Park City Mathematics Institute
Secondary School Teacher Program

Reflection on Practice Class: Day 12
Akihiko Takahashi

Gail started our discussion by comparing two ways of writing objectives:

Set one:
Reinforce algebraic methods for solving systems of equations.
Review forms of linear equations.

Set two:
Develop relationships betweens lines and a point.
Develop relationships between multiple lines through the same points.

In set one the mathematical expectations are explicit.
In set two the mathematical expectations are less obvious. What type of relationships might be developed?

Gail emphasized the need for visible mathematical expectations.

Aki started by noting that when teachers write the goals of a lesson or a class, sometimes they mix up goals and tasks. Tasks relate to process. Usually the subject of a task is teacher. A task is a process, not a goal. The subject of a goal is the student. What we are to do in a class is not the goal, it is the task. The ultimate goal of a lesson is to provide something new to students. It should be different from what they did last year. If there isnŐt something new, we waste the students' time.

We spent the rest of the hour working on our open-ended problem.

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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.