Struggling With Pre-Algebra

[momofsix]

My ds is an 8th grader whose is mildly dyslexic. 

We have been using TT up to this point but he is just struggling with Pre-Algebra.

Wondering if there are any suggestions for a different curriculum?

[Targhee]

Which topics is hardest? Or is it related to the dyslexia and left-right/up-down nature of doing math?

[momofsix]

It's related to the nature of doing math. The crazy thing is he does calculations in his head rapidly, but gets confused when writing them on paper. 

This has been an ongoing issue with him. So now that he has to write things out, it's frustrating to him.

I'm thinking a different curriculum might work.

[forty-two]

My oldest dd has a lot of stealth dyslexic characteristics, and it's taken a lot of effort from both of us for her to learn how to show her work.  I think it took all of her 4th grade year before writing the needed equations went from pulling teeth to something she could do fairly fluently.  I walked her through the thought process and the writing process for months before she really internalized it.  Now we've embarked on Pre-Algebra, and there's a new way of showing the work, and teaching her the new way - and how it's really very similar to the old way (not the entirely new and confusing thing) - has been one of the more time-consuming parts of Pre-A for us.

There was a thread a few months ago on showing your work, and lewelma had a really insightful post that nailed our experience perfectly.  Her post was about how some kids have problems "showing their work" because what they did in their head really isn't *showable* at all.  It's not that they did the usual linear steps, but in their head instead of on paper, but that they didn't do any of the linear steps at all.  Learning to show the usual work isn't a matter of just learning to write down what they did, but actually requires them to learn a whole new way of thinking about math.  It's more learning to show *the* work, not learning to show *their* work.  I'm quoting her post here in full because it's that good 🙂:

On 10/6/2018 at 3:11 PM, lewelma said:

An event 3 years ago really impacted how I perceive of showing your mathematical workings. My younger son was struggling to write, so we took him in to get tested for dysgraphia. They worked him through a battery of tests that took 2 days and about 5 hours. I was in the room because he wanted me to be. He was 11 at the time. For the math section, the final question was something like you have 5 oranges and 8 apples costing $20, and 8 bananas and 6 oranges cost $18, and 9 applies and 3 bananas cost $21. How much does each fruit cost? (this is not the question, just something like it). I got out a piece of paper and simply coded it as three equations and three unknowns, but then realized I was going to get fractional answers.  Yuck!  Well, my ds had not started algebra certainly had never done simultaneous equations, had never seen a problem remotely like this, plus he could not write. Although he was allowed to use paper, he did not touch it. It took him 15 minutes to get the answer. He did it in his head.  To say that the examiner and I were flabbergasted, would be to undersell our response.  Neither of us could figure out how he did it. It was an amazing display of both raw intelligence and memory. When we got home, I was really curious about how he did it.  So we talked. I pulled out a piece of paper so I could actually write down what he did since he could not write, and what he explained made no sense.  Clearly, he was using ratios in some way. But we had not yet covered ratios, so he had no words to describe his intuition.  His 15 minutes of insight could not be coded into standard mathematical language. At least not by me. I was at a loss.

Because my ds could not write, he did all of his math in his head, and had for years.  I often scribed for him, but it was more me showing him what to write down rather than just writing verbatum what he told me to write.  So that week during math, I tried to scribe for him by just writing exactly what he told me to write, and it became very clear that he had no idea. None.  He could get the answer because of his mathematical insight, but he could not code it.  Over the next year I came to understand that this was a piece of his dyslexia.  He could not *code* his thinking into mathematical language of expressions and equations. He thinking was web-like and based on intuition, it was not linear or really logical, and certainly not structured in a standard way.  And I came to believe that this was going to be a bigger and bigger problem as he advanced in math.  Given his amazing mathematical intuition, it would be sad for him to be limited in math because he could not write it down. His mathematical insight needed a strong linear, logical foundation of writing to be put to great use in higher math.

This was the beginning of my journey to *teach* him *how* to show his work.  It was absolutely not about showing *his* work because *his* work was a jumble of insight that could not be written down.  It was about rewiring a piece of his brain so that he could take that jumble and code in into linear logical steps.  This took 3 years. But this process showed me that there is more than one reason why students don't show *their* work. My son had to be trained not just which steps to write, but how to *think* like a mathematician. Intuition is a wonderful ability to have, but it simply won't get you far in math without proper mathematical thinking.  And writing is thinking made clear.  If you cannot write it, you are not thinking it.

My point is, to ask a student to show *her* work, is the wrong approach in my opinion.  You need to train a student to write the workings in a certain way, and that certain way when repeated day after day, year after year, will train a student to see math differently.  It is no different than practicing scales in violin, over many years you train the ear to hear if notes are out of tune. Drill is what is required.  So for my son, he had to drill proper workings to be able to train his brain to think linearly and logically. To do it the other way -- show your jumbled workings so I can see what you are thinking -- is to miss half of what teaching kids math is all about.

Ruth in NZ

 

 

[lewelma]

I loved re-reading this.  Wow, I wrote clearly that day.  🙂  

[TCB]

37 minutes ago, lewelma said:

I loved re-reading this.  Wow, I wrote clearly that day.  🙂  

That was really interesting to read. I'm wondering about this a little with my dd. She seems to have a natural understanding of math that she doesn't understand some times and I'm wondering about the whole showing her work thing. How did you go about teaching him to do this?

[forty-two]

17 hours ago, TCB said:

That was really interesting to read. I'm wondering about this a little with my dd. She seems to have a natural understanding of math that she doesn't understand some times and I'm wondering about the whole showing her work thing. How did you go about teaching him to do this?

Not lewelma, but with my dd we did a lot of working backward.  She'd solve the problem first, and then I'd walk her through the standard problem solving steps, having her answer each question in turn.  Here's an example of problem solving steps (from our Dolciani Pre-Algebra book):  1) Read the problem carefully.  2) Decide what is asked for.  3) Look at the facts given.  4) Decide which operations to use.  5) Perform the operations.  6) Check your answer with the statements in the problem. 

So, with my dd, first she'd solve the problem.  Then we'd go back through the steps.  I'd have her read the problem aloud to me (Step 1 in the above list).  Then I'd ask her what she was trying to find and, once she told me, I'd ask her if she had enough information to find it right now, or if she needed to find something else first (Step 2).  Once we'd worked back through the chain of Things We Need to Find to a starting point, something we could find with the information given in the problem (Step 3), we'd start working forward.  So what do you need to do to find that first thing - what operation do you need to do and with what numbers? (Step 4)  Once she could tell me that (sometimes I'd have to prompt her "So, do we add?  Subtract?  Multiply?  Divide?", but she could usually identify what to do from there, once I'd broken down the options and went through them one-by-one), I'd have her write down the equation and solve it (Step 5).  Then we'd look at the next link in the chain: now what do you need to do? (Back to Step 4)  And once she could tell me, I'd have her write the equation and solve it (Step 5 again).  We'd keep working our way forward step-by-step through our list of Things To Find till she'd found what the problem was asking for.  Then I'd have her write the answer in a sentence, which required her to look back at the problem and check that what she found was what the problem wanted her to find (Step 6).

I think we spent the better part of 4th grade working together through Intensive Practice in that way before she really internalized it.  When she got stuck on a step, I'd go back to the usual teaching methods for whatever concept it was, I'd often pull out manipulatives, I'd work through a bar diagram with her - whatever it took for her to make the connection between her intuitive understanding and the logic of the steps.

13 hours ago, square_25 said:

Not sure where I'm going with this (I should really be asleep already)... maybe I'm just curious how you train someone in logical progressions that aren't intuitive to them without them starting to think that what they are doing are black boxes?  

With my n-of-1, I did it by a) letting dd solve the problem her way first, so that she had an intuitive understanding to build on, and b) by making sure each step made sense to her, that she at least understood why it was a mathematically valid, legitimate step to take, that it connected to her intuitive understanding of math in general even if she didn't necessarily see how it connected to her intuitive approach to this problem in particular.  If she felt like something I wanted her to do made no sense, we'd stop and look at it from as many directions as it took for her to understand.  It definitely helped that she flat out won't do anything she doesn't understand.  If something was a black box to her, she'd balk and refuse, instead of go through the motions to get it over with.  So I always knew if she was having a problem understanding.