Lesson Plans -> Mathematics

This is a template one of my instructors in the Michigan State Teacher Education program asked our class to use to plan a discussion. It expanded my thinking, and allowed me to conceptualize discussion in mathematics classrooms differently. By thinking through possible student interpretations, as well as my own interpretations, of the problems, I had to not only understand the problem, but understand how it relates to previous knowledges, and how students might relate to the problem. I was able to see how students' thinking drove the discussion, built off each other's ideas, and worked toward a conceptualization of graphing that reflected how one could represent an equation. Framing discussions with student work that continuously builds off of and expands the ideas and understandings of students shows them their work and thinking are valuable additions to the classroom, which helps offset the inequity experienced in a typical classroom and teach students to respect and value other's opinions.

This lesson bridges from the discussion above to help students begin to understand quadratic equations, functions, graphs, and other representations. This lesson assumes students have already explored ideas similar to the discussion above, recognizing that equations that link one variable to another using only integer multiplication, division, addition, and subtraction are linear, and look like a line on a graph. Now, they are asked to consider another way in which we can make patterns or sequences that aren't linear. I attempt to make this connection explicit during the lesson, to build on students' existing knowledges. Further, by having students explore the patterns on their own, I am showing that their ways of thinking and reasoning are valid tools in the classroom.