A Research Programme for Mathematics Education

After reading the title, I predict that the article will focus on students' mathematical thinking. My

reading of the first paragraph makes me realize that this article covers a range of research ideas related to learning and teaching math. The project coordinator, Wheeler, publishes the proposals of Nesher, Bell, and Gattegno, who are the co-authors of the article.

Among the three educators, Nesher seems to be most concerned about interdisciplinary aspects

of math acquisition. He points out that the general public is strongly against “New Math” and demands “back to basics” because students are struggling with New Math. She wonders what makes math so difficult for students to learn compared to how easily they learn and master natural languages. She believes that current research totally overlooks the cognitive processes involved in learning math. To improve the ways students learn math, she suggests that a new research program examine the types of cognitive processes involved in learning math “as a language system (p.27)” in relation to its real-life interpretation and practicality as well as artificial intelligence, psychology, and sociology.


On the other hand, Bell suggests a program that examines methods of teaching which may affect
students' understanding of math. The reason he chooses to look at the teaching aspect is that many
students cannot understand fully the math concepts taught in their lessons. He points out that many
students can add two positive numbers or two negative ones or subtract a larger negative number from a smaller negative one accurately. But, some fail to subtract a smaller negative number from a larger negative one (for example, -5 – -12) logically without using a number line. Lastly, she believes that research should look at ways of teaching which help students understand the meanings of the math concepts taught and eliminate their math misconceptions.

From a mathematician's perpective, Gattegno states that the three “mother structures - order, algebra and topological (p29)” are fundamental to the development of classical math. He relates them to the structures and activities of the human mind on which math education needs to be based. He thinks that students generally learn math through seeing, hearing and other senses and that computer

technology can improve their learning of math. Therefore, he believes that a research program
examining the effect of technology on students' ways of learning math can help develop a better math
curriculum.

I think all of the authors' perspectives are valid and interesting. On the one hand, Nesher and Bell have different focal points on math educational research. While Nesher talks about the importance

of learning math effectively, Bell emphasizes the instructional aspects of math education. I believe that effective learning cannot occur without effective teaching and vice versa. To me, both are equally significant. Since there is no single teaching method best for teaching all math concepts, it is important to examine a variety of teaching techniques to improve student learning. In the same way, there is no one method most effective in learning math. Since different students have different learning styles, they can develop multiple ways of learning math concepts. Their preferred learning methods may shape lesson planning and class activities. On the other hand, Nesher and Gattegno consider math education from interdisciplinary views on their research interests which focus on cognitive processes and computer technology. These aspects are certainly important. Today's technology is more advanced than when this article was published. The use of computers can certainly increase students' interest and understanding of math. In terms cognition, if we think about how children think mathematically through task-based interviews, we can come up with different ways of teaching the subject in a fun-filled manner.