Why some students are good at math and others lag behind

"Former math teacher explains why some students are good at math and others lag behind"
The title of a news article shown on todays Yahoo site,
https://www.yahoo.com/news/former-math-teacher-explains-why-122744193.html

Looking in the section called "
Why are some students ‘good’ at math and others can’t solve basic problems?
", the article explains there something which is very reasonable, so to me seems credible. Other reasons are also possible, in my own opinion. But from that section of the article, effort + support + motivation is what makes success in Mathematics happen.

From the article:

It’s not true that some kids are good at math and others aren’t.

Does this include children with "learning difficulties" or Down's syndrome, for example? A corollary of this statement is that our brain's are all essentially identical. In other words, our DNA can affect our physical attributes, but not under any circumstances can it affect our cognitive abilities. That's politically correct hogwash, IMHO.

PeroK said:

From the article:

It’s not true that some kids are good at math and others aren’t.

Does this include children with "learning difficulties" or Down's syndrome, for example? A corollary of this statement is that our brain's are all essentially identical. In other words, our DNA can affect our physical attributes, but not under any circumstances can it affect our cognitive abilities. That's politically correct hogwash, IMHO.

Maybe the article is missing a few things. Excluding learning disabilities and some other diseases, I can accept that one particular section "Why some are good,... others can't solve basic..."

symbolipoint said:

Maybe the article is missing a few things. Excluding learning disabilities and some other diseases, I can accept that one particular section "Why some are good,... others can't solve basic..."

What is a learning disability? It stands to reason that, like everything else, learning abilities and disabilities are on a spectrum. We all have our strengths and weaknesses. The funny thing is that certain "disabilities" lead to someone being highly skilled mathematically.

The other funny thing is that if we were all identical, then there would be no civilisation. We need people who are good at maths, of course, but we also need practical people who can build things. It would be a terrible thing if our brains really were all much the same.

symbolipoint said:

effort + support + motivation is what makes success in Mathematics happen

I didn't see that in the linked piece, I guess this is your summary. Either way, isn't "effort + support + motivation" what makes success in any endeavor? I don't see where mathematics is special in this way.

All students are good at math, except those with learning disabilities. How do you tell if a student has a learning disability? They aren't good at math!

How can you argue with that kind of logic?

Vanadium 50 said:

All students are good at math, except those with learning disabilities. How do you tell if a student has a learning disability? They aren't good at math!

How can you argue with that kind of logic?

Its the way of operational definitions.

This article was not very well written. The title discussion was limited to one paragraph with only one explanation and did not comment on other possible theories. She presumably depended on a brain plasticity effect to support her proposition that all students can learn math. I guess she believes that with selected teaching techniques customized to each student, they will be successful in learning math.

One point that makes me a little wary about her research program is her statement that direct instruction works for 20% of students which she supports with a link to an article on Edgar Dale's Cone of Experience.
This article discusses Dale's work and states that "There is no scientific evidence to back up the percent-remembering numbers. " (emphasis his) when you read the full article which is not that long.

gleem said:

One point that makes me a little wary about her research program is her statement that direct instruction works for 20% of students which she supports with a link to an article on Edgar Dale's Cone of Experience.
This article discusses Dale's work and states t

That link there is pretty good. "Do the real thing", also consistent to some extent with more-practice and to applying what is being learned or studied.

does it matter what we consider as "math"? I was good at adding, but subtraction was hard, and still is. I was good at plane geometry, but calculus, and then sheaf cohomology, were really hard. and if someone tries to explain to me that "stacks" are just "categories fibred in groupoids", I turn the page.

mathwonk said:

does it matter what we consider as "math"? I was good at adding, but subtraction was hard, and still is. I was good at plane geometry, but calculus, and then sheaf cohomology, were really hard. and if someone tries to explain to me that "stacks" are just "categories fibred in groupoids", I turn the page.

The first part of that passage quoted reminds me of a time a elementary school student receiving tutoring for Mathematics asked, while becoming satisfied about long-multiplication, "why is Division so complicated?"

mathwonk said:

does it matter what we consider as "math"?

Thanks for the lead-in. In reading the OP link I discovered a video of an interview of Jo Boaler, Professor of Math in the Department of Math Education at Stanford. Stanford has been doing research in Math Ed for about 40 years. She discusses your question. The video is 1.5 hrs but a lot of ground is covered in Math Ed.
It rambles a little but on the whole, if you are interested in Math Ed give it a look.

She created the website YouCubed which makes available Math Ed research to school teachers who might otherwise not read because of cost or lack of time.

There is a disconnect between people who scientifically study what does and does not work educationally, who often sit in subject-matter departments like physics and math, and those who advocate for what they would like to be true, who often sit in education departments.

Vanadium 50 said:

There is a disconnect between people who scientifically study what does and does not work educationally, who often sit in subject-matter departments like physics and math, and those who advocate for what they would like to be true, who often sit in education departments.

Sure thing - easy to accept.

Someone really should ask the students, especially ask the students who have had trouble at any time along their educational Mathematics paths.

symbolipoint said:

ask the students

Not so easy.

Student evaluations really answer the question "how entertaining was the class?" and "how lenient were the evaluations?" You can try and get around this by evaluating the Calc II class after the student is done with Calc III, asking "how well did Calc II prepare you?". That has its own problems, but a big one is that it selects for successful students.

Couple that with the general problem of asking someone who doesn't understand the material to explain what is going wrong and you have a mess.

The best work I have seen along these lines was a multiple choice test where each distractor was the product of a particular misunderstanding. Analyzing not just which questions were wrong but which wrong answers was selected was enlightening. But you can't put this much effort into every single assessment.

Vanadium 50 said:

Not so easy.

Along with the rest of that post, great experienced discussion.

My thoughts were to include the much less-advanced students. If you ask many of them why are not good at Mathematics, two kinds of responses will pop-out at you.
(1) The very imprecise, "I just don't get it."
(2) The just as bad one of, "I just does not click." (not much different from "(1)" ).
(3) the very discouraging, "I will never use this stuff".

And when I say "much less-advanced students", I mean BOTH adults and children.

I mean, I'm curious, is there any special reason you're focusing on Math, rather than, say, Physics, Chemistry, etc? Does something hold for Math that doesn't for other areas?

WWGD said:

I mean, I'm curious, is there any special reason you're focusing on Math, rather than, say, Physics, Chemistry, etc? Does something hold for Math that doesn't for other areas?

If that is to me, not really much special reason. I am just telling about the article I found online.

WWGD said:

I mean, I'm curious, is there any special reason you're focusing on Math, rather than, say, Physics, Chemistry, etc? Does something hold for Math that doesn't for other areas?

Here is a possible opinion on why the article and other discussions like it focus on Mathematics.
Fundamental skill, fundamental knowledge, necessary to include "general Mathematics" for elementary school education. Part of basic literacy. Mathematics may seem to stray from basic literacy just after "Algebra 1" as taught in high school.

I am pretty good at math. Better than the average bear.

Unless the numbers have dollar signs attached. Then I suck donkey chunks.

I don't mean arithmetic ... 13% of $1.79 kind of math is trivial for me. I mean accounts payable/receivable kind of math. I was unable to complete my tax form because the final number was either positive or negative, and I had not the slightest concept of whether that meant I was getting money or losing it. I literally did not know which of two boxes on the very last line of my tax form to put it in, and it utterly paralyzed me into paying someone to finish it.

I am currently doing billing for a living and I simply cannot learn any new tricks because of this.

It is not about being good or bad at it; it is about the richness of the models in my head and the degree of stimulation I get from manipulating them. I am utterly uninterested in the flow of money, and so cannot force enough neurons to fire.

But maybe that's just me.

DaveC426913
I do not know what to say about your posting #20. I will try. One of the most interesting conditions you describe. You are so likely like some other people. For myself, I am also uncomfortable with some money-handling and money-discussion situations. The language used feels odd and I cannot think clearly what I hear in conversation; and if put onto paper, I could still be confused. On contrary, basic algebra for use in communication in a structured way both on paper (or some display board) combined with conversation is more comfortable and generally more understandable (for ME, that is).

This brings me back to an earlier thread I started: Kids are born scientists.

These two posts - and the link I refer to in both - really sum up my thoughts about the subject:

• https://www.physicsforums.com/threads/kids-are-born-scientists.942137/post-6112938
• https://www.physicsforums.com/threads/kids-are-born-scientists.942137/post-6114176

jack action said:

This brings me back to an earlier thread I started: Kids are born scientists.

These two posts - and the link I refer to in both - really sum up my thoughts about the subject:

• https://www.physicsforums.com/threads/kids-are-born-scientists.942137/post-6112938
• https://www.physicsforums.com/threads/kids-are-born-scientists.942137/post-6114176

The prima facie evidence is that humans have a range of natural abilities in all respects: music, language, mathematics, social skills etc. We appear to be all different, in other words.

I met a successful sculptor once and we talked all afternoon. His brain was so different from mine. He wasn't a born scientist. He was a born artist.

When I started on PF ten years ago I had done effectively no maths for nearly thirty years. I had no right to be helping current university students with their homework. Also, when I was a student I was often ahead of the lecture - predicting where it was going and ploughing ahead myself. That was a particular skill I seemed to have. There were three others in my class who were ultimately just as good as me. But, none of them could just "see stuff" as quickly as I could. I used to have the strong impression that the material was already in my brain and the lectures only shone a light on what was already there.

This started at the age of about 14, when I shocked my maths and physics teachers a few times by just seeing stuff that I hadn't been taught.

Ultimately, i wasn't a brilliant mathematician and went into a career in IT. So, mathematics ability is not one dimensional. I had a huge ability to see undergraduate material very quickly. But, that doesn't necessarily translate to being a successful mathematician.

Even those of us who are naturally good at maths are good in different ways.

PS I don't remember what age I was at the time, perhaps 12-14, but here's a story.

There was a book of card games in the house and it had the odds of being dealt each poker hand, from a pair to a royal flush. I put the book to one side and worked out all the probabilities.

I don't remember whether I got them all exactly right first time, but I do remember realising that the exotic ones, like a straight flush, were much easier to calculate than more likely things like a pair.

How does that tie in with the theory that all kids can do that? I didn't even know probability theory was a thing! It was just something I could do from pure, natural ability.

PeroK said:

How does that tie in with the theory that all kids can do that? I didn't even know probability theory was a thing! It was just something I could do from pure, natural ability.

That is much different than the less-advanced topics which elementary and lower-secondary students are expected to learn. Not many students will be talented at Mathematics, but more of them can learn the expected material than they believe. Effort, good instruction, and practice.

A mid-ground is a possibility (opinion). Some students may be "good at mathematics", some will always "lag behind"; but between those two kinds is another kind - Maybe not as talented as those who are good-at-mathematics but can learn most/all of basic arithmetic and general consumer-level stuff and at least a little beyond Algebra 1, before really starting to struggle.

PeroK said:

I met a successful sculptor once and we talked all afternoon. His brain was so different from mine. He wasn't a born scientist. He was a born artist.

Being good at something doesn't mean you cannot do something else.

You don't have to be the best at what you do to claim to be able to do it.

Not that long ago, people would have said not everybody can read and write; some better stick to manual labor. Since school is mandatory, it appears everybody can read and write. Does that mean that everybody can write a 1200-page novel? No. Do we say that someone reading 50 words per minute (wpm) doesn't know how to read because someone else can read 350 wpm? No.

If you are not a good race car or semi-truck driver, does it mean you can't drive? No.

Humans are born readers. They are born runners. They are born artists. They are born scientists. We can expect all of that from a human, any human.

Some of them will perform better in one field than in another. Nurturing them in one field will most likely increase their chances of excelling in that field. Discouraging them in one field will most likely destroy their self-confidence in that field.

Genetics do play a role. You prefer a Collie for herding livestock, a Cocker Spaniel to hunt, and a Doberman for protection. That doesn't mean they can't do anything else. A dog is a dog: they can all run, they can all play catch, and they can all be trained even if some are better than others at certain tasks.

Not being the best at something doesn't mean you shouldn't do it and leave others to do it for you.

That's why we have hobbies.

jack action said:

Since school is mandatory, it appears everybody can read and write. Does that mean that everybody can write a 1200-page novel? No. Do we say that someone reading 50 words per minute (wpm) doesn't know how to read because someone else can read 350 wpm?

I thought you were talking about everyone being approximately equal. There is a huge range of linguistic abilities across the population.

If you're wrong you're making life miserable for a huge number of kids by forcing them down the academic route.

There are millions of young people in the UK saddled with crippling student debt to achieve a largely worthless degree. All because of ill-founded ideas that everyone should be going to university and performing academically.

jack action said:

Being good at something doesn't mean you cannot do something else.

You don't have to be the best at what you do to claim to be able to do it.

Not that long ago, people would have said not everybody can read and write; some better stick to manual labor. Since

Jack action makes a good point!

jack action said:

If you are not a good race car or semi-truck driver, does it mean you can't drive? No.

....and he continues to make that point; like what was just said, in-between the talented and the 'laggers'.

PeroK said:

There are millions of young people in the UK saddled with crippling student debt to achieve a largely worthless degree. All because of ill-founded ideas that everyone should be going to university and performing academically.

Some people can make the argument to support vocational training. Both academic achievement AND vocational training (job skills) are important. BOTH should be encouraged.