dyscalculia

If you look under LD in Depth- the button is at the top of this page- under Math- you will find some stuff. There is not much you can do in two weeks- but if he is on an IEP since he has been evaluated- he will have some accommodations and modifications already.
Robin

I am new to the concept of dyscalculia. I work in a private school where testing is not a norm. However, I have four students in a general math class who are not progressing beyond basic math facts. Three of the four students are B students in all other classes, causing me to wonder if there could be a specific disability in mathematics. What type of assessment was administered to your student to identify dyscalculia? Recent reading material consistently complains of the lack of accurate testing tools for dyscalculia; however, I need a starting point. Any suggestions or leads would be greatly appreciated.

There are several excellent articles about dyscalculia in the “LD In Depth” section of LD OnLine (there’s a box on the top of the page that will get you there).

True “dyscalculia” is truly rare. However, other difficulties with processing symbols or dealing with abstractions (either because of a processing problem or lack of good instruction) can wreak havoc with learning math — and since a whole lot of elementary teachers are math avoiders, they tend to hand the problems down.

Why is dyscalculia truly rare? I have just started reading about it, but I was under the impression that most math processing problems fell under the umbrella “dyscalculia”.

Dyscalculia is like dyslexia — there are a small number of true cases of genetic origin, and these students need special teaching and intense individual tutoring and if possible early intervention.
Swamping these are a huge number, I estimate ten times as many, cases of bad teaching and teaching of bad attitudes.

If elementary teachers use math as a punishment (if you do that again I’ll give you ten math problems for detention) and avoid math as a reward (class, you were so good today, no math homework tonight; aren’t we lucky tomorrow, birthday party, no math class) — and both of these are extremely common — then it is no surprise that they raise another generation of math phobics and math avoiders.

If elementary teachers can get their degrees and teach with no more than Grade 10 math (and most of them do; their college courses in “math education” do *not* generally teach college level, but review Grades 1 to 5) and never do any more math in their lives, then it is no surprise that many kids in school are taught things that are dead wrong as well as methods that are tremendously inefficient and/or dead ends.

If elementary texts are bought by committees of non-math people who buy the publisher’s flashy sales pitches — read Richard Feynman’s [Nobel Physics winner] story about being on the New Math committee in California, and being sold “textbooks” that were showy covers with blank pages inside, because the books were being sold before they were even written; and those that were written contained huge errors of fact — then it is no surprise that both teachers and students are just scraping through confusing and confused texts with no idea of what the work means or where it is supposed to go.

Read the Third International Math and Science Study to find out how badly North American schools stand in math teaching — the most money, the most time, the most computers and extra materials, and among the lowest results in the industrialized world. Kids with the highest self-esteem and lowest performance. And in the rest of the world,. teachers spend the majrity of their time “developing concepts” (ie actually teaching) whereas in the US teachers spend the majority of their time shuffling papers and doing bureaucratic tasks.

This is not to blame the teachers — they do what they are told to do and they teach as they were taught.
But when a student has trouble with math, nine times out of ten it is a case of never having “developed the concepts”.

Would a math assessment distinguish between a math processing problem and a lack of developing the concept????

Why is it rare? I could come up with evolutionary theories… most math processing problems aren’t problems with the math — the concepts of number quantities and adding and subtracting and understanding that 12 is 12, wheter it’s 2 x 6 or 3 x 4 (in rows and columns or area or whatever). I believe it’s the Kate Garnett article that explains it best but it might be one of the others.
I think it is really important for people to understand the difference between having a problem processing and understanding symbols — or a problem making the connection between those symbols and the comprehensible concepts — and having a disability with math. ‘Way too often the issue is teaching the math as if it were a bunch of symbolic manipulations wiht their own littel rules and procedures, in a code too arcane for hte masses to grasp.

I think we are saying the same thing.

True dyscalculia is like true dyslexia — a difficulty in processing the concepts.

This has to be distinguished from bad teaching and bad programs, where the student has developed a totally erroneous idea of reading as guessing from pictures or of math as shoving symbols around.

It’s exactly the same problem as a reading assessment for dyslexia: is the student making errors reading because he really does not process the symbols, or because he has been taught for four years to look at the pictures and guess? Is the student making math errors because he really does not understand the concepts that have been taught, or because he was never taught the concepts and told only to manipulate symbols?

This is why you search out a respected and experienced professional to make the assessment; the tester is not only checking off right and wrong on a paper, but looking for nuances of behaviour and interviewing the student to try to get at concepts. This is also why you don’t immediately label every weak reader as dyslexic or every weak math student as dyscalculic.

Cathy wrote:
>
> Would a math assessment distinguish between a math processing
> problem and a lack of developing the concept????

Nope. OFten the solution is the same, though — going back and teaching the concepts. And hopefully this would be done with a diagnostic eye so that if there were processing issues the teacher would slow things down and address those.

One difference between reading and math is that most people *do* end up processing verbal language an awful lot, whether it’s spoken or written. It’s everywhere. Many mathematical tasks *can* be left on the workbook pages. This means that bad processing habits, as well as anxieties or even phobias, can quietly develop. I see an awful lot of returning students who are in a *serious* rut of “what’s the recipe” and who resist making the connection to the rest of the world. No, math is this awful thing they must endure to pass this pointless class that they will never use. Well, they *will* never use the stuff they are thinking is math. If they could step out of the recipe box they’d see that it *does* connect to understanding how the world works. It’s almost as if a disability had been created in these folks.

This is true—this created disability, not to discount real disabilities. My best friend in college and I took an accounting class for nonmajors. We studied together. I got an A and she got a D. She understood it as well as I. She just froze when she had to do anything with numbers. \

Now, 20 years later, she actually does book keeping as part of her job. She has learned to face her fears and has proved to be competent.

Beth

Hi,

My daughter - almost 11 - has exactly this problem. Her IQ was 120 when she was 7. Her reading age is three years above her chronological age. She is well above average in Science. But in maths she is about two years behind. I hope someone has some answers. It is really frustrating.

No magic wands. But try the basic principles of good teaching in any subject:

(1) Find out what she really knows. Take some time and ask some searching questions. 90% of the time she stopped understanding a grade or two before the level people are trying to teach her on, so of course she is frustrated.

(2) Start at the level she last mastered. That may be adding numbers under 100 and not subtracting. OK, so that is her real mastery level, so work from that base.

(3) Teach one thing at a time. She understands adding two-digit numbers; OK, work on base ten, meaning of hundreds, and adding three-digit numbers. Work on carrying as an application of base ten. Work on basic subtraction as undoing addition. Work on these basics until she really feels confident with them and has mastered and overlearned them. Then and only them move on to the next operation.

(4) Use real-life examples and concrete objects, always. If an abacus helps, use an abacus. Use it until she decides herself that she knows the material anyway and can do without it.

A lot of teachers, and some students who have absorbed their attitudes, resist going back so far because it’s “too easy” or “babyish”. I keep reminding these people that if you fail Grade 3 three times in a row, you have still failed Grade 3 and have wasted three years in pointless activity and failure and frustration; but if you start at Grade 1 and *learn* Grades 1, 2, and 3, you have spent the *same* three years and have gotten some value out of it. Which will catch you up faster?

My son has some form of this but they have not tested him yet. He is in the 9th grade and has always had A’s in class until last year in Algebra 1. His teachers from last year and this year cannot for the life of them figure out what his problem is. they say that he is a global thinker. He turn his equations upside down. The top number is now on the bottom and the bottom on the top. Can you help?
laurie

This is such a common problem I feel like a broken record repeating myself.

Kids are *taught* a certain way of working and a way of thinking that goes with it. They do elementary arithmetic by recipe and rote and magic abracadabra formulas: pick up this number here and move it over there; move the decimal point this way; turn this fraction upside down; cross out these two numbers; this number “becomes” (by a magic wand?) this other number. The student does not invent this worldview of math as mysticism by himself; he absorbs it from teachers who themselves are working by rote. A student with a good memory for facts and recipes and abracadabras and a cooperative personality can go a long way without having any logical connection to what math is all about.

Then it hits. Sometimes in long division, often in fractions, and very often in algebra and geometry. The math being presented is either longer than the memorization capacity, or requires logic and understanding. The student is lost without a rudder. The system he has learned — and again, only what people taught him to do, rarely his own idea or decision or fault, so blang the student is pointless — is not effective for what is now being demanded, and he feels like he is in a foreign language (actually, he is).

The solution is to go back to the start of algebra and work on logic: theequation is a *balance* The stuff on the left side equals (in weight, on the balance) the stuff on the right side. If six oranges weigh four pounds and two ounces, how much do a dozen oranges weigh? Eight pounds and four ounces. How did you get that answer? Doubled. What did you double? EVERYTHING, *all* numbers on both sides of the balance. Etcetera. Teach the *logic* rule: do exactly the same *mathematical* operation to both sides of the equals sign, period. Absolutely resist quick tricks like picking up a number here and moving it there, and refuse to eversay that a number can magically change sign. False, you are actually subtracting, and it is important to stress the mathematical operation and eschew magic. If you make numbers magically change sign when they “cross” the equals sign (flying magically?) then what happens with division? this “rule” is wrong 50% of the time, not a very effective rule.

You solve an equation by “undoing”: to get rid of an addition, subtract; to get rid of a subtraction, add; to get rid of a multiplication, divide; to get rid of a division (= fraction), multiply. And you “undo” in the reverse order to doing arithmetic; you “do” multiplication and division before addition and subtraction, so you “undo” or solve by getting rid of addition and subtraction before
multiplication and division. The wonderful thing about this rule is that it is not only simple and crystal clear, but it works all the way through advanced university math. Instead of twenty different formulas and five hundred different rules, you need only one simple clear principle.

Even before that, if necessary, re-teach the idea of using letters to stand for numbers; every letter is just a number that we haven’t filled in yet. Teach missing number problems like 5 + ? = 8, and point out that the unknown x in algebra stands for the missing number that in arithmetic we noted as ? or an empty box.

Teach directly the symbolism of algebra, that when you run two letters next to each other or a number or letter next to a parenthesis you mean *multiply* and why we don’t use x for multiply any more is that x is standing in for our missing number and it would get too confusing. Often kids get lost on this symbolism and the rest of the course goes over their heads.

Give him models of correctly solved problems and insist that he write down every line and every step; shortcuts are a very good way to get lost in math as in life.

If you re-start like this and teach a good foundation of logic and thinking and *systematic* problem-solving (no guessing, no magic, no long lists of special rules), the subject becomes clear. It may take a month or two to re-teach the foundations; be patient. Most students pick up and move ahead after they get a good start.

Please give some recommendations on math assessment tools that will accurately pinpoints strengths and deficits. Thanks, Cathy in Georgia

I can give you an answer that may or may not help you, depending on your situation.

I use an intensive-extensive personal interview during the first two or three hours of tutoring. I ask the student what he/she is having problems with and give sample problems either from my own knowledge or a text, and I ask them what to do to solve the problem, each step, as I write it down; then I ask them to do one on their own. The student shows exactly how his/her thinking is operating, and weaknesses are easy to pinpoint. For example, if you try to do a two/three-digit multiplication problem with carrying, acting as a scribe you very quickly find out if place value is confused, if the multiplication facts are known or not, if numbers get miscopied or lost, and in the final step if addition facts are weak. If a student tells me five times seven is forty-two, and six plus seven is fourteen, and adds the carries before multiplying, I know exactly what is going on. Having the student write out and solve a problem shows if the numbers are written so badly that the student can’t read his/her own work (a common problem by the way) and therefore makes errors of misreading, if place values are lined up, if steps are omitted, and so on. The same with reading problems and setting up multi-step solutions — can the student read the words? Does the student comprehend those words? Does he/she have any idea of a systematic system for problem-solving, or do they just fold up and say they can’t do it? (again very common), or do they grab the first number at hand and wildly choose any arithmetic operation out of the air (the other very common problem). Does he/she write something sensible, or just scribble all sorts of numbers all over a sheet of “scrap” paper (which I ban absolutely, by the way; my work is not trash, thank you very much) and then do they copy some random “answer”, without explanation, on another sheet? Does the student wait expectantly for marks as the only validation (or insist on marking their own paper as a necessary ritual), or try to actually see if the work makes some sense?

If you really want to get a grip on the student’s thinking processes and real strengths and weaknesses, this is the most effective way possible.

If you are forced by bureaucratic rules to get some sort of “objective” numerical measurement, there are lots and lots of tests out there; check the archives of this board with the search button, look for test or evaluation etc., and I’m sure you can find some names and possibly websites.

Thank you so much! I believe I can use both and satisfy all.victoria wrote:
>
> I can give you an answer that may or may not help you,
> depending on your situation.
>
> I use an intensive-extensive personal interview during the
> first two or three hours of tutoring. I ask the student what
> he/she is having problems with and give sample problems
> either from my own knowledge or a text, and I ask them what
> to do to solve the problem, each step, as I write it down;
> then I ask them to do one on their own. The student shows
> exactly how his/her thinking is operating, and weaknesses are
> easy to pinpoint. For example, if you try to do a
> two/three-digit multiplication problem with carrying, acting
> as a scribe you very quickly find out if place value is
> confused, if the multiplication facts are known or not, if
> numbers get miscopied or lost, and in the final step if
> addition facts are weak. If a student tells me five times
> seven is forty-two, and six plus seven is fourteen, and adds
> the carries before multiplying, I know exactly what is going
> on. Having the student write out and solve a problem shows if
> the numbers are written so badly that the student can’t read
> his/her own work (a common problem by the way) and therefore
> makes errors of misreading, if place values are lined up, if
> steps are omitted, and so on. The same with reading problems
> and setting up multi-step solutions — can the student read
> the words? Does the student comprehend those words? Does
> he/she have any idea of a systematic system for
> problem-solving, or do they just fold up and say they can’t
> do it? (again very common), or do they grab the first number
> at hand and wildly choose any arithmetic operation out of the
> air (the other very common problem). Does he/she write
> something sensible, or just scribble all sorts of numbers all
> over a sheet of “scrap” paper (which I ban absolutely, by the
> way; my work is not trash, thank you very much) and then do
> they copy some random “answer”, without explanation, on
> another sheet? Does the student wait expectantly for marks as
> the only validation (or insist on marking their own paper as
> a necessary ritual), or try to actually see if the work makes
> some sense?
>
> If you really want to get a grip on the student’s thinking
> processes and real strengths and weaknesses, this is the most
> effective way possible.
>
> If you are forced by bureaucratic rules to get some sort of
> “objective” numerical measurement, there are lots and lots of
> tests out there; check the archives of this board with the
> search button, look for test or evaluation etc., and I’m
> sure you can find some names and possibly websites.