Active Learning in Sophomore Mathematics: A Cautionary Tale

Math 245: Multivariate Calculus, Linear Algebra, and Differential Equations with Computer I is the first half of a year-long sophomore sequence that emphasizes the subjects\u27 interconnections and grounding in real-world applications. The sequence is aimed primarily at students from physical and mathematical sciences and engineering. In Fall, 1998, as a result of my affiliation with the Science, Technology, Engineering, and Mathematics Teacher Education Collaborative (STEMTEC), I continued and extended previously-introduced reforms in Math 245, including: motivating mathematical ideas with real-world phenomena; student use of computer technology; and, learning by discovery and experimentation. I also introduced additional pedagogical strategies for more actively involving the students in their own learning—a collaborative exam component and in-class problem-solving exercises. The in-class exercises were well received and usually productive; two were especially effective at revealing normally unarticulated thinking. The collaborative exam component was of questionable benefit and was subsequently abandoned. Overall student performance, as measured by traditional means, was disappointing. Among the plausible reasons for this result is that too much material was covered in too short a time. Experience here suggests that active-learning strategies can be useful, but are unlikely to succeed unless one sets realistic limits to content coverage

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Supporting students with learning disabilities to explore linear relationships using online learning objects

The study of linear relationships is foundational for mathematics teaching and learning. However, students’ abilities connect different representations of linear relationships have proven to be challenging. In response, a computer-based instructional sequence was designed to support students’ understanding of the connections among representations. In this paper we report on the affordances of this dynamic mode of representation specifically for students with learning disabilities. We outline four results identified by teachers as they implemented the online lessons

Developing mathematics teaching: What can we learn from the literature?

In this chapter we address the extensive literature which can inform the teaching of mathematics drawing on our own experience of using and finding value in the literature to enhance our own knowledge and practice in teaching mathematics at university level. Three areas of literature are recognised and addressed: professional literature, in which we gain insights into the ways in which other teachers/lecturers have thought about their teaching and the approaches/strategies and frameworks they have used; research literature which offers what is known, findings from research that can enable more informed approaches to teaching; and pedagogical literature that deals overtly with developing and enhancing teaching, through the lecturer engaging with new ideas (for example those offered in the professional literature), attending to research findings or using specific tactics or teaching approaches recommended by the authors. Many examples are provided, both of particular sources in the literature and of approaches to learning and teaching in mathematics, with an extensive reference list. This approach is intended to be informative to mathematics teachers at university level who look for knowledge and ideas to inform their teaching and support its development

Preservice teachers’ creation of dynamic geometry sketches to understand trigonometric relationships

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. This paper looks at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. We identify common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. Lastly, we discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended

Developing mathematics teaching: what can we learn from the literature?

In this chapter we address the extensive literature which can inform the teaching of mathematics drawing on our own experience of using and finding value in the literature to enhance our own knowledge and practice in teaching mathematics at university level. Three areas of literature are recognised and addressed: professional literature, in which we gain insights into the ways in which other teachers/lecturers have thought about their teaching and the approaches/strategies and frameworks they have used; research literature which offers what is known, findings from research that can enable more informed approaches to teaching; and pedagogical literature that deals overtly with developing and enhancing teaching, through the lecturer engaging with new ideas (for example those offered in the professional literature), attending to research findings or using specific tactics or teaching approaches recommended by the authors. Many examples are provided, both of particular sources in the literature and of approaches to learning and teaching in mathematics, with an extensive reference list. This approach is intended to be informative to mathematics teachers at university level who look for knowledge and ideas to inform their teaching and support its development