More than meets the eye: patterns and shifts in middle school mathematics teachers’ descriptions of models

Modeling is a major topic of interest in mathematics education. However, the field’s definition of models is diverse. Less is known about what teachers identify as mathematical models, even though it is teachers who ultimately enact modeling activities in the classroom. In this study, we asked nine middle school teachers with a variety of academic backgrounds and teaching experience to collect data related to one familiar physical phenomenon, cooling liquid. We then asked each participant to construct a model of that phenomenon, describe why it was a model, and identify whether a variety of artifacts representing the phenomenon also counted as models during a semi-structured interview. We sought to identify: what do mathematics teachers attend to when describing what constitutes a model? And, how do their attentions shift as they engage in different activities related to models? Using content analysis, we documented what features and purposes teachers attended to when describing a mathematical model. When constructing their own model, they focused on the visual form of the model and what quantitative information it should include. When deciding whether particular representational artifacts constituted models, they focused on how the representations reflected the system under study, and what purposes those representations could serve in further understanding that system. These findings suggest teachers may have multiple understandings of models, which are active at different times and reflect different perspectives. This has implications for research, teacher education, and professional development.     

Community-based inquiry improves critical thinking in general education biology

National stakeholders are becoming increasingly concerned about the inability of college graduates to think critically. Research shows that, while both faculty and students deem critical thinking essential, only a small fraction of graduates can demonstrate the thinking skills necessary for academic and professional success. Many faculty are considering nontraditional teaching methods that incorporate undergraduate research because they more closely align with the process of doing investigative science. This study compared a research-focused teaching method called community-based inquiry (CBI) with traditional lecture/laboratory in general education biology to discover which method would elicit greater gains in critical thinking. Results showed significant critical-thinking gains in the CBI group but decreases in a traditional group and a mixed CBI/traditional group. Prior critical-thinking skill, instructor, and ethnicity also significantly influenced critical-thinking gains, with nearly all ethnicities in the CBI group outperforming peers in both the mixed and traditional groups. Females, who showed decreased critical thinking in traditional courses relative to males, outperformed their male counterparts in CBI courses. Through the results of this study, it is hoped that faculty who value both research and critical thinking will consider using the CBI method.