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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 2: Teachers Guiding Student Discovery

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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2.	Teachers Guiding Student Discovery
	Responses in this category are still fundamentally based on a behaviorist view of learning; however, in this category student thinking is valued.  Responses indicate that the respondent sees the teacher’s role as setting up situations that lead students to the specific ideas important to the lesson. This implies a greater sense of student agency than in Category 1 because students are being asked to “discover” ideas predetermined by the teacher.  Unlike in later categories, once the work of discovery is underway, the teacher is less sensitive to the ideas that the students are generating and more sensitive to making sure the “discovery” doesn’t go awry.  Unlike responses in Category “1,” there may be some attention to student thinking but the main focus of the response is the teacher. However, unlike responses in category “3,” where the teacher would be seen as “asking open-ended questions,” or “getting student strategies out,” responses in Category “2” will focus on whether the teacher is bringing students to the pre-determined right answer. If the response mentions student readiness, the concern will be for whether or not the students “get” the ideas that the teacher wants them to get, rather than a more nuanced interest in what students understand. If the response mentions confusion, it will be seen as something to be avoided. If the response includes mention of discovery/inquiry/constructivist learning/problem solving/critical thinking, and the like, these will be described as very general characteristics of the lesson.
	Indicators and Illustrative data
	Response demonstrates that in interpreting the scenario, principals indicate that they approve of classrooms in which the teacher is Aiming for students to get a particular understanding or answer Example: “Ask questions to get the learning you desire.” Arranging for students to arrive at certain, specific, answers/ideas (in any of a variety of ways) The initiator, sustainer, and director of student thinking. Example: She was leading the students through a thinking process.” If respondent uses terms like inquiry/constructivist/discovery learning/higher order thinking skills/critical thinking skills/problem solving, and the like, they will be used as very general characteristics of the lesson Example: “The teacher placed the students in the position to do some higher order thinking.”
	Sample Responses for the Category 2 Scoring Scheme (Note that all sample responses represent a principal’s entire response and are taken verbatim from study participants’ responses.)
	a. Yes, I think she was expanding the children’s thinking power because students can consider a different problem that is not a typical one. Instead of correcting the student who said 5 divided by 39, she made it a teachable moment. b. The teacher did not correct a student’s response but asked a question so that students’ thinking power could be started. Yes, it is good teaching because the students are building self-reliance and are considering/using their math knowledge. I just hope that the students have received instruction on math concepts so they can use those experiences to think about possible answers. T.C. seemed to think that his statement is true, and I wouldn’t want him to have an incorrect answer. c. The teacher posed a different problem in the discussion. Yes, it is good teaching because it led students to consider a real world problem that they could use their prior knowledge, and it helped lead the students to discover the answer. This example would open their understandings, and it might be an easier problem that students could relate to.