Lehman Lesson Study Session Two: Exploring Functions through Geometry

Wednesday, October 25, 2017

First order of business was to agree on the statement of our broader goal for our students that we hope to be manifested in our research lesson.

Here’s what we came up with:

Connecting to a Broader Goal: Students will enjoy math as a conquerable challenge by building on successes and developing a systematic approach to problem-solving.

We want students to see math as a challenge, not as a problem. They will have the confidence to not view struggle as a negative statement about their own ability, but as an expected part of learning. They will use their personal experience and the information given to approach mathematical situations with the spirit of a scientist, with the confidence to move forward and try things that may not work. With each challenge they work through, they will gain confidence in their ability to use a systematic approach as they make sense of unfamiliar situations or problems.

Next we talked about challenges of teaching functions. The goal is to think about the challenges and then look at some problems exploring function concepts through geometry. One we settle on a problem, we’ll consider it through the lens of what is missing from the CUNY HSE Framework and meeting specific standards assessed in those domains on the TASC.

Content Brainstorms

What function concepts are difficult for students?

  • understanding that functions are generalizations and that there are sometimes infinite possibilities for x and y
  • different uses of variables – they always want to put numbers in for x and y
  • that a function is about the relationship between x and y, not about a specific x and y
  • going back and forth flexibly between the graph, chart and rule
  • creating functions to describe a situation or relationship
  • translating data to a workable function
  • graphing functions
  • understanding what points/graphs of functions mean – how does the graph connect to the situation

What functions topics are difficult to teach?

  • exponential functions
  • distinguishing between independent and dependent variables
  • quadratic functions
  • geometry within functions
  • volume
  • coordinate geometry
  • the concept of a variable
  • capturing different ways of seeing and understanding them as different equivalent functions or expressions

Finally, we looked at 8 possible problems, on our own and then in pairs. The goal was to find problems we enjoyed from the bunch and then to start considering them in terms of the student/teacher challenges mentioned above.