Teaching, Learning & Technology
Sharing best practices from faculty around the world who are using technology to transform teaching and learning.

Mathematical Repesentations, Part 2

If I examine every other entry, starting from the first, I get 1.047..., 7.330...,  13.613... This sequence has a common difference of 6.283 or 2*pi. Likewise, the other sequence has 2.094..., 8.377..., 14.660... These terms also have a common difference of 2*pi. I am now in a position to write the two solutions as X=pi/3 + 2*pi*n or X=2*pi/3 + 2*pi*n, where n is any integer.

 

I can return to Symbolic view now and enter both Y=sin(X) and Y=sqrt(3)/2 (Figure 6). In Plot view (Figure 7), I see the larger context. I can use this in my next lesson.

 

Blog6.png     Blog7.png

                                                 Figure 6                                                                                                    Figure 7

 

In Figure 7, the tracer is set to jump from one intersection to the next of V2 and V3.

 

In this blog, we have used a set of mathematical representations to promote a conceptual understanding before focusing on the computations and algorithms required to obtain the solutions by hand. This is a fundamental aspect of my own teaching style. Although I am an HP employee and a member of the team that developed the HP Prime graphing calculator, what I have expressed here are my own views and not those of HP.

 

If you are going to the NCTM AAnnual COnference in New Orleans, please stop by the HP booth and say hello!

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About the Author
I am part of the HP Calculator team, working on the HP Prime graphing calculator. I taught mathematics for 20 years and have extensive exper...


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