I am linking up with Sarah and Courtney today from Adventures in Guided Math to discuss chapters 1 and 2 of the book Teaching Student-Centered Mathematics by Van de Walle, Lovin, Karp, and Bay-Williams. This book is a great read, if you can I would encourage you to read it. It is already opened my eyes to new ideas regarding guided math.
Chapter 1: Teaching Mathematics for Understanding
Chapter one begins by explaining that understanding is "being able to think and act flexibly with a topic or concept. It goes beyond knowing; it is more than a collection of information, facts , or data. It is more than being able to follow steps in a procedure. One hallmark of mathematical understanding is a student's ability to justify why a given mathematical claim or answer is true or why a mathematical rule makes sense (Council of Chief State School Officers, 2010)." This statement is powerful because it made me think of my accomplishments and struggles this year in the classroom. I took from this that students need to know the how and why of a problem, instead of just the answer. They have to be able to justify an answer. This year we focused on this in my classroom. I noticed that many of the students are better at memorization or they focus on strategies that they have been taught but can not explain their thinking with them.
One of the biggest challenges that I found in 2nd grade at my school is that the students want to use the regrouping strategies to solve addition and subtraction problems. They can not explain why they regrouped. Even after giving the students many different strategies to use they wanted to go back to that strategy. This chapter made me realize that most of my students in my classroom were use to the instrumental approach of understanding for these type of problems and that I had to take them to the relational approach of understanding by the end of the year. One great way to help with this situation was to incorporate daily number talks. It does help the students begin to think differently about math.
Chapter 2: Teaching Mathematics through Problem Solving
Problem solving helps children develop relational understanding. In reflection, I took from this chapter that we should find task that challenge the students to problem solve. Also, make sure that these task or activities do not lend to memorization or procedures that do not lead to mathematical connections. We need to allow the students opportunities to solve and explain the problems without necessarily giving them the answers all the time.
Please come back Wednesday to see what chapters 3 and 4 are about.
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