math instruction for language based LD students

There is one school of thought that has tried to limit the language demands in math texts or even remove language entirely, leaving only drill sheets.

Alas, in the real world, nobody presents you with a drill sheet. People have this habit of communicating in words and language. So the graduates of the simplified language programs didn’t do as well as they were expected to when they hit the next level, high school or college.

I don’t know of a simple answer to this one. Yes, teach math skills any way you can. But be prepared for math demands to show up anywhere in life — one of my students, a theater major, found herself calculating the area of a circle to figure out how much light intensity they were going to get from a spotlight.

I would work very very hard on the language skills and teach the language of math directly as part of the math lesson.

The recommendations with regard to teaching math are roughly the same as for any content class- preteach the vocabulary, provide instruction in the “grammar” (syntax) of equations, present new conceptual stuff slowly and teach to mastery before moving on…provide visual supports for complex processes.

You are right on the money about the impact of language processing problems on math understanding. Math teachers, by and large, don’t understand this IMHO- and the ones who do are a treasure beyond price. SLPs and resource folk can be a big help in this area, sometimes simply by including math vocabulary in their lessons. You do have to go around and find out what it being done however. The most helpful (beyond directly reteaching math assignments in resource) thing that I have done is to cross-contextualize all that vocabulary- we would dissect the words in reading, web them, use them in a variety of situations and develop visual cues for them. (I loved it when words would come up in multiple classes) I always shared this with the teachers-some took it quite seriously and understood it - and therefore had great ideas or would come and let me know about new vocab in advance- and some would smile politely and say thank you. Sigh… Many times the SLP and I would plan together- who did which words or taught what skill- that was always helpful. In addition to teaching the words, you need to teach kids with Language issues HOW to apply them in different situations and how to pick the correct meaning.

One thing that I often recommend now, in addition to coordinating stuff this way, is that teachers look for algorhythms than are visually simpler than the ones we grew up with and don’t allow students to rely so heavily on rote positioning of numbers. My favorite resource is a very inexpensive book developed at the Landmark School in Mass. called the Landmark Method for Teaching Arithmetic. (landmarkschool.org) It is a great book, specifically developed for students with language based LD’s (which is the school’s population.

This is a great question!

Robin

Martha,

You’ve hit a nerve here so I’ll weigh in although I am not an SLP. We discovered serious language problems in my son just before he turned six. He did have, however, an affinity for numbers, so I decided to supplement math to give him something he could do well in. I chose Saxon math and found, to my delight, it was helpful with the language issue. I did not slavishly follow it due to lack of time—had him do the workbook and went back to the manual when he had problems. One of these: he could not name a number between 20 and 30. The manual, as it turns out, anticipated a problem here and called for working on the concept of “between” before presenting this problem. Following the instructions, I put a fork between a knife and spoon and said “The fork is between the knife and spoon.” Then I varied it, and then asked him to put one utensil between the other two. We did this for several nights and then I asked him to name a number between 20 and 30, which he did promptly. The numbers weren’t the problem, the meaning of “between” was. After that, I was hooked on Saxon.

I think the vast majority of grade school teachers believe that all kids having trouble with math suffer from dyscalculia. So they address this problem by lots of drill. It doesn’t occur to them that a child can be very good in calculation and pure number concepts like prime numbers, exponents, and square roots, but are stumbling over more language intensive concepts like fractions. Poor language constructs used in the texts, and reiteerated in oral presentations, are the main culprit. (Grade school tachers generally are not specialized in math and just follow the textbook—the majority of these are incredibly awful.) When I compare Saxon to the texts in my son’s parochial school, I get very frustrated—the math could be so much better if they just changed the books.

Saxon in my view does an excellent job of presenting concepts incrementally and thoroughly reviewing them before moving on. And ongoing review is incorporated to make sure that a learned concept has stuck. If you want to help your son, you will probably have to do it yourself. Many homeschoolers use Saxon because the materials make it is easy to teach. Go to www.saxonpub.com. They have a placement test online, which you could give your son, in order to order the appropriate text. (Since he is 14 I probably wouldn’t go lower, though, than Math 65, which is for fifth and less advanced sixth graders.) Mary MN, who posts here often, advocates Singapore Math, which I haven’t used. She may want to add something here.

Finally, a word about Chicago Everyday Math—my dd is in a school that uses it—she is very verbal and it has worked well for her. (Her school supplements with a lot of math facts practice, which Chicago is somewhat weak in). However, this is math for future lawyers—kids who are very verbal and not too strong on the calculation end of things. My son would have been overwhelmed by it and would never have been able to live up to the high language skills assumed in this approach.

Yes, you are absolutely right that the typical elementary math texts are pitiful and that teachers are in general very poorly trained. A good program that actually explains what it intends to teach is worth its weight in gold — definitely look into Saxon or Singapore programs.

I have also heard less-than-stunning reviews about the Chicago program; I would avoid it.

A good math lesson teaches the vocabulary and concepts in a meaningful way as an integral and inseparable part of the lesson.

One of the problems we have to deal with is un-teaching the bad habits of students who have not learned math in a meaningful way, but merely do mystical magical manipulation of symbols which they fear and misunderstand.

Robin:

I’ve noticed that the math assessments (KeyMath-R, WIAT etc.) that we use for initial assessments, annual reviews and triennials really do not measure the skills needed in current math curriculums, because of the amount of language required. In other words, those LD students with language deficits (most of them), may do extremely well on the above math assessments, but are failing miserably in their classrooms. Do you know of any new standardized math assessments that will be more accurate in determining a student’s skills?

I posted a few weeks about this, but no one provided any suggestions.

Marilyn

Hi-
Sorry I missed your post before!
No, and I do not think that the normed assessments will reflect the changes in curriculum any time soon either. Actually, I am not sure that they could, any more closely than they do, until the new curriculum has been around long enough to change the results in the norming sample. The grade level score on a normed assessment is the LEAST accurate number generated by the results. One item can, depending on where it is in the test and how old the student is, jump a student an entire grade level. In another section, one item may only mean a couple of months- or less. The grade levels are relative numbers derived from the distribution of the norming sample and bears little resemblance to what actually happens in a classroom. As the the “new, more demanding curriculum” is more widely taught, one would expect that students would know more- and what that would do is raise the definition of “average score” on the tests. However- you wouldn’t even really see that until the tests were renormed again- and this only happens about every ten years or so.

So, the situation you describe can happen easily. What I generally do, if this is the case, is provide a fairly complete description of what sorts of skills the child has (I was a teacher for a LONG time before I started consulting) and describe their performance relative to skills, capacity, and processing pattern. Then I make recommendations that will even things out a little (hopefully)- so that the difference between actual skills and performance will narrow. I might suggest alternate presentations of content, or specific accommodations with regard to assignments or presentation. It depends on the child- and how big the gap is between performance and skills.

Does this help? I hope I haven’t been completely confusing.

Robin

Robin:

Thanks so much for your thoughtful response!

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I agree with this statement, although the KeyMath has until recently been one of the few tests that did correspond well with functioning levels. At our team meetings, we only use standard scores to decide on whether students will qualify for services, and I should have indicated that in my previous post. However, even the standard scores are quite inflated due to the difference in curriculum.

Marilyn

Keymath is a pretty detailed math test relative to most of the others around. I am not sure the standard scores are really inflated on the WJIII etc. though. Remember, average describes a relative position within the population. So all you are really saying is that compared to the rest of the population, so and so is average. Average, partcularly when you are in the low nineties, does not necessarily mean very skilled. A child with standard scores of 91-95 is still missing some stuff and may struggle. They may need to work quite hard to maintain their progress and acquire new learning in a classroom setting, especially given the sequence and pace of some classroom math programs. (as well as the manner in which they are implemented)

Robin

Hi Martha,

This may sound a little contradictory in light of the qustion you asked, but please hear me out. One thing I have learned by being an adult with a huge gap between (low) math and (high) verbal skills, is that I need to ask LOTS of questions in order to learn, understand, and retain information about numbers, symbols and mathematical processes. I generally don’t have trouble processing language, but that isn’t true when it comes to language used for discussing some abstract concepts. When I approach algebra, it almost feels like my brain is shifting from one gear to another, and the low gear causes me to have a very bumpy, uncomfortable ride in which I often feel lost. Sometimes I never get to my “destination” which can be very frustrating. For a child who does not know what is happening, it can be totally deflating to his or her self-esteem, especially after working so hard. When math failure happens over and over, it can become a fear or source of anxiety that takes on a life of its own. Does any of this sound familiar?

Aside from needing to have as many concrete representations as possible, I suspect that your son may be needing to ask many more questions than are practical in a regular or even a special classroom for students with math LDs. It might be helpful next time you two are working on an assignment or concept, to allow HIM to do most of the talking by letting him ask questions. You might be surprised at how many questions he has, once he realizes it’s OK to ask, and that you will remain patient no matter how long it takes. Keep in mind that when someone else does all the talking, the child may be distracted by questions that arise during the instruction period. He may be trying hard to remember his questions, and not be in a position to process or attend to the words that come afterward.

The end result of helping your child question and talk his way throught the lesson may be that he can “hold on to” the information better because he has come to understand it in his own words.

If you like reading educational journal articles at home to learn more, you might want to sign up for the electronic library. For about $10 per month, you can access articles from such journals as the Journal of Learning Disabilities. I found an article in the 1/01/97 issue that discussed the “Educational aspects of math disorders” and addressed some of your concerns. Hope this is helpful. JJ

Where can I get a copy of the Saxon program?victoria wrote:
>
> Yes, you are absolutely right that the typical elementary
> math texts are pitiful and that teachers are in general very
> poorly trained. A good program that actually explains what it
> intends to teach is worth its weight in gold — definitely
> look into Saxon or Singapore programs.
>
> I have also heard less-than-stunning reviews about the
> Chicago program; I would avoid it.
>
> A good math lesson teaches the vocabulary and concepts in a
> meaningful way as an integral and inseparable part of the
> lesson.
>
> One of the problems we have to deal with is un-teaching the
> bad habits of students who have not learned math in a
> meaningful way, but merely do mystical magical manipulation
> of symbols which they fear and misunderstand.

See my post just below on So true..Try Saxon. Website is given there. Marie