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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

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Sample for MATH-IN-USE Category C: Expanding MIU

Coding Scheme for A Classroom Reflection: BELIEFS

Coding Scheme for A Classroom Reflection: MATH-IN-USE (MIU)

Strand-Coding Scheme for Static Ccorers on A Classroom Reflection

Click here to view all of the MIU Coding Categories with Indicators.

C.	Expanding MIU
	Respondents’ comments about the math do more than just reflect back what is in the scenario. Respondents describe in their own words what is going on mathematically, and in doing so, they demonstrate a degree of engagement with the mathematics. While they may make references of a general nature to the mathematical thinking of the students or teacher, they do not provide detail about or unpack the general statements they make. Respondents refer to math that is not already part of the scenario, e.g., · Fraction · Decimal · Percents · A piece of a whole · Parts of a group · Quotient, dividend, divisor · Numbers less than 1 · Fair shares, partitive, quotitive · Order of division · Whole numbers being divided into parts · Ratios   Respondent writes about how using the pizza as an example can further the students’ mathematical understanding of this problem. Respondent provides a basic mathematical reason why (such as pizza can be divided into parts). Respondent only notes that the kids’ examples of objects to divide do not work well mathematically; respondents do not say why they don’t work well. Respondent indicates that 1 divided by 4 is easier numerically to divide than 5 divided by 39, but does not recognize that 5 divided by 39 is a different challenge in division. Respondent might say that kids often have trouble with X (a specific math topic).  But, the respondent would not provide a perspective on why they have trouble with it or what to do about it. Respondent writes about math process (conjecturing, proving, claiming, etc). Example: "The teacher continued to ask probing questions.  She asked, 'Is it true?' – give me some proof – she wanted the students to mathematical [sic] defend their answer."
	Sample to illustrate Category C: Expanding MIU Note that all samples represent a principal's entire response and are taken verbatim from study principals' repsonses
	a. The teacher was getting the students to think about the mathematical concept of division. Obviously, you can divide 5 by 39, but the students seemed to be confusing the mathematical notation 5÷ 39 vs 39 ÷5. It was excellent teaching assuming that the teacher carried it further into a discussion of fractions. b. The teacher was stimulating student thought about T.C.’s statement. Again, good teaching because the teacher was facilitating mathematical thinking. c. The teacher was putting the concept into a context that all 4th graders can understand — pizza. Excellent teaching! This stimulated thinking about fractional parts of a whole.