Class Notes

The McGraw-Hill Ryerson PreCalculus 12 Text is used as the Main Resource.

Assignments in the Powerpoint Lesson Plans refer to pages and questions in the PreCalculus 12 text.

 1.1A Horizontal Translations

 1.1B Horizontal and Vertical Translation

 

 

Digital Resources to Support Visualization and Differentiate Instruction

1.1A Family of Functions

1.1B Move It

Pedagogical Shifts: TRANSFORM, Moving from Traditional to Student-centered

Shifting from Student as Knowledge Recipient to Student as Inquirer and Creator

Shifting from Memorization to Higher-level Thinking

Shifting from Competitive to Collaborative Learning

 

   

I wanted to begin my jouney of transforming my teaching and student learning by taking steps to move students away from lecture style learning. I presented the idea of horizontal transformations in my usual style of presentation with powerpoint notes and digital resources (1.1A Family of Functions above) for students to visualize the mathematics. They had a good grasp of the concept and were able to explain the effect on the graph of a parent function when the parameter h in y = f(x - h) was changed. They understood that  y = f(x - 3) meant a translation of the graph of a function three units to the right. The next step in my lesson was to teach the effect of vertical translations and the image function equation (the effect of k). Rather than teaching in the same lecture and digital visualization style, I decided to TRANSFORM. Students were placed in groups of two or three. The problem asked was open ended and went something like this..."Does the function equation for a vertical translation behave in the same manner as a horizontal translation?" Students must provide algebraic proof of their findings.

Students were reluctant as first since many of them had only experienced math in a lecture style. Students began by asking questions... What letter do I use for the transformation? Where does the parameter go in the function equation? They wanted to be told what to do but this is not supporting higher-level thinking nor does it support student as inquirer and creator. I reponded to students by asking them questions. Is the letter used important? What would you like to use? What letters should not be used? It was interesting how students directed their own learning once they found out that I was not going to tell them what to do.

Once students were finished with their algebraic proof of their understands, they did a gallery walk  to see what other groups had done. At the end of the activity we summarized vertical translations.

What did I learn from my students???? They were able to discover the effect of k on the graph of a function in BOTH forms  y - k = f(x) and  y = f(x) + k.