Mathematical and Statistical Reasoning in Compelling Contexts: Quantitative Approaches for building and Interrogating Personal, Disciplinary, Interdisciplinary and Worldviews

David L. Ferguson – Stony Brook University

This paper calls for increased emphasis on a vision of mathematical and statistical reasoning that situates these subjects in compelling contexts (compelling from the students’ viewpoints) and thereby allows for the development of core mathematical concepts that can be interconnected to a variety of interests and purposes. That vision suggests a modest core of mathematical concepts and methods, developed through a constructivist approach. Students will build on that core to both extend their understanding to new mathematical ideas/approaches and enhance their understanding of complex (dirty) domains in which mathematics contributes to their evolving knowledge. This approach recognizes that, both within the core and beyond the core, students’ knowledge will evolve in different ways. Such student-initiated learning paths will demand creative and flexible assessment methods that not only gauge progress on benchmarks but reveal insights about learners’ unique experiences on personally meaningful projects. From the paper’s conclusion.

Topics of Interest to the SENCER Community

Quantitative Reasoning

  • Key elements of a reformed environment for engaging students in mathematical and statistical reasoning.
  • A discussion of role of motivation in learning mathematics and statistics
  • A provocative discussion of the role of rigor in quantitative reasoning

Modeling and Decision Making

  • A discussion of the design of SENCER Model Course in view of learning research and goals for broad mathematical competency in the population.

Full Report

Download (PDF, 319KB)

Related Resources

About the Author

Ferguson David L. Ferguson
Professor, Stony Brook University
347 Harriman Hall
Stony Brook, NY
(631) 632-8763

David L. Ferguson is Distinguished Service Professor of Technology and Society and Applied Mathematics at Stony Brook University. He is Chair of the Department of Technology and Society in the College of Engineering and Applied Sciences. Dr. Ferguson has been P.I. or Co- P.I. on numerous projects, including several NSF projects, aimed at improving undergraduate and graduate education in science, technology, engineering and mathematics (STEM). He is faculty contributor in the calculus reform movement. He co-directed the NSF-supported Algorithm Discovery Development Project and two NSF-funded Faculty Enhancement workshops on the teaching of introductory computer science courses. Under support from the Sloan Foundation, he developed a course in applications of mathematics for liberal arts students. He was Co-P.I. on a multi-campus project, funded by NSF, on Mathematical Sciences and Their Applications Throughout the Curriculum. He is coordinator for the Math and Computer Science cluster of Science Education for New Civic Engagements and Responsibilities (SENCER), an NSF-funded National Dissemination grant. He was Co-P.I. on a project entitled “Real-time Multidimensional Assessment of Student Learning” funded by NSF’s Program in the Assessment of Student Achievement in Undergraduate Education. Also, he is Co-P.I. on a project on Innovative Approaches to Human-Computer Interfaces, funded by the Combined Research and Curriculum Development Program of NSF. Professor Ferguson is the author of numerous papers on problem-solving, quantitative reasoning and educational technology. He is the editor of two books on educational computing.

In 1992, Professor Ferguson received the State University of New York Chancellor’s Award for Excellence in Teaching. He is a New York State and national leader in programs to enhance the participation of underrepresented minority students in science, technology, engineering and mathematics programs. He is director of both the NSF-supported SUNY Louis Stokes Alliance for Minority Participation and the NSF-supported SUNY Alliance for Graduate Education and the Professoriate. In 1997, he received the U.S. Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring. Professor Ferguson served as a member of the executive committee of the NSF-supported Recognition Award for the Integration of Research and Education (RAIRE) at Stony Brook. From 1998 to 2002, Professor Ferguson directed Stony Brook’s Center for Excellence in Learning and Teaching (CELT). The New York Academy of Sciences named Dr. Ferguson as the Academy’s 2004 recipient of its Archie Lacey Award, which is presented nationally to an individual who has made extraordinary contributions to the participation of underrepresented minority students in STEM fields.