The class is a philosophy seminar.

The class is a philosophy seminar.

​As I explained on the Home page, I constructed metaphors to help me implement authentic mathematical practices. I wanted to see students engaging in genuine mathematical inquiry, for them to see the activity of problem solving as a creative process, and most importantly, for them to see themselves as mathematical thinkers.

The vision that I had for the teaching and learning that I wanted to construct was one where students could dig into problem sets, give their best attempt, come to class with their thoughts, and then talk it out. Through talking it out, I wanted students to question each other’s arguments, wonder why certain concepts “worked” or were true, and feel the urge to seek deep understanding. I found that whenever I thought of the classroom in this way, I was always referencing my experience in studying philosophy. So, the metaphor, “My classroom is a philosophy seminar” came to be.

I unpack the words that I am using to replace “mathematics class” in this statement, and search find the implied activities and meaning. Then, I apply them to the classroom, to reveal the activities in which student participate in this environment.

Unpack: Philosophy



                   necessary and sufficient

And when I look up the dictionary definition, I find:
            Merriam-Webster definition:
                 : the study of ideas about knowledge, truth, the nature and meaning of life, etc.
                 : a particular set of ideas about knowledge, truth, the nature and meaning of life, etc.
                 : a set of ideas about how to do something or how to live

Unpack: Seminar
                   Small class

When I look up the definition of seminar, I find:
            Merriam-Webster definition:
                 : a meeting in which you receive information on and training in a particular subject
                 : a class offered to a small group of students at a college or university

 Unpack: Philosophy Seminar
             A course about truth, ethics, and logic, where students argue, analyze, think, and write in a discussion-oriented setting.

Apply: Implied activities/meanings

If my class is actually a mathematics course, then the metaphor functions in the following way:

A mathematical thinker Reads and Analyzes a problem, organizes a Systematic approach to solving the problem, and Writes her Proofs. Students of mathematics need to know the Truth of the concepts that they are discovering and devising by Questioning the why and how the theorems and formulas work. They are Critical of each other's Arguments, and debate about them. 

In order to make this happen, students need to be given the chance to Think Deeply and Logically about the content, and to Discuss solutions with each other.

Developing these activities has facilitated a Culture of mathematical thinking and doing, to deepen student understanding of mathematics.

“The essence of metaphor is understanding and experiencing one kind of thing in terms of another.”
-George Lakoff and Mark Johnson, Metaphors We Live By