Conceptual Teaching and Learning of Math

Ramblings: When I was a wee undergraduate student, I was a research assistant to a math education professor. My thesis had a title with words like "novel," "linear relationship," and "student thinking."Basically, for a year I was immersed into the idea that conceptual understanding is paramount in math education. And I totally drank the Kool-Aid. A professional goal I set for myself most ears is to try and incorporate as much conceptual understanding into each lesson as possible. However, with district and state tests, sometimes it can be very overwhelming to teach students conceptual understanding, make sure that develops into fluency, ensure students able to apply said concepts to new situations, and teach test-taking strategies. It is so exhausting. Huh, I just realized this whole spiel wasn't even related to what I wanted to post about: an excellent problem I did with 3rd grade. I guess I just needed to vent! Here begins my real post:

Last week, I started reading Principal Actions: Ensuring Mathematical Success for All, which is a National Council of Teachers of Mathematics (NCTM) publication. Of course they promote this conceptual understanding of mathematics and encourage giving students real-world scenarios, letting them experience a "productive struggle," work collaboratively and solve the problem in many ways. I gave my 3rd graders the following problem from the book:

There's going to be a talent show and the principal wants to set up 7 rows with 20 chairs in each row, and possibly an aisle down the middle for people to walk. How many chairs should she order to be pulled out of storage? 

I didn't print this out and give this to them on a worksheet. I had a small group of 3 students (of similar ability levels) and gave them the question verbally. They were to tell me how they thought they could solve it before they started to write it on individual whiteboards. I was SO impressed with what they came up with. Between the three of them, they were able to represent the situation with a picture, counting by 10s, counting by 20s, and with a multiplication equation. It even concluded with two of the students representing the solution in various ways after I kept questioning.

This activity reminded me that it is not too difficult to incorporate conceptual-based tasks into your day. This one was about 10-15 minutes and it let me spend time with 3 students while the rest were on computers working independently on subtraction fluency. The students enjoyed this, and I can't wait for Monday to pull a new group of 3 students to see how they wow me.

Happy weekend!

Disclaimer (not sure if I need one or not): I am NOT affiliated in any way with NCTM. I just enjoy reading the book and have learned a lot!