Sandra Crespo

Praising and correcting prospective teachers investigate their teacherly talk

Abstract Despite recent calls for teachers to promote and increase students’ communication and discussion in their classrooms, prospective teachers have limited opportunities to explore issues of classroom talk during their teacher preparation programs. In this study, prospective teachers attending a mathematics methods course were encouraged to attend to and investigate their developing teacherly talk through a letter writing exchange with school students. This paper reports on their tendency to respond to the correct answers with praise and to supply the answers when students reached an incorrect result. It explores the ways in which they began to interrogate and problematize such practices and to consider alternative forms of teacher responses to students’ right and wrong answers. Features of the courses field-related experience and the teacher educators’ interventions that promoted and supported the preservice teachers’ investigations are also discussed.

Cross-platform learning: children's learning from multiple media

Educational media projects often span several platforms (e.g., games, TV, hands-on materials), under the assumption that multiple platforms elicit greater learning than a single medium. To test this assumption, 672 fourth graders were assigned to use different combinations of math-based Cyberchase media for eight weeks: DVD Only, Web Only, DVD + Web, All Materials, or No Exposure (control). Mathematical problem solving was assessed via hands-on, pretest-posttest tasks, and by tracking software that recorded performance in three Cyberchase online games. Consistent with past research, significantly greater problem solving gains appeared among Cyberchase users than the control group. Pre-post effects were often stronger in the DVD + Web group than in groups that used either medium alone. Moreover, users of multiple media employed significantly more sophisticated mathematical strategies -- and produced more correct responses -- while playing online games. Thus, a unique benefit of cross-platform learning seems to lie in transfer of learning, i.e., applying educational content learned from one medium (e.g., television) to support learning in another medium (e.g., games), resulting in richer engagement and greater posttest gains.

Research on Improving Teacher Knowledge and Pedagogical Approaches: From a Comparative to a Collaborative Perspective

International studies in education have been part of the research and policy landscape for more than five decades. They are often associated with the inevitable declaration of educational winners and losers and tend to be overshadowed by the media frenzy that accompanies any research reports that highlight world rankings. However, the organizational, political, methodological, and social skills required to design, implement, and disseminate these kinds of international comparative studies cannot be underestimated. In this commentary I first provide a brief overview of salient and widely discussed challenges and benefits of international studies and consider them in relation to the focus of this section on improving teacher knowledge and pedagogical approaches. I then highlight how each of the chapters in this section attends to some of these challenges and benefits. I close with reflections and future questions for international research focused on this area of study.

Truth, Lies, and Videotapes: Embracing the Contraries of Mathematics Teaching

As videos of teaching become increasingly available and used as tools for analyzing classroom practice, it is important for researchers and practitioners to reflect on the nature and purposes of video representations of teaching. Too often classroom videos are made and viewed in ways that narrow interpretations about the nature and quality of instruction. This article discusses and illustrates a different perspective for making and working with videos of teaching, one that embraces rather than rejects contradictions in the work of teaching. This approach seeks to disrupt researchers and practitioners’ tendencies to generate and use overly evaluative frameworks and language when describing and analyzing teaching practice. Implications for researchers and practitioners of teaching and teacher education are discussed.

A Collection of Problem-Posing Experiences for Prospective Mathematics Teachers that Make a Difference

Without significant work on problem posing during teacher preparation, prospective teachers will enter the profession with limited vision and strategies for mathematics teaching. Based on previous and ongoing research on problem posing, the author proposes three essential strands for a problem posing framework that strives to teach prospective teachers to: (a) mindfully pose problems to students; (b) engage in problem posing with their students; and (c) pose personally and socially relevant mathematics problems. These strands engage prospective teachers with enduring questions for teachers of mathematics: What makes a mathematics problem educational? Who poses mathematics problems in the classroom? and Why do people spend time posing and solving mathematics problems? These three strands, individually and combined, can empower prospective teachers as problem posers and as teachers of mathematics who will pose rich and engaging problems to and with their future students.

Generating, Appraising, and Revising Representations of Mathematics Teaching with Prospective Teachers

Facilitating whole class discussions is a complex practice to learn during teacher preparation. Hence much of the curriculum and pedagogies of mathematics teacher education aim to support beginning teachers to learn to facilitate meaningful and equitable mathematical class discussions. Although there are multiple approaches to address this complex teaching practice, in this chapter the author shares a task that bridges pedagogies of inquiry and enactment in teacher education and aims to empower prospective teachers by positioning them as producers, not just as consumers of representations of mathematics teaching. The “Create and Sort a Classroom Dialogue” invites prospective teachers to generate a representation of a mathematical discussion and to then sort and appraise the quality of their imaginary classroom dialogues. Prospective teachers are also invited to revise these dialogues to further refine their descriptions and representations of what high quality mathematical discussions might look and sound like. The author argues that the phases of generating, appraising, and revising representations of practice provide an important framework for engaging and empowering prospective teachers as future teachers of mathematics. These three phases are illustrated and used to discuss the affordances of engaging prospective teachers with representations of practice that they themselves have generated.

Television, Games, and Mathematics: Effects of Children's Interactions with Multiple Media

Research has shown that educational media, such as television series or interactive games, can promote significant learning. However, it is quite common for producers to create several interconnected media, such as a television show and an associated web site, under the assumption that multiple platforms elicit greater learning than a single medium would. The research reported in this paper uses Cyberchase media as the setting in which to investigate the effectiveness of multiple media as a tool for mathematical learning for elementary school children. The study includes both a naturalistic phase, which mirrors childrens typical use of the media, and an experimental phase, which allows for causal inference to be drawn about their learning outcomes.