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Quantitative reasoning (QR) enhances and lengthens lives. In this article, the author discusses how his team is improving QR instruction in U.S. higher education and explain the 5C model of student engagement in quantitative reasoning: (a) Critical thinking, (b) QR Competencies, (c) student Collaboration, (d) real-world Contexts, and (e) mathematical and statistical Concepts. Critical thinking is the heart of quantitative reasoning. QR Competencies and student Collaboration help students connect real-world Contexts to mathematical and statistical Concepts to make decisions about meaningful personal and professional issues. 

Inquiry-based learning (IBL) is a form of active learning that engages students in cognitively demanding tasks—involving students’ attention, reasoning, problem solving, and communication. In the rest of this article, we look at IBL—past, present, and future. IBL has a storied history and a growing literature of theory and research to support its efficacy as a method for teaching for entry-level postsecondary (i.e., gateway) courses in mathematics. The 20th-century roots of teaching mathematics via IBL built a foundation for recent theory-building and for research that demonstrates how IBL teaching improves students’ mathematical proficiency, their ownership of and confidence in their own thinking and reasoning, their level of classroom engagement, and their success in mathematics class and throughout their lives. Despite this positive evidence, the mathematics teaching community faces challenges in implementing IBL in the classroom. Thus, we provide practical information on overcoming obstacles to IBL teaching, examples of IBL tasks, and tips for implementing IBL instruction. With the backing of AMATYC, its sister organizations—the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics—and the growing number of IBL practitioners and researchers, the future for IBL seems bright. 

This is one of three responses to two articles by James E. Schultz on how mathematics education in Ohio—and especially at Ohio State University—has influenced mathematics teaching and learning across the United States and beyond. Every mathematics teacher in Ohio should know this story. Schultz’s two contributions are oral histories in written form and possess a biographical and even autobiographical flavor. My response will follow suite. After a brief introduction, I reflect on—and add to—Schultz’s “Laying the Groundwork” article (2024a) and his “Incorporating Technology” piece (2024b). I then consider how the issues and legacy presented in these articles connect to mathematics teaching and learning today and how Ohio continues to influence mathematics education beyond its borders. I close with an epilogue on how I first met several key characters in this mathematical narrative. 

Despite a growing emphasis on Quantitative Reasoning in education, particularly as universities develop courses that move beyond traditional mathematics, its role in fostering critical citizenship remains underexplored. The research reported herein explores the perspectives of instructors on teaching Quantitative Reasoning at university and examines how these courses can promote critical citizenship. By evaluating practical teaching approaches, the study highlights the evolving role of quantitative reasoning in preparing students for thoughtful civic participation. 

Abstract A tertiary course in Quantitative Reasoning (QR) has the potential to develop key practical and intellectual skills for citizenship, such as critical thinking, problem solving, quantitative literacy, and oral and written communication. In this article, we present research conducted on four instructors of such a QR course for students enrolled in a wide variety of nonscience degree programs at a university in the United States. The course used a student-inquiry approach to proportional reasoning, probability, statistical reasoning, and mathematical modeling. The findings are framed by a 5 C model of QR, which entailsCritical thinking to link real-worldContexts to mathematicalConcepts supported by studentCollaboration and QRCompetencies. The research addressed the questions of how university instructors support student development of the skills needed for critical citizenship and how this support relates to the 5 C model. We found that three of the four instructors viewed critical thinking as a central goal of the QR course and as supporting citizenship education. All four engaged students in tasks designed to develop a combination of skills associated citizenship, including critical thinking, self-questioning, collaboration, and communication. The discussion addresses such issues as the course’s merits and challenges, student engagement, the relative importance of the five Cs, the importance of instructional autonomy, and recommendations for related professional development and future research.