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© Education Development Center, 2006-2008

Thinking About Mathematics Instruction
Leadership Content Knowledge
Elementary and Middle School Principals’ Survey

Table of Contents

1. Introduction
2. Overview and comparison of the Pre- and Post-surveys
3. Pre-Survey
4. Post-Survey
5. Assembling Your Own Mathematics Content Knowledge Section
6. Coding Schemes and Sample Responses
7. Validity and Reliability Considerations

Indicators and Illustrative Data for Category 5: Instructional Decisions Guided by Students’ Mathematical Thinking

Click here to return to the complete Coding Scheme for A Classroom Reflection: BELIEFS. To view illustrators for other categories, click on the appropriate link below.
Category 1	Category 2	Category 3	Category 4	Category 5	Category 6

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5.	Instructional Decisions Guided by Students’ Mathematical Thinking
	In this category, responses are now solidly based on a consideration of ideas as opposed to behaviors.  Comments focus on how the teacher is working to get a sense of students’ thinking and how the teacher elicits students’ thinking to guide his or her teaching. If comments address the issue of “readiness,” they will consider whether students are at a point in their mathematical understanding to work with the ideas under discussion. If comments include reference to misunderstandings or confusions, they will be seen as important to probe.  Unlike 6s, comments in this category about students’ knowledge will be focused on the group as a whole rather than on individuals.
	Indicators and Illustrative data
	Response indicates that in interpreting the scenario, the respondent’s writing reflects that the following is important to good classroom practice: Using student thinking to guide his or her teaching Example: “Her question allows students to express their thinking and also allows her to hear their ideas.  I would think this information would be useful to her, when she is ready to address division of a smaller by a larger number. ” If respondent talks about student confusion, s/he will see the teacher as working with student confusion/misunderstanding – i.e., tries to understand what is causing the confusion/misunderstanding. Example: “Her teaching is looking to get towards the meaning of division … rather than just correcting a student and then moving on without probing a possible misunderstanding.”
	Sample Responses for the Category 5 Scoring Scheme (Note that all sample responses represent a principal’s entire response and are taken verbatim from study participants’ responses.)
	a. The teacher was trying to see if the students understood the difference between what was in the book and how it was communicated. It was good teaching because the teacher was clarifying and redirecting the student and using his/her understanding to help drive instruction. b. Again, the teacher was checking for understanding and/or trying to extend or enrich the lesson based on student perception. It was good teaching because the teacher was asking questions to see if the students really knew about division or if they just understood an algorithm. He or she was checking for their number sense. c. Here, the teacher was seeing if the students could relate their thinking to a similar situation. Again, I feel this is good teaching because she’s/he’s teaching them how to solve a problem and not just putting down a correct answer. The teacher is allowing the students to build knowledge.