What We Know About Deepening Teachers' Content Knowledge: Engaging Teachers with Developing Conceptual Maps of Mathematics/Science Content

Programs for mathematics and science teachers can work to deepen teachers' understanding of disciplinary content. One strategy used to deepen teachers' knowledge of mathematics and science concepts is engaging teachers in developing conceptual maps. Developing conceptual maps involves working with a particular concept or set of concepts and identifying the relevant ideas that make up the concept(s) as well as the relationships among those ideas. When engaged in this intervention, teachers may be asked to identify both the ideas and their relationships, or they may be provided with the ideas and asked to focus only on the relationships among them. Advice from experienced practitioners offers guidance for efforts to engage teachers with developing conceptual maps of mathematics and science content as a strategy for deepening their content knowledge. Insights provided by a group of expert practitioners with diverse backgrounds included the following ideas:

• While it is important in all professional development to build an atmosphere of trust, respect, and openness to ideas, it is particularly important when constructing conceptual maps of mathematics/science content since teachers' thinking is open to public examination.
• During the concept mapping process, it is important to keep the focus on the key mathematics/science concepts and their relationships.
• Invalid content is likely to surface during concept mapping, and professional development providers must be prepared to guide teachers to correct content understandings.

Teacher Content Knowledge Matters

Empirical evidence demonstrates that teachers' mathematics/science content knowledge makes a difference in their instructional practice and their students' achievement. Consistent findings across studies include:

• Teachers' mathematics/science content knowledge influences how teachers engage students with the subject matter.
• Teachers' mathematics/science content knowledge influences how teachers evaluate and use instructional materials.
• Teachers' mathematics/science content knowledge is related to what their students learn.

Research on Engaging Teachers with Developing Conceptual Maps of Mathematics/Science Content

The literature search identified one research study of a professional development program that engaged teachers in developing conceptual maps of mathematics content, as one of several strategies. The study provided preliminary evidence of positive effects on teachers' mathematics content knowledge (Clark & Schorr, 2000). This study focused on the middle grades, with teacher participants ranging from grade 6 to grade 8. Topics in number and operations were addressed. Although the study did not investigate the unique contribution of the strategy of engaging teachers in developing conceptual maps of content, the positive results suggest that the use of such maps is a potentially useful professional development strategy and a fruitful area for future research.

The literature search surfaced one research study of a professional development program that included engaging teachers with developing conceptual maps of science content (Shymansky, Woodworth, Norman, Dunkhase, Matthews, & Liu, 1993). The study focused on teachers of grades 4 through 9, with various physical, life, and earth science concepts targeted among different groups of teachers. Although the study was not designed to systematically study the particular strategy of using concept maps for deepening teacher content knowledge, there was some support for the claim regarding its effectiveness in deepening teachers' science content knowledge.