Unit Plan & Lesson Plan

Battleground Schools

I found the history of mathematics education discussed in the article very informative. Although I knew that teaching biology and history is usually influenced by ideologies, I have never thought that the politics and ideologies, especially in countries that have democratic governments, could influence the mathematical education policies.   It was very interesting to learn that the politics of the cold war was responsible for the New Math program; a program that continued in Iran even during the years that I was a high school student despite the fact that its ineffectiveness had become clear long before that time and the program had been changed in the States where it had been originated.

I found the progressive/conservative dichotomy used to categorize the conflicting views on mathematical education useful. But what I really liked was the author’s awareness of the danger of oversimplification and the discussion of the shared views of these parties.

When I think about the math textbooks that are currently used in Canadian high school, I am reminded of the description of pre-reform math textbooks in the article. Unfortunately, the math that is taught is reduced to a series of algorithm to solve artificially created problems. Students are expected to master these rules and use them to solve problems that they are given in their homework and tests. Neither are they taught why these algorithms work nor the importance or the beauty of the problems that they are used to solve. I only can hope that the next reform pays more attention to the progressive views and incorporates more of Dewey’s ideas.

John Mason on questioning in math class

John Mason on questioning in math class 

I found Mason’s ideas interesting and applicable to inquiry-based learning. In particular, I think they provide useful insights in conducting p4c-style method of teaching that I’m especially interested in. The role of the facilitator in community of inquiry is to help the learners to ask themselves questions that lead them to the solution to the problem, rather to lead them to solutions by asking them questions that lead to answer. I found the distinction between “asking as telling” and “asking as asking” which is based on the distinction between “listening-for an expected response and listening-to what students are saying (and watching what students are doing)(p. 515)” insightful. This idea can help the facilitator in community of inquiry to find ways to engage the learners in such a manner that they lead to ask useful questions and in the course of answering those questions learn the subject that they are supposed to learn. Another interesting idea discussed in Mason’s paper is asking students “to construct examples of mathematical objects meeting various constraints. By carefully choosing the constraints so as to force students to think beyond the first (usually rather simple) example that comes to mind”(p. 516). I will try to come up with ways to use the method of formulating questions by students and constructing examples when I plan my lesson for the long practicum.

 

Reflection on micro teaching:

Based on self-reflection and the feedback, I think there purpose of our activity wasn’t clear and made students a bit confusing. We also could have allocated more time for the activity and engaging students in learning so that they could have had enough time to express their ideas and solution methods.