Papers

Mathematics Education and the Multiple Intelligences

Here is a paper by Mark Wahl that gives a taste of the power of using the multiple intelligences to convey math problem-solving and process. You can go straight to a page to rapidly obtain copies of his books that relate to this kind of teaching (for instance, Math for Humans: Teaching Math through 8 Intelligences ).

Or, read the paper now:

Multiple Intelligences — Power Up Math Teaching

Results are still flowing in from the Third International Math and Science Study (TIMSS) that examined the curricula, student performance, and teaching styles of math and science programs in fifty countries. They indicate that math instruction in the U.S. can be characterized as “a mile wide and an inch deep.” That is, it sips many dozens of topics, but pauses little to drink of their essences. A further finding was that, in general, U.S. students’ “number sense” lagged behind the average of the other countries mainly because focus on procedures takes precedence over true math thinking and problem solving in classrooms.

The Problem and Many Limited Solutions

The findings weren’t surprising to me because I regularly encounter numerous parents who are worried that their children aren’t really “getting it” in math, even while earning a B. The “it” they long to see demonstrated is that elusive spark of “number sense” and depth of response to math ideas linked with the confidence and dexterity to tackle real-life problems. Instead, the parents sense that their child is turning into a “math robot” in the daily repetitive lessons.

Experts have been aware of the problem and there have been many solutions proposed. The National Council of Teachers of Mathematics, for instance, supports the use of more projects, investigations, open-ended questioning, and “constructivist teaching” in which students are guided and encouraged to build up meaning as they participate in activities. This is valuable, but, we have more “learning channels” available than that. To use multiple-intelligences language, I see the NCTM approach as geared primarily to the logical-mathematical intelligence. In some students this is not the strongest asset, so even “reformed math instruction” leaves them somewhat cold.

A Broader Solution

We must tap the other intelligences of all the students in our quest to engender a “felt sense” in mathematics. A sense of depth is not just conceptual but personal — a feeling that math strikes me “where I live.” For instance, a musically intelligent student may really break through on number pattern recognition when that pattern is translated to piano keys or rhythms, and a spatially intelligent student may get an “Aha!” from a lively diagram, mind map, or guided inner “movie.”

A Detailed, Surprising Example

To amplify the case for using more than the logical-mathematical intelligence in math, consider this story problem: “A student is sorting into sacks a room full of food donated by the school for a local food bank. He sorted 1/3 of it before lunch then sorted 3/4 of the remainder before 3:00 p.m., the end of school. What part (fraction) of all the food will be left for him to sort after school?” (Take careful intrapersonal note of your intrapersonal responses to reading this problem and being asked to solve it — I’ll address them later.)

This problem defeats many students just in its wording. They may go into a blur, seeing all the fractions at once, and proclaim it hopeless to sort out. Some even say to themselves “It’s probably a trick” or “I hate those kind,” then give up. Others not so defeated jump in with memorized fraction tools flying, just hoping that the right ones will be chosen and they’ll “get the answer.”

Switch Intelligence “Channels”

Using other intelligences would yield more progress. They would be wise to tap their linguistic and interpersonal intelligences by pairing off and paraphrasing the problem to each other until they are sure they understand the question. With the spatial and bodily-kinesthetic intelligence they can “feel” or visualize the portions in that food-sorting process. This not only helps them to get oriented in the problem but it can lead to an estimate of the answer. (Estimates should always accompany problem-solving to screen for “wild results” from a calculation.)

Here’s how it would go. Feeling the process and visualization convey that a pretty big chunk of the job (1/3) got done before lunch. It can be felt that the lion’s share (3/4 of the remainder) got done before school was out. The sense is that there will be only a small part of the job left for after school — something like an eighth, seventh, sixth or fifth perhaps.

A more precise use of the spatial intelligence is to make a rectangle to represent all the food, then to divide it up into three equal parts, marking the top third done “before lunch.” Then the remaining two thirds are divided into four equal parts and three are marked done “Done before 3:00.”


Careful examination of your picture will reveal that there is only 1/6 of the food left to be sorted — the correct solution. Spatial persons feel a real “Aha!” at seeing the answer this way.

 

An intrapersonal task for you right now, and for your students, is to reflect for a moment on your feelings when encountering the solution in this form. Did you feel you understood it better? Did it seem like this was “not legitimate” as a way to solve?

 

And Don’t Forget to Bridge to the Logical Mathematical

The insights from the figure can then lead the way to, and make visual, the logical-mathematical method: fraction multiplication to find 3/4 of 2/3 = 1/2 = three of the rectangles in the diagram: done before the end of school. Then add this 1/2 to the 1/3 done before lunch to find that 5/6 is finished, leaving 1/6 to do.

Follow-ups

A linguistic, interpersonal and spatial follow-up is to ask each group in class to re-create the solution process, including a recall of the key turning points in their thought processes, and come up with a group write-up that totally conveys the solution process in complete sentences, with labeling on a diagram, or with a flow chart.

An intrapersonal follow-up would be to ask students what their first reaction to the problem was, including internal dialogue, regardless of how confident or how crazy or negative that reaction was. Students are reminded that if we track what we were thinking and feeling in a process we can increase our effectiveness as a problem-solver. We can keep doing what helped and learn to weed out negative self-talk, imprecise assumptions, and ineffective strategies.

Contrast This With the Usual Approach

The use of the various intelligences, even Gardner’s latest, the naturalist intelligence, with its sorting, naming and classifying strengths, creates more of a sense of total involvement with a problem. It gains relevance to a student with certain intelligence strengths, and the number relationships make sense. Compare this broader experience to the usual way this problem would be taught by, for instance, reading the problem, having students try it, showing a fraction calculation on the board, and moving on. An awareness of many intelligences can keep fresh approaches coming in math class and can include students who otherwise might drift off when only talk or calculations are being offered.

I have only scratched the surface — there are many other ways to tap the power of these intelligences for math learning that I go into in my book Math for Humans: Teaching Math through 8 Intelligences.

To get the book mentioned plus other resources and ideas Click here