Janet Bowers

Cognitive and Situated Learning Perspectives in Theory and Practice.

In their recent exchange, Anderson, Reder, and Simon (1996 Anderson, Reder, and Simon (1997) and Greeno (1997) frame the conflicts between cognitive theory and situated learning theory in terms of issues that are primarily of interest to educational psychologists. We attempt to broaden the debate by approaching this discussion of perspectives against the background of our concerns as educators who engage in classroom-based research and instructional design in collaboration with teachers. We first delineate the underlying differences between the two perspectives by distinguishing their central organizing metaphors. We then argue that the contrast between the two perspectives cannot be reduced to that of choosing between the individual and the social collective as the primary unit of analysis. Against this background, we compare the situated viewpoint we find useful in our work with the cognitive approach advocated by Anderson et al. by focusing on their treatments of meaning and instructional goals. Finally, we consider the potential contributions of the two perspectives to instructional practice by contrasting their differing formulations of the relationship between theory and practice.

Adapting the mathematical task framework to design online didactic objects

Designing didactic objects involves imagining how students can conceive of specific mathematical topics and then imagining what types of classroom discussions could support these mental constructions. This study investigated whether it was possible to design Java applets that might serve as didactic objects to support online learning where ‘discussions’ are broadly defined as the conversations students have with themselves as they interact with the dynamic mathematical representations on the screen. Eighty-four pre-service elementary teachers enrolled in hybrid mathematics courses were asked to interact with a series of applets designed to support their understanding of qualitative graphing. The results of the surveys indicate that various design features of the applets did in fact cause perturbations and opportunities for resolutions that enabled the users to ‘discuss’ their learning by reflecting on their in-class discussions and online activities. The discussion includes four design features for guiding future applet creation.

A Case Study of Change in the Teaching and Learning of Precalculus to Calculus 2: What We Are Doing with What We Have.

Abstract This article presents a case study that details the successes and lessons learned by faculty and administrators at San Diego State University (SDSU) who are in the process of implementing a substantial improvement to the Precalculus to Calculus 2 sequence. Improvement efforts have been informed by national studies of successful programs and center on the department as the primary agent of change. The majority of the article will discuss the particular changes that are being enacted at SDSU, with special attention to how they came to be as they are, how they are being implemented, and how we have identified and addressed salient concerns during the process. We conclude with how we intend to continue and expand our efforts to improve student success in introductory mathematics courses and a discussion of the lessons we have learned along the way.

Integrating active learning labs in precalculus: Measuring the value added

ABSTRACT The need to incorporate active learning (AL) in higher education has become a prominent issue discussed by major leadership organizations such as the Conference Board of Mathematical Sciences (CBMS, 2016). These calls for AL are based on a large and growing body of research documenting the correlation between AL use and reduced failure rates, deeper conceptual understanding, and increased retention in STEM (science, technology, engineering, and mathematics) courses. However, the dependent variables in these studies are usually final grades or results of tests. At this point, there is a need to devise new ways to measure the specific role that AL use plays in enhancing student engagement practices. To that end, this article first discusses the validity of a survey to measure students’ views of how their opportunities to engage in AL practices differed between lecture and break-out sessions and then discusses the results of the survey. The nature of the survey enabled us to identify two student engagement practices that were most enhanced through the use of AL: (a) opportunities to explore novel solutions to real-world situations and (b) opportunities to critique the reasoning of others.

Topic Models: A Tutorial with R

This tutorial presents topic models for organizing and comparing documents. The technique and corresponding discussion focuses on analysis of short text documents, particularly micro-blogs. However, the base topic model and R implementation are generally applicable to text analytics of document databases.

Mentoring Student Participation in Undergraduate Research: A Case Study of Twists and Turns from Two Perspectives

Abstract Undergraduate research experiences provide excellent examples of high-impact practices. They rely on inquiry-based learning to provide important capstone experiences for the students. However, they are time-intensive for mentor faculty. In an attempt to scale up our faculty’s ability to offer such experiences, we combined a number of projects into one class: the Biomathematics Workshop. This article chronicles the experiences of one student from that class interspersed with comments from his mentor. Our goal is to illustrate some of the twists and turns in his journey and the unexpected but valuable lessons the student (and the mentoring team) learned.