Math and Diversity

So what does "carry" really mean? What does "carry the 1" really mean. Several years ago David Pimm, a British linguist, calls this "teacher patter", a word or phrase used by teachers to get children to learn to do something by rote, The "guzintas" as in "2 guzinta 10 five times" is another example of teacher patter.

The word carry" is of course a metaphor used to shortcut the process of regrouping the 14 ones into 1 ten and four ones. It was done for generations, and sadly still is, so that children could learn a procedure quickly without any sense of what was really happening in the quantitative relationship between the two quantities, 15 and 29. Without any sense of the concepts behind what was happening children were never able to develop the skill any further, were never able to check their accuracy, other from memory, and develop absolutely no sense of what the number system was all about.

This is bad enough for neurotypical children but presents greater problems for children who have  special needs or math anxiety. Teaching such meaningless rote bits of knowledge to children who will most likely never be able to apply this skill to anything meaningful is a terrible waste of everyone's time, especially the children.  Instead, it is so much better to teach children with special needs what addition and subtraction mean and when these operations should be used, and then use calculators to do the arithmetic.

For English language learners there are similar problems with the use of metaphorical language. In many other languages the linguistic equivalent of "carry" is used but in some languages different words such a "put" are used where math instruction is based on rote learning. Other metaphors such as "reduce" when changing 4/8 to 1/2 also cause learners to develop misconceptions between. Most children, and many adults, who have been taught fractions with the use of this word will think 1/2 is smaller than 4/8 because a) "reduce" means to make smaller and the numbers 1 and 2 are smaller than 4 and 8.

In my graduate course GED612 Math and Diversity this fall we will discuss many issues related to teaching math to children who have diverse needs. Here are soe resources for Math and Students with Special Needs and Math and English Learners.