How Does One Design or Evaluate a Course in Quantitative Reasoning?

Abstract

In the absence of generally accepted content standards and with little evidence on the learning for long-term retrieval and transfer, how does one design or evaluate a course in quantitative reasoning (QR)? This is a report on one way to do so. The subject QR course, which has college algebra as a prerequisite and has been taught for 8 years, is being modified slightly to be offered as an alternative to college algebra. One modification is adding a significant formal writing component. As the modification occurs, the current course and the modified one are judged according to six sets of criteria: the six core competencies of the Association of American Colleges and Universities rubric on quantitative literacy; the five mathematical competencies from the National Research Council (NRC) study report, Adding It Up; the eight practice standards from the Common Core State Standards for Mathematics; the five elements of effective thinking as articulated by Edward Burger and Michael Starbird, the summary research findings on human cognition from the NRC study report, How People Learn; and the ten principles gleaned from applying the science of learning to university teaching. The QR course, as described by ten design principles, is determined to be generally well aligned with most of the overlapping criteria of the six sets, providing cogent evidence of high educational value.

Alignment Between Learning Objectives and Assessments in a Quantitative Literacy Course

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“…However, greater learning is possible with a focus on practicing core quantitative reasoning competencies embedded in EDDIE modules such as: interpretation, representation, calculation, analyses, synthesis, assumptions, and communication. 13 Part of increasing instructor buy‐in may therefore include providing orientation in how students learn inquiry and quantitative reasoning and support for trying out new teaching approaches.…”

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“…Mathematics literacy is defined as being able to identify what is learned in everyday life and understanding the role that knowledge plays in the world (Ojose, 2011). Demonstrating confidence, or a "productive disposition" (Madison, 2014), when engaging in situations that involve using what has been learned is a mark of literacy (Bybee, 2013). Thus, to develop literacy students need opportunities to learn, develop, and practice their literacy skills in an authentic, experience-based environment.…”