Teaching HFA - executive function limitations

[CliffStamp]

I currently volunteer to teach high school kids math/physics. I have a number of high functioning autism kids who have the following concerns :

• they won't try a problem (write anything down) until they can see the full solution in their head
• when they can't do this, they get frustrated readily, when they get frustrated almost at all, they will act out, refuse to do work, etc. .

With one kid, if I attempt to suggest to him to write down anything, just try a solution, he will put his hands on his head, put his head down, make noises, etc. . If I do more than make a suggestion this behavior will escalate. At his school, he ended up into a physical altercation with a teacher, so I have to take care to keep his frustration very low, because he will act out and it can snow ball very fast.

With another kid, as soon as he gets frustrated he will stop working and call his mom who comes and picks him up.

In short, I am looking for suggestions on how to get these kids to :

• attempt any solution when the answer isn't obvious
• to increase their frustration tolerance (under the limits noted in the above)

Now with kids not on the spectrum, it is often just a manner of noting clear rules like :

• all problems need at least one clear attempt

and have a structured response type :

• note what is given
• the relevant equations/relationships
• draw a diagram

etc. . But if I even suggest to these kids to follow that they will refuse and it can set off their disruptive behavior.

Anyway I am open to any reading resources, or anything that would help me understand how to get these kids to be more productive on these types of questions.

 

[Judge]

Thoughtful post, Cliff. Welcome to AF.

I can't help but wonder how your students themselves perceive such class exercises. That while you perceive them giving a very structured response, do they really perceive the exercise itself to be sufficiently structured so as not to frustrate or intimidate them?

I ask given it's my understanding that those on the spectrum with executive functioning deficits are more prone to having great difficulty with much of anything they regard as appearing to be "open-ended or unstructured" tasks. Potentially compounded if in fact these type of deficits are neurologically "hard-wired" for them. Where there may not be any way of really reaching them along such lines in the first place.

What I'm wondering is whether or not when you develop such exercises and problems, if there is some way of compartmentalizing them in a manner that makes it more conducive for your students to attempt to work the problem? Thinking of the prospect that giving the task more structure may encourage a student to work the problem rather than just shy away from it.

All of which may well resemble a sort of placebo effect. But hey...if it works, who cares?

 

[the_tortoise]

You may be encountering kids who have difficulty with the linguistic parts of math....all the stuff that gets written down to show the calculations and offer proofs.

They may be able to do the math, but have difficulty with writing out the equations.....in a similar vein, they may be capable of understanding the concepts but struggle with traditional teaching methods.

All I can suggest is to try and find as many practical and concrete applications of the math you're teaching as you possibly can, and allow them to provide answers without showing their work -- you won't know if it's a wild guess or not, I suppose (unless someone regularly gets it right), but if you give them the benefit of the doubt it may encourage them to trust you and to make an attempt without as much fear and stress.

Then again, you may just have kids with massive frustration tolerance issues, in which case all I can suggest is to stress that it's okay to get frustrated and take time to calm down -- stress to them that it's okay to get upset, to take a break. Don't freak out when they want to go home. Give them credit (like praise, not like academic credit) for coming back to class and trying again. Try to keep yourself and them focused on the positive efforts they do make -- not the times when they give up and go home. Tell them all that matters is that they do the best they can. (For all you know they are doing their best, and you just can't see it because their efforts are happening inside their heads....maybe they can't do the problem and write it down at the same time, maybe it's not possible based on how their cognition works. Don't assume this is "won't", or that it's a very simple "can't" where you just have to teach them some trick or show them what you perceive to be a better/easier way of doing things....your way of doing things may be impossible for them, or maybe it's not quite that bad but your "easy" may be their "hard" and vice versa.)

I am not saying to have no expectations; I am just saying that if they do not do what you expect (whether it is a blatant and obvious refusal or not) it is helpful to remain calm and accepting; Feel free to explain the consequences of not doing the math, keep asking them to try again, just try to be calm and accepting when they cannot or will not do what you want. (And don't assume that your HFA students can't see it when you get frustrated -- some autistic kids can't read nonverbals at all, while others are highly attunded to them but have difficulty with understanding the reasons and perspectives behind the emotional reactions they see and no idea how to respond...... And both groups of ASD kids may, in a situation where they are not meeting your expectations (whether intentionally or despite massive effort), be expecting something terrible to happen to them simply because of past situations where they did not meet a teacher's expectations and were misunderstood/unfairly judged and mistreated as a result.)

 

[BK201]

Maybe it helps if you don't give out all the instructions at the same time. For instance, ask them to just note what is given and don't move on to the actual problem solving until they've done that. Then, work through each equation/relationship separately, one step at a time. It works for me, anyway. When I have to do something complicated, if I look at the whole picture, I get dizzy, so I try to break it down into small tasks.

 

[Progster]

Maybe it helps if you don't give out all the instructions at the same time. For instance, ask them to just note what is given and don't move on to the actual problem solving until they've done that. Then, work through each equation/relationship separately, one step at a time. It works for me, anyway. When I have to do something complicated, if I look at the whole picture, I get dizzy, so I try to break it down into small tasks.

I agree with this. Break it up into chunks, or stages, make sure that the student understands each stage, and provide clear, written examples to follow. Give lists of steps with illustrations where appropiate, just like you get in an instruction manual. Guide the student to discovering the answer himself/herself, rather than dictating. Make sure they understand what the point is, what it is that they need to achieve or practise, and why it is useful - give real life examples.

 

[Gritches]

I had trouble with math. I understand that frustration, and for me the frustration came from the pressure. The teacher would hover over my shoulder and go over the same technique over and over and I felt so much pressure to hurry up and "get it" that it would frustrate me and I'd have some of those bad reactions.

When I finally did understand a mathematical concept, it was never in the same way the NT kids learned it. Ironically, I'd usually get it as soon as the teacher stopped pressuring me and I could actually analyze the concepts at play and understand them at a fundamental level rather than merely performing a technique like it was a magic trick without understanding why these things worked the way they did.

I did fine that way until college algebra, which is probably more like what you're referring to. What helped there was, again, not getting individual attention. A rigid technique became necessary at that point, and watching the prof perform the techniques on the board (for the whole class rather than just me) over and over and over while I dissected and analyzed them was helpful.

I scraped by with a C- in college algebra, an absolutely embarrassing grade, because eventually the teacher would move too fast and move on before I had caught on to the previous concept.

POST OVER
*tired 6 AM rant here*: Screw the square root of -1. They called it i, an "imaginary number". That's where I put my foot down and say "no, you cannot do that. You can not have imaginary numbers. You can have three apples (3), you can owe your friend Antwan 3 apples (-3), or you can have a basket full of apples in an unknown quantity (x). Any which way, the apples involved are real, because you know what you have if you have i apples? If you have an imaginary number of apples? You frickin starve, because you have no apples. Imaginary apples will not sustain you, so therefore you can NOT have an imaginary number. Something is either a number or it's not a number; that's the only two states in which any given thing can exist. So which is it? Is the square root of -1 a number, or is it not a number? If we're imagining that it's a number, it's a number. But if it's not a number, then it's not a number; which means that neither you nor Antwan have any apples, and the entire village starves to death because they were trying to eat imaginary apples in this madhouse of mass delusion in which you believe something you're imagining is real. So if you have i apples, do you have apples or not?

Frickin math.

 

[Fridgemagnetman]

You can have three apples (3), you can owe your friend Antwan 3 apples

Before negatives... They invented zero apples.

They laughed at the guy.

You can't have nothing of anything you idiot.

I guess he got through to them eventually.

Al - words are usually Arabic.

But I read the history of zero ,quite interesting.

Aleph.
Algebra
Alcohol...
Zero... Ah well.

 

[Mary Anne]

I was one of those kids. I tried and tried and tried in math and could not get better than D-minus. I struggled with fractions, decimals, and percentages. I had summer school, and math is the reason I never completed my bachelors degree. Algebra and geometry are indiscernible “languages” to me. To this day 50-plus years later, I am math phobic. I cannot do anything beyond add, subtract, divide, and multiply.

Is there a way to teach math in a more approachable way? A visual way? A more interesting, creative way? A non-numerical way?

I have heard now in college that art, knitting and crochet, and sculpting are sometimes used to teach math. I certainly would have been able to get through math using those techniques. We had none of such creativity back then. We were even forbidden to bring a new type of technology to class called a “calculator” back in the early 1970s.

 

[Gracey]

If those children ‘lose it’ in class, send the problem home with them to be completed at home and brought to the next class for marking?
(Ask parents to help make sure it gets done)


If your delivery is moving too fast they may miss important parts of the sequence, or won’t be able to see how values change in their minds.
Break it down, step by step.
(If you’re already doing that, break it down further)

Cliff would you be kind enough to give an example here of a problem where the answer isn’t obvious please?
(I can’t see what you mean)

Welcome to A F

 

[Mary Terry]

I've been teaching young adult HFAs for years as a volunteer for the GED program and have experienced this many times. Other posters have offered good suggestions here.

One of the things I do is to solve math problems, one step at a time, on the chalk board so they can all follow along with each step. After we do numerous math problems on the board, I start asking them to tell me what would be the next step to solve the problem. Repetition and practice helps some students understand how to methodically solve the problems by breaking them down into each small step. The GED exam requires them to show each step in solving the problem so it is important for them to be able to display what they are doing. Some are so smart that they can solve incredibly complex problems in their heads but cannot demonstrate or explain how they do it.

A lack of understanding of negative and positive numbers is often the problem, as well as not knowing order of operation, so we have to go back to the basics before we can advance to the tougher problems.

When students make noises, stim, or shut down, I just whisper or quietly say "discipline" to them to remind them to try to get a grip on their reactions. If they appear near meltdown, we take a break so they can walk around, get a drink or snack, and I turn off the horrible humming overhead lights for a while.

 

[Progster]

I've been teaching young adult HFAs for years as a volunteer for the GED program and have experienced this many times. Other posters have offered good suggestions here.

One of the things I do is to solve math problems, one step at a time, on the chalk board so they can all follow along with each step. After we do numerous math problems on the board, I start asking them to tell me what would be the next step to solve the problem. Repetition and practice helps some students understand how to methodically solve the problems by breaking them down into each small step. The GED exam requires them to show each step in solving the problem so it is important for them to be able to display what they are doing. Some are so smart that they can solve incredibly complex problems in their heads but cannot demonstrate or explain how they do it.

A lack of understanding of negative and positive numbers is often the problem, as well as not knowing order of operation, so we have to go back to the basics before we can advance to the tougher problems.

When students make noises, stim, or shut down, I just whisper or quietly say "discipline" to them to remind them to try to get a grip on their reactions. If they appear near meltdown, we take a break so they can walk around, get a drink or snack, and I turn off the horrible humming overhead lights for a while.

You sound like an awesome teacher!

 

[Judge]

One of the things I do is to solve math problems, one step at a time, on the chalk board so they can all follow along with each step. After we do numerous math problems on the board, I start asking them to tell me what would be the next step to solve the problem. Repetition and practice helps some students understand how to methodically solve the problems by breaking them down into each small step.

This is precisely what I meant in my post about trying to find methods of compartmentalizing the exercise. But obviously you explained it in so much better terms. To give the students much more structure which they need to persevere and solve the problem.

 

[Bella Pines]

I'm HFA and made it to my 40s.

Lots of people here have HFA and made it to adulthood and so will want to help, including myself.

However.

Ironically, you've only posted half a problem and until I see the full solution I cannot propose any ideas

The way my mind works is like a jigsaw puzzle. I'll take in as much information as I can and then consider the picture that forms. I do this with everything. For example, a while back I was looking to buy my eldest son a jacket. I looked at every online store available, browsing 30 different websites. I then went in and out of every high street store that sold kids jackets. I then repeated the process throughout... London. Finally the landscape formed in my head, I had enough data to make a decision and bought a jacket from the 15th online store. I'm convinced that the jacket is exactly what I was looking for and all is well. I'm rarely wrong and if on a rare occasion I am wrong then it's because I have been working off faulty or insufficient data (or with illogical human beings).

So it's a bit like a computer. If you are filling in a form, it won't allow you to submit until all the fields are filled in.

So in order for us to propose a full solution and a way forward, can you post specific examples? Like pose the questions to us?

 

[CliffStamp]

Is there a way to teach math in a more approachable way? A visual way? A more interesting, creative way? A non-numerical way

Yes, I work with kids with learning disabilities all the time, some of them severe to the extent of dyscalculia. I don't have any concern there, that is usually a simple problem to solve, it just takes effort to find the right reframing.

What has to be done on a fundamental level is to represent the concept in a way/language that it can be understood to the listener. For some people this may be very abstract, others more concrete, some more physical, some verbal, some like written etc. . In general if you pay attention to the way an individual expresses themselves, what they talk about and frame it about that, in that way, mirror them, generally it will be understood.

The challenge for most is to understand that you can say something which makes perfect sense to you but is complete nonsense to someone else, hence you have to keep reframing, paying attention to the language (to make sure that isn't a barrier) until you succeed. The real danger, once you get familiar with a subject, is not falling to the trap of assuming far too much in an explanation.

For example saying something like "disjoint sets just have the empty set as the intersect" won't help out someone who is just learning set theory. Even if they know all the terms a typical HS student here won't have enough of a grasp on them to both try to integrate all of them and at the same time remember the sentence. Hence it usually works better if you say something like "the set of animals is disjoint from the set of plants because there are no plants which are animals" .

Generally, though it varies, we typically learn better often from examples rather than rigid definitions. If you think on how you know what a chair is for example, it likely isn't that someone defined it, you just were shown a bunch of chairs and your brain figured out what it meant. We have a massive ability to do this, so take advantage of it when you can. There are some people who like definitions though, so you basically try lots of things until you find what sticks for someone and then focus on that.

 

[CliffStamp]

Cliff would you be kind enough to give an example here ...

So there are two main concerns, the first is where the reluctance to write things out causes them to bottom out mentally.

f'=f (1 +/− v/c)

This is the doppler shift for light, it tells you how the color of light you see (f') depends on how fast an object which sends out the light moves (v).

A typical question exam question would be something like

"Given a wavelength of light produced by an object, and an observed frequency, what is the velocity (magnitude and direction) of the object? "

This is an attempt to test their ability to :

• do unit conversions as most quantities won't be in the right units
• understand if you are given wavelength you can get frequency as they are related
• to realize this is a doppler question (and of light, they also do sound)
• which formula is used for dopper of light
• to understand what the parts mean
• to be able to actually use numbers in scientific notation and understand prefixes
• finally, to do the algebra

The kids don't have any issues with the first six, but they will fail at the last because this is what they will attempt to do :

• in their head remember the formula that converts wavelength to frequency and do that getting the result (on the calculator)
• similar with unit conversions as necessary (figure them out mentally, do them on the calculator)
• recall the doppler formula, try to re-arrange that in their head to come up with the series of manipulations which solve for the v
• then punch all of the numbers in on the calculator while trying to retain that list of operations and then carry them out, all while remembering what numbers correspond to what

The questions get more complex, but this is the kind of thing where they will typically bottom out, usually get a wrong answer and end up getting 0/5 on a long answer, which could be worth 15-20%. Note I am not assuming this, I know they are doing it because that is what they say they are doing, they typically ask me to verify the algebra. On the more involved questions, they won't attempt it because it becomes obvious you can't mentally manipulate all of the quantities.

For example :

"There is a block on an incline of an angle of 10 degrees which has a frictional coefficient of 0.15. If there is an applied force of 15% of the weight of the block at an angle of 30 degrees above the incline, what is the acceleration of the block."

There are many ways to approach this, a standard method would be something like :

• identify all the forces
• decompose them into x, y parts
• write out f= ma for x and y
• solve the equations

This could require solving multiple equations at the same time by combining them. This would be extremely difficult to juggle mentally.

 

[CliffStamp]

I am not saying to have no expectations; I am just saying that if they do not do what you expect (whether it is a blatant and obvious refusal or not) it is helpful to remain calm and accepting; Feel free to explain the consequences of not doing the math, keep asking them to try again, just try to be calm and accepting when they cannot or will not do what you want.

My issue isn't that they are not doing what I ask, it is that I don't know how to direct them that will enable them to progress. If I can't get them to change these habits they will bottom out in math/sciences. I want to find a way to get them to :

• see the paper as a tool which saves precious mental resources
• explore problems which don't have obvious solutions

The latter is fairly important outside the classroom, it is rare in live to know what you are supposed to do, at times the most you can do is try to do something which seems like it can move you forward, taking feed back as it happens and correct as necessary.

 

[CliffStamp]

Like pose the questions to us?

Here is a typical math problem where the solution is very difficult unless you work it on paper and the more the structure the better :

"Mary has a rectangular garden with dimensions 10 m by 4 m. She extends it by a common border so it is 50% bigger. How big is the border?"

Note there is no formula here that just relates the numbers to the answer like area = pi r^2 or similar. You actually have to make the formula you have to solve by laying a bunch of concepts :

• When it says bigger, it means the area.
• What it means to say you border an area
• How to use percents
• How to get the area of a rectangle
• How to produce the equation from the above
• Realize that it is a quadratic
• Solve it using the quadratic formula (it won't be factorable)
• Realize one of the answers isn't sensible and reject it

The general method to do this would be :

1. draw a picture
2. label it
3. calculate the original area and the new one
4. write out the equation involving the areas and the border (new = old + 50%)
5. solve it
6. reject insensible answers (realize negative lengths are NPV's)

So again, the kids typically will look at this for awhile, not see how to solve for the border. I need some way to get them to approach problems in a more structured manner similar to the above, not necessarily the same. For example you could just guess border widths and very rapidly estimate an answer versus solving a quadratic directly.

 

[CliffStamp]

Thinking of the prospect that giving the task more structure may encourage a student to work the problem rather than just shy away from it.

All of which may well resemble a sort of placebo effect. But hey...if it works, who cares?

The problem is on the test they won't get the structure, hence I have to be able to get them to explore problems which are not scaffolded. For example, they do a section of proofs in math, you will be given some tangle of lines, cord, triangles and circles and be given a bunch of things and asked for some angle/length.

The kids who are willing to play with the problem get this easily because each step is very simple, but the problem is there is no way to know what ones lead to the solution aside from trying a bunch and seeing if they go anywhere.

For example, this is about the simplest question you can get asked :

http://86.23.108.180/MathFiguredOut/Images/image639.jpg

The typical way to do this would be something like :

• get BDC from applying the property that the sum of the interior angles of a triangle are 180
• get DBA by applying the property of equivalence of alternate interiors of parallel lines
• get the unknown finally by reapplying the sum of the interior angles of a triangle is 180

Final exam questions will be similar, just bigger diagrams which require you to move further through the thing and apply a wider variety of principles (there are about a dozen which are testable and you can be asked to use any combination of them).

 

[Progster]

My biggest issue with maths is that I need to visualise a problem for it to have any meaning. So geometry and trigonometry were always a lot easier and I really struggled with algebra. Also, in demonstrations I didn't know how they got from one stage in solving it to the next. I could solve a problem if it was demostrated in stages, and I understood how the teacher got from one stage to another, but as soon as something was slightly different, I didn't know what to do. Or I think I get it, then try doing something on my own, my answer is wrong but I don't understand why, and then frustration kicks in.

If it was a simple 'solve for x' equation, I could do it. But if it was a complex equation asking me to simplify or reduce it, then I was lost.

 

[Gracey]

Thanks for your examples and explanation Cliff,


I’m going to ask the obvious,
(At the risk of embarrassing myself)

You’ve explained this to the two, in the same way you’ve explained it on here to me/us?

The examiner wants to see how well they interpret and process the information and isn’t a medium or clairvoyant.
Give the examiner proof on paper that they (the students) understand what’s going on.

I’m guessing Mary’s border is 20 meters squared.
But I don’t know the difference between a border and common border.

(I don’t know what NVPs are or negative lengths.)

I saw a 50% increase of 40m2 to be 60m2.
The difference being 20m2- the difference is the border.

How would you teach me to prove to an examiner I knew what just happened?