Gifted Issues Discussion homepage Forums Twice Exceptional IEP goals for writing down math reasoning?

DS9 qualified for an IEP in spelling, writing (composition), and language (mostly related to social & figurative speech). There are no fine motor deficits. Maximum split in performance scores is 92 points.

One great weakness we see at home is writing down his mathematical reasoning. In the Applied Problems section of the WJ, he used scratch paper for just 3 of the 30 (or was it 40?) problems he solved (still with a sky high SS; already multiply accelerated in math). We note that he often has no concept of how to write down his math reasoning when doing his homework, despite the fact that he's clearly shown it in class. This will very quickly limit his ability to learn to solve more complex problems. I'm getting a little sick of "well, he's just so smart...." It's time to learn it.

The issue from my perspective is that he needs direct instruction along the lines of "first write this number, now put an equal sign, now write the next thing..." sort of instruction, then enforcement to do it every single time, and then reteach and reteach and reteach.

I'm looking to get a sense of what potential "writing down your math reasoning" goals could look like.

An alternate perspective: my PG sib did not write down any math reasoning until calculus (well, maybe for geometry two-column proofs)--mainly because, why, there were no steps! Went on to collect multiple STEM bac and post-bac degrees. And actually, had no issues with demonstrating reasoning at the collegiate and higher level. When my sib was age 9, my parents were still advocating for grading on accuracy of answers only...and take your lumps (i.e., no partial credit) if the answer is wrong.

It is not necessarily the case that your DS does not know how to write down steps. I'd want to probe a bit, first, to see what his actual process is, or if it just seems too obvious to him to spell out.

FWIW, we have found that writing down math steps when he didn't find it necessary for getting the answer was a real sticking point with DS8 who is very high PG in math. If he can explain the reasoning, then is the issue more about how to know when he should write out his steps (to avoid making simple errors, etc.)?

I would be more concerned if he couldn't explain the reasoning.

He cannot explain his reasoning.

I'm a STEM professor with multiple degrees myself. This as a genuine deficit. Waiting for things to get more complicated is going to make things worse, not better, even if he does make it there with his self-esteem in tact. Accuracy ranges from <30% to 100% from one day to the next. Taking his lumps is not being instructive.

The school sees the same deficit, and views my concerns similarly. I'm currently confronted with a lack of imagination on how to construct an IEP goal in which a child is "only" performing 3 standard deviations above the mean.

Ah, I misread your post, sorry about that -- if he can't explain the method or reasoning that does seem another matter.

Given that, it would seem instruction on what's necessary to write down (with examples at the level he's working at) would be a good step in the right direction. Ideally, it seems that would then help isolate any patterns in the mistakes he's making (referencing the wide fluctuation in accuracy).

I see. Well, what can he do at the moment, with regard to explaining his reasoning? (On the IEP goal, this would be the "current performance level" section.) Can he state the problem/question? Identify what the end product should look like? Look at a problem and identify how he would set about solving the problem (using problems without actual numbers, to avoid the issue of just naming the answer)? To what extent can he do any part or whole of these?

Also, what level of mathematics is he working at? It would be easier to offer suggestions for IEP goals and objectives with that information. And this might sound a little crazy for someone at +3 SD in math, but has he had in-depth assessment in mathematics, not through a survey instrument like the WIAT, WJ, or KTEA, but through a diagnostic instrument, like the KeyMath-3? (Separates concepts, operations, and problem-solving strategies.) The standard scoring software for that actually generates suggested IEP goals and objectives, based on error analysis, which might at least start some conversations and balls rolling on the part of the school staff. The companion intervention manual has even more, also keyed to the error analysis.

http://www.pearsonclinical.com/psychology/products/100000649/keymath3-diagnostic-assessment.html

Oh yeah, the keymath test. He ran off the end of the test in 2nd grade in just about all areas -- only the subtest that included percents and decimals did he not run out of questions before hitting the stopping criteria. I recall in the meeting about the 3rd grade acceleration notes that he did most of the work in his head, consistent with the WJ observations.

Looking for such a math IEP goal is starting to look ridiculous.

The most concrete way in which present levels of performance that can be quantified, though, is the number of problems for which he uses pencil and paper. Homework is on Pearson's digits, and he's supposed to show his work in a spiral notebook. He's filled two just pages since December for his daily homework. The underlying issue appears to be related to the language difficulties, certainly not in the mathematical skills. The SLP is so wowed by his math skills, she's not able to really meaningfully discuss this. The math teacher is so stuck on "well, I showed him how to do it one on one, and he did it, so it's fine" that she doesn't really understand the underlying language issues. At the same time, she marveled to me yesterday that just once, she'd like a peek into his brain to see how it is that he figures this stuff out, because she knows it's often so radically different than the intended.

This effect seems most closely tied to his writing struggle, in which the language issues, together with the spelling problems, conspire to make it difficult for him to write anything down.

I have an awesome IEP team that wants to help him. If it's a reasonable request, I'm comfortable asking. The end result might not be as requested, but I'm fairly confident that something rational can be hung on the writing or language goals.

"You see exercises sometimes to find the error in the student's reasoning. How does he do on these?"
The teacher removes these from the tests. I'll have to go back into his homework to see how he does. I think he generally does ok.

"Is he typing the rest of his work, writing it? Is his work spatially organized?"
The answers are being typed into the computer for homework, written on the page for tests. His spatial organization leaves quite a bit to be desired, to put it mildly. Thanks.

"So for goals, it might be something like "show intermediary steps for solving math problems" and methods would be to use a graphic organizer with prompts in the form of steps to choose."
OK, that plus the 3 column structure (not sure I fully understand your explanation, but I've got my own spatial organization I impose on my students...) might be good. It needs to be written generally enough to adapt to the hodge podge of topics they cover in middle school math.

OK, that's about what I guess it was. Thanks. That's almost exactly how I was taught...

I almost hate to mention this at all-- but if the "homework" in the math classes he's taken is all answer and no 'work' then this may well be a matter of hearing mixed messages on the relative importance of doing this in the first place.

I saw this with my DD. Oh, sure-- Mom and Dad kept telling her to "show her work" but she did "fine" in math without doing that-- because everything was about entering the RESULTS (not the "work") into the computer, which then presented an output related to the correctness of said result.


Needless to say, this was not exactly helpful in convincing our DD to write things out. At all.

Just for her, I started doing spot-checks of her notebooks-- and if she got less than 80% accuracy, I specifically asked to see work related to that task, and if she couldn't produce it, she did it again.

I have no idea what I would ask for here, in an IEP, but clearly with kids who have difficulty, a lot of scaffolding may be needed to convince them to do it. DD is better about this now-- but far from what I'd call awesome. It burned her in calc and chemistry during her first few midterms in college, by the way.

And I rubbed her nose in it. Yes, I did. Because I've been telling her for years.


With that said-- does he understand WHY he must write out his work? That is, does he understand that it's not for his own benefit, but that of a third party to follow what his brain is doing? That really did help my DD to understand WHY she was doing it, and helped her to differentiate what needed to be on the page. Well, it helped, anyway. It didn't do so all at once, by any means.

Another idea would be to perhaps have a teacher select a representative problem and have him work through it with verbal explanations (on a whiteboard or smartboard), and SCRIBE the problem as he goes-- then coach him using that "transcript" so that he can see which steps probably should be written in order for another person to follow his logic.

Adding that what really made my own DD better about this was tutoring math. Because there, she got feedback immediately into what other human beings needed to see/hear in order to follow the math.

I'm assuming that he knows how to do the problems-- obviously this is far from enough if there are other underlying difficulties there.

I am not sure how to put this in IEPs. My DS struggled with understanding why he had to show steps because he does math intuitively and in his mind and really did not know how or why to show his work. He is in a school that is very picky about showing work (for 2nd grade) that he lost 15 to 20 points in math on weekly tests even when he got it all correct. Both the teachers and we coached him for a few weeks. For him, pictorial representations worked better than writing long winded explanations of the type "x happened because of y ..." . So, we taught him the SM bar diagram models, number line depictions, pictorial depictions (boxes with grouped pictures to represent multiplication/division, pictures of clocks for time problems, stick people nicely labeled and ordered for problems with ordering/logic etc) and sat with him to do his homework with him for 2 weeks and tutored him as to what exactly was needed.

After those 2 weeks, we told him that if he could show his work satisfactorily, he was free to move on to other stuff of his choice. But, if the "showing work" part was unclear, he needed to do an extra word problem and show work again. This turned out to be the best strategy for us - he figured that he could do less problems if he could show work effectively and ever since, showing work is not an issue.

If you go to a large state school, you don't have to worry about showing your work in calc/physics etc.

You just have to get the right answer on the multiple choice tests.

One problem with showing your work is that it sometimes makes you partially unable to *do* the work, since you don't necessarily know *how* you do it, you just do it automatically and get the correct answer.

It's kind of counter-intuitive but it might be better if you treat it as a separate skill to be developed from the grounds up. While I was mildly annoyed at the time (early elementary) at the show work requirements, I have become rather grateful that our schools actively taught this skill from an early age and made it impossible to get an A without mastering it.

It is entirely normal to be disinclined to show work, particularly if you have high ability in math and have to reverse and slow down your thinking processes to provide an intelligible description. However, the fact that your DS' accuracy is not very high should be an additional persuasive argument for showing some of his work. I think there is a wonderful article in the AOPS database by Richard Rusczyk that related to an AIME contestant learning the value of writing down some of his work. I plan to show DS11 when the time is right. At present, he can do most of the AMC8 and much of the AMC10 problems in his head but he does so to his detriment and ends up averaging a couple of careless errors per test. I haven't push this point on multiple choice questions because he tends to make fewer (sometimes none) mistakes on exams that are easier than the AMC exams(county benchmarks, state assessments, MAP, SAT, etc.).

However, DS has mastered the art of showing work in essay type questions and the following has helped: At the early stages, it may be helpful to encourage your DS to do the problems twice and compare the answers - once all in his head and once on paper as if he had to explain to another student. It may also be helpful to show him completely different approaches (pictures, words, number sentences or a combo) to showing work so he can decide which method is least painful to him. Ultimately, he needs scaffolding (such as provided to elementary students) for each problem type. The teacher needs to identify and explain step by step what he needs to write and once he has assimilated the steps, then he needs to apply those exact same steps to another similar problem. For example, if he is given an elementary geometry problem such as find the volume of a rectangular prism, one approach would be to identify the formula (volume = length x width x height), identify the value of each constant/factor (l=9, w=7, h =5), input the values into the formula (v = 9 x 7 x 5), and provide the answer (v = 315 cubic units).

What I am suggesting is to separate out the writing down of steps from math instruction until he has gain some basic skills. Teach him to identify the general steps for particular types of problems. Have him study actual model answers and have him practice on similar problems. Although DS still prefers to do everything in his head, he is able to apply the same technique to new problems and provide written "proof" when called to do so. In fact, I think that this type of training has made writing geometric proofs very natural for him.