This session will describe the study of a professional development project based in a museum that resulted in an enhancement of teachers’ abilities to recognize and incorporate mathematical concepts into the planning of their instruction.

First, the speaker will briefly describe the framework of the study (3 minutes). Connecting school mathematics to the real world appears to be beneficial, because it enhances students’ understanding of fundamental mathematical ideas and motivates mathematics learning and applications (e.g., Gainsburg, 2008; NCTM, 2000). Nevertheless, most inservice and preservice teachers tend to favor nonrealistic solutions, to exclude real-world knowledge and considerations when solving problems (Gainsburg, 2008; Verchaffel, De Corte, and Borghart, 1997), and make no effort to connect instruction to students’ backgrounds (Daley & Valdes, 2006).

Research shows that learning at informal sites enhances science teachers’ subject matter knowledge (Kelly, 2000), knowledge of pedagogy and knowledge of students (Anderson, Lawson, & Mayer-Smith, 2006; Chin, 2004; Anderson et al., 2006). In addition, learning mathematics through modeling and making connections between mathematics and real world phenomena support secondary mathematics preservice teachers’ ability to identify mathematics applied in informal sites of their choice (Munakata, 2005).

Therefore, the study adopted a situated cognition perspective, which assumes that the knowledge is inseparable from the context and activities within which it develops (Borko & Putnam, 2000),  to investigate the following questions: (1) In what ways does instruction on mathematical concepts involved in informal sites impact secondary mathematics teachers’ ability to recognize mathematical concepts in other informal sites?, and (2) In what ways do teachers’ abilities to recognize mathematics in informal settings influence their ability to integrate informal education applications into the planning of mathematics instruction?

Next, the methodology used in the study will be addressed (7 min). The study took place in the Museum of Science and Industry (MSI), in Chicago, IL. Seven teachers, certified by their state to teach secondary mathematics, and pursuing a Masters in Mathematics Education degree at a private Midwest university, volunteered to participate in the study. The researcher met with the teachers four times at MSI over the two-month period, for a total of approximately 16 hours.

During the first meeting at MSI, the teachers toured the museum on their own, and searched for the exhibits that could be, in their opinion, used as resource for teaching mathematics. The second meeting involved instruction at the exhibits selected by the researcher. During the third meeting, the teachers explored mathematical concepts through activities developed by the researcher in the context of the particular museum exhibits. The last meeting at MSI once again provided teachers with the opportunity to, on their own, search for mathematics in the museum. After each meeting, the group met for a discussion regarding the experience.  The teachers shared ideas regarding the mathematics identified in the museum exhibits and about learning activities that could be used with students to address particular mathematical concepts in the context of the museum exhibits. In addition, the teachers expressed their concerns with respect to the teaching and learning at informal sites.

Ethnographic methods (e.g., audiotapes of instruction, teachers’ written work) of data collection and analysis were used to capture teachers’ learning in the context of MSI exhibits (Lave, 1988). Lave’s methodology considers “person-acting (in setting) as an integral unit of analysis” (Lave, 1988, p. 180). Accordingly, the data collection and analysis were organized around two tasks: identifying mathematical concepts represented in the exhibits and creating lesson ideas to address identified mathematical concepts. The data collection included audiotapes of the group discussions and the instruction at the exhibits, teachers’ written work, and teachers’ reflections papers completed at the end of the study. The process of data analysis consisted of multiple interpretative passes through the data. An ethnographically grounded approach to discourse analysis (Gee and Green, 1998) was used as a framework for the analysis across data types.

Finally, the speaker will present the results of the study and its educational significance (5 min). Results showed that in order to identify mathematics in the museum exhibits, the teachers initially relied on explicit representations of mathematical concepts, specifically numbers, geometric shapes, and geometric figures. Additionally, they overlooked many exhibits, because they believed that the exhibits solely represented scientific phenomena, hence they made no attempt to even contemplate what possible mathematical concepts existed in those exhibits. Through discussions with the researcher and with each other, the participants began to realize that the explicit representation of mathematical concepts in the form of numbers, geometric shapes, and geometric figures is not vital to identifying mathematics in the museum exhibits, as well as to view mathematics and science as closely interrelated topics. 

The data analysis also indicated that once they identified mathematical concepts represented in the exhibit, the teachers had little difficulty to think of a teaching idea to address identified concepts, or to specify where in the curriculum they would utilize the idea. However, the analysis revealed several obstacles that prevented teachers from incorporating informal education into their teaching: lack of support from schools; the limited amount of readily available resources; and the constraints of the curriculum and testing. The teachers also thought that they did not have enough training and experience to teach through making connections between mathematics and the real world.

The results of the study indicate that providing secondary mathematics inservice teachers with opportunity to explore mathematics through modeling at informal sites contribute their ability to identify applied mathematics in those informal sites, as well as helps them understand what connections could be made and how. Therefore, teacher educators should design education courses that incorporate informal education experiences for both inservice and preservice teachers, in order to prepare teachers to teach mathematics through modeling and making connections to the real world, as recommended by the NCTM (2000).

Throughout the session, the audience will have the opportunity to pose questions as well as engage into discussion regarding teaching and learning of mathematics in informal settings such as museums.