This question has been on my mind a lot because I'm wrapping up running a study on the development of math concepts in four and five year olds. Part of this study involves assessing their current level of math knowledge using a standard test developed by a leader in this area of research. It includes questions on counting, comparing two quantities, adding and subtracting, with one and two-digit numbers, with and without manipulatives and visual aids. Because the children are so young, parents observe the entire study and see how they answer these questions, and are often surprised both by the difficult questions their children answer correctly and the more basic ones they fail even to understand.
For example, our participants all answer the following question incorrectly: "how many numbers are between 7 and 9?"
A few of them don't understand the question at all, and guess some random one-digit number. Most of them reply, "8." They know the number 8 goes in the middle. They do not take the next step, realize we're asking about the number of numbers--a second order question--and give the correct answer (1 or 2).
This is not supposed to be one of the more difficult questions. It's grouped amongst all the other questions about one-digit numbers presented without visual aids--all assumed to be at the level of the average six year old. A level that, incidentally, the local population of four and five year olds in this high socioeconomic status area seems to have already reached.
The problem is that they don't understand the word "between." Ask them the other "between" question on the test--"how many numbers are between 2 and 6"--and they almost never give you a sensible answer, and sometimes they'll look at you blankly. It doesn't help to use gestures (use a hand on one side of the table to represent 2, another to represent 6, and gesture to the space in the middle). It doesn't help to use different phrasing, such as "how many numbers do you have to jump over to get from 2 to 6." They just don't get what you're asking them, probably because it's not the sort of math question they're used to being asked.
Another hard one is "is 5 closer to 6 or 5 closer to 2?" (where we present a visual aid, a triangle with these numbers at each of the points, with 5 at the topmost one). The blank looks and wild guesses indicate that some children don't understand the question. I don't blame them; I'd be confused about whether they were talking about the relative length of the sides of the triangle I'm holding up or the abstract relationship between the numbers. I've rephrased it "is a five year old closer to a six year old, or closer to a two year old?" to make the distance more palpable, but even this was too confusing for one four year old I tested recently.
In general, the language of math, not math itself, is what trips them up. They'll answer a question wrong because of how it's phrased when they've already demonstrated through earlier questions that they know the concept being assessed.
This always surprises parents. It's never occurred to them that math has its own language, its own jargon. That kids don't just have to learn how to count and add and subtract, but they have to learn the verbal cues to perform each of these operations.
Their faces light up in that "wow, I just learned something new today" way and I can see the wheels turning as they think about how to help their child learn the language of math. (This reaction always makes my day).
It would be fascinating to do a training study where we demonstrate something like this to parents and then follow them over the next couple of years and see how their kids achieve in math compared to kids with the same educational and socioeconomic background who didn't receive this sort of training.
Have you or your child struggled with the language of math? Do you think this would be a productive area for education to focus on? Let me know what you think!
Benno (nickname) qualifies for double time accommodations in Math(Dyscalculia) and 1.5 in Writing (Dysgraphia). In every other area of Psycho-educational testing, he scores at the 95%tile or higher (ss, science, reading). He scores @ the 8%tile in math calculations, but in the 90%tile in reasoning. That is a dramatic discrepancy ...and so similar to dyslexia, only with numbers. They make no sense to him, as symbols. The fact that he has never had the manual dexterity to do math is in there somewhere, too. Maybe there is a motor aspect to learning calculation. This same child couldn't sign his learner's permit without looking at a visual cue at age 17. It made sense to me when I learned there is a motor aspect to writing, too. Our muscles learn and repeat a motor function. (I'm going here, somewhat sloppily, as I read your next post where you discuss the sensory/motor aspect of autism. I am so easily distracted...)
ReplyDeleteAnyhow, when I read this post, I thought "YES!" because my Benno was language delayed. In kindergarten, he could not yet participate in conversation. He could only repeat long strings of words used on videos that he had memorized that may or may not have anything to do with what you were talking about. Something triggered them, though, in his mind. For one year, ages 4-5, I had spent 2 hours every day after developmental preschool presenting words to him in a visual/kinesthetic context. He knew nouns, because he could visualize them, he had seen pictures, and the words associated with them. But words like between, he had to be visually, or kinesthetically shown a few times before he had any understanding. Math at school must have sounded like "blah, blah, blah apples blah apples blah blah apples, Ben?". Simplified, but if you didn't understand the meaning of the word "take", "plus"," equals"---how could you even go there? He was echolalic, which means "a pretend communicator-making the noise without the understanding" up until grade 4, where he began to answer freely with the vocabulary he had.
YOU GO GIRL...these poopy-heads have no empathy for children who are plopped in a world set out to make them feel like failures. The real failures are those who punish them for things totally beyond their control. If we demanded of teachers to teach the way kids learn, most of them would look pretty stupid. I was trained as a teacher, and I would be right there with them. But you learn and you grow for love of this most magnificent brain your child has been endowed with.
>>>Have you or your child struggled with the language of math? Do you think this would be a productive area for education to focus on? Let me know what you think!<<<<
ReplyDeleteYES!!!!!!!!!!!!!! Just wanted to reiterate. Kids with Dyslexia have had adaptive teaching for years (Lindamood-Bell among others). I don't know of a similar adaptive teaching program for Math, although it may be out there.