1. T. Stevens, G. Harris, Z. Aguirre-Munoz, and L. Cobbs Southern Right Delta (ΣΡΔ'09) Gordons Bay, South Africa, December 3, 2009

2. Support provided by the National Science Foundation Math Science Partnerships Program under Award No. 0831420. The opinions expressed in this presentation are those of the WTMSMP personnel and associates and do not necessarily reflect those of NSF.

3. Math Science Partnerships 1. Reduce the number of teachers who are teaching outside of their field. 2. Encourage more students to take advanced coursework. 3. Increase challenging curricula in schools.

4. West Texas Middle School Math Partnership 1. Develop a deep understanding of elementary mathematics in middle level math teachers. 2. Develop teachers’ self- efficacy to improve the mathematics self-efficacy of their students. 3. Develop teachers’ self- efficacy to teach mathematics to diverse student populations.

5. Purpose  Evaluate the use of a case study approach employed in a workshop as a strategy to increase teachers’ conceptual knowledge for teaching and understanding of self-efficacy. Do teacher participants possess the same learning preferences? Do teacher participants learning preferences vary depending upon the content taught?

6. The case utilized in this study was designed to elicit teachers’ content knowledge and their ability to identify student misconceptions as well as engage them in critical reflection. In this way, this case offered an opportunity to explore and develop teachers’ sensitivity to student difficulty and needs (with respect to content and self-efficacy) as well as an ability to provide pedagogically sensitive and mathematically precise feedback to the student. Incorporated into a 2 hour workshop at a regional meeting of the Mathematics Association of America.

7. Procedure  Workshop participants were presented with the case study to discuss mathematical issues. shown a video describing self-efficacy and its sources. provided with the workshop manual. asked to review the case study to identify issues related to self-efficacy.

8. Case Study Approach  Authentic  Allows for a variety of viewpoints and potential outcomes  Fosters high levels of critical thinking and reflection  Promotes process skills that complement content knowledge

9. Q Methodology “Q Methodology is a research method used to study people’s “subjectivity”– that is, their viewpoint.” “Refers to “a selected population of n different tests (or essays, pictures, traits or other measurable material), each of which is measured or scaled by m Individuals.” Correlates individuals across a sample of variables.

10. Q Methodology QualitativeQuantitative  Determination of all possible statements that could be said about the learning strategies used in the workshop.  Development of the Q set.  Selection of the P set.  Q sorting.  Factor analysis.  Varimax rotation.  PQmethod.

11. Q Set  Lecture done by workshop faculty  Projected PowerPoint slides…  PowerPoint slides handout…  Large group activity (e.g., index card…)  Small group discussion  Case study provided…  Specific examples provided by others  Specific examples provided by faculty  General comments made by others…  Formal question and answer period  Informal discussion with workshop participants  Informal discussion with workshop faculty

12. Factors– Conceptual Knowledge  Autonomy Factor 1– participant led activities preferred Factor 2– instructor led activities preferred Factor 3– participant and instructor preferred  All agreed the case study was beneficial.  No demographic differences observed across factors.

13. Factors– Self-Efficacy  Degree of content application Factor 1– preferred activities that required basic knowledge. (10.33 avg.– public school teaching) Factor 2– preferred activities that required applied knowledge. (no public school teaching) Factor 3– preferred a blend of basic and applied activities with limited peer interaction.  Factor 1, comprised of mostly public school teachers, did not prefer the case study.

14. Conclusions  Do teacher participants possess the same learning preferences? Participants did not prefer the same learning strategies, but agreed the case study was helpful in learning math concepts.  Do teacher participants learning preferences vary depending upon the content taught? Public school teachers did not prefer the case study approach when studying self-efficacy.

15. Conclusions  Q methodology was useful in evaluating workshop effectiveness when time was limited. longitudinal analysis was not feasible. sample size was small.  If systemic, sustainable change in mathematics education is to be achieved, researchers must work to understand what aspects of professional development are responsible for increases in targeted variables from subjective as well as objective sources.