"5 Practices for Orchestrating Productive Mathematics Discussions" is a book written by Margaret S. Smith and Mary Kay Stein, and it is published by The NCTM (National Council of Teachers of Mathematics). The Five Practices is a framework for teaching through problem solving that helps teachers to deepen their content knowledge, broaden their understanding of what strategies to anticipate and notice students using, and then how to orchestrate that whole class debrief at the end, once students have solved the problem. It makes you think about why you are choosing a particular problem and what you want students to learn from it, and there is an organizer that you can use to collect evidence of student learning, misconceptions, the strategies, models and tools they are using. This pedagogical documentation tool is really useful for collecting assessment "for" and "as" learning evidence, and it helps teachers to name and make connections between the various student strategies, making it much easier to connect their ideas to key mathematical big ideas or enduring understandings during the debrief.
The Five Practices that teachers need to do before, during and after problem solving are: 1. ANTICIPATING likely student responses to challenging mathematical tasks 2. MONITORING students' actual responses to the tasks (while students work on 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 (page 8 in the book)
The book goes on to explain each practice using classroom case studies and the problems that they solved, and it is has incredibly small print, but is a fast and interesting read, a mere hundred and four pages! We have included a pdf that nicely summarizes The Five Practices and gives you an example of the organizer tool. The most important part of The Three Part Lesson is the whole class discussion, or the debrief, because that is where students clarify misconceptions and consolidate their learning of important mathematical ideas. The discussion is productive when "accomplishes something that is important mathematically and that the mathematics to be learned by the students", students can "expand on , debate and question the solutions being shared, make connections among the different strategies that are presented [and] look for patterns (pages 78-79). This book is exactly what we are trying to do and accomplish when teaching through problem solving.
Sample pedagogical documentation of a co-planned lesson using this framework, with a sample organizer:
Where's the Math?
"5 Practices for Orchestrating Productive Mathematics Discussions" is a book written by Margaret S. Smith and Mary Kay Stein, and it is published by The NCTM (National Council of Teachers of Mathematics). The Five Practices is a framework for teaching through problem solving that helps teachers to deepen their content knowledge, broaden their understanding of what strategies to anticipate and notice students using, and then how to orchestrate that whole class debrief at the end, once students have solved the problem. It makes you think about why you are choosing a particular problem and what you want students to learn from it, and there is an organizer that you can use to collect evidence of student learning, misconceptions, the strategies, models and tools they are using. This pedagogical documentation tool is really useful for collecting assessment "for" and "as" learning evidence, and it helps teachers to name and make connections between the various student strategies, making it much easier to connect their ideas to key mathematical big ideas or enduring understandings during the debrief.The Five Practices that teachers need to do before, during and after problem solving are:
1. ANTICIPATING likely student responses to challenging mathematical tasks
2. MONITORING students' actual responses to the tasks (while students work on 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
(page 8 in the book)
The book goes on to explain each practice using classroom case studies and the problems that they solved, and it is has incredibly small print, but is a fast and interesting read, a mere hundred and four pages! We have included a pdf that nicely summarizes The Five Practices and gives you an example of the organizer tool. The most important part of The Three Part Lesson is the whole class discussion, or the debrief, because that is where students clarify misconceptions and consolidate their learning of important mathematical ideas. The discussion is productive when "accomplishes something that is important mathematically and that the mathematics to be learned by the students", students can "expand on , debate and question the solutions being shared, make connections among the different strategies that are presented [and] look for patterns (pages 78-79). This book is exactly what we are trying to do and accomplish when teaching through problem solving.
Sample pedagogical documentation of a co-planned lesson using this framework, with a sample organizer:
Short article explaining this framework, with a sample organizer: