Teaching Mathematics to Non-sequential Learners

In our case files, we have dozens of students who show superior grasp of mathematical relations, but inferior abilities in mathematical computation. These students consistently see themselves as poor in mathematics and most hate math. This situation is terribly unfortunate, since their visual-spatial abilities and talent in mathematical analysis would indicate that they are "born mathematicians."

Visual-spatial abilities are the domain of the right hemisphere; sequential abilities are in the domain of the left hemisphere. The test performance patterns demonstrated by this group of students seem to indicate unusual strengths in the right-hemispheric tasks, and less facility with left-hemispheric tasks. In order to teach them, it is necessary to access their right hemispheres. This can be done through humor, use of meaningful material, discovery learning, whole/part learning, rhythm, music, high levels of challenge, emotion, interest, hands-on experiences, fantasy and visual presentations.

Sequentially-impaired students cannot learn through rote memorization, particularly series of numbers, such as math facts. Since the right hemisphere cannot process series of non-meaningful symbols, it appears that these spatially-oriented students must picture things in their minds before they can reproduce them. For example, in taking timed tests, they first have to see the numbers before they can do the computation. This material apparently gets transmitted to the left hemisphere so that the student can respond. This takes twice as long for them as it does for students who do not have impaired sequential functioning; therefore, such tests appear cruelly unfair to them.

I have found that students can learn their multiplication facts in less than two weeks if they are taught within the context of the entire number system. I have them complete a blank multiplication chart as fast as they can, finding as many shortcuts as possible. That may take some assistance, but it enables them to see the whole picture first, before we break it down into parts. I ask them to look for shortcuts to enhance their ability to see patterns. After it is completed, we look mournfully at the table and bemoan the fact that there are over 100 multiplication facts to memorize. Then I ask how we cut down the number of items to learn.

First, we eliminate the rows of zeros, since anything times 0 equals 0. Then we eliminate the rows of 1s, since anything times 1 equals itself. Then, we do the tens and the student happily announces that these are easy, since you just put a zero after the multiplier. By this time, the student usually notices that there are three rows of zeros, ones, and tens, and that one half of the chart is a mirror image of the other half. When we fold it on the diagonal, from the top left corner to the bottom right corner, that becomes even clearer. I ask how this happens and the student discovers the commutative principle: that a x b = b x a. This certainly cuts down on the task of memorization considerably! If one knows 4 x 6 = 24, one also knows that 6 x 4 = 24.