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I think I am on to something…Concept Maps: Bubbles and Arrows.

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.

Trig CM

Transformation CM1

Transformation CM2

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.


Reflecting on NCTM 2014

I’m glad to finally have the opportunity to attend the NCTM conference after 9 years of teaching…and I found it professionally invigorating!  Conference-wise, it was like any other math conference I have attended: there were some hits, many misses, and the cool kids were still the cool kids (like Dan Meyer and them).  But most importantly, I came home with renewed excitement and new ideas about teaching that grew from being surrounded by, simply stated, ‘good people’ in math education.   My most memorable moments were the times before sessions, in-between sessions, and after sessions.   And if any of you were a part of those moments, I am grateful and look forward to sharing ideas and using some of your ideas in the near future.

Things I learned at NCTM:

1) Make MP explicit for the students by incorporating them into your rubric.

2) Engagement in Tasks should include: 1) Launch 2) Investigate 3) Debrief

3) “Smart” has no racial lines.  Create a classroom environment where the students feel like they are a part of a ‘union’ such that they are doing, experiencing, and achieving TOGETHER.

4) Concept Maps …Concept Maps… Concept Maps…  You can have an overarching one, one for the unit, one for the lesson, one for the day…You can never have enough of them!

5) I was right about Synthetic Division… the algorithm is easy to teach, the context is way more challenging.

6) [In regards to] Parenthesis: “Use them”