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Baxter, Juliet A.
Summary

This study attempts to answer three questions, which can be simplified into, “What does writing reveal about the students’ conceptual understanding, strategic competence, and adaptive reasoning?” They studied middle school students who were in “reform mathematics classrooms” to find how particular students responded to writing assignments. They observed the classroom, and also used information from interviews with the teacher and student journals. In one situation where writing was used in the classroom, the teacher asked if students should be able to use calculators. Responses were short, but got students involved in writing informally. The study went on to analyze individual students across the entire year. Certain students simply recorded information from the teacher, while others generalized the information. Some, who had trouble understanding, just wrote “I don’t know” multiple times. In a comparison between the students in the “reform” classroom and students in a regular classroom, they found the “reform” students wrote more recording or summarizing style, while the regular students generalized much more often. Also, “reform” students tended to write in a conversational style (conversing with the teacher), while other students tended to be less conversational.

Response

The classroom journals seemed to help students express themselves. Even the students who rarely spoke in class had opinions when asked to write about calculator usage. However, a concern was raised in the article regarding taking time to read students’ responses. While it could take more time, this strategy would also lessen the amount of time needed for one-on-one teaching with the students outside of class. Students would hopefully leave class with a deeper understanding of the topic and would not need to seek as much extra help.

Usefulness

This approach to writing in the math classroom could change how I taught in the future. Having never learned in this kind of environment, it was enlightening to see how effective this could be. I feel like students would enjoy having an outlet to discuss their opinions, while it would also help them learn. I can imagine using this kind of writing to summarize a class period, or to provide a break from the teacher speaking the entire time.

Bossé, Michael J.
Summary

This article by Michael Bossé examines why it would be effective to bring reading and writing back into the math classroom, and how we could do it. In many secondary education classrooms mathematics is simplified to the study of equations, while it is certainly more complex than this. This means that while the students are able to learn and recite the knowledge required for state testing, they do not understand the meaning behind the numbers they use. Bossé first reports that reading in the classroom is severely lacking. Most students (and teachers) do not even read out of the assigned textbook, instead only referring to diagrams and formulas. Likewise, writing is kept to a bare minimum. If writing is necessary, such as for school or district requirements, teachers assign biographical research papers. While the students are technically writing, these types of assignments do very little to further mathematical understanding. Bossé says it’s not enough to have students writing about math, they should be writing in math. This is why writing a biography doesn’t really cut it. Bossé states, “…reading and writing biographies of famous mathematicians has upstaged reading and writing regarding the nature and uses of the discriminant of a quadratic polynomial.” In this case, writing a paragraph on how we can use a function contributes to mathematical growth, whereas a biography is simply an interesting bit of history. As the purpose of the course is to teach mathematical concepts, the former is obviously preferable.

Response & Usefulness

I can personally attest to the lack of reading and writing included in high school math. In fact, many textbooks highlight necessary definitions, and as such students never have to read even a paragraph to find what is needed for their homework. Bossé recommends a few different approaches to math through writing, as can be found in the article. The benefit of writing in mathematics is similar to the reasons behind writing in any field. In order to write effectively students are required to understand the relationship between abstract ideas and concrete mathematics. Overall, Bossé presents many useful tips to include writing in the secondary education classroom. In his article, he goes on to include many specific examples of writing opportunities. This is a valuable resource for anyone looking to teach mathematics at any level.

Montague, Marjorie, Craig Enders, and Samantha Dietz
Summary

This study led by Dr. Marjorie Montague of the University of Miami examined the effects of Cognitive Strategy Instruction on middle school students with learning disabilities, specifically in the field of mathematics. 24 middle schools in the Miami-Dade County Public Schools continued the study to its end, using a program called “Solve It!” that was added to the traditional curriculum. Instead of belaboring equations and formulae, this method focuses more on how to think about problems in the math classroom. Students learn how to tackle difficult problems by breaking them down into components and learning how to construct solutions in their own way. After studying the 24 middle schools, Dr. Montague found positive results in every school using the new curriculum, while those using the old curriculum remained unchanged. Many schools in Florida are now adopting the curriculum created for this research.

Response & Usefulness

The "Solve It!" program completely redesigned how content literacy was explored in the classrooms using it. The students not only learned the required material, but also developed a greater understanding for problem solving for real life applications. The impact of this study is spreading as more and more schools are adopting the improved curriculum. I certainly recommend this article for anyone teaching mathematics at any level.

Kirchner, Mary Kay, and Reza Sarhangi.
Summary

When most people think of mathematics, they usually relate it to computers, architecture, physics, or just about any other kind of analytical science. The last thing that comes to mind is artwork. However, a couple of math teachers in Maryland are working on closing the gap between art and numbers in students’ minds. Using traditional weavings from Navajo culture allows a blend of cultural learning and applied mathematical concepts in the classroom. Professor Reza Sarhangi and high school teacher Mary Kay Kirchner have begun utilizing the Navajo patterns to teach elements of symmetry. The basic concepts of symmetry consist of reflection, translations, and rotations. All of these are used in Navajo artwork to create a large piece out of one small, simple pattern. As shown in Sarhangi’s and Kirchner’s work, it is common to see a pattern appear as much as 32 times in different forms in a small rug. This allows students to study real world applications of math while learning about Navajo history. It is important to acknowledge the importance of harmony and balance in Navajo culture, as these are recurring themes in mathematical symmetry.

Response & Usefulness

One difficulty many students face with math is that it is so abstract. There is no way to see or feel equations. Even those who are able to memorize the equations are completely lost when they need to apply the equations in real situations. To this end, I feel that applying mathematical concepts to physical objects will help many students grasp the meaning behind the equations. Also, the Navajo rugs potentially provide a cross-curricular opportunity unique to this sort of experience. I whole-heartedly recommend this study to math teachers.