Math calculation v. math reasoning

Arguably, u can be good at math calculation with only a good memory
to recall the steps in the calculation procedure, without a basic understanding.





David

That's the deal. I could understand someone being good at calculations but bad at reasoning but I don't get the other way around -- which is the way around Mo is -- he can write the equation but he can't get the answer (he can if he uses a calculator).

It's interesting that you mention "visual type things" because they had some fairly serious concerns (neurological, perhaps) about visual processing and short term memory.

He 's doing algebra at his age ?

could he be bored with the math calculations? I mean doing calculations can be boring - one math problem after another and maybe he isn't being careful as a result. Whereas reasoning (at least to me) is more interesting - it is requiring you to come up with a solution - pretty resolving a problem.

Does he like to solve things? Figure things out?

I wish it was boredom.

No.

I've got a client right now who has the same results as Mo (at least in this particular area). Her math reasoning is 96th percentile, math calculation is less than 10th percentile. It's problematic as there aren't a lot of jobs (given her other abilities/limitations) that can use the reasoning without the calculation ability. There are apparently different parts of the brain involved. I've been reviewing her neurology reports with a neuropsych friend for a while, trying to figure out what kind of assistance would be useful.

Thanks, ehBeth. We've been wondering if a neuro evaluation might give us more insight into ways we can help. Do you think it would?

I really wish I knew. I'm a big fan of neuro and neuro-psych assessments, but I'm also really aware that I've got an enormous bias in favour of science (v. social work and psychiatry for example).

I know that in the case of the client I'm trying to assess that the neuro assessment (which we had done on the recommendation of an occupational therapist - another of my favourite practical specialties) added so much information AND made her feel better. It hasn't made academic/vocational planning much easier for me, but she feels so much better knowing that she's not stupid - which she's been told for about 30 years. She is off the chart brilliant on spatial relationships but struggles to read at the grade 4 level. Finding a way for her to learn is challenging - but she is giddy knowing that there are things she is really good at (and having proof).

Two things.

First of all don't pay too much attention to these tests. They aren't very useful because they don't predict much of anything. You should take them with a big grain of salt and focus on your individual kid's real needs and wants.

That being said, I worked as a math teacher. One of my big pet peeves was kids who could memorize and repeat the calculations perfectly without having a clue about the ideas behind them. This isn't what real mathematicians do in real life. Math isn't about calculation, it is about ideas and critical thought and logic or what is otherwise called reasoning.

Calculation is much easier to teach than reasoning. And, one you leave school there is very little need to do calculation since we have software (or grad students) to do the calculation for us.

Math Reasoning is far more important than math calculation (if it were possible for a fill-in-the-blanks test to accurately measure either on of these).

I don't claim any expertise other than working with a lot of math and people who work with math, but compare an architect and a carpenter. It doesn't necessarily follow that someone who can envision a design for a building in all its detail would be able to actually build it the way a skilled carpenter could. I think people put a lot of value in math reasoning and see calculation as almost a given, but often the challenge is in seeing the relationships of the numbers, how to simplify, how to substitute, how to drive down to an answer. The good news in your case it that it is probably a lot easier to teach calculation. That's something schools used to really focus on (think math drills) but have now moved away from.

lots of real-life applications of calculation are important

my client wouldn't be able to tell you whether she's being ripped off in nearly any real-life financial transaction. she can tell you the theory involved in determing compound interest, but she wouldn't be able to determine if the monthly mortgage rate she's being quoted makes sense. She doesn't know if she's been given the right change at the grocery store.

She'll be right on in determining if a two-dimensional representation of a three-dimensional object is correct, but don't ask her to get the coffee and donuts and expect to get the right change back. No laziness or disinterest on her part, her brain can't do it.

I don't think that is so hard to understand.

True story - Last evening, one of the kids from down the street knocked on our door selling, candy and cookies for school. We bought three items. My wife, the kid and I all were able to reason out that we just needed to add up the cost of the 3 items. My wife said, "I guess we need a calculator". The kid agreed. I told them the total.
17.50 + 15.50 + 14.00

Doing math is a skill that is easily lost if you don't continue to do it. I know I can't do complex calculations in my mind like I used to be able to. I even find myself at times having to stop and think about the multiplication tables to make sure I have the right answer.

In my experience, except in rare circumstances, human beings can learn to do the level of calculation they need to.

I have always been focused on reason which meant I didn't do so well in math. Then the school had the good sense to put me into an independent study class. Once I was given problems that were interesting to solve I excelled since I would do the work I wanted to do. I did calculus in high school this way.

As a teacher I worked with many very bright kids who were the same way. I am now a computer engineer and many of us in that industry had similar experiences. Reasoning above calculation certainly works well in my highly technical field. Of course none of us are at the extreme of not being able to calculate correct change.

A few years ago I found a hobby that requires the ability to do quick calculation when I started playing poker. To play poker well I need to be able to consider possibilities and come up with a fairly accurate estimate of the probability of each one. These estimates need to be done in my head in a matter of seconds so I can make a quick decision at the table.

Poker is the first thing I have ever done where I actually need to focus on calculation. I have even taken to memorizing tables. Before this I never memorized anything including multiplication tables.

Funny I found that when I had a good reason to be good at calculation, I figured it out pretty quick and did whatever I had to do to learn something I felt was worthwhile.

I think this is a sign of intelligence. Many really bright kids have trouble being motivated at rote exercises that don't have an immediate purpose. The key with this type of kids is to focus on problems that interesting.

Inspiring curiosity is the most important part of education process.

Weird.

That sounds like my father's early symptoms of Alzheimer's -- he could still manage big concepts but day to day life was becoming difficult.

Which, in a way, is kind of the same with Mo.

I suppose I should be glad that his strength lies in reasoning but it just seems so impractical at his age. Thank you. I feel better!

Maybe I need to teach Mo to play poker. The opportunity to win some money off of me might encourage him to make the effort!

That makes a lot of sense. I'm reminded of countless conversations with our contractor. He often things my ideas are a bit wacky but working together we've managed to solve some problems.

I think the problems he has with calculation are related to the problems with short term memory. I need to find a way to push those basic facts into his long term memory with is very, very good.

Thank you.

Interesting.

My mom insists that she's bad at math but I have never seen anyone do basic calculations in their head as fast as she can. You can give her a list of numbers and she will give you an answer in seconds. She has never understood why anyone would need a calculator.

The brain is a weird thing.

Thank you.

I had a chemistry teacher who used to multiple 4 digits x 4 digit numbers in her head - I think her brain was a calculator.

Hi guys

Thank you for your valuable suggestion, That makes a lot of sense. I am reminded of countless conversations with our contractor. He often things my ideas are a bit wacky, but working together we have managed to solve some problems. I think the problems , He has with calculation are related to the problems with short -term memory. I need to find a way to push those basic facts into his long- term memory with is very, very good.

Thank and regards
Andy Charles

I am trying to figure this out as well. How can someone be good at math reasoning, but stink at math calculation? Observing kids, I see that they can problem solve in their heads, but when it comes to writing down equations to show their work, it falls apart. They often say, I know the answer, but can't write it down. I've searched and what often comes up is dyscalculia which is a math disability but what I understand it to be is that if you have this then you struggle with math calculation and math reasoning. I have suspicions that it may have to do with visual perceptual skills, spatial relationships which can mean a person can have difficulty with relationship of how numbers are placed for equations and recognizing that the symbol present tells us how to solve the problem. This also can include visual discrimination and visual figure-ground and also, maybe, visual form constancy. The other thing is that although these people struggle with calculating problems with pencil and paper, some are able to solve them using calculators. How important is it to write and solve problems on paper if you're able to do them math in your head or with the use of a calculator?