Ear to the Ground features voices from various corners of the mathematics education world.

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### Kelly Curtis, Katrina Lindo, and Amanda Jansen

When a ninth-grade teacher used discourse moves aligned with responding to students’ thinking and explicitly promoting productive dispositions, her students reported having positive experiences.

### Amanda Jansen and Alison S. Marzocchi

This edited volume, *Vital Directions for Mathematics Education Research*, is a significant contribution to our field because each chapter highlights grand problems that researchers must tackle to improve mathematics learning and teaching. The ambitious goals of the chapters could be summarized in a central question: How can research contribute to understanding and improving mathematics teaching so that we can further understand and support students' meaningful learning of mathematics? From this book, readers will draw inspiration for their research endeavors, and they will be able to situate their studies in broader perspectives about mathematics teaching and learning.

### Amanda Jansen, Joseph DiNapoli, and Kristin McKenney

Mathematics educators incorporate affective constructs into their research as they seek to understand phenomena related to teaching and learning. Some prominent findings in mathematics education research suggest that beliefs provide explanations for some perplexing behaviors. For instance, if students stop working on a challenging task after a short period of time, one explanation may be that they believe that if you understand mathematics, you can solve problems in 5 minutes or less (Schoenfeld, 1988).

### Eva Thanheiser and Amanda Jansen

Engaging prospective elementary teachers (PTs) in participating productively by making their exploratory (rough draft) thinking public during class discussions remains a constant challenge for instructors of mathematics content courses for teachers, in part because of perspectives incoming PTs may hold about interacting in academic settings. In this article, we share the effects of an intervention designed to confront PTs' incoming perspectives. PTs were provided with opportunities to label the level of completeness and correctness of their thinking before they displayed and discussed their written work publicly during a mathematics content course for teachers. Results indicated that labeling their work increased PTs' level of comfort with sharing their thinking and awareness of the value of doing so. PTs also reported that the label served as a reflection tool. The label increased the PTs' productive disposition in terms of comfort level with taking intellectual risks when doing mathematics and reflecting on their work.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

### Amanda Jansen, Brandy Cooper, Stefanie Vascellaro, and Philip Wandless

This article describes a useful approach, called rough-draft talk, to create a classroom culture in which talking is used as a tool in the classroom.

### Jon R. Star, John P. Smith III, and Amanda Jansen

Research on the impact of *Standards*-based mathematics and reform calculus curricula has largely focused on changes in achievement and attitudes, generally ignoring how students experience these new programs. This study was designed to address that deficit. As part of a larger effort to characterize students' transitions into and out of reform programs, we analyzed how 93 high school and college students perceived *Standards*-based and reform calculus programs as different from traditional ones. Results show considerable diversity across and even within sites. Nearly all students reported differences, but high-impact differences, like *Content*, were not always related to curriculum type (reform or traditional). Students' perceptions aligned moderately well with those of reform curriculum authors, e.g., concerning *Typical Problems*. These results show that students' responses to reform programs can be quite diverse and only partially aligned with adults' views.