TMI

Thinking About Mathematics Instruction


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TMI is a project in EDC's Center
for the Development of Teaching

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Funded by the
National Science Foundation
Grant EHR-0335384

 

© 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

STRAND-coding Scheme for Static Scores
on A Classroom Reflection

The pre-survey scores for over 1/3 of the respondents in our sample who scored either 2 or a 3 on A Classroom Reflection were the same as their post-survey scores on the same item, indicating no apparent change in their pedagogical beliefs over the period of the study.  Because this proportion was so high, we developed a coding scheme known as the STRAND-coding scheme to identify indicators of changes in beliefs of finer grain than our original scoring scheme allowed us to capture.

Overview of the STRAND-coding scheme  
(For a STRAND-by-STRAND description with examples, click here)

The STRAND-coding scheme allowed us to take into consideration data that may have been picked up by the original scoring scheme but which did not end up determining the ultimate categorization of the response because of the presence of other more influential data.  For example, by using the STRAND-coding scheme, a pre-survey 2 response with elements of some 1 in it can be distinguished from the same respondent’s post-survey 2 response with some elements of a 3 in it. Using our original coding scheme this respondent’s beliefs would appear not to have changed.

There are three STRANDs for picking up movement pre to post among the static scorers (Pleae refer to Scoring Sheet (PDF)):

  1. Attention to Students, where the focus is on what respondents say about the students.
  2. Attention to Teaching, where the focus is on the teaching. This STRAND is comprised of two different DIMENSIONs: what the respondent says about what teacher is doing and what, if anything, the respondent says about students being confused.
  3. Rationale, where the focus is on whether the rationales that respondents provide for the teacher’s moves are math-based or generic in nature.

In order to measure change pre to post, we divided the first two STRANDs into three BANDs.  This allowed us to measure whether respondents changed from one BAND to another on either of the first two STRANDs (See Scoring Sheet):

  • the left-most BAND (1s and 2s from the BELIEFS coding scheme) includes comments that reflect traditional ideas. We used the letter “t” to indicate responses that reflect traditional ideas.
  • the right-most BAND (5s and 6s from the BELIEFS coding scheme), includes comments that reflect socio-constructivist ideas. We used “c” to indicate responses that reflect socio-constructivist ideas.
  • the middle BAND (3s and 4s from the BELIEFS coding scheme) includes comments of a mixed nature in that they refer to ideas that have moved beyond traditional thinking but do not reflect fully developed socio-constructivist thinking. We used the letter “m” to indicate that a response that has been placed into this BAND.

For the math rationale STRAND, there are no BANDs; instead, we measured change by whether or not the principal’s comments about the teacher’s motivation for moves she made shifts from non math-based reasons to math-based ones. 

Below we provide an example of how we coded raw data. Assigned codes are in brackets.  Within the brackets, the number is the STRAND number followed by the DIMENSION letter and then the BAND indicator letter.

Example of Coded Raw Data

Again, the teacher became a facilitator/coach to propose a problem or scenario to get her students thinking. [2Am] Using a real life situation – 1 pizza and 4 kids – was a good way to bring the math concept into their world.[3A] The teacher, still focusing on the concept of division, used the situation to introduce a new concept. I think that this type of probing – thought provoking technique is a good strategy. [2Am; 3B] This teacher got her students thinking about division – the concept not just working on computation. [2Am]

Click here for a STRAND-by-STRAND description with examples

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