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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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Overview and Comparison of the
Pre- and Post-Surveys

Due to our research design in which principals completed a survey both before and after a randomly assigned group of them took a professional development course, there are two versions of the survey: one taken before the course was given (pre-survey) and one taken after the course (post-survey).

The Pre-survey has three sections whereas the Post-survey has four. Both versions take about 2 hours to complete. The three sections of the Pre-survey are as follows:

1. The Background Information section collects relevant background information including the length and nature of administrative and teaching experience, level of education, high school and college level math courses completed, general self-reported estimate of comfort level with mathematics, recent professional development participation, and curricula currently in use at principals’ schools.
   
   On the Post-survey, this first section is re-named About You and Your School, and principals are asked to update the professional development activities they have participated in since completing the pre-survey.
   
   In addition, several items from the Background Information section in the Pre-survey (questions about education, administrative experience, teaching experience, and mathematics coursework) were moved to the fourth section of the post-survey which is called Demographics and Professional Experience.
   
2. The Teaching and Learning of Mathematics section assesses beliefs about mathematics learning and teaching through two sub-sections.
   
   Section A
   A Classroom Reflection was designed to assess the degree to which respondents took “constructivist” or “non-constructivist” views of learning. It is an open response item that presents a short description of an elementary mathematics class* that captures part of a discussion in a 4th grade class about what it means to divide 5 by 39. Respondents respond to three questions about the teacher’s actions during the lesson.
   
   Two additional questions, What were the mathematical ideas in this classroom scenario? and What can students learn in this class? follow the questions about the teacher’s actions. The purpose of these two additional questions is to assess more directly the degree to which respondents can identify the mathematics at play in the episode.
   
   A Classroom Reflection also provides a measure of respondents’ Math-in-Use which is the extent to which they attended to the mathematics at play in the classroom in their interpretation of the episode.
   
   Section B
   Because this item did not yield clear results, we are omitting it from this website.
   
   Section C
   Views about Math is a quick-score instrument we used to assess general beliefs about effective instructional methods for mathematics and beliefs about student learning using Likert scales**.
   
   Note that the Teaching and Learning of Mathematics section is the same on the Pre- and Post-surveys.
   
3. The Mathematics Content Knowledge for Teaching (Doing Mathematics) section is drawn from assessments designed by Ball et al. as part of the Study for Instructional Improvement (SII) which developed and administered mathematics content items to elementary school teachers. One of the reasons we chose to use items from the SII is that the items are very well constructed and address important concepts of elementary mathematics. They also have been field-tested and analyzed for validity and reliability.
   
   Our collection of items was designed to measure “mathematics knowledge for teaching”, content knowledge that is particularly relevant to supervision of elementary and middle school mathematics instruction. In general, the items are couched in the context of student learning and are specific to the mathematics that teachers teach and use in their teaching as opposed to the mathematics used by accountants, engineers, or members of other professions. It is important to point out that this instrument is not designed to provide an absolute measure of mathematical knowledge but is appropriate for making within and between group comparisons and measuring change in content knowledge over time.
   
   As previously mentioned, because items from the Mathematics Content Knowledge for Teaching Section are still in use, we cannot provide the set of items we used on the survey. We do, however, provide detailed information about the contents of this section. If you would like to put together your own set of mathematics items, click here for the website for the Learning Math for Teaching Project at the University of Michigan. Here you will find information about attending their free training in Michigan, a necessary step that must be completed in order to use their survey items in your project.
   
   Note that the Mathematics Content Knowledge for Teaching section is the same on our Pre- and Post-surveys.

The Post-survey has an additional section entitled Demographics and Professional Experience. It comprises several items from the Background Information section in the Pre-survey (questions about administrative experience, teaching experience, mathematics coursework, professional development and education), and three questions about the principals’ race and gender. These items were taken directly from the School and Staffing Survey (SASS), so we would be in a position to compare our data to this national sample.

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*   The scenario is excerpted from a case in Developing Mathematical Ideas (Schifter, et al., 1998).
** Based on the TELT belief scale (National Center for Research on Teacher Education, 1985).