Secondary Lenses on Learning:

Leadership for Mathematics Education
in Middle and High Schools - Survey

1. Survey Overview 3. Assembling Your Own Mathematics Knowledge 2. The Survey - section by section for Teaching Section Part 1 Background Information (pdf) 4. Coding Schemes and Sample Responses Part 2 Teaching and Learning Mathematics (pdf) a. Coding Scheme for a Classroom Reflection   Section A A Classroom Reflection (pdf)   BELIEFS Scoring Scheme Sample Responses   Section B Views About Math (pdf) b. Making Sense of the Leadership Function Data   Part 3 Doing Mathematics (note that on the survey, itself, this is labeled Part 2, Section C)

---

Categories of Belief with Indicators for Coding

The indicators in each of the categories below characterize the attributes of a respondent’s writing.  For example, responses categorized as “2” can be identified as such by the presence of indicators listed under category “2”.  In order to be in a particular category the response does not have to include all of that category’s indicators.  Further, a response may have individual sentences that are coded in several different categories. When coding a piece of data we coded every codable sentence in the written text and then looked at the whole picture in order to arrive at a single category label for the text. The category used to describe the entire piece of writing was based on the preponderance of evidence in the text. We indicated whether a response was at the low end of the category, in the middle, or at the upper end by adding a + or a -.  So, a low three was represented as 3-, a middle three as 3, and a high three as 3+.

1.	Direct Instruction
	Respondents view teachers as presenting information that students absorb, or providing opportunities for students to practice skills, with positive reinforcement for correct answers. Responses also indicate that the teacher should follow the lesson plan and avoid confusion. Responses in this category indicate a preference for direct instruction.
	Click here for illustrative data and samples of Category 1: Direct Instruction.
2.	Teacher Guiding Student Discovery
	Responses indicate that the respondent sees the teacher’s role as setting up situations in which students can discover the specific ideas important to the lesson. Responses will focus on whether the teacher is bringing students to the predetermined right answer.
	Click here for illustrative data and samples of Category 2: Teacher Guiding Student Discovery.
3.	Teacher and Student Behaviors Associated with NCTM Standards
	Respondents write about the characteristics of standards-based pedagogy but do not connect these to the thinking students would do when engaging in them.  Respondents appear to have a checklist of desirable teacher behaviors.  They tend to over-generalize. Responses in this category have a more open feel than those in category 2.
	Click here for illustrative data and samples of Category 3: Teacher and Student Behaviors Associated with NCTM Standards.
4.	Attention to Students' Mathematical Thinking
	Class is seen as fundamentally about ideas and thinking.  Respondents attend to the student thinking in the scenario and see the teacher’s behaviors as directed toward encouraging student thinking.  Respondents attribute more agency to students than in earlier categories.
	Click here for illustrative data and samples of Category 4: Attention to Students' Mathematical Thinking.
5.	Instructional Decisions Guided by Students' Mathematical Thinking
	Focus on how teacher is working to get a sense of students’ thinking and how teacher elicits students’ thinking to guide teaching. I.e., once student thinking is out there, there is something to work with.
	Click here for illustrative data and samples of Category 5: Instructional Decisions Guided by Students' Mathematical Thinking.
6.	Instructional Decisions Integrate Individual and Group Mathematical Thinking
	Responses include mention of both individual and group thinking.  Respondents view the teacher as knowing enough about the thinking of the individuals in the class to be able to select individual students’ ideas for discussion because they know how others will also benefit.  Respondent views the teacher as trying to find the “forward” place of where the students are.  That is, respondent views the teacher as knowing that students will only think about what they can think about, so she has to find the point at which student thinking and her agenda can merge.
	Click here for illustrative data and samples of Category 6: Instructional Decisions Integrate Individual and Group Mathematical Thinking.

 

---