## Tuesday, January 13, 2015

### #5Practices Book Study: Chapter 1 "Introducing the Five Practices"

The purpose of the five practices is to provide teachers with a structure to control student-centered discussions in order to achieve the mathematical goals set for the lesson.

Chapter 1 Introduces the five practices,
1. Anticipating likely student responses to challenging mathematical tasks
2. Monitoring students' actual responses to the tasks (while students work on the tasks in pairs or small groups)
3. Selecting particular students to present their mathematical work during the whole-class discussion
4. Sequencing the student responses that will be displayed in a specific order
5. Connecting different students' responses and connecting the responses to key mathematical ideas
Anticipating: This step is all about working out your problem in as many different ways as you can and with different representations.  Saving student work samples or jotting down misconceptions will help you when you teach the lesson again.  It's important to anticipate how students might interpret and solve a problem, both correctly and incorrectly.

Monitoring: This involves paying close attention to how students go about solving a math problem and what strategies they use. Teachers should do more than just listen and observe they need to be questioning students to help them explain and clarify their thinking.  These questions can be preplanned based on anticipated responses and solutions to the problem. Questioning a student while they work on a task allows them to refine or revise a strategy they are using before sharing ideas during a whole group discussion and gives me feedback on what the students are understanding about or struggling with the problem.

Selecting: The teacher needs to carefully select students to share responses based on the goals of that lesson.  By selecting the responses you want shared with the whole class, you can maintain control of the discussion while encouraging student participation.

Sequencing: By very thoughtfully planning the order in which you have students share their responses you can maximize the chance of achieving your mathematical goals for you class discussion.

Connecting: The teacher should help students draw connections between the different strategies and representations presented during the sharing of solutions. The goal is for the student presentations to develop powerful mathematical ideas by carefully building on one another.

Discussion Questions: (my thoughts in blue)
1) How do you currently plan a lesson?  To what extent do you focus on what you will do versus what students will do and think?  I currently plan a lesson by looking at how I will structure the problems in my workshop format: opener, mini lesson, work time, sharing & reflection.  I make sure I work out all problems and make notes where I think students may have misconceptions.  I definitely spend more time thinking about what I am going to do during the workshop rather than what students will think and do.

2) Anticipating is an activity that is likely to increase the amount of time spent planning a lesson.  What would you expect to be the payoff for this investment of time?  The payoff for spending planning time on anticipating student responses is you would be prepared for multiple representations and solution strategies.  By anticipating student errors you can make sure to emphasize possible misconceptions and discuss those with students.  When we spend time in team planning discussing different strategies for solving a particular problem I am often introduced to methods I may not have considered myself.

3)  Why is connecting important?  What is the teacher's role in helping students make connections? Connecting is important so students can see that there are other ways to solve problems and multiple ways to represent solutions.  It is important to show them that some strategies are more effective than others.  By observing the solutions of others students are able to check the accuracy of their own solutions.  This can create rich discourse as students use mathematical practice standard #3 to  construct viable arguments and critique the reasoning of others.

Thanks for reading and joining in the book study.  I look forward to hearing your thoughts on Chapter 1.