This Lampert book just keeps getting better and better. She’s so good at breaking down and analyzing her individual “teacher moves,” and in this chapter she talks about the menu of moves that she selects from while she’s teaching. She analyzes a whole group discussion she leads, and in one six-minute section of the lesson she counts 15 teacher moves, as detailed here:
Teaching and Studying Event #1: Teacher Formulating and Asking a Question to Begin the Discussion
Teaching and Studying Event #2: Teacher Calling on a Particular Student to Answer
Teaching and Studying Event #3: Student Asserting and Teacher Repeating His Assertion
Teaching and Studying Event #4: Teacher Asking a Student to “Explain His Reasoning”
Teaching and Studying Event #5: Student Interpreting “Explaining” and Responding
Teaching and Studying Event #6: Teacher Making Representations of Student Talk
Teaching and Studying Event #7: Teacher Interpreting Symbols in Terms of an Alternative Representation
Teaching and Studying Event #8: Teacher Highlighting Patterns to Give Meaning to Multiplication
Teaching and Studying Event #9: Student Interpreting the Public Representation
Teaching and Studying Event #10: Teacher Relating the Idea of Groups to Practicing the “Times Tables”
Teaching and Studying Event #11: Teacher Again Asking for an Explanation
Teaching and Studying Event #12: Teacher Linking the Explanation to the Public Representation
Teaching and Studying Event #13: Teacher Representing, Student Asserting
Teaching and Studying Event #14: Student Evaluating Earlier Assertion
Teaching and Studying Event #15: Teacher and Student Reason Collaboratively
(She discusses each event in detail… these are merely the titles of each of these sections.)
In this six-minute episode, she gets at how she manages the tension of working with one student while the other students watch, making sure that in the next episode she contrasts this with more involvement from the rest of the class.
She also talks a great deal about her overall goal, which is getting students to “make sense” of the mathematics. She is much more concerned with this than answer getting. (I heard a lot of echoes of this at this year’s NCTM conference in Boston.)
“…Students’ engagement in mathematical sense-making is the foundation on which studying mathematics by working on problems is built,” Lampert writes. “If they learn to expect me or their classmates to step in when they do not make sense, rather than learning to get themselves out of a difficult spot, they will not be likely to do mathematics when completing the assigned problems.”
Finally, here are the unedited notes I made on the menu of teacher moves she presents:
Variety of moves… to address the problems of getting mathematics into the conversation and getting that mathematics to be studied. Elements of the work of teaching within this structure include:
• Creating visual representations of the ideas under discussion as a common record of the class’s journey and referent for our discussion;
• Deciding who to call on from among those who are and are not bidding for attention;
• Simultaneously teaching individual students and engaging the group as a whole in worthwhile mathematical activity;
• Keeping the discussion on track while also allowing students to make spontaneous contributions that they considered to be relevant;
• Monitoring the pace of the discussion with attention to the scheduled end of the class period; and
• Adjusting to the few students who need to leave or enter the room during the period.
The actions I take to address these problems are both managerial and intellectual. They serve both to move the discussion along for everyone and to infuse its content with the mathematics students are to study.
How to begin each new segment of discussion…
• Choosing the question to begin a segment of discussion;
• Choosing who has the floor in response to a question;
• Choosing to give someone who is bidding for the floor an entrée into the discussion.
When a student responds… There are several subsequent moves that can be made to turn that response into a resource productive of teaching and studying:
• When an assertion is made, choosing to stay with the student who made it and requesting an explanation;
• When an assertion is made, choosing to stay with the student who made it and suggesting my interpretation;
• When an assertion is made, moving to other students and requesting a counterspeculation; or
• When an assertion is made, moving to other students and requesting an explanation.
Whichever of these actions is chosen, the teacher can continue by
• Asking additional students to comment on another student’s thinking;
• Rephrasing a student’s explanation in more precise mathematical terms and asking him or her to comment; or
• Creating a representation of the students’ talk on the chalkboard.
To address the problem of infusing mathematics into the discussion in conjunction with attending to social issues, a teacher can:
• Alternate between persistent engagement with one student and quick moves around the class, or
• Alternate between single student answers and chorus-style participation.
At any point in the discussion the teacher can step out and
• Comment on what kind of problem or what kind of work this is, or
• Name a process or a kind of number with either a contextually invented term or a term from the public domain of mathematics.
Each move is designed and enacted in a particular moment to bring a particular piece of mathematics to students and particular students to mathematics. The work of teaching is not only deciding what to do at each of these levels, but also doing it, and keeping track of the studies it enables for students.
The teacher consistently works at teaching students both mathematics and how to study mathematics by asking students to reason, to explain, to attend to and interpret the assertions of others, and by reasoning, explaining, attending, and interpreting the mathematics herself in concert with their responses.
I left this chapter with a much better sense of the types of teacher moves that exist, which I had wondered about since reading Elizabeth Green’s Building a Better Teacher last summer. It would be interesting to videotape my own lessons and try to break them down and analyze them in this way. I can only imagine the amount of growth that would help me make going forward.