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Creating Environments for Fostering Effective Critical Thinking in Mathematics Education (Math-EFFECTs)

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2014 ASEE Annual Conference & Exposition


Indianapolis, Indiana

Publication Date

June 15, 2014

Start Date

June 15, 2014

End Date

June 18, 2014



Conference Session

Changing the Classroom Environment in Mathematics Education

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Page Count


Page Numbers

24.332.1 - 24.332.8



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Paper Authors


Rebecca Bourn Tribeca Flashpoint Media Arts Academy

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Dr. Bourn designed the math curriculum for the Core Studies Program at the Tribeca Flashpoint Media Arts Academy. She received her Ph.D. in applied ,athematics from the University of Virginia School of Engineering and Applied Science.

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Sarah C. Baxter University of South Carolina

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Dr. Baxter is a professor in the department of mechanical engineering at the University of South Carolina. She received her Ph.D. in applied mathematics from the University of Virginia School of Engineering and Applied Science.

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Creating Environments for Fostering Effective Critical Thinking in Mathematics Education (Math-EFFECTs)The objective of this work is to present a strategy for the development and implementation of theEnvironments for Fostering Effective Critical Thinking (EFFECTs) pedagogical framework in amathematics classroom, called Math-EFFECTS. A primary goal of Math-EFFECTs is toenhance the timely integration of mathematical solution techniques with engineering, technologyand applied science applications.EFFECTs was developed by a team of researchers at the University of ____ under funding fromthe National Science Foundation. It has been disseminated via the web and has almost a dozenpractitioners who have applied the framework to concepts such as geotechnical engineering,thermodynamics, mechanics, numerical methods, and scientific visualization, working withstudents at all stages of their engineering education. The central learning goals of engineeringEFFECTs are to (i) improve the understanding and retention of a specific set of concepts thatprovide core knowledge and (ii) encourage students to recognize and develop critical thinkingskills that lead to earlier growth in engineering judgment. The primary application of EFFECTshas focused on enhancing the understanding of underlying engineering concepts and developingcritical thinking. However, the framework can also be used to more effectively present and teachcore mathematical concepts, encourage the critical mathematical thinking associated with real-world problem solving, and effectively link formal mathematics concepts to students’applications of mathematics at an earlier stage in their education.The developmental framework for instructors using EFFECTs begins with the identification ofthe core concepts being studied. Next, these concepts are associated with active learningactivities; each concept could be associated with a single activity or multiple concepts can belinked or combined in progressively building activities. The third step in the process is to identifyan application that has at its base a solid understanding of the core concepts. Finally, the generalapplication is placed in a real context, putting the application in a setting that resonates withstudents and gets them invested in creating the final solution. From this context an overalldriving question is developed.The instructional framework operates in reverse. The process for the students begins with thereal world context. Students are then presented with a decision worksheet, directly linked to thecontext, that poses a driving question. Driving questions are deliberately offered with justenough information so that students are encouraged to perform estimations and must begin toevaluate their own learning needs in the context of the application. In response to the drivingquestion, students are prompted to start asking conceptually-based questions that motivate activelearning modules. Thus the goal of the EFFECTs framework is to create an integrative, ratherthan additive module based approach.In this paper we present an overview of the developmental framework and strategies for adaptingthe EFFECTS approach to the study of mathematics, Math-EFFECTs, and illustrate theinstructional framework with specific examples. Challenges to adopting this approach in formalmathematics settings are discussed and framework adaptations are suggested. The specificexamples presented focus on the core concepts of estimation and statistics, elementary linearalgebra/systems of linear equations, and polynomial root-finding.

Bourn, R., & Baxter, S. C. (2014, June), Creating Environments for Fostering Effective Critical Thinking in Mathematics Education (Math-EFFECTs) Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--20223

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