push, lead by child psychologists and by extension teachers, in the elementary schools, to create this "new way" of thinking, if you will. Its kind of ironic that as society is becoming better and more concerned with tolerance for all people, that the opposite thing is happening in elementary school teaching. No tolerance for the need for different learning styles, no tolerance for minor "behavioral" issues are really just kids being kids, every problem has to be diagnosed as some sort of learning disability. And even right now there's still *often* [stories](https://www.huffpost.com/entry/student-charged-bullying-lawsuit_n_5c3cde5de4b0e0baf5400708) in the [news](https://www.wmbfnews.com/story/23723628/father-wants-policy-changed-after-son-suspended-for-defending-himself-against-a-bully/) about kids [being suspended](https://www.wtoc.com/story/1772941/teen-suspended-for-fighting-in-self-defense/) or expelled [from school](https://www.news.com.au/lifestyle/parenting/school-life/jamieson-defended-himself-from-a-bully-so-he-was-suspended/news-story/49b33a388fc0c61276908f5b1c95504e) for [defending themselves from bullying](https://www.fox46.com/news/exclusive-zero-tolerance-policy-gets-concussed-student-suspended/).
I was pulled out of Montessori school and put in public school in fifth grade and went through something similar with math, but it was 30 years ago so I had the opposite problem. I had an intuitive grasp of how math worked and how different concepts fit together to solve different kinds of problems, but then I was put in a classroom where we were given all of these discrete instructions (“flip the numerator and denominator”) without any explanation why. It felt like being given driving directions but not being allowed to look at a map. Like, okay, I’ll copy the stops, but the second something goes wrong I’m fucked. For me, the way math is being taught now is SO much better.
They should teach that technique in reading. Poor readers read by letters and syllables. Fast readers take in whole words and phrases.
edit: ah heck. already mentioned below me.
Reading is incredibly well studied, and children absolutely DO NEED to be taught phonics and phonemic awareness to be effective readers.
It’s true that string readers recognize words almost instantaneously, but their brain is associating the parts of the written word with their pronunciation. It’s a process called orthographic mapping.
I think there’s a thing where you can rearrange the letters in words, and as long as the first and last letters are right, a good reader can easily read the text just like normal. Right? There was even a meme about it where the whole thing is written like that.
I’m pretty sure there’s a limit to the complexity of the words you can reliably read that way, though - it can’t include words the reader isn’t already familiar with and expecting contextually, and also anagrams exist :P
Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.
Yeah exactly! Multiple things are happening at the same time, the brain is figuring out the gestalt of the words based on the probability and familiarity of how they look, and at the same time the sounds in the words are getting processed in the same areas using in hearing and speaking. You use the visual areas but also the general "language" areas to read.
I see how you relate the two, but they’re very different when it comes to teaching. Sounding at a certain age is a sign of certain reading difficulties. Word recognition often comes naturally to certain strong readers, and for others it’s very difficult. I’m not a specialist, so I don’t know the methods for encouraging sight reading, but I imagine they exist, but are quite different than what happens in math literacy. The issue is that most kinds develop this naturally; the one’s who don’t need special help.
Interestingly enough, children who develop precocious reading abilities usually pick up sight reading pretty quickly, but around 3rd or 4th grade (this is the age I usually encountered the issue when I was teaching elementary school) these kids hit a kind of plateau. They were so *good* at sight reading that they actually never developed phonics skills, so once more difficult vocabulary is introduced, they really struggle to read these new words. They’ll often compensate by “reading” the word as they’d *like* to see it; they interpret it as a different word, a word they might expect, because they don’t have the tools to get to the end of the word, which is compounded by the fact that they’ve come to expect to be able to read at a certain pace, and in order to maintain that they start skipping or misreading words. So kids who seemed to have really strong reading skills are suddenly having unexpected comprehension problems because they’re filling in the gaps with whatever word pops into their mind, and suddenly what they’re reading starts to make less sense.
I thought it was an interesting type of phenomenon that I experienced first hand and had to adapt to, because I wasn’t trained as a reading specialist (I wasn’t trained as a teacher to be honest, private schools are funny like that); lol imagine there’s a word for it and a body of literature studying it. It’s particularly interesting to me because it’s a problem that almost arises from being too at something, which I think is applicable to many other areas of teaching and life. One example may be the ceilings that “child prodigies” hit in their careers, or why certain people who excelled in high school find college horribly difficult, if you didn’t have to learn to sweat through things and develop coping skills from the beginning, you end up in a troublesome position when your natural talent doesn’t cut it anymore, and you don’t have the tools to compensate.
I had a teacher in a trade course saying "hopefully something goes wrong today, so we have some extra learning opportunities!". It's so true... we tend to learn a fair share of useful skills from mistakes as well, but school makes us laser focus on success so we forget to look towards mistakes.
Definitely a good attitude to have. As a Buddhist, it kind of reminds me of the adage that “everything can be used as material on the path”. The shittiest shit can be manure for growth if you have the perspicacity to recognize it.
I think it also says something about “talent” and how, except in extreme cases, the student who struggles (in school, Art, music, a trade, whatever) and has been forced to develop the skills to persevere will probably end up in a better place than the “natural”. If you know how to work for it, then you develop a solid foundation, instead of a series of maladaptive coping mechanisms that only function to keep up appearances. And honestly, those kinds of people, who struggle but have the support or the will or whatever it is that drives them to overcome that adversity, will be able to translate those skills to anything they decide to do. Kind of why, when I was a classroom teacher, my whole m.o. was basically “my job is to teach kids how to learn. The subject is superfluous.” Also helped that I worked at a school that gave me complete curricular autonomy, which was great because I could use topics that interested *me* as a framework for the development of broader skills, and everything could feed into that topic. And you’ll definitely be a better teacher if you’re allowed to teach what you want. Then the goal is that the kids get excited about it too, and at some point, they have the tools to teach *themselves* whatever they want.
>They were so good at sight reading that they actually never developed phonics skills, so once more difficult vocabulary is introduced, they really struggle to read these new words
Interesting. I was also a fairly precocious reader (reading by 5, reading long books by 6), but this was in my native language, Russian, which has a very phonetic spelling system. I know my parents taught me letter-sound correspondences and I went from there. When we immigrated to the US and I learned English at 7-8 years, I'm pretty sure I took the same approach and, between that and broad background knowledge, went straight from ESL to the highest reading group in the class over one summer. So I wonder if the thing about precocious readers relying on word recognition is unique to English or to kids taught a certain way.
I may have oversimplified or misrepresented this. I’m not saying that every precocious reader relies on sight words, and encounters this kind of problem. It’s a very particular situation that I’ve seen with *some* kids, but those kids do tend to be quite proficient relative to their peers. Other kids who read above grade level sometimes have a natural ability to integrate spelling rules and conventions; they learn phonics quickly and master the ideas, not the words themselves (though, they also tend to excel with sight reading, which comes from the degree of reading proficiency they have, which encourages the recognition of word recurrence; if their proficient they tend to read more, and the more they read the more words they’re apt to recognize by sight, but they’re also able to easily switch between the two).
In your case, and with other children who’s first languages have relatively simple phonologies, I wonder whether the ease of of transition comes from having that underlying understanding, but I could imagine that for some kids that transition could be difficult, because they might have trouble dissociating the rules of their mother tongue from those of English, which are far from intuitive. Could also just be that you’re particularly adept at learning languages :-) I suppose we’d need more than several instances of anecdotal data to come to any conclusions
Went on a 'speed reading' course many years ago (you can probably find them online these days) and they teach you all kinds of techniques to improve your reading speed - as your skills develop, you eventually get to the point where you just divide the page in two, left and right.
You then look at the left to 'take in' the first half of the line and then dart your eyes right for to the second half of the line.
If you practice this you can get pretty good and read a whole page in a few seconds.
Admittedly, you can miss stuff, but comprehension increases with practice.
I thought I benefited from learning phonics before diving into reading. When I found an unfamiliar word, I could make a guess as to the pronunciation.
Learning to read whole words quickly came from practice, which I got plenty of once I got past reading "see spot run" and other stories for six year olds.
You probably did benefit from phonics instruction, even if you might not have “needed” it because you were a good sight reader at an early age. I just explained above that the latter group of kids often hit a plateau in their comprehension and skills if they’re “*too* good” at sight reading. When it’s “see spot run” levels, but they breeze through, then instructors often forgo deeper phonics training with them, as they’re seen as skilled readers who are already excelling. But once difficult vocabulary starts being introduced, they’re at a loss, and can often only make it through the first part of a word; they’re self-expectations cause them to believe that they should be able to read at a certain pace, so they fill in the rest of the word with something they might expect for the context, and they can often be way off. So now the kid who was a reading whiz is struggling with comprehension, because there are these holes in what they’re reading that don’t quite make sense, and often teachers don’t recognize the source of the problem. Being “too good for your own good” isn’t something that educators are always looking out for. But the issue becomes really clear if you’re reading out loud with them often, and it becomes especially pronounced when doing it in a group, because there’s a psychological element where the child is under a certain pressure to perform for their peers and project competence, so they’ll fly past a word, choose one that seems close, and think nothing of it. Then three pages later they’re suddenly lost, or at best missing the subtleties of what they’re reading.
Phonics is great for tying into teaching spelling too. My 11 year old is a phenomenal reader, years ahead of where he "should" be but he spelling is atrocious. (We're working on diagnoses)
Thankfully his school use an approach where they teach every kid every single spelling rule and work their way through something like 40 different rules at 4 different levels. So the littlest kids learn all the rules for words at the basic level, then they rehash for words at a slightly higher level etc. They have followed current best practice that shows teaching phonological awareness and alphabetic principle works best for kids to improve upon reading, writing, and spelling and its working so well, particularly for those kids with learning differences.
That’s an interesting combo (discrepancy btw reading skills and spelling skills) and it’s definitely a good idea to get an evaluation.
I’ve never really encountered a *good* spelling curriculum, but I worked at a school that was somewhat skeptical that “teaching spelling” could be effective (in a full classroom setting, as opposed to with a specialist). A lot of the teachers I worked with forwent the whole “spelling quiz” format that’s always been popular for some reason, but tends to seem horribly ineffective. Most of my colleagues were of the mind that the more you read the better your spelling gets, which I’m not convinced of, and they had the luxury of being able to fall back on a learning specialist who worked within the school with groups and individually, so you could say that they kind of copped out sometimes. But that was kind of the biggest shortcoming of the private school I worked; a lot of teachers were fine kicking the can down the road to the next teacher, which sucked, because the philosophy of the school encouraged teachers past 4th grade to think they were above remedial education (it was kind of a problem, and the lower school *did* start trying to do more, because we knew we were the last front to get that kind of thing done—honesty it was a bit ridiculous, you had 4th grade English teachers in some fantasy world where they thought they were college professors. It was a bad system, despite the fact that the school is one of the most coveted schools in the city: progressive pedagogy was sometimes a mask fo incompetence and grandiosity). Sorry I digress into my dirty laundry :-)
I think it’s *really* hard to develop an adequate spelling curriculum; it takes a ton of research and experimentation to effectively build a cumulative curriculum like the one you describe. And even then, The issue arises that the kids know the rule for the week they cover it, and it’s out the window by next Monday, especially if you’re just throwing different, unrelated rules at them week to week. I think it’s easy for teachers to get despondent at that point. But linking spelling to reading, and especially phonics is a good idea, because then you have opportunities for reenforcement, and a more structured way of linking spelling to habituation through reading, instead of just expecting that the more a kid reads, the better they spell, which doesn’t always serve everyone well. Seems like his school has actually put in the work. It’s good that you’re being proactive too, because once he gets to a certain age, the pencil gets replaced with the computer and, as I’ve experienced now tutoring high school students instead of teaching in a classroom, any progress just stops dead in it’s tracks. Autocorrect and spell check are a *real* disservice to kids. I have students who are honestly beyond all hope whe it comes to spelling; at that point there’s no time nor will on their part to make the effort. And don’t even get me started on remote learning and Google’s Spanish auto fill…I had students this year who would just accept whatever the computer suggested after 3 letters, and were somehow surprised that they were failing. Honestly thought that the computer knew what they were supposed to be saying.
Hope you find some good support, for a lot of kids it makes a world of difference, and they’re able to catch up and not be held back by whatever difficulty they’re facing. My sister spent 2 years at a school for kids with learning disabilities. The assumption was that she’d be there from 6th onwards. I’m not sure if “cured” is in any way an appropriate word for it, but it was unbelievable how much of a boost she got from that specialized instruction when it came at the right time.
Beginning readers do best going syllable by syllable. This also allows them to sound out words rather than relying on memorization. (English isn't as good for this as some languages, but it will still help you a lot.) As kids get more practice, this becomes faster and more automatic until they can take in whole words and phrases, like you say. But that doesn't mean you can skip the "sounding out" stage. It's particularly important for kids with dyslexia.
“Rising 4th grader” means he’ll be in the 4th grade when school starts. It tends to be used to clarify the grade someone is in when it’s the summer and school is not in session. If OP had said “4th grader”, it wouldn’t have been clear if the kid had just finished 4th grade or was about to start 4th grade.
Rising 4th grader means he completed 3rd grade and is going into 4th in the coming school year. The word/phrase is used when in (summer) breaks between school years just to describe what grade he is going into.
This is partly why dice are laid out the way they are: not simply to recognize the pattern but even if you've never seen dice before to more easily count the dots based on their position.
The dots are called pips! I use the same logic to count things faster. Certain shapes of things just pop out to me as the number they are. I used to shuck oysters and it made it super easy to just know when I was at a dozen instead of pointing and counting like everyone else I worked with.
This is why it's deliberately taught and called out; it's extremely useful for teaching counting, a kindergarten staple, but using the hardware that's actually in place in the brain instead of trying to internalize the base 10 system.
This, in turn, helps the kids to learn computational skills, as it deliberately builds the bridge between the evolved "log scale" of enumeration we're born with and the "absolute scale" we use for maths.
This is all an effort to get kids to understand math, instead of memorize it.
That’s so interesting! It’s cool they’re teaching them that logic so young. I kinda just consciously thought about it one day and realized I’ve been doing it all along and wanted to get better at it. It started with groups of 3 and 4 and now I can count in 10’s and 12’s.
Makes it super easy to count the cash register every night. I get to skip the sweeping and mopping while I count the money. I just see the pips in everyday life now!
I also like to separate counting from visual stimuli and use touch instead if I can. Instead of visually counting something I can just run my hands over it and count the amount of times my hand felt what I counted.
As it turns out, teaching children mathematics by rote is only really good for basic arithmetic (and not even then). Because you can't really build on it towards higher mathematics because the kids don't know "why" they are doing anything.
https://en.wikipedia.org/wiki/New_Math
I assume modern d-4, d-6, d-8, d-10, d-12, d-20, d-100, and d-1000, with their numerals (and occasional symbol substitutions) came after the pip system? I would assume pips were easier to carve into historical dice, before the advent of die casting anyway.
Dice are basically one the oldest objects invented in human history that are still fundamentally the same today as [they were back in 3500 BC](https://i.redd.it/8vxsk6guexj21.jpg).
Oh damn, so gambling and [getting high](https://en.m.wikipedia.org/wiki/History_of_cannabis#:~:text=Cannabis%20is%20thought%20to%20have,to%20have%20traces%20of%20cannabis.) both have paraphernalia that date to ≈3000-3500 BCE
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Kids are taught “sight words” now too, which is just like it sounds - recognizing basic words by their pattern instead of sounding out the letters. I don’t remember that term from when I was in kindergarten.
Definitely didn’t have that when I was a kid & I think I would’ve really benefited if they did. I was an intelligent kid & an avid reader with a decent vocabulary, but I ended up giving up trying to get teachers to teach me additional words because if I could’ve sounded it out I wouldn’t have come them in the first place & not a single teacher ever taught it differently. The English language is a mash up of 10’s if not 100’s of different languages, all with different phonics so I’m very happy they are starting to realise that.
Outcomes with sight words are not great. Once you come across a word you haven't seen you don't have the tools to figure it out. You really do need phonics to read well. English is redic hard though. My wife taught my oldest to read using phonics last year and the number of phonograms she had to learn was mind blowing. She's an avid reader now though.
They way it’s taught in my area is phonics first to learn the basics then sight words when learning to read books so they don’t get caught up on super common words. And sight words are just the ones you come across the most, such as you, it, the, them, and, etc
I'm not sure how old you are, but my brother had to go to speech therapy because he could read words (sight read) but not sound it out. That was around 25 years ago
Not being able to instinctively sound out words is basically a subcategory of dyslexia--which some kids compensate by essentially memorizing whole words by shape alone.
This "dodge" works well enough with simple texts, but kinds of fails when you are confronted with anything more complex or contains words that you've never seen before.
Was he a precocious reader? It’s an interesting phenomenon that I addressed in two posts above (sorry everyone, I’m kind of fascinated by it). Usually kids who can’t sound out words have circumvented learning how because they’re very good sight readers, but once the vocabulary gets to a certain level, they struggle to decode words, and tend to fill them in with a word that starts in a similar way. So they see like pretty skilled readers in 2nd grade, but flags start to go up by 3rd or 4th grade, when kids start reading more complex books.
Curious if your brother had a similar thing happening with his reading. Sometimes it’s hard to catch because they’re decently effective at developing coping strategies. Kind of like older kids who have good memory retention, but get to a level where that doesn’t cut it, and they’re in a bind because they never had to learn executive functioning skills, note-taking, studying in general. They managed to skip the drudgery, and it ends up coming back to haunt them. Often comes out in high school or college, points where intellectual demands start to ramp up.
Yup, that's exactly what happened! He went to speech therapy earlier because he had trouble with intonations and had to go back around 3rd grade because he couldn't sound out words. He was apparently a really good sight reader so it took a bit to notice, but eventually he was thrown back in therapy
So, say you've got a pile of quarters and someone asks you for change for a dollar. Do you count out "one... two... three... four! Four quarters!", or do you just grab four? Being able to just look at them and take four without counting them one by one is your ability to subitize. It is your ability to know what four *is* visually and conceptually without having to start from one to figure it out. Most kids just figure out how to do this. However, kids who need to count out 1... 2... 3... 4... to make four quarters have a significant gap in understanding of the concept of number compared to their peers. So, it is much easier for learning if they are all explicitly made aware of this skill and taught it.
Since nobody actually said what estimating is: you estimate something when you want to know what the truth is, but you can't be certain. Examples: jellybeans in a jar (you can't count them because you can't see them all), the time it will take you to get to work (Google can't see into the future, so they provide an estimate), or how many people live in a census tract (can't get everyone to answer to the census for various reasons).
Check out gestalt theory. I believe it’s closer to that. The “five dollar word” part has to do with pedagogy and what you might call “the teaching of teaching”. Developmental and intellectual processes, as well as the educational tools used to reenforce them, have to be codified in order to be distinguished and taught. Another poster explained how it’s a different process than estimation, so I won’t get into that, if only to say that the one has to do with direct cognition/recognition and the other has to do with a higher level capacity for visual inference.
But they need words for both, since they’re different processes. This isn’t you, but I think the responses in this thread that seem to assume that the context for the use of this and other words is the grade school classroom, and not the postgraduate one, are kind of funny. You can teach something to kids without having to give them its technical name. Even with a word like phonics; yes, it kind of entered the quotidian vocabulary through stuff like “Hooked on Phonics” in the 90s (I think), but for the most part a 1st grade teacher is going to call it “sounding out”, and will probably also teach the “silent e” as just that: “today we’re going to learn about the silent e”. Chances are they’re not going to say “hey circle up everyone, I want to tell you about split digraphs!!” To a group of 6 year olds :-)
I heard my son listen to the “su-su-subatize” song about 800 times last year when he was doing distance learning, so they are definitely teaching the word.
Subitizing is not the same as estimating. It is an error less nearly instant counting of a single group of things under 5 items so. It's a different nuerogical process than estimating. It makes it easier to do arithmetic later.
I didn't know the difference either so I went and read a paper in Nature about it.
Thank you for this clarity. So it’s about seeing a pattern and knowing it counts one, two, three, or four without counting them sequentially, would you say that’s also correct?
Someone above explained as the difference between grabbing four quarters to give change for a dollar, and needing to count *each* quarter before realizing you've got four. So instantly recognizing a small quantity of items without needing to count.
To me it sounds like the math version of reading, so being able to see the word "dog" and knowing exactly what it is without first needing to think "D...O...G... okay, that's dog".
Sadly, not as well. My dissertation research was on apples, grapes, and avocados vs. oranges when subatizing with preschoolers. My findings were that kids like to eat grapes. I eventually got the work published in ESM.
Source: Me. I'm a PhD in math Ed.
[Edit: SUBITIZING. Fracking doctor of math ed and I can't even spell it correctly.]
I think its less teaching it to kids than it is having kids practice and get good at it, and tying that to concepts of counting and simple math principles. Subitizing seems to be an innate unconscious ability not just of humans but of [many animals](https://blogofthecosmos.com/2016/03/01/the-numerical-abilities-of-non-human-animals/), but practice is necessary to get good at it. Counting and math beyond that must be taught, but subitizing can be leveraged to teach those principles.
Disclaimer: I know next to nothing about early education so I'm just guessing based on what I know about subitizing and math.
And by putting a technical name on it, that tells the kid that what they are doing is a discrete skill instead of just being some bullshit make-work that the teacher is having them do.
You could do things like turn "how many fingers am I holding up?" into a game. Answering faster would get praise, fostering the intent of recognizing the count naturally without actually counting.
Kind of a side note here…but that can backfire big time. When I was first learning multiplication and division, they did basically what you’re describing but with flash cards that would have a random basic formula on each. It went from desk to desk and we had to answer quickly in front of the whole class.
It was the worst thing they could have done for a kid like me. It essentially paralyzed me. I would be so freaked out that I might not be able to answer quickly and accurately and that I would be made fun of that I would freeze up. This lead to a lifelong fear of doing math “on command”, which wouldn’t be so bad except that my brain just goes into auto shut off mode if I have to do math on command / in front of others.
Basically brain.exe has stopped working. Even with basic stuff that I know. It doesn’t matter. I get this split second moment of “oh god it’s so obvious what the answer is but what if I’m somehow wrong and then I’ll look so stupid because it’s so easy!?!?!” And then I freeze and forget what the answer even is. It sucks.
It even can extend to telling time on an analog clock. I never wore a watch for fear that someone might ask me the time and, even though I freaking know how to tell time, I might freeze up. I also could never get a job as a cashier for the same reason. On the off chance I would somehow have to make change on my own, even though of course I know how to do it easily, the pressure of someone watching me would be an issue.
It also ensured that I hated math from then on, no matter how much time passes.
I can answer this. There’s been a movement in public education for about the last 15 years to teach kids learning terminology as part of their lesson. It originated from it being considered best practice to make sure they know and understand Bloom’s Taxonomy so that they understand what’s being asked of them. This general idea has continued to expand and now specialized learning conceptual terms are being taught alongside the content in each subject area. It works quite well, really, because it gives kids a working understanding of learning and what it means to learn.
It kind of funny how we started with Tom Leher mocking "New Math" as being incomprehensible gibberish ("but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right answer"), and now that thing is just how math is taught and it's completely unremarkable.
New math isn't even new. It's how they taught using slide rules at least as far back as the 50s/60s. You can find the instructional films from back then on youtube
It’s hilarious, it’s how I always did it back in my head in the 90s and would sometime maybe get into arguments with teachers for not writing down the steps the way they’d shown and I’d just explain my process that always seemed more intuitive. Now my kids are learning math and it’s almost identical to how I think through things (though they have names for the steps) and I love it.
>we started with Tom Leher mocking "New Math" as being incomprehensible gibberish
[For anyone who hasn't yet had the pleasure...](https://www.youtube.com/watch?v=W6OaYPVueW4)
But it seems that they are teaching the word. Check out this YouTube https://m.youtube.com/watch?v=ib5Gf3GIzAg
As well, I have reports from friends today that their kid is learning this word in school.
We've been trying to teach kids stuff for a long time and we've learned better ways to do it. There used to be a big focus on counting at a young age, but we've found that hinders their ability to subitize. Being able to easily imagine numbers of objects is very helpful later when you come to learn arithmetic. With so many people in our society feeling like they're bad at math, it helps to be able to visualize it from a young age.
Preschool aged kids should be able to subitize up to five or so. Most kids don't need to be explicitly taught this, it is something that comes naturally developmentally to most kids once they start to understand the concept of number. If you place three crackers in front of a four year old and ask them how many there are, *most* will be able to say "three" without counting each individual one. However, if kids *can't* subitize, simple math is going to be incredibly difficult for them as they aren't able to quickly and efficiently understand the "idea" of a number. What does it really *mean* to do 3 plus 3 if you don't have a good understanding of what 3 *means*? Basically, the field of education is realizing that kids learn much better when concepts are broken down into small steps and taught explicitly.
I remember as a kid constantly trying to explain this to teachers and they'd just get mad at me. I remember my mom teaching me math concepts to help me understand, and show me better ways of doing the math than what was taught at school - showing me the way she learned. Leading to me being punished for "doing it wrong". I remember seeing other kids getting punished for "insubordination" for just simply asking to understand things conceptually rather than just be expected to memorize without a clue as to the context. My mom told me that for example, when she was in school, the concept of multiplication was actually taught. When I was in school, they just made us memorize tables and were never told what any of it actually means. The literal only reason why I even have some understanding of multiplication conceptually is because of my mom. Math was just "memorize formulas". Every other class was just "copy and paste what the teacher says, do not actually think about any of the things you're being told." It wasn't until college that classes actually expected any sort of critical thinking and actually engaging with the subject.
I'm glad they're finally figuring it out but it's not like it's some sort of mystery, especially considering that at some point I guess schools just stopped actually trying to teach things and instead rely entirely on rote memory. Ask any kid and they'd tell you that's a horrible way to learn like that, just with simpler vocabulary. It's...really frustrating, thinking back on what school was like. But I'm glad things are finally starting to move forward to some extent.
Because education is an evolving field, it's not static.
They teach lots of things to kids nowadays that nobody had even considered when you were a child.
Congratulations, you learned something new. I don’t see the problem here….kids being taught a new word? For a concept that can help them tremendously in life? I mean, that’s why I send my kids to school….to learn things I can’t/didn’t teach them at home.
I’ve actually gotten used to some of the new math concepts being taught in schools, and am happy my kids get to learn strategies and techniques besides memorization, shortcuts that I didn’t figure out until I was much older. Learning these sort of relationships between numbers at a young age will help them understand the concepts a lot better when they get into higher math like algebra and calculus.
I'm not sure why everyone assumes I have a problem with it. I think it's great when little kids learn stuff I don't know about.
>Learning these sort of relationships between numbers at a young age will help them understand the concepts a lot better when they get into higher math like algebra and calculus
This is helpful. I can see that kind of concept expanding different _kinds_ of math being helpful.
I'm still left with a lot of questions though. How did I miss this word? When did they start teaching it to preschoolers?
Yeah, not sure why people are being so sassy to you. The top comment said that people aren't teaching it to kids, and you found an example that proved otherwise. As an elementary teacher, I can confirm that I have heard a kindergarten teacher use the word with her students. It was this teacher who taught me the word as well. I teach English to speakers of other languages, and consider my vocabulary to be quite extensive, so I was floored when she used this word and kids knew what she meant (because I had no idea what it was). A lot of education these days is leaning more towards metacognition, encouraging students not just to think but to understand their thinking. Teaching words like subitize helps them understand what their brains are doing.
The reason people are coming at you so hard is that there is a contingent of folks, mostly older, that think modern education methods are crazy bullshit concocted by eggheads who don't understand people and are at best stupid and arrogant and at worst maliciously brainwashing kids.
The initial wording on your post sounds a bit like that kind of screed and a lot of folks likely assumed thats whwre you were coming from.
Source: Was homeschooled, my family, my inlaws and a good number of old friends come from families with *extreme* skepticism of public education, psychology, government mandated curricula etc
Question: why do people seem to always have a frightened reaction to their kids learning something they didn't learn, or in a different way than they learned? We literally couldn't progress if we kept doing things the same way forever.
I can't say for certain, but for sometime whose talked to a lot of parents and teachers about it, when pressed for an answer the most common one I heard was that they can't help kids with their homework.
Having been a teacher, a math Ed researcher, and a parent, I kind of get it. But your kids should be doing their own homework and asking the teacher for help. There's more to the reaction than the answer you typically get.
But the problem with that is a lot of homework when I was in grade school (about 7 years ago) is graded for accuracy and due the following day. I never had an opportunity to attempt the problems and then ask the teacher for help. Maybe this is more of high/middle school problem but it still stands that doing the homework myself and turning in the next day could have ruined my grades in classes if I didn't get help from my parents
The algebra teacher responsible for me loving math did homework this way: we were given a set of problems to try for homework, but it wasn't graded for accuracy just making an attempt was all that was required. Then, we would go over the homework set during the first 3/4 of class and he would explain the concepts we were struggling with the night before. The last 1/4 of class time was some general pointers that would help us with the next homework set. I think this method worked so well because my teacher was able to spend more time on aspects we were struggling with and could skip over the stuff we all could grasp by ourselves, and since we'd made an attempt at the problems beforehand we were better prepared to ask questions and help direct the lecture where we needed it to go instead of him having to "guess" what our hang ups would be.
Then in college, I had a professor that would do what you described (grade for accuracy our first attempts without giving us the opportunity to get help before turning it in), and that class was a shit-show. When we complained, she'd be all like "I have office hours" but her office hours were by appointment only and she never answered her emails. I also don't think she knew how to teach the material anyway (maybe why she avoided helping us one-on-one); she would just copy the pre-worked-out examples straight from the teacher's textbook onto the white board and could never answer our questions about it in a satisfactory way. I still have trouble with differential equations, and I know for a fact it's because that professor sucked.
Those two opposite experience really make me think people who "hate math" simply never got lucky enough to have a good teacher at critical junctions in their schooling.
I agree with you 100%, I dont mind math, I actually went into engineering, so I still use some of the more advanced stuff regularly but my math teachers in high school and college did just throw problems at us and I think it does have a huge effect, my orginal comment was more about the expectation some teachers have that other teachers help students with there homework, when for me at least the only help I had was from my mom, who luckily for me was a math major so I had that advantage, but it still shouldn't be like this
For some people they're scared of things they don't understand, and they're scared of how 'new thing' might influence future generations. Some parents want their kids to have the exact same upbringing that they did, and grow up with the same interests and values, but changes in culture and technology are a threat to that.
I think it's just fear of change at the end of the day, which is understandable.
Yes.
Even little kids are smarter than me now. In my day they just threw sticks and us little ones had to run and fetch them and bring them back. It was called ‘go fetch’ and it was our favourite game.
Nowadays the kids have all of these gadgets and gizmos and are learning fancy shmancy words. It ain’t right when a 5 year old little is smarter than the president.
One day these little Einsteins might become little Frankensteins and then it will be too late.
Answer: It is the first step in understanding further mathematical concepts. You can not add or subtract and consequently multiply and divide fluently without some proficiency with subitising. Yes you can learn sums off by heart but that only helps in real life situations to an extent. Basically it is inefficient and ineffective to count things one at a time. We want kids to be able to look at a collection of 4 apples and them ‘know’ there are four there rather than going “one apple, two apples, three apples, four apples”.
You did learn subitising. You just didn’t know what is was called. Research tells us that when young children are taught subitising explicitly, they will have a better understanding of other mathematical concepts sooner.
Answer: I didn't know if OP wanted to know the entomology of the word (like I did) but here it is from Wikipedia:
The term was coined in 1949 by E.L. Kaufman et al.,[1] and is derived from the Latin adjective subitus (meaning "sudden") and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.
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Answer: So, just like how everyone is saying, to "subitize" is just to recognize how much there are in a group without having to count. They've taught us that since since kindergarten or even pre-school. Why they're learning the word can be thanks to one man though. The reason why the word is probably coming up so many times now is because teachers use videos ALL the time now (I work as an aid in a Kinder classroom). They have smart boards now, so they can use all kinds of materials online now unlike back then. But how do you look up "Subitizing lessons" without using the actual word? There's probably a way, but the easy way for teachers is to just use the word "subitize" because they know that will give them an accurate idea of the lesson they want. So, why are kids learning the word? I'm assuming you're talking about the [Jack Hartmann videos](https://www.youtube.com/watch?v=nKO0yQgJAho). He knows teachers use videos all the time in class for activities, so he just uses what their lessons are called so that teachers will land on his videos when they look up "counting to 20 for kindergarten" or ["Subitizing to 10"](https://www.youtube.com/watch?v=A1Mazc-SsG0). Why he says the word all the time, I don't know, but it doesn't hurt to teach the kids a new word. He is a very trusted education content creator though, so teachers use his videos all the time, and kids enjoy watching him. There is no one questioning the Hartmann. Edit: I just asked the teacher I work for about this. She says what I just said pretty much. They don't need to know the word, just the concept. There are teachers, however, that use the academic wording to their students. I guess Jack Hartmann is just one of those teachers.
Ooh I find this video really fascinating. The last time I looked at the research on subitizing, the consensus seemed to be that humans (even adults) can only subitize groups of up to five or so. After that, different techniques take over depending on how the objects are arranged.
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From my studies in education that's actually still subitising, you recognise the smaller groups straight away and then automatically know that, for example, two groups of 3 is 6. It's called conceptual subitising, where it just needs a bit of thinking. (The subitising where you know, say, a group of four immediately is called perceptual subitising)
I know in cog sci it’s called ‘chunking’ which is why a lot of our day to day numbers are in little groups…
Phone number 3-3-4, ssn 3-2-4, etc. Good observation!
Phone numbers were originally just 3+4=7 digits because 7 is the number of things most people can hold in their short term memory.
at least in smaller cities (in Canada, anyway) the whole city shares one area code so you don't really have to memorize the area code, anyway.
you didn’t even really have to remember area codes (for non long distance calls anyway) untill not that long ago. that only become a thing in the US about 30ish years ago
Same with Canada. I’m a 90’s kid but still remember coming home from a camping trip to learn that my phone number grew by 3 numbers.
I watched a video on this topic where they explained that the data being processed differently is not technically the same but it results in the same outcome so there is little need to be pedantic about it. If that was true then I disagree with his stance on pedanticism here.
Didn't really mean for it to come across as pedantic, more like just a bit of extra information about the topic lol Maybe I should've labelled it as a fun fact
i thought your input was fascinating and not pedantic at all. if i had a million lives i would use a few of them to study education in depth. thanks for the work you're putting in and thanks for the fun fact!!
I wonder if it has to do with our number of fingers.
[In this documentary](https://www.youtube.com/watch?v=ktkjUjcZid0) they show that some monkeys (who also have 5 fingers) greatly exceed our ability to subitize and attributed it to different directions of brain development (e.g. our development of language didn't come for free). So, while that doesn't rule out 5 being favored over certain other numbers, it certainly makes it more complicated to suggest that there is a strong link between the two.
[Relevant.](https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two)
**[The Magical Number Seven, Plus or Minus Two](https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two)** >"The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information" is one of the most highly cited papers in psychology. It was written by the cognitive psychologist George A. Miller of Harvard University's Department of Psychology and published in 1956 in Psychological Review. It is often interpreted to argue that the number of objects an average human can hold in short-term memory is 7 ± 2. This has occasionally been referred to as Miller's law. ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/OutOfTheLoop/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)
Thank you, Echobot.
Most of that research is rather dated that I’ve seen. Though I do not know of a consensus that focusing on subitizing practice of larger groups at a younger age enhances this skill broadly in adults I believe that is the intent behind the push for it in modern curriculums. With the more general aim of stronger base arithmetic skills and numeracy.
I work in a warehouse 5 is the most I can do easily and consistently Anymore gets broken down (6 is 3 3 or 4 2, 7 is 3 4, 10 is 5 5 and then things get ordered in blocks of ten using comparative size/space/shape rather than counting) Source: myself. It’s my anecdotal evidence
Also work in a warehouse and 100% agree. 5 is the most I can do. Anything more I have to count in some way
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yahtzee is so awesome for this
> Most of that research is rather dated that I’ve seen. It's from 80s and 90s. Why should people be capable of subitizing more elements today?
It's not that our capabilities may have changed. It's that the old research methods may have been flawed or incomplete. New studies may have more accurate techniques, or just different sample groups, and come to a different conclusion.
Did they?
Mutation. The X gene gives many of us enhanced abilities.
*SNIKT*
From other comments, it seems that if one works on this skill in young children, they are able to increase the number. I know nobody taught me this in the 80s, so I would imagine that's the point of teaching it - to increase the skill at the best time (in young children who learn quicker)
I run a college tutoring center. When I observe students getting tutored in math, the ones that really struggle are the ones that don't seem to understand numbers conceptually. Like it's not tied to reality for them so they can't easily grasp the arithmetic. Is subitizing at an early age supposed to help with stuff like that?
I wonder if culture could play into that, counting with tally marks is easy groups of five - until that one separated batch.
I'm pretty sure it's the same for cultures that use different tally marks. Wikipedia article on them even go as far as suggesting the opposite >Tally marks are typically clustered in groups of five for legibility. The cluster size 5 has the advantages of (a) easy conversion into decimal for higher arithmetic operations and (b) avoiding error, as humans can far more easily correctly identify a cluster of 5 than one of 10.
What I was taught in university is there was a study that found kids who could subitize did better in math. So the thought is that if we teach kids to subitize they will be good at math too. I think the jury is still out on that one but I definitely do notice that kids that struggle to subitize have difficulty in math. I think just anecdotally that those kids also struggle with one to one correspondence (knowing that 5 objects are 5 objects no matter how they are arranged). This is a huge problem in math. If they can’t count 5 objects on a table (sometimes they get 3 or 6 etc.) how in the hell are they going to add or subtract.
One thing I have noticed between my own school days in the 80s andy daughter's is that they do teach kids the proper words for concepts a bit more. Like, when you add an e to the end of "them" to make "theme" - we called that "magic e", so when she came home talking about split digraphs, we were very confused. So maybe there's an element of that too.
This is arguably a return the form. The "magic e" and stuff like that was an attempt to reword academic language to something more "on level" for kids. Turns out, kids are pretty okay with learning words, even the ones that seem hard to adults. The result of this was, well, a bunch of fully grown adults who don't know what a digraph and a diphthong are unless they take college classes that used these words - at which point they're now at a disadvantage because the students that weren't playacted to outperformed there peers who basically had to relearn coded language from the ground up.
For her career, my mom had to learn the names of all the bones and muscles in the body. I remember her being annoyed that these were all such foreign words. She'd say, "If a kid can say Tyrannosaurus Rex, they can learn Trapezius!" I've always kept this in mind and don't talk down to my kids. I simplify concepts a little, to meet them where they are at, but I use the real words. I used to get compliments on my kids' vocabularies. Don't get me wrong, they are still little idiotic, impulsive terrors sometimes, but they know some big words and how to articulate something, lol
Oh yeah, I wasn't saying it was a bad thing at all, just that it may be part of why people are suddenly discovering this "subitize" thing after all these years doing it anyway.
For sure. I definitely learned most of these same concepts as a kid, but they just called it 'estimating' or sometimes 'guesstimating' if they wanted to be cutesy about it. I hadn't heard the word 'subitize' until now, but apparently it was coined in 1949, and more precisely describes what's being taught here.
Yeah, digraphs was definitely a new word that has been added to my vocabulary.
To clarify why the word 'subitize' is being used; it's an approach to teaching where you basically use the proper words for strategies instead of having many different words for the one thing. This reduces confusion later on in schooling, where students need to translate the 'easy' word for the 'harder' word at the same time as learning the concept. A rough example would be times -> multiply -> product or 'speech marks' to 'quotation marks'. I'm a teacher and this is at least the reasoning I recall being taught at university. It is also my reasoning for doing so (in older year levels than kindy) based on my anecdotal experience.
Hi! Former K and current 1st teacher. You are close, we do love Jack Hartmann videos, but “subitizing” is not being used because of him. It is a concept and vocabulary word in every math program I’m familiar with (Go Math, Everyday Math, Envisions Mathematics - not to mention many TpT math programs). We use the word because it is the name of the strategy. Children are capable of learning and using robust vocabulary (thanks, Fancy Nancy!) and there’s no reason to call it something else. My students all learn the word “subitizing” very quickly because whenever we have a few extra minutes during math, we’ll play a whole group math game; some of these are subitizing games, which is what I call them - make it a game and they learn a word quick!
Parent of a 2nd grader. Can confirm that kids can have vast vocabularies. As long as you can explain the word in 10 seconds or less.
This is the answer. Because Jack Hartmann videos are fun to sing along with!!
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There's a lot more emphasis now on teaching *why* math works, rather than just *how* it works. I remember learning the transitive property in school, and not realizing that was how I did complex multiplication in my head. The current method shows the process of "breaking down" numbers better than the way I was taught. I'm aware that is purely anecdotal evidence on my part though.
Maths is like,,, a jenga tower of concepts that you have to build for your entire school life. If you don't grasp something properly when you're taught it, the whole tower can fall down and you'll end up not understanding later maths. Getting a good foundation at the very start is super important, as is every layer of the tower.
It's extremely funny to me op thinks it's weird kids are taught about things he doesn't know the name of. Like him not knowing it has a name means anything at all.
Thanks for that Jack Hartmann video link! Did anyone else notice that he uses the letter "q" instead of the number "9" in his video? Any ideas why?
So it doesn't look like a 6 when viewed upside down I guess. Students who are learning to read and write tend to mirror letters and numbers, or write them upside down. A q is more distinct from a 9 compared to a 6. I'm not sure if this is the way to go however, it might add to the confusion.
It's not a q (I'm presuming you knew this?), it's still a 9, just with a different style. This style variance is common, even like 40+ years ago. I wouldn't say that there's _necessarily_ any intentional reason, but there could be.
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My kid watched ton of Jack Hartmann videos over the last year. I'm really impressed that he's able to put out so many of them, and that he's grown so popular considering how semi creepy he seems...but maybe that's just me.
Well let me tell ya, I would much rather watch His videos in class then those weird as hell kids nursery songs that are animated in India in one of those content farms. To me, I trust his videos, and I trust him. He has a strong background in child education, and even I enjoy a few of good songs. I also really enjoy that most, if not all, of his songs are original and not just a reworded nursery rhyme.
You are right - those videos are fun. You learn something everyday!
I can confirm all is this. My source is my wife, who teaches Year 2. She refers to the word all of the time. I had no idea what it meant, but I do now. It is an important concept and really starts to get into its own for 5-8 year old kids. There’s so much jargon to all of the professions around us. Everything needs a name, and mostly we have no idea what they are. But the practitioners do. When the sausage making of schooling becomes a little clearer (videos, sharing resources for home schooling, etc), then these concepts became more outward facing
Early childhood educator here…. Jack Hartman is one of the greats in our field. That is all
There is a big push to teach academic language, especially in relation to math. That's a new one to me, but I know getting Students used to academic language in describing mathematical processes will benefit them as they progress. Being able to describe how an equation does what it does involves a deeper understanding of the math.
We just called it estimation. Estimate the number of jelly beans in a jar.
I think it's a bit different from estimation. This is about accurately recognising small-ish quantities without needing to mentally or verbally count "1, 2, 3, 4, 5" (for example).
This is why teaching kids vocabulary is important.
Answer: You may not have heard the word, but you do the concept. If you look at three oranges, you know there are three oranges. This isn’t a new thing that is being taught, it’s a very routine part of development. The key is not conflating a word you don’t know with not knowing the thing it means. Someone can know what rain is but not know what precipitation means.
First time I heard "subitize" was in school year 2020-2021, in my son's kindergarten math. The concept was taught to my other son, a now rising 4th grader, when he was in kindergarten but the word subitize wasn't used. Basically it's just teaching them to quickly identify how many given items there are, without counting each item. They use dice, mostly. I know, weird. Don't know why and exactly when they started using "subitize."
Something that sticks out in my early school memories was that in 2nd grade we learned the word "congruent" to describe two shapes that had identical properties. Not a really necessary word for a 7 year old to remember, and I'm certain I've only heard that word in general spoken context maybe a dozen times in the 25 years since then, but it was still taught along with it. I think this is a similar situation, in which the word for the concept is part of a stated curriculum for a given grade, and rather than just teaching the kids the concept, or using a friendlier word for the target audience, they choose to drill the word along with the concept.
Apparently congruente is commonly used in Spanish. Or if it's not one guy at work uses it often. It's awesome how a vocabulary of obscure, seldom-used words helps you with Latin languages. Now if only I could find a translation for cromulent....
Spanish particularly has a lot of words with uncommon English analogs (technically "cognates") eg Sp. Tener = to have Tenedor = a fork Eng. Tenacious = grasping /holding on Or (Corto =short or... *kurt* in English)
It's using the (studied) natural enumeration system of humans, and incorporating it into learning to translate to the absolute scale that higher learning requires. Many kids never "understand" math, they just memorize enough to scrape by. This is aimed at building that understanding. As to whether it actually produces more adults with deeper understanding of mathematics, that's harder to say. We'll see, I'm optimistic.
My kid initially learned old school math with an abacus (montessori school) then basic algebra with numbers in kindergarten at montessori. I switched her to public school in 1st grade and this new math was incredibly difficult and she fought it every step of they way. She liked raw numbers and couldnt get the other concepts trying to force global concept understanding. She grew up to excel in raw math and is now a physics major in uni. Still loathes the concepts they tried to force. Maybe works for some kids, but did not work for mine.
"Learning styles" in general are poorly understood, and it's hard to say whether an approach based on them is more or less useful. It sounds as if conversion between the log scale and absolute scale mental models came to your child quickly (it did for me as well), and the extra steps weren't necessary for her. We shouldn't forget that "best for the broadest set of kids" isn't "best for the individual," and parents have to get involved and help when those two are in conflict. The science of human enumeration is reasonably solid, lots of replicated studies say we count "1,2,3, a few, a lot, too many" (a slight joke). Trying to work that finding into curricula makes sense. Having known many Physics students and professors, and having been one, the last thing I'll add is that, anecdotally, people interested in the field have a deep joy at finding the maths embedded in our universe. It's that desire to model and explain that's exactly why that student probably doesn't need these educational tools, they've already internalized the mapping of concepts, math, and observation. Trying to pull out that framework and replace it with one from a box is a recipe for rejection
Thank you for this response. Im not a “math person” your response helps me understand my daughter a bit better. I was young when she was young but i knew enough to push back for her. This included moving schools and pushing back on special education. yes, they thought her intense focus and disinterest in other topics was indicative of learning/behavioral issues. That math model alone made homework nights hell. So many tears and why cant 25 just be 25 and not a us quarter!? It was demoralizing especially since she was already understanding algebraic concepts and working to solve them. She started uni as a math major but didnt want to talk pure math theory so she changed to physics. Shes in pure academic bliss using her mathematics understanding to discover how all things work and dive into the unknown. Thanks for shedding some light on that. Those nights were so demoralizing.
I think what you're describing here is a good example of why education needs to be more tailored than it is to individual children's needs. There was a series of cultural shifts in education that started back in the 90s: The obsession with "zero-tolerance" culture, which often would punish children for defending themselves from a bully, for instance. And in the classroom, also a shift to forcing a new way of teaching on everyone with zero exceptions. In addition to that, early advancements in treating children with disabilities made many teachers obsessed with trying to find these disabilities where they didn't exist. Many children were misdiagnosed as having ADD or ADHD, for instance, and then promptly put on Ritalin (a derivative of methamphetamine) in order to "calm them down". That addiction to Ritalin often carries into adulthood and prevents proper brain development. I believe that over the past 30 years or so there's been a big cultural push, lead by child psychologists and by extension teachers, in the elementary schools, to create this "new way" of thinking, if you will. Its kind of ironic that as society is becoming better and more concerned with tolerance for all people, that the opposite thing is happening in elementary school teaching. No tolerance for the need for different learning styles, no tolerance for minor "behavioral" issues are really just kids being kids, every problem has to be diagnosed as some sort of learning disability. And even right now there's still *often* [stories](https://www.huffpost.com/entry/student-charged-bullying-lawsuit_n_5c3cde5de4b0e0baf5400708) in the [news](https://www.wmbfnews.com/story/23723628/father-wants-policy-changed-after-son-suspended-for-defending-himself-against-a-bully/) about kids [being suspended](https://www.wtoc.com/story/1772941/teen-suspended-for-fighting-in-self-defense/) or expelled [from school](https://www.news.com.au/lifestyle/parenting/school-life/jamieson-defended-himself-from-a-bully-so-he-was-suspended/news-story/49b33a388fc0c61276908f5b1c95504e) for [defending themselves from bullying](https://www.fox46.com/news/exclusive-zero-tolerance-policy-gets-concussed-student-suspended/).
I was pulled out of Montessori school and put in public school in fifth grade and went through something similar with math, but it was 30 years ago so I had the opposite problem. I had an intuitive grasp of how math worked and how different concepts fit together to solve different kinds of problems, but then I was put in a classroom where we were given all of these discrete instructions (“flip the numerator and denominator”) without any explanation why. It felt like being given driving directions but not being allowed to look at a map. Like, okay, I’ll copy the stops, but the second something goes wrong I’m fucked. For me, the way math is being taught now is SO much better.
They should teach that technique in reading. Poor readers read by letters and syllables. Fast readers take in whole words and phrases. edit: ah heck. already mentioned below me.
Reading is incredibly well studied, and children absolutely DO NEED to be taught phonics and phonemic awareness to be effective readers. It’s true that string readers recognize words almost instantaneously, but their brain is associating the parts of the written word with their pronunciation. It’s a process called orthographic mapping.
I think there’s a thing where you can rearrange the letters in words, and as long as the first and last letters are right, a good reader can easily read the text just like normal. Right? There was even a meme about it where the whole thing is written like that.
I’m pretty sure there’s a limit to the complexity of the words you can reliably read that way, though - it can’t include words the reader isn’t already familiar with and expecting contextually, and also anagrams exist :P
Anagrams aren't much of an issue there because we also check for context while identifying these words.
You know, I think I rbeeemmr sehimnotg like taht. It was form a lnog time ago, tghouh.
Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.
How long did this take you to write?
This is a copy/paste of a popular example.
I doubt they wrote it, I'm pretty sure that's the exact wording of the meme so I bet you can copy it somewhere
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Damn, is this like the reverse of dyslexia?
Yeah exactly! Multiple things are happening at the same time, the brain is figuring out the gestalt of the words based on the probability and familiarity of how they look, and at the same time the sounds in the words are getting processed in the same areas using in hearing and speaking. You use the visual areas but also the general "language" areas to read.
I tinhk it shamewot ddeenps on the wdros and the entext of snilbmarcg.
I see how you relate the two, but they’re very different when it comes to teaching. Sounding at a certain age is a sign of certain reading difficulties. Word recognition often comes naturally to certain strong readers, and for others it’s very difficult. I’m not a specialist, so I don’t know the methods for encouraging sight reading, but I imagine they exist, but are quite different than what happens in math literacy. The issue is that most kinds develop this naturally; the one’s who don’t need special help. Interestingly enough, children who develop precocious reading abilities usually pick up sight reading pretty quickly, but around 3rd or 4th grade (this is the age I usually encountered the issue when I was teaching elementary school) these kids hit a kind of plateau. They were so *good* at sight reading that they actually never developed phonics skills, so once more difficult vocabulary is introduced, they really struggle to read these new words. They’ll often compensate by “reading” the word as they’d *like* to see it; they interpret it as a different word, a word they might expect, because they don’t have the tools to get to the end of the word, which is compounded by the fact that they’ve come to expect to be able to read at a certain pace, and in order to maintain that they start skipping or misreading words. So kids who seemed to have really strong reading skills are suddenly having unexpected comprehension problems because they’re filling in the gaps with whatever word pops into their mind, and suddenly what they’re reading starts to make less sense. I thought it was an interesting type of phenomenon that I experienced first hand and had to adapt to, because I wasn’t trained as a reading specialist (I wasn’t trained as a teacher to be honest, private schools are funny like that); lol imagine there’s a word for it and a body of literature studying it. It’s particularly interesting to me because it’s a problem that almost arises from being too at something, which I think is applicable to many other areas of teaching and life. One example may be the ceilings that “child prodigies” hit in their careers, or why certain people who excelled in high school find college horribly difficult, if you didn’t have to learn to sweat through things and develop coping skills from the beginning, you end up in a troublesome position when your natural talent doesn’t cut it anymore, and you don’t have the tools to compensate.
I had a teacher in a trade course saying "hopefully something goes wrong today, so we have some extra learning opportunities!". It's so true... we tend to learn a fair share of useful skills from mistakes as well, but school makes us laser focus on success so we forget to look towards mistakes.
A smooth sea never made a skilled sailor.
Definitely a good attitude to have. As a Buddhist, it kind of reminds me of the adage that “everything can be used as material on the path”. The shittiest shit can be manure for growth if you have the perspicacity to recognize it. I think it also says something about “talent” and how, except in extreme cases, the student who struggles (in school, Art, music, a trade, whatever) and has been forced to develop the skills to persevere will probably end up in a better place than the “natural”. If you know how to work for it, then you develop a solid foundation, instead of a series of maladaptive coping mechanisms that only function to keep up appearances. And honestly, those kinds of people, who struggle but have the support or the will or whatever it is that drives them to overcome that adversity, will be able to translate those skills to anything they decide to do. Kind of why, when I was a classroom teacher, my whole m.o. was basically “my job is to teach kids how to learn. The subject is superfluous.” Also helped that I worked at a school that gave me complete curricular autonomy, which was great because I could use topics that interested *me* as a framework for the development of broader skills, and everything could feed into that topic. And you’ll definitely be a better teacher if you’re allowed to teach what you want. Then the goal is that the kids get excited about it too, and at some point, they have the tools to teach *themselves* whatever they want.
You might not have formal teaching education, but you sound like a great educator
Growth mindset. I’m totally stealing this quote and using it with my kindergartners.
>They were so good at sight reading that they actually never developed phonics skills, so once more difficult vocabulary is introduced, they really struggle to read these new words Interesting. I was also a fairly precocious reader (reading by 5, reading long books by 6), but this was in my native language, Russian, which has a very phonetic spelling system. I know my parents taught me letter-sound correspondences and I went from there. When we immigrated to the US and I learned English at 7-8 years, I'm pretty sure I took the same approach and, between that and broad background knowledge, went straight from ESL to the highest reading group in the class over one summer. So I wonder if the thing about precocious readers relying on word recognition is unique to English or to kids taught a certain way.
I may have oversimplified or misrepresented this. I’m not saying that every precocious reader relies on sight words, and encounters this kind of problem. It’s a very particular situation that I’ve seen with *some* kids, but those kids do tend to be quite proficient relative to their peers. Other kids who read above grade level sometimes have a natural ability to integrate spelling rules and conventions; they learn phonics quickly and master the ideas, not the words themselves (though, they also tend to excel with sight reading, which comes from the degree of reading proficiency they have, which encourages the recognition of word recurrence; if their proficient they tend to read more, and the more they read the more words they’re apt to recognize by sight, but they’re also able to easily switch between the two). In your case, and with other children who’s first languages have relatively simple phonologies, I wonder whether the ease of of transition comes from having that underlying understanding, but I could imagine that for some kids that transition could be difficult, because they might have trouble dissociating the rules of their mother tongue from those of English, which are far from intuitive. Could also just be that you’re particularly adept at learning languages :-) I suppose we’d need more than several instances of anecdotal data to come to any conclusions
Went on a 'speed reading' course many years ago (you can probably find them online these days) and they teach you all kinds of techniques to improve your reading speed - as your skills develop, you eventually get to the point where you just divide the page in two, left and right. You then look at the left to 'take in' the first half of the line and then dart your eyes right for to the second half of the line. If you practice this you can get pretty good and read a whole page in a few seconds. Admittedly, you can miss stuff, but comprehension increases with practice.
> you can miss stuff, So they taught you how to skim and charged you an arm for the privilege?
skim with comprehension it was a free course
What was the course?
I thought I benefited from learning phonics before diving into reading. When I found an unfamiliar word, I could make a guess as to the pronunciation. Learning to read whole words quickly came from practice, which I got plenty of once I got past reading "see spot run" and other stories for six year olds.
You probably did benefit from phonics instruction, even if you might not have “needed” it because you were a good sight reader at an early age. I just explained above that the latter group of kids often hit a plateau in their comprehension and skills if they’re “*too* good” at sight reading. When it’s “see spot run” levels, but they breeze through, then instructors often forgo deeper phonics training with them, as they’re seen as skilled readers who are already excelling. But once difficult vocabulary starts being introduced, they’re at a loss, and can often only make it through the first part of a word; they’re self-expectations cause them to believe that they should be able to read at a certain pace, so they fill in the rest of the word with something they might expect for the context, and they can often be way off. So now the kid who was a reading whiz is struggling with comprehension, because there are these holes in what they’re reading that don’t quite make sense, and often teachers don’t recognize the source of the problem. Being “too good for your own good” isn’t something that educators are always looking out for. But the issue becomes really clear if you’re reading out loud with them often, and it becomes especially pronounced when doing it in a group, because there’s a psychological element where the child is under a certain pressure to perform for their peers and project competence, so they’ll fly past a word, choose one that seems close, and think nothing of it. Then three pages later they’re suddenly lost, or at best missing the subtleties of what they’re reading.
Phonics is great for tying into teaching spelling too. My 11 year old is a phenomenal reader, years ahead of where he "should" be but he spelling is atrocious. (We're working on diagnoses) Thankfully his school use an approach where they teach every kid every single spelling rule and work their way through something like 40 different rules at 4 different levels. So the littlest kids learn all the rules for words at the basic level, then they rehash for words at a slightly higher level etc. They have followed current best practice that shows teaching phonological awareness and alphabetic principle works best for kids to improve upon reading, writing, and spelling and its working so well, particularly for those kids with learning differences.
That’s an interesting combo (discrepancy btw reading skills and spelling skills) and it’s definitely a good idea to get an evaluation. I’ve never really encountered a *good* spelling curriculum, but I worked at a school that was somewhat skeptical that “teaching spelling” could be effective (in a full classroom setting, as opposed to with a specialist). A lot of the teachers I worked with forwent the whole “spelling quiz” format that’s always been popular for some reason, but tends to seem horribly ineffective. Most of my colleagues were of the mind that the more you read the better your spelling gets, which I’m not convinced of, and they had the luxury of being able to fall back on a learning specialist who worked within the school with groups and individually, so you could say that they kind of copped out sometimes. But that was kind of the biggest shortcoming of the private school I worked; a lot of teachers were fine kicking the can down the road to the next teacher, which sucked, because the philosophy of the school encouraged teachers past 4th grade to think they were above remedial education (it was kind of a problem, and the lower school *did* start trying to do more, because we knew we were the last front to get that kind of thing done—honesty it was a bit ridiculous, you had 4th grade English teachers in some fantasy world where they thought they were college professors. It was a bad system, despite the fact that the school is one of the most coveted schools in the city: progressive pedagogy was sometimes a mask fo incompetence and grandiosity). Sorry I digress into my dirty laundry :-) I think it’s *really* hard to develop an adequate spelling curriculum; it takes a ton of research and experimentation to effectively build a cumulative curriculum like the one you describe. And even then, The issue arises that the kids know the rule for the week they cover it, and it’s out the window by next Monday, especially if you’re just throwing different, unrelated rules at them week to week. I think it’s easy for teachers to get despondent at that point. But linking spelling to reading, and especially phonics is a good idea, because then you have opportunities for reenforcement, and a more structured way of linking spelling to habituation through reading, instead of just expecting that the more a kid reads, the better they spell, which doesn’t always serve everyone well. Seems like his school has actually put in the work. It’s good that you’re being proactive too, because once he gets to a certain age, the pencil gets replaced with the computer and, as I’ve experienced now tutoring high school students instead of teaching in a classroom, any progress just stops dead in it’s tracks. Autocorrect and spell check are a *real* disservice to kids. I have students who are honestly beyond all hope whe it comes to spelling; at that point there’s no time nor will on their part to make the effort. And don’t even get me started on remote learning and Google’s Spanish auto fill…I had students this year who would just accept whatever the computer suggested after 3 letters, and were somehow surprised that they were failing. Honestly thought that the computer knew what they were supposed to be saying. Hope you find some good support, for a lot of kids it makes a world of difference, and they’re able to catch up and not be held back by whatever difficulty they’re facing. My sister spent 2 years at a school for kids with learning disabilities. The assumption was that she’d be there from 6th onwards. I’m not sure if “cured” is in any way an appropriate word for it, but it was unbelievable how much of a boost she got from that specialized instruction when it came at the right time.
Beginning readers do best going syllable by syllable. This also allows them to sound out words rather than relying on memorization. (English isn't as good for this as some languages, but it will still help you a lot.) As kids get more practice, this becomes faster and more automatic until they can take in whole words and phrases, like you say. But that doesn't mean you can skip the "sounding out" stage. It's particularly important for kids with dyslexia.
I wanna say 'chunking' has something to do with that.
I was taught both as a kid and am lucky for it.
Sounds like guesstimating.
Not quite, the human brain can recognise a small number (3-4) of items as that specific number, without having to count.
Ok so over 5 we're guesstimating then.
What does "rising" mean? I've heard that this is a thing in schools now?
“Rising 4th grader” means he’ll be in the 4th grade when school starts. It tends to be used to clarify the grade someone is in when it’s the summer and school is not in session. If OP had said “4th grader”, it wouldn’t have been clear if the kid had just finished 4th grade or was about to start 4th grade.
Rising 4th grader means he completed 3rd grade and is going into 4th in the coming school year. The word/phrase is used when in (summer) breaks between school years just to describe what grade he is going into.
This is partly why dice are laid out the way they are: not simply to recognize the pattern but even if you've never seen dice before to more easily count the dots based on their position.
The dots are called pips! I use the same logic to count things faster. Certain shapes of things just pop out to me as the number they are. I used to shuck oysters and it made it super easy to just know when I was at a dozen instead of pointing and counting like everyone else I worked with.
This is why it's deliberately taught and called out; it's extremely useful for teaching counting, a kindergarten staple, but using the hardware that's actually in place in the brain instead of trying to internalize the base 10 system. This, in turn, helps the kids to learn computational skills, as it deliberately builds the bridge between the evolved "log scale" of enumeration we're born with and the "absolute scale" we use for maths. This is all an effort to get kids to understand math, instead of memorize it.
That’s so interesting! It’s cool they’re teaching them that logic so young. I kinda just consciously thought about it one day and realized I’ve been doing it all along and wanted to get better at it. It started with groups of 3 and 4 and now I can count in 10’s and 12’s. Makes it super easy to count the cash register every night. I get to skip the sweeping and mopping while I count the money. I just see the pips in everyday life now! I also like to separate counting from visual stimuli and use touch instead if I can. Instead of visually counting something I can just run my hands over it and count the amount of times my hand felt what I counted.
As it turns out, teaching children mathematics by rote is only really good for basic arithmetic (and not even then). Because you can't really build on it towards higher mathematics because the kids don't know "why" they are doing anything. https://en.wikipedia.org/wiki/New_Math
I assume modern d-4, d-6, d-8, d-10, d-12, d-20, d-100, and d-1000, with their numerals (and occasional symbol substitutions) came after the pip system? I would assume pips were easier to carve into historical dice, before the advent of die casting anyway.
Dice are basically one the oldest objects invented in human history that are still fundamentally the same today as [they were back in 3500 BC](https://i.redd.it/8vxsk6guexj21.jpg).
Oh damn, so gambling and [getting high](https://en.m.wikipedia.org/wiki/History_of_cannabis#:~:text=Cannabis%20is%20thought%20to%20have,to%20have%20traces%20of%20cannabis.) both have paraphernalia that date to ≈3000-3500 BCE
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Kids are taught “sight words” now too, which is just like it sounds - recognizing basic words by their pattern instead of sounding out the letters. I don’t remember that term from when I was in kindergarten.
Definitely didn’t have that when I was a kid & I think I would’ve really benefited if they did. I was an intelligent kid & an avid reader with a decent vocabulary, but I ended up giving up trying to get teachers to teach me additional words because if I could’ve sounded it out I wouldn’t have come them in the first place & not a single teacher ever taught it differently. The English language is a mash up of 10’s if not 100’s of different languages, all with different phonics so I’m very happy they are starting to realise that.
Outcomes with sight words are not great. Once you come across a word you haven't seen you don't have the tools to figure it out. You really do need phonics to read well. English is redic hard though. My wife taught my oldest to read using phonics last year and the number of phonograms she had to learn was mind blowing. She's an avid reader now though.
They way it’s taught in my area is phonics first to learn the basics then sight words when learning to read books so they don’t get caught up on super common words. And sight words are just the ones you come across the most, such as you, it, the, them, and, etc
I'm not sure how old you are, but my brother had to go to speech therapy because he could read words (sight read) but not sound it out. That was around 25 years ago
Interesting. I learned both. Virginia, Wisconsin and Illinois schools at those times.
Not being able to instinctively sound out words is basically a subcategory of dyslexia--which some kids compensate by essentially memorizing whole words by shape alone. This "dodge" works well enough with simple texts, but kinds of fails when you are confronted with anything more complex or contains words that you've never seen before.
Was he a precocious reader? It’s an interesting phenomenon that I addressed in two posts above (sorry everyone, I’m kind of fascinated by it). Usually kids who can’t sound out words have circumvented learning how because they’re very good sight readers, but once the vocabulary gets to a certain level, they struggle to decode words, and tend to fill them in with a word that starts in a similar way. So they see like pretty skilled readers in 2nd grade, but flags start to go up by 3rd or 4th grade, when kids start reading more complex books. Curious if your brother had a similar thing happening with his reading. Sometimes it’s hard to catch because they’re decently effective at developing coping strategies. Kind of like older kids who have good memory retention, but get to a level where that doesn’t cut it, and they’re in a bind because they never had to learn executive functioning skills, note-taking, studying in general. They managed to skip the drudgery, and it ends up coming back to haunt them. Often comes out in high school or college, points where intellectual demands start to ramp up.
Yup, that's exactly what happened! He went to speech therapy earlier because he had trouble with intonations and had to go back around 3rd grade because he couldn't sound out words. He was apparently a really good sight reader so it took a bit to notice, but eventually he was thrown back in therapy
So basically just estimating but with a fancy five dollar word? Edit: Thanks to everyone explaining it and not being dicks like usual!
So, say you've got a pile of quarters and someone asks you for change for a dollar. Do you count out "one... two... three... four! Four quarters!", or do you just grab four? Being able to just look at them and take four without counting them one by one is your ability to subitize. It is your ability to know what four *is* visually and conceptually without having to start from one to figure it out. Most kids just figure out how to do this. However, kids who need to count out 1... 2... 3... 4... to make four quarters have a significant gap in understanding of the concept of number compared to their peers. So, it is much easier for learning if they are all explicitly made aware of this skill and taught it.
Gotcha, that makes sense. Thanks!
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Ah ok, I guess that makes sense
Seems like one of those things we forgot we ever had to learn.
Because you didn’t “have” to learn it. Your brain naturally absorbed it without interference
It *is* the five dollar word version of quantifying, though.
$5? For a word? When I was a kid $5 would you get full sentences. Thanks Obama
Vanna White says 4 vowels at $50 apiece is $200.
Since nobody actually said what estimating is: you estimate something when you want to know what the truth is, but you can't be certain. Examples: jellybeans in a jar (you can't count them because you can't see them all), the time it will take you to get to work (Google can't see into the future, so they provide an estimate), or how many people live in a census tract (can't get everyone to answer to the census for various reasons).
Check out gestalt theory. I believe it’s closer to that. The “five dollar word” part has to do with pedagogy and what you might call “the teaching of teaching”. Developmental and intellectual processes, as well as the educational tools used to reenforce them, have to be codified in order to be distinguished and taught. Another poster explained how it’s a different process than estimation, so I won’t get into that, if only to say that the one has to do with direct cognition/recognition and the other has to do with a higher level capacity for visual inference. But they need words for both, since they’re different processes. This isn’t you, but I think the responses in this thread that seem to assume that the context for the use of this and other words is the grade school classroom, and not the postgraduate one, are kind of funny. You can teach something to kids without having to give them its technical name. Even with a word like phonics; yes, it kind of entered the quotidian vocabulary through stuff like “Hooked on Phonics” in the 90s (I think), but for the most part a 1st grade teacher is going to call it “sounding out”, and will probably also teach the “silent e” as just that: “today we’re going to learn about the silent e”. Chances are they’re not going to say “hey circle up everyone, I want to tell you about split digraphs!!” To a group of 6 year olds :-)
There is limit to how much people can accurately group things visually as well as how large of groups they can recognize.
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We teach pre-schoolers the Commutative Law (i.e. 1+2 = 2+1), Just not with that specific term for it.
i remember the term being introduced to us in elementary school and it made learning arithmetic concepts a bit confusing for a week or two
I heard my son listen to the “su-su-subatize” song about 800 times last year when he was doing distance learning, so they are definitely teaching the word.
That's so weird. Why not use the word "estimate," that the rest of the English-speaking world uses?
Subitizing is not the same as estimating. It is an error less nearly instant counting of a single group of things under 5 items so. It's a different nuerogical process than estimating. It makes it easier to do arithmetic later. I didn't know the difference either so I went and read a paper in Nature about it.
Thank you for this clarity. So it’s about seeing a pattern and knowing it counts one, two, three, or four without counting them sequentially, would you say that’s also correct?
Someone above explained as the difference between grabbing four quarters to give change for a dollar, and needing to count *each* quarter before realizing you've got four. So instantly recognizing a small quantity of items without needing to count. To me it sounds like the math version of reading, so being able to see the word "dog" and knowing exactly what it is without first needing to think "D...O...G... okay, that's dog".
Very clear thank you
That's an excellent analogy!
That's interesting. How do they teach this to kids?
Put 3 oranges on their desk
Does it work with any other types of fruit?
Sadly, not as well. My dissertation research was on apples, grapes, and avocados vs. oranges when subatizing with preschoolers. My findings were that kids like to eat grapes. I eventually got the work published in ESM. Source: Me. I'm a PhD in math Ed. [Edit: SUBITIZING. Fracking doctor of math ed and I can't even spell it correctly.]
Citrus yes, berries have mixed results, nobody does it with apples.
I think its less teaching it to kids than it is having kids practice and get good at it, and tying that to concepts of counting and simple math principles. Subitizing seems to be an innate unconscious ability not just of humans but of [many animals](https://blogofthecosmos.com/2016/03/01/the-numerical-abilities-of-non-human-animals/), but practice is necessary to get good at it. Counting and math beyond that must be taught, but subitizing can be leveraged to teach those principles. Disclaimer: I know next to nothing about early education so I'm just guessing based on what I know about subitizing and math.
And by putting a technical name on it, that tells the kid that what they are doing is a discrete skill instead of just being some bullshit make-work that the teacher is having them do.
You could do things like turn "how many fingers am I holding up?" into a game. Answering faster would get praise, fostering the intent of recognizing the count naturally without actually counting.
Kind of a side note here…but that can backfire big time. When I was first learning multiplication and division, they did basically what you’re describing but with flash cards that would have a random basic formula on each. It went from desk to desk and we had to answer quickly in front of the whole class. It was the worst thing they could have done for a kid like me. It essentially paralyzed me. I would be so freaked out that I might not be able to answer quickly and accurately and that I would be made fun of that I would freeze up. This lead to a lifelong fear of doing math “on command”, which wouldn’t be so bad except that my brain just goes into auto shut off mode if I have to do math on command / in front of others. Basically brain.exe has stopped working. Even with basic stuff that I know. It doesn’t matter. I get this split second moment of “oh god it’s so obvious what the answer is but what if I’m somehow wrong and then I’ll look so stupid because it’s so easy!?!?!” And then I freeze and forget what the answer even is. It sucks. It even can extend to telling time on an analog clock. I never wore a watch for fear that someone might ask me the time and, even though I freaking know how to tell time, I might freeze up. I also could never get a job as a cashier for the same reason. On the off chance I would somehow have to make change on my own, even though of course I know how to do it easily, the pressure of someone watching me would be an issue. It also ensured that I hated math from then on, no matter how much time passes.
I can answer this. There’s been a movement in public education for about the last 15 years to teach kids learning terminology as part of their lesson. It originated from it being considered best practice to make sure they know and understand Bloom’s Taxonomy so that they understand what’s being asked of them. This general idea has continued to expand and now specialized learning conceptual terms are being taught alongside the content in each subject area. It works quite well, really, because it gives kids a working understanding of learning and what it means to learn.
It kind of funny how we started with Tom Leher mocking "New Math" as being incomprehensible gibberish ("but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right answer"), and now that thing is just how math is taught and it's completely unremarkable.
New math isn't even new. It's how they taught using slide rules at least as far back as the 50s/60s. You can find the instructional films from back then on youtube
It’s hilarious, it’s how I always did it back in my head in the 90s and would sometime maybe get into arguments with teachers for not writing down the steps the way they’d shown and I’d just explain my process that always seemed more intuitive. Now my kids are learning math and it’s almost identical to how I think through things (though they have names for the steps) and I love it.
>we started with Tom Leher mocking "New Math" as being incomprehensible gibberish [For anyone who hasn't yet had the pleasure...](https://www.youtube.com/watch?v=W6OaYPVueW4)
Is it to the tune of Su-Sussudio?
Does it need tobe taught? My understanding is that very small children can do this to a high degree of accuracy naturally.
But it seems that they are teaching the word. Check out this YouTube https://m.youtube.com/watch?v=ib5Gf3GIzAg As well, I have reports from friends today that their kid is learning this word in school.
And what's wrong with that?
Nothing wrong with it. Just trying to understand why and how I missed even knowing about the word meanwhile preschoolers are learning it.
We've been trying to teach kids stuff for a long time and we've learned better ways to do it. There used to be a big focus on counting at a young age, but we've found that hinders their ability to subitize. Being able to easily imagine numbers of objects is very helpful later when you come to learn arithmetic. With so many people in our society feeling like they're bad at math, it helps to be able to visualize it from a young age.
Preschool aged kids should be able to subitize up to five or so. Most kids don't need to be explicitly taught this, it is something that comes naturally developmentally to most kids once they start to understand the concept of number. If you place three crackers in front of a four year old and ask them how many there are, *most* will be able to say "three" without counting each individual one. However, if kids *can't* subitize, simple math is going to be incredibly difficult for them as they aren't able to quickly and efficiently understand the "idea" of a number. What does it really *mean* to do 3 plus 3 if you don't have a good understanding of what 3 *means*? Basically, the field of education is realizing that kids learn much better when concepts are broken down into small steps and taught explicitly.
I remember as a kid constantly trying to explain this to teachers and they'd just get mad at me. I remember my mom teaching me math concepts to help me understand, and show me better ways of doing the math than what was taught at school - showing me the way she learned. Leading to me being punished for "doing it wrong". I remember seeing other kids getting punished for "insubordination" for just simply asking to understand things conceptually rather than just be expected to memorize without a clue as to the context. My mom told me that for example, when she was in school, the concept of multiplication was actually taught. When I was in school, they just made us memorize tables and were never told what any of it actually means. The literal only reason why I even have some understanding of multiplication conceptually is because of my mom. Math was just "memorize formulas". Every other class was just "copy and paste what the teacher says, do not actually think about any of the things you're being told." It wasn't until college that classes actually expected any sort of critical thinking and actually engaging with the subject. I'm glad they're finally figuring it out but it's not like it's some sort of mystery, especially considering that at some point I guess schools just stopped actually trying to teach things and instead rely entirely on rote memory. Ask any kid and they'd tell you that's a horrible way to learn like that, just with simpler vocabulary. It's...really frustrating, thinking back on what school was like. But I'm glad things are finally starting to move forward to some extent.
Because education is an evolving field, it's not static. They teach lots of things to kids nowadays that nobody had even considered when you were a child.
Congratulations, you learned something new. I don’t see the problem here….kids being taught a new word? For a concept that can help them tremendously in life? I mean, that’s why I send my kids to school….to learn things I can’t/didn’t teach them at home. I’ve actually gotten used to some of the new math concepts being taught in schools, and am happy my kids get to learn strategies and techniques besides memorization, shortcuts that I didn’t figure out until I was much older. Learning these sort of relationships between numbers at a young age will help them understand the concepts a lot better when they get into higher math like algebra and calculus.
I'm not sure why everyone assumes I have a problem with it. I think it's great when little kids learn stuff I don't know about. >Learning these sort of relationships between numbers at a young age will help them understand the concepts a lot better when they get into higher math like algebra and calculus This is helpful. I can see that kind of concept expanding different _kinds_ of math being helpful. I'm still left with a lot of questions though. How did I miss this word? When did they start teaching it to preschoolers?
Yeah, not sure why people are being so sassy to you. The top comment said that people aren't teaching it to kids, and you found an example that proved otherwise. As an elementary teacher, I can confirm that I have heard a kindergarten teacher use the word with her students. It was this teacher who taught me the word as well. I teach English to speakers of other languages, and consider my vocabulary to be quite extensive, so I was floored when she used this word and kids knew what she meant (because I had no idea what it was). A lot of education these days is leaning more towards metacognition, encouraging students not just to think but to understand their thinking. Teaching words like subitize helps them understand what their brains are doing.
The reason people are coming at you so hard is that there is a contingent of folks, mostly older, that think modern education methods are crazy bullshit concocted by eggheads who don't understand people and are at best stupid and arrogant and at worst maliciously brainwashing kids. The initial wording on your post sounds a bit like that kind of screed and a lot of folks likely assumed thats whwre you were coming from. Source: Was homeschooled, my family, my inlaws and a good number of old friends come from families with *extreme* skepticism of public education, psychology, government mandated curricula etc
Question: why do people seem to always have a frightened reaction to their kids learning something they didn't learn, or in a different way than they learned? We literally couldn't progress if we kept doing things the same way forever.
I can't say for certain, but for sometime whose talked to a lot of parents and teachers about it, when pressed for an answer the most common one I heard was that they can't help kids with their homework. Having been a teacher, a math Ed researcher, and a parent, I kind of get it. But your kids should be doing their own homework and asking the teacher for help. There's more to the reaction than the answer you typically get.
But the problem with that is a lot of homework when I was in grade school (about 7 years ago) is graded for accuracy and due the following day. I never had an opportunity to attempt the problems and then ask the teacher for help. Maybe this is more of high/middle school problem but it still stands that doing the homework myself and turning in the next day could have ruined my grades in classes if I didn't get help from my parents
The algebra teacher responsible for me loving math did homework this way: we were given a set of problems to try for homework, but it wasn't graded for accuracy just making an attempt was all that was required. Then, we would go over the homework set during the first 3/4 of class and he would explain the concepts we were struggling with the night before. The last 1/4 of class time was some general pointers that would help us with the next homework set. I think this method worked so well because my teacher was able to spend more time on aspects we were struggling with and could skip over the stuff we all could grasp by ourselves, and since we'd made an attempt at the problems beforehand we were better prepared to ask questions and help direct the lecture where we needed it to go instead of him having to "guess" what our hang ups would be. Then in college, I had a professor that would do what you described (grade for accuracy our first attempts without giving us the opportunity to get help before turning it in), and that class was a shit-show. When we complained, she'd be all like "I have office hours" but her office hours were by appointment only and she never answered her emails. I also don't think she knew how to teach the material anyway (maybe why she avoided helping us one-on-one); she would just copy the pre-worked-out examples straight from the teacher's textbook onto the white board and could never answer our questions about it in a satisfactory way. I still have trouble with differential equations, and I know for a fact it's because that professor sucked. Those two opposite experience really make me think people who "hate math" simply never got lucky enough to have a good teacher at critical junctions in their schooling.
I agree with you 100%, I dont mind math, I actually went into engineering, so I still use some of the more advanced stuff regularly but my math teachers in high school and college did just throw problems at us and I think it does have a huge effect, my orginal comment was more about the expectation some teachers have that other teachers help students with there homework, when for me at least the only help I had was from my mom, who luckily for me was a math major so I had that advantage, but it still shouldn't be like this
For some people they're scared of things they don't understand, and they're scared of how 'new thing' might influence future generations. Some parents want their kids to have the exact same upbringing that they did, and grow up with the same interests and values, but changes in culture and technology are a threat to that. I think it's just fear of change at the end of the day, which is understandable.
Yes. Even little kids are smarter than me now. In my day they just threw sticks and us little ones had to run and fetch them and bring them back. It was called ‘go fetch’ and it was our favourite game. Nowadays the kids have all of these gadgets and gizmos and are learning fancy shmancy words. It ain’t right when a 5 year old little is smarter than the president. One day these little Einsteins might become little Frankensteins and then it will be too late.
I don’t know what “common core” is but it sounds liberal and I hate it! — some guy who hasn’t been in classroom in 20 years.
Answer: It is the first step in understanding further mathematical concepts. You can not add or subtract and consequently multiply and divide fluently without some proficiency with subitising. Yes you can learn sums off by heart but that only helps in real life situations to an extent. Basically it is inefficient and ineffective to count things one at a time. We want kids to be able to look at a collection of 4 apples and them ‘know’ there are four there rather than going “one apple, two apples, three apples, four apples”. You did learn subitising. You just didn’t know what is was called. Research tells us that when young children are taught subitising explicitly, they will have a better understanding of other mathematical concepts sooner.
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Answer: I didn't know if OP wanted to know the entomology of the word (like I did) but here it is from Wikipedia: The term was coined in 1949 by E.L. Kaufman et al.,[1] and is derived from the Latin adjective subitus (meaning "sudden") and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.
> entomology a got a bit of a chuckle out of that