Michaele F. Chappell, a researcher in the Department of Secondary Education at the University of South Florida, has studied the ability of African-American students to create, and to re-create, geometric patterns.
In a paper based on a study of inner-city elementary students, she found that those with “high-spatial ability” can generally discern abstract patterns in geometric figures, and use those patterns to construct new mental images. By contrast, those with “low spatial ability” cannot generate such images.
The inability to create such abstractions, she argues, may confound students in other areas of mathematics, where the concept of pattern is vital.
Ms. Chappell recently presented some of the results of her study during the annual meeting of the National Council of Teachers of Mathematics in New Orleans.
She discussed her research with Staff Writer Peter West.
Q. What attracted you to this area of study?
A. One of the things that we are con6cerned about in mathematics education is building cognitive models based solely on the performance of African-American students. At present, we have no such models.
We have some established models, but they have been built [by using data from] different [racial] groups. When you use these to compare [performance] across groups, we’re finding that this is just not fair.
Which is not to argue that African-American students necessarily approach problems differently from other students, but we simply don’t know.
I also was concerned about ... visual imagery and its helping to enhance mathematic ability. ... I wanted to ask the question, “What is the role of imagery in mathematics learning.”
Q. Could you explain the connection between visual imagery and success in mathematics?
A. We’re hoping that there’s a connection; there are two different bodies of research that we have on that.
There’s one that says, well, there’s not really a connection, [and] ... that imagery may well hinder [math performance]. But there’s also a a body that says the opposite.
When I use the word imagery, I’m not referring to the [concept of an] image on a piece of paper. I’m talking about the ability to contruct an idea mentally.
For example, if you say “pyramid” to students, what are some of the images that students have constructed around that concept?
Some students may see a three-dimensional square pyramid ... but some students may see a triangle, which is a different notion.
What we’re finding out is that some students are constructing very static images of some of these ideas. Therefore, when we expect them to move up into the more abstract areas [of math], then it is harder for them.
Q. What does your study specifically tell us about the use of image-building in math?
A. All of the students were able to reconstruct primary images.
But what I found out is that the high-spatial students were able to go beyond that.
Looking at a geometric pattern, and asked to say what they saw, they might say, “Well, I saw a hill moving up and down.”
But my low-spatial students primarily stayed at the level of forming static images. And when they had an opportunity to use their images in a dynamic way, they still used them in a static way.
Q. Does your research indicate any immediate changes that need to be made to help African-American students achieve in math?
A. Certainly I can’t say that this happens for all 5th-grade African-American students. This model is something that has to be continually refined.
And at some point we may want to go out and compare its results to [those of] some other ethnic groups.
A lot of the implications concern things that we have to look at in the curriculum. At some point in our curriculum, we may need to key in on patterns more carefully than we are now doing, because patterns are out there in the real live world.
Q. What are the implications for teachers in this work?
A. Teachers need to be aware of how [students] go about developing imagery.
Teachers, for example, tend to draw triangles in very static ways. They need to be more aware of the mental process of creating images.
One of the key problems that we have [as students] is drawing a three-dimensional object on a two-dimensional blackboard.
I can recall when a teacher would draw a three-dimensional axis on the blackboard, I would recall a corner, and that image would be comfortable for me.
But [the] child who hasn’t made that construction yet, he may just be in La-La land.
