Sepideh Stewart

Taking clickers to the next level: a contingent teaching model

Over the past decade, many researchers have discussed the effectiveness of clickers and their potential to change the way we teach and interact with students. Although most of the literature revolves around elementary usage of clickers, the deeper questions of how to integrate this technology into teaching are largely unanswered. In this paper, we present an implementation of a teaching model in a third year undergraduate Bayesian statistics class. The model is based on Schoenfelds interactive teaching routine and it is enhanced by Draper and Browns contingent teaching and Beatty et al.s Question Driven Instruction (QDI) and the use of clickers. It illustrates a teaching paradigm which is flexible, contingent to students’ needs, makes use of the most up to date information from students’ feedback via clickers and benefits from the teachers decision making at appropriate moments. We will discuss the pedagogical implications of this model in teaching.

Digital Game based Learning for Undergraduate Calculus Education: Immersion, Calculation, and Conceptual Understanding

This study has two goals: First, to investigate the effectiveness of using a digital game to teach undergraduate-level calculus in terms of improving task immersion, sense of control, calculation skills, and conceptual understanding. Second, to investigate how feedback and visual manipulation can facilitate conceptual understanding of calculus. 132 undergraduate students participated in a controlled lab experiment and were randomly assigned to either a game-playing condition, a practice quiz condition, or a no-treatment control condition. The authors collected survey data and behavioral-tracking data recorded by the server during gameplay. The results showed that students who played the digital game reported highest task immersion but not sense of control. Students in the game condition also performed significantly better in conceptual understanding compared to students who solved a practice quiz and the control group. Gameplay behavioral-tracking data was used to examine the effects of visual manipulation and feedback on conceptual understanding.

Crossing New Uncharted Territory: Shifts in Academic Identity as a Result of Modifying Teaching Practice in Undergraduate Mathematics.

The changes in academic identity a teacher may undergo, as they modify their teaching practice, will vary depending on their experiences and the support they receive. In this paper, we describe the shifts in academic identity of two lecturers, a mathematician and a mathematics educator, as they both made changes to their teaching practice by implementing new questioning techniques in a large undergraduate mathematics course. Both the lecturers were members of the research group, which became their community of practice. Our findings recommend that lecturers endeavouring to step out and try changes to their teaching practice, particularly with large groups of students, belong to a community of practice. The community of practice provides a place for shared reflection, new learning, and opportunities to negotiate new identities.

Accommodation in the formal world of mathematical thinking

ABSTRACT In this study, we examined a mathematician and one of his students’ teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Talls framework of three worlds of mathematical thinking as well as Piagets notion of accommodation to theoretically study the narratives. This paper reveals the pedagogical challenges of proving an elegant theory as the events unfolded. Although the mathematician was conscious of the students’ abilities as he carefully made the path accessible, the disparity between the mind of the mathematician and the student became apparent.

Moving Between the Embodied, Symbolic and Formal Worlds of Mathematical Thinking with Specific Linear Algebra Tasks

Linear algebra is made out of many languages and representations. Instructors and text books often move between these languages and modes fluently, not allowing students time to discuss and interpret their validities as they assume that students will pick up their understandings along the way. In reality, most students do not have the cognitive framework to perform the move that is available to the expert. In this chapter, employing Tall’s three-world model, we present specific linear algebra tasks that are designed to encourage students to move between the embodied, symbolic and formal worlds of mathematical thinking. Our working hypothesize is that by creating opportunities to move between the worlds we will encourage students to think in multiple modes of thinking which result in richer conceptual understanding.

Teaching Linear Algebra

Research on students’ conceptual difficulties with linear algebra first made an appearance in the 90’s and early 2000’s (e.g. Carlson, 1997; Dorier & Sierpinska, 2001). Over the past decade, research on linear algebra has concentrated on the nature of these difficulties and students’ thought processes (e.g. Stewart &Thomas, 2009; Wawro, Zandieh, Sweeney, Larson, & Rasmussen, 2011). The aim of the discussion group is to initiate a multinational research project on how to foster conceptual understanding of Linear Algebra concepts. Key questions and issues to be discussed are listed below:

Algebra Underperformances at College Level: What Are the Consequences?

Many college instructors consider the final problem-solving steps in their respective disciplines as “just algebra”; however, for many college students, a weak foundation in algebra seems to be a source of significant struggle with solving a variety of mathematics problems. The purpose of this chapter is to reveal some typical algebra errors that subsequently plague students’ abilities to succeed in higher-level mathematics courses. The early detection and mindfulness of these errors will aid in the creation of a model for intervention that is specifically designed for students’ needs in each course.

School Algebra to Linear Algebra: Advancing Through the Worlds of Mathematical Thinking

Linear algebra is a core subject for mathematics students and is required for many STEM majors. Research reveals that many students struggle grasping the more theoretical aspects of linear algebra which are unavoidable features of the course. Working with vectors and understanding new concepts through definitions, theorems, and proofs all indicate that a sudden shift has occurred, and despite carrying the name “algebra,” in many respects linear algebra is significantly more complex than school algebra. In this chapter we will employ the Framework of Advanced Mathematical Thinking (FAMT) to describe the type of thinking that is required for linear algebra students to succeed at college level.

Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm.

Abstract For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper conceptual ideas that are necessary for an effective diagnosis of MCMC output. In this paper we discuss MCMC simulation conceptually in the context of a Bayesian paradigm without revealing the formal algorithm first. We propose a tactile simulation method with a two-state discrete parameter where a coin supplies the proposal values and given the acceptance sets, the die value determines whether be not to accept the proposal.

Teaching Bayesian statistics to undergraduate students through debates

This paper describes a lecturer’s approach to teaching Bayesian statistics to students who were only exposed to the classical paradigm. The study shows how the lecturer extended himself by making use of ventriloquist dolls to grab hold of students’ attention and embed important ideas in revealing the differences between the Bayesian and classical paradigms. The results show that the dolls were vital and novel to the lecturer in bringing out the differences between the paradigms and the students found them interesting, funny and helpful in regard to their understanding.