Here we go, first week of the

*Teaching Student-Centered Mathematics*by Van de Walle, Lovin, Karp, and Bay-Williams*book study being hosted by Adventures in Guided Math.*I shared in my last post the reason why I was so excited to be jumping into this book study. The first two chapters of the text certainly did not disappoint. We haven't quite gotten into the meat of strategies to use with children but are learning about a larger framework of theories which will help us to choose math activities which will allow our students to best make connections and learn.

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__Chapter 1__

__Chapter 1__

Children learn through opportunities to construct meaning by connecting new information to ideas and understandings they previously held. Children also learn through the opportunity to work with and hear ideas from those who are more knowledgeable.

The authors point out that these are theories of LEARNING, not theories of TEACHING. Which was a subtle but important point for me to consider. The question is then how we teach in a way which allows students to have opportunities to connect ideas, through explorations of their own as well as through opportunities to work with and hear from those who are more knowledgeable.

Asking students to solve a problem in a way that makes the most sense to them but also exposing students to the ideas and strategies of their peers and exposure to direct instruction which will expand a student's bank of strategies and opportunities to explore with those strategies will all lead to deep relational understanding.

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__Chapter 2__

__Chapter 2__

*through*problem solving as opposed to for the purpose of being able to apply mathematics to problem solving. This approach involves selecting a task with a variety of entry and exit points which will allow students to choose or develop a strategy. The focus of problem solving is not simply on achieving a correct answer but rather on ideas and sense making. This type of teaching allows for flexible critical thinking skills.

This chapter also describes the type of problems that you could use to teach through problem solving. A problem may be an open ended story problem - for example-

**Jose wants to have blue and green candles on his cake for his 6th birthday. How many combinations of blue and green candles could his grandma use to show 6 candles?**A question about a simple equation could also be a high level task that students could investigate from multiple angles or perspectives. Similarly, a procedural question such as "How could you solve 45 x 3? Find 2 ways to justify your result. Could result in high level thinking. The authors stressed that just because a word problem is based in a story doesn't mean it will help students to clarify a concept and just because a problem is based in numbers alone doesn't mean that it couldn't lead to critical thinking. The way a task is presented and the expectation of the students leads to the quality of the activity.

An interesting section of this chapter focused on "How Much to Tell and Not to Tell". When discussing a student's work or solution, it is best to clarify their ideas and hold back from evaluating their answer leaving that to the other students in the class. If you are introducing a convention or symbol, the best approach is to introduce the concept and THEN assign a symbol or term to that concept. Lastly, if your students aren't coming up with a strategy or solution that you are interested in them using, you shouldn't shy away from introducing the strategy as another possible solution.

Come back on Wednesday as we delve deeper into this text!

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