I recall my first years of teaching: I followed a district created pacing plan that started at Section 1.1, then to 1.2, and so on and so on until you finish Chapter 1, give a test, then move on to Chapter 2, and so on. While I had a good math background, my preoccupation with the teaching profession did not allow me the insight to think about the logical progression of the content that I was presenting to my students; but rather, it was just the progression outlined by the book. Not to take anything away from the authors of my book, there was a logical progression of content, but I soon realized that it was overwhelmingly influenced by the vast amounts of Standards required by the California Mathematics Framework.

After years of teaching Trigonometry, I started seeing deeper connections between the concepts; and admittedly, it is currently still developing. So if I am still developing these connections, I wonder what my kind of connections that my STUDENTS have made and will continue to make. I was not only curious to see the connections students were able to make, but more curious about the ones they didn’t. For the ones that didn’t make the connections, I almost felt bad for them. These students sit in my class day in and day out learning math that, in their minds, seems disjointed. So, I decided to give it a go…I asked them explicitly to show me how they see the concepts connected. After teaching the students Chapter 4: Trigonometric Functions, we made a list of the concepts we have covered. And then, I said to the students: “I want you to go home draw me a picture…with the ‘Unit Circle’ in the center, draw how you see all these concepts connected.” To be honest, I didn’t know what to expect, so there were no further instructions nor rubric.

And these things the students have turned in, however you may want to call them: Trees, Diagrams, or Concept Maps, etc., have given me exceptional insight into what students have learned and failed to learn. I was amazed, shocked, and at a loss for words when I first looked at the students’ submissions. Sure enough, the CM that I envisioned was different from what each student saw. Each student’s submission was unique, almost like a blueprint of how Trigonometric concepts developed in their brain. So I took a bold step, I placed them on the document reader…one by one. To my amazement, it sparked students’ curiosities; they wanted to know why a certain Map had so many arrows while some had a few. And since then…Bubbles, Arrows, and Concept Maps came to be.

Have you done something like this in your class? How can we make this better? Any idea what a rubric will look like? Suggestions and comments are appreciated.