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.\u00a0\u00a0 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.<\/p>\n
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\u2019t.\u00a0\u00a0 For the ones that didn\u2019t 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\u2026I asked them explicitly to show me how they see the concepts connected.\u00a0\u00a0 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: \u201cI want you to go home draw me a picture\u2026with the \u2018Unit Circle\u2019 in the center, draw how you see all these concepts connected.\u201d To be honest, I didn\u2019t know what to expect, so there were no further instructions nor rubric.<\/p>\n
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\u2019 submissions. Sure enough, the CM that I envisioned was different from what each student saw.\u00a0\u00a0 Each student\u2019s 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\u2026one by one. To my amazement, it sparked students\u2019 curiosities; they wanted to know why a certain Map had so many arrows while some had a few. And since then\u2026Bubbles, Arrows, and Concept Maps came to be.<\/p>\n
Trig CM<\/a><\/p>\n Transformation CM1<\/a><\/p>\n Transformation CM2<\/a><\/p>\n Have you done something like this in your class?\u00a0 How can we make this better?\u00a0 Any idea what a rubric will look like?\u00a0\u00a0 Suggestions and comments are appreciated.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" 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 … Continue reading I think I am on to something\u2026Concept Maps: Bubbles and Arrows.<\/span>