How can an executive deficit affect maths?

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jw

Well, executive function deficit has implications for math. What most people mean by "math" is manually performing algorithmic procedures, such as arithmetic calculations (eg the notorious long-division algorithm), algebraic symbol manipulations (eg factoring), calculus (eg taking derivatives) and so on. In most students' experience, only geometry differs substantially from the usual math. Almost all high-school and college level math is doing algorithms by hand, and that's basically using your executive function ability.

To perform math algorithms, you have to remember each step and do it in the right order. You must also work neatly to keep track of what you're doing. You must also be accurate, and actually write down the numbers you intend to write down in the correct order. As you progress, you must remember everything that you've done before when you need it. Calculus is an extreme example, because as you start applying calculus to solve problems, you basically have to be able to recall instantly everything you've ever done in trig, geometry (particularly area and volume), and every algebra technique.

Speed is also an issue. You know the old saying, good fast cheap - pick any two. People with AS could do good work, with neatness and accuracy, but they wouldn't do it fast because of the executive function issues.

All of this is difficult for someone with AS. The more numbers you see on a page, the more jumbled they get in your mind.

I think the main difference between AS and someone who just struggles at math is that someone with AS knows what they need to do, they just can't do it either because of memory issues, executive function issues, or neatness issues. I don't think it's a coincidence that people with AS heavily shaped the computer industry, since we have programs to do artificial handwriting (LaTeX, word processors), math algorithms (calculators), and symbolic manipulation (Maxima). All of these compensate for the executive function issues.

Last edited by Trencher93 on 15 Aug 2012, 10:41 am, edited 1 time in total.

I was going to answer this, only to discover that Trencher already had.

For what it's worth, I have pretty much every problem Trencher mentions, and I still got up to differential equations (and applications thereof in engineering). I take about twice the time that everyone else takes, I get extended time on tests, I have to write out every little step, so I use lots of paper--but I get it right just as often as the other decent students in my class do. Math is a weakness for me academically, but because I'm a good student overall and have learned ways to compensate, I've grown to love it and use it competently. So if you like math but find it difficult--take heart; there are ways to work with your unusual cognitive style and learn to do math anyway.

I remember in college (long time ago now!) taking Calculus II and there was a point where my brain just couldn't hold everything I needed to know. I barely passed that class, and since that was the last math class I needed for my degree, I just gave up and forgot about it. What happened was like a house of cards collapsed. My mental concept of math just fell apart after a certain point. I could no longer absorb new concepts easily, and began struggling to remember old concepts. I probably approached the limit of a D- as close as any student ever came, but I passed somehow and just never looked back.

Only as an adult did I develop an interest in set theory and the philosophy of math. That's something you almost ever get exposed to in a normal high school and college education. A lot of people say they don't like "math" when what they're really saying is that manually grinding through algorithms is boring and they're not interested in doing what a machine can do for them. But that's only the tip of the iceberg for math.

When I solve a problem, I tend to try to do everything at once.

Instead of re-organizing I rush in putting all of the information at once and I get confused.


Like a shape game, where you're meant to re-organize the shapes in the correct hole but instead I'm pushing all the shapes in one hole at once.

Is that considered an executive problem? Do you know how you would deal with that too?

I would say that's an executive function problem, because you are overwhelmed by the number of steps you need to perform and have trouble putting them in the order they need to be done. I tend to run into this more with writing than math. I know I need to say A, B, C, and D but actually putting them into a coherent order and making sense tends to be the hard part. I guess math is more sequential and I don't notice it as much.

In the game of basketball, some teams run a full-court pressing defense. A wise coach described why they do this, and it's stuck with me. He said they do it because they want to speed you up so you will make mistakes. I tend to use this as a metaphor. If I start getting overwhelmed, I remember that something is trying to speed me up, and I will make mistakes, so I slow myself down until I am operating at my own speed.

I have NVLD, and after great difficulty with visual-spatial material, my biggest math hinderance is knowing what to do when given a word problem, as well as when the steps/material are presented in a different way or different order.

The only math I'm good at is algebra, because algebra is mostly solving equations, which is very logical, rule-based, sequential, and formulaic. There's not really much you need to "understand" about algebra, conceptually speaking, unless you are doing word problems or higher-level math applications. To this day, I still have only a partial understanding of the algebra behind coordinate geometry, and a large chunk of that understanding came when I took calculus and learned why the slope of a regular line won't give information about instantaneous change.

But even with algebra, I am doomed when it comes to word problems. I just do not have the ability to pick out the relevant information given from the extraneous information. And it's also difficult for me to remember or know how to obtain a needed value if it's not explicitly given. I have taken a great many chemistry courses, and to this day, I still do not understand stoichiometry. I also have difficulties with percent word problems, because I just don't "get" decimals and percents when used outside of a statistics meaning (i.e., "59% of participants tried placebo," or p < 0.05). Ever since elementary school, I only understand fractions. Even though fractions and decimals/percentages are equivalent, I just get lost without the fractions. When calculating a 15% tip at a restaurant for example, I have to take the total and multiply it by 3/20. The percent part just isn't concrete.

In this case, my math executive function problem is one of a failure to overgeneralize. And it always made me so mad in school when teachers would think I "didn't study enough" or something when I failed to overgeneralize. The way I made it through word problems was from memorization of steps and types of calculations that matched to certain patterns in the words asked in the word problem. No matter how many times I do the problem, it just doesn't "click." It's not that I can't do the actual math or computations. It's that I can't set up the problem. And it's doubly worse when it's a word problem where you have to draw a picture to understand what is happening. This is a big reason why, in calculus, I actually understand differentiation, both mathematically and conceptually, fairly well. There are rules to follow, and the rules are mostly algebra-related. Integration, on the other hand, is something I never mastered. For one thing, even the basic conceptual understanding of integration involves visual-spatial drawings, and I never could get the hang of how integrating was differentiating BACKWARDS. I never was able to do basic integration problems without showing every step, so when the rest of the class could do the steps in their head after two or three days, I was lost.

So, in summary, math executive function problems aren't always a matter of not being able to know how to the actual math computations.

How do you think I can deal with it?

Btw, if anyone can help me.

This is what kinda happens visually


http://tinypic.com/view.php?pic=35816i0&s=6


and an example:

If there were 193 episodes, 25 minutes each and I only had 3 weeks and 4 days to watch them all how many would I have to see per day?

With this problem, instead of doing 193/25

Everything mixed up, I gathered the information but I had a hard time organizing it all. I followed the same ideology involved but everything messed up.


Basically what I'm talking about. With my problem.

Someone please help me what I can do.

I don't think word problems are taught very well, either. I see vague advice like "take time to completely understand the problem" which doesn't tell you where to start. The basic thing is to parse the words, and look for adjectives and nouns that describe quantities, and verbs that describe what to do with the quantities. The key words like "is" (equals), "of" "than" etc (multiply), etc help you make the equation. Then you'll probably recognize a pattern you've seen before and know how to put all this together. Maybe I should write a word problem tutorial?

I'm not sure there's a specific strategy, but writing things down in steps would help. Knowing keywords helps. Let's take the example:



Per is the key word here. It means you're going to divide something by something. Here it's "per day", so you'll be dividing by days. This is what I mean by parsing the word problem.

A textbook problem would say "193 episodes OF 25 min each" and "of" is another keyword that means multiply.

Estimation helps you a lot in cases like this. Just say each episode is 30 min, so you could watch about 50 per day. So 200 episodes would take 4 days (non-stop) to watch. You can then get more precise and fill in the numbers. There are 1440 minutes per day, so you could watch 57.6 episodes in a day. That's about 3.4 days to watch all of them, which is reasonably close to the estimate.

Here is a typical word problem from the web: "The older brother Bob is two year older than his little sister Alice. Taken together, the sum of their ages is 8." What are their ages?

Key word: "than" - this compares one thing to another. Since one is "older than" the other, we'll have the other one be the variable and write the "older than" in terms of it.

Alice age = X
Bob age = X + 2

The next keyword is "is" - the sum of their ages is 8.

SUM = 8

So the sum of their ages is X + X + 2, or just 2X+2.

This starts looking like algebra now:

2X+2 = 8
2X+2-8=0
2X-6=0
X-3=0
X=3

So Alice is 3, and Bob is 5. Be sure not to just stop at the end of the algebra part, and always go back and answer the question. Here we want to know BOTH their ages.

Also, check your answer. Here it's obvious 3+5=8, but it's not always this obvious. Plug the values you get back into the equation and make sure they are right (time permitting).

These sorts of problems are common: "Two consecutive odd integers have a sum of 48. What are the two odd integers?"

The key word here is "have a sum", or "the sum is", so we're going to add two things and get a total. The things are "odd integers".

This type of problem relies on you knowing: An even number is a multiple of 2. An odd number isn't. Given any even number 2x, the odd number before it is 2x-1 and the one after it is 2x+1. This is what you have to know ahead of time to do this sort of thing. This is like your tool kit. If you don't have this tool available, you will have problems.

So:

2x - 1 + 2x + 1 = 48

2x+2x = 48

4x = 48

x = 12

Now, again, you have to answer the question. We've found x, but we need the two numbers.

2x - 1 = 2(12) - 1 = 24 - 1 = 23
2x + 1 = 2(12) + 1 = 24 + 1 = 25

Check: 23+25 = 48 yes, that's right, and 23 and 25 are consecutive odd numbers.

I can do math but I take a while to work out the problem. its a good thing we live in an age were you have a calculator on you at all times.

I still wonder how much of the problems aspies encounter in math is due to the teaching style that is forced on us. I still can't do calculations the way I was taught in school. I think many of us who encounter problems with math would not have a problem if it was taught in a way that is intuitive to us. We're taught to go through unnecessary steps and to sub-vocalize to 'talk through' problems. This is a disaster for those of us who have a visual system of calculating. Trenchers very simple algebra examples... I looked at the word questions and knew the answers, no 'talking it out', no sequential steps as taught in school, just visual. How am I supposed to show my work? Draw a f*****g picture? Yet I'm forced to show these extra steps that I don't use to arrive at an answer. For more complex calculations I do go through steps but still not the steps that I was taught in school. It's like telling a person to run a race and, "oh by the way we're going to strap this ball and chain to your ankle". I'm still going through this crap in college but at least I've had some understanding instructors that have cut me some slack in showing work.

There are many things that can cause problems for aspies when it comes to math but I think the methods forced on us in school permanently f***s many of us up in math because they conflict with intuition.

I think this is my problem, I also have a problem that I was not taught math from the 3rd to 8th grade as I was in a "special needs class" the teachers did not teach they just sat around their desk and talked all day and gave everyone in the class a packet of busy work to do.