# Chapter 2: 5 Practices for Orchestrating Productive Mathematics Discussions

Chapter 2: 5 Practices for Orchestrating Productive Mathematics Discussions

This chapter has really made me think about the learning targets I have written for all my units. What I took from this chapter is that you want explicit learning targets. You don’t want to write learning targets that have students just sitting and getting or performing like robots. From there you find problems or lessons that fit those learning targets.

I wrote my graduate paper on problem solving. The information below is from that paper and I thought fit in pretty well with this chapter.

For years students have been solving problems at the end of each lesson in a math textbook. There are questions, however, about to what extent these problems are actually problematic for students. Hiebert states, “that for problems to be problematic they need to be problems that are just within the students’ reach, allowing them to struggle to find solutions, and then examining the methods they have used” (Hiebert, 2003, p.54). According to the statement above, most problems that I have observed in traditional math textbooks would not be considered problematic. The problems found at the end of a lesson in most traditional math textbooks utilize the same skill as the lesson and students don’t have to struggle with solving the problems. This results in students not developing a deep mathematical understanding from these tasks. The teacher, however, can improve student learning by modifying how the problems are stated or selecting problems from other sources (supplementing).

Heibert et al. also state “that to be problematic means allowing students to wonder why things are, to inquire, to search for solutions, and to resolve incongruities” (Heibert, et al., 1996, p. 12). This means that teachers need to focus on the methods used by students and allow students to learn from their mistakes. Teachers need to step back from giving a prescription of how to solve a problem and allow students time to discuss and investigate different strategies they might use to solve a problem. Hiebert and Wearne (2003) state, “the key to allowing mathematics to be problematic for students is for the teacher to refrain from stepping in and doing too much of the mathematical work too quickly” (p. 7). According to the National Council of Teachers of Mathematics (NCTM, 2000), “good problems give students the chance to solidify and extend what they know and, when well chosen, can stimulate mathematical learning” (p.52).

Again, I am so glad that my school district adopted CMP (Connected Mathematics) as the problems are problematic for students but still within their reach. I am not having to search for appropriate problems or create them on my own.

-Sarah