Response to "Why you should learn geometry" - Walter Whiteley

This article is a response to another article that was published in the print edition of the Los Angeles Times. The published article, “Why you should learn algebra”, was written by an English professor, David Eggenschwiler. Dr. Eggenschwiler's article was addressed to the Times readers' complaints about the usefulness and necessity of algebra in high school curriculum.

In Dr. Whiteley's response, he notes how algebra is associated with mathematics. The notion that studying algebra fosters rational, abstract, and systematic ways of thinking, reduces the significance of other equally important areas, specifically geometry, of mathematics. Several prominent figures, like Michael Faraday and James Clerk Maxwell, used alternative approaches to provide effective reasons for their pioneering work.

Dr. Whitely seems to suggest that exclusive promotion of traditional views on learning mathematics may be counter-productive. This could be because of potential talents and worthwhile contributions, from learners who excel through alternative ways of doing or understanding mathematics, may go unrecognised or disregarded.

Contact Info. . .

Hi Murugan.


Can you send me your e-mail?

Mine is dharris@sd44.ca


Cheers,
David Harris

Response to "Proofs as bearers of mathematical knowledge" - Gila Hanna andd Ed Barbeau

This article is composed of two parts. The first part of the article delves into Yehuda Rav's paper, "Why do we prove theorems?" According to Rav, who completed his undergraduate and graduate studies at Columbia University, proofs can be used as "methods, tools, strategies and concepts for solving problems." Rav identifies (or differentiates) proofs to be either derivation proofs("application of rules of logical inference") or conceptual proofs. A conceptual proof "does not have a precise mathematical definition, mathematicians would readily understand its overall structure and could verify the correctness."

The second part of the article discusses about proofs as being expressions of mathematical knowledge. Numerous aspects of proofs, such as cognitive, intuitive, reasoning, logical, etc., are identified by Hanna and Barbeau in order to teach mathematical methods and strategies by mathematics educators. Several examples are provided as case studies to show how proofs may be incorporated into a secondary level for improving problem solving techniques. The authors acknowledge that their outlines (suggestions) were not tested in actual classrooms.

The authors of this article seem to approach the issue of proofs from a theoretical point of view, which may be in line with Kilpatrick's line of thought for an effective research program. 

Response to "Models and Maps from the Marshall Islands: A Case in Ethnomathematics" - Marcia Ascher

This paper focusses on Marshall Island navigators' (natives) use of stick charts to examine their experiential and representational knowledge with modern scientific and mathematical ideas and knowledge. These charts were made of palm ribs, coconut fibre, and shells attached and organized to display sophisticated geometrical models of ocean wave propagation. The abstract models represented shapes and motion of waves and land/sea features, which were used for navigating vast area and for training future navigators.

The stick charts were similar to diagrams on a modern-day blackboard. Information that was considered essential where represented by geometrical figures and objects. It is interesting to note how valuable this knowledge was when individuals learn to understand these representations. Marshall Island navigation techniques were kept secret and their future navigators, from noble lineage, were selected and trained by master navigators.

As knowledge seekers, today's students are selected, coached, and trained by educational institutions. How is today's tradition of gaining specialized knowledge in an educational institution (formal) different from other tradition?

Response to "A Linguistic and Narrative View of Word Problems in Mathematics Education" - Susan Gerofsky

In this article, the author looks at the nature of word problems in mathematics education by using three methods. The three methods are pragmatics (the branch of linguistics dealing with language in use and the contexts in which it is used), discourse analysis (approaches to analyze written, vocal, or sign language use or any significant semiotic event), and genre studies (a branch of general critical theory in several different fields, including the literary or artistic, linguistic, or rhetorical). Among other structures of word problems, the author describes the break-up of generic word problems into three components ("set-up", "information", and "question").

This is how I generally tried to solve word problems. I wasn't interested in the problem set-up. I would try to find all the variables involved in solving the problem and then identify the relationship to find the answer. Once I come up with an answer, I would go to the back of the book to check the answer. If my answer was identical to the book's, I would move on. Otherwise, I would re-read the problem to find where I went wrong. Whether the problems were word problems or abstract algebraic problems, I employed the same techniques. This could be why I hated word problems. Whenever I tried to come up problems to solve in the class, the problems were often times identical to those found in textbooks. The author cites John Lave to describe this phenomenon.

Finally, the author goes on to wonder why word problems in mathematics have persisted for so long. I am curious to know if the author has found some answers to the purpose of word problems in mathematics education.