**Using concept maps to assess change in teachers’ understandings of algebra: a respectful approach**

By: Sarah Hough, Nancy O’Rode, Nancy Terman, Julian Weissglass

### Abstract

*The purpose of this study was to explore teachers’ growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their understanding about mathematics, their ability to implement effective mathematics practices in their classrooms, and their knowledge of working with English Learners. Results indicate that teachers’ algebraic knowledge structures became more complex and connected as a result of their professional development. In addition, they were able to adapt their knowledge networks to incorporate important aspects of algebra into them. Concept maps are recommended to other leaders of mathematics professional development as a means of assessing change. *

**Keywords**: Assessing change, Concept maps, Equity, Knowledge structures, Knowledge packets, Lead teachers, Multiple analysis of variance (MANOVA), Mathematics, Professional development

### Conclusion

The results reported indicate that participants’ understandings of algebra changed as a consequence of participating in the project’s activities. The structural and content analytic techniques, used to analyze participants’ concept maps, illustrated how their subject matter knowledge had increased in terms of breadth, depth and connectivity. These techniques allowed us to examine how adaptation of pre-institute knowledge occurred in order for new knowledge to be assimilated into the network structure. Further, for both of these analyses, participants’ own reflective writings were used to triangulate results. Participants themselves felt that they had gained a greater understanding of concepts. They particularly saw self-growth in graphing, functions and patterns. They further felt that their maps represented the greater connectivity of their understanding of algebra concepts. Thus we feel confident in recommending concept maps in conjunction with reflective writing as a means of assessing participants’ understanding in specific mathematics topics, especially those that may result from professional development.

Concept maps are a respectful approach to assessing teacher’s growth in mathematical understanding.

- Concept maps provide opportunities to build participants’ collective understanding and vocabulary of algebra at the beginning of an institute and hence enhance the building of community. Having the participants discuss their pre maps in pairs, share with the whole group and then contrast and discuss different representations of algebra allowed participants to build a common picture of the topic.
- Concept maps are in themselves a valuable learning activity in which participants reflect on their own understanding.Participants were given time to reflect on both their own and other participant’s understandings of algebra as well as the chance to compare and comment on their own growth after the institute.
- Concept maps validate the mathematical knowledge that each participant holds. Teacher participants were asked to begin the institute by reflecting on their existing knowledge of algebra, which communicated respect for their thinking and validated the knowledge they brought to the institute. In addition, teachers were asked their opinion of how well the maps measured their own growth.
- Concept maps provide an assessment of important mathematics consistent with the project philosophy. Creating the concept maps asked teacher participants to articulate and to make connections between the mathematical ideas or concepts that they hold, thus re-enforcing the idea that mathematic is more than discrete facts and skills.
- Concept maps document growth among a group of participants with radically different understandings of subject matter.

Growth in algebraic understanding was captured by looking at each participant’s map from where they began at the start of the institute to where their thinking was at the end, hence relative change was captured. In this study we used triangulation of concept map data with the reflective writings of participants to establish their use as a credible method to measure change in important mathematical content as described in this paper. To give more credence to the use of concept maps as a scientific measure of growth in mathematics content understanding in general, further study that tests their concurrent validity is needed. For example, structural variables could be correlated with task-based assessments that require participants to connect learned concepts to other areas of mathematics.

Source: (2007). Journal of Mathematics Teacher Education, Springer Netherlands, 10(1), pp 23-41

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