Park City Mathematics Institute
Secondary School Teacher Program

Reflection on Practice Class: Day 1
Akihiko Takahashi

Aki started off Day 1 by asking, rhetorically, "What type of classroom is not building math?" We are all teaching mathematics in the classroom. How can we move from what we are doing to building math in the classroom? What does it mean to build math in the classroom?

Aki had just returned from a conference in Thailand. "In Thailand, people are talking about mathematics for all students. But teachers don't have time to accomplish this. It is difficult for teachers to work collaboratively. They don't have open doors (to their colleagues). Each of the countries represented at that conference is struggling with these issues. Singapore and other countries are very aggressive trying to improve teaching of mathematics."

He showed us a slide from the TIMSS study which compared 8th grade teaching in 3 countries: Germany, Japan, and the US. The chart showed the percentage of lessons rated as having low, medium, and high level of mathematical content. In Germany, 34% of the lessons had a low level of mathematical content, in Japan 11% of the lessons had a low level of mathematical content, and in the US 89% of the lessons had a low level of mathematical content. Teachers in each of the countries need to work to try to get 100% of the lessons focused on a high level of mathematical content.

He asked us for our thoughts. Some of the responses were: "Is there too much of an emphasis on having fun in grades leading up to high school?" "Is math presented so dryly and piecemeal in elementary school?" "Is there too little willingness to study rigorous subjects in school?" "What are the cultural effects outside the classroom? In Germany or Japan is it socially acceptable to be not good in math? In the US, it isn't acceptable to say I can't read, but it is OK to say that about math."

"Is the problem teacher preparedness?" "Do teachers tell kids that they can't do math? How are we going to convince the students that understanding mathematics is necessary for everyone?" "Should we expect more mathematical rigor in the requirements for all teachers?"

"How much time are we willing to wait before we step in to give help? How much time are our students wiling to work before they ask for help?"

"What are the differences between medium and high levels of math content in the classroom?"

Aki: "What can we do?" He showed us a graphic which illustrates: "Math people can pour their math knowledge into students." This technique works for some people. But how can we help all of the students?

Aki showed us the response of one of his students, who wrote: "Our first activity in class was to discuss in groups what we expected from this class. We found that most of our expectations were quite similar to those of other groups when the class reconvened as a whole. In particular, our class was concerned about how to make mathematics fun and relevant for our students. Many of us also felt the need to become more comfortable with mathematics ourselves. We agreed that a majority of Americans feel anxious about mathematics; mathematics is regarded as something that only 'math people' or geniuses can understand, but in order for us to be effective mathematics teachers we need to embrace the idea that mathematics is something everyone can do."

Aki: "In the traditional model of mathematics teaching, teachers are very busy at the beginning of class and students are busy at the end. In the new model, students are busy at the beginning and teachers are busy at the end after students come up with their own solutions."

Aki showed us a parallelogram made up of four strips of plastic (polystrips) joined at the corners. As he slid the top, it changed to a differently shaped parallelogram. Our task was to find relationships among sides, angles, area of the shapes made from polystrips as the shape changed.

We worked on this problem in our group and wrote up our results on poster paper.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.