Janet Bowers

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Dynalogue: Teacher Candidates Collaborating to Learn and Teach Proportional Reasoning

Computer Supported Collaborative Learning, Jun 1, 2013

DynaLab is an interactive, Web-based resource for teacher educators to use with beginning teacher... more DynaLab is an interactive, Web-based resource for teacher educators to use with beginning teachers, helping them learn to teach mathematical reasoning. This demonstration focuses on one aspect of this hands-on curriculum, DynaLogue. Participants will collaborate to compose simulated dialogues between a hypothetical student and teacher, including a whiteboard to draw and write visual representations. They will discuss and share their ideas for how to understand student thinking around a proportional reasoning problem, thus building a repertoire of explanations and broadening their knowledge of how to teach complex mathematical ideas.

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Running Head: Every Picture Tells a Story Linking Algebraic Concepts and Contexts: Every Picture Tells a Story&apos

This paper reports on efforts to design a computer-based instructional unit for 7th grade student... more This paper reports on efforts to design a computer-based instructional unit for 7th grade students that would not only address state standards but would also provide some groundwork for the students ' subsequent formal study of algebra. SimCalc Mathworlds software was used to explore the same motion from different perspectives. The overall objective is to build on what students know and to provide learning experience on which they build. Instructional sequences implemented and students ' comments regarding what they thought they had experienced during the instructional sequences are included. (KHR) Reproductions supplied by EDRS are the best that can be made from the original document. a71-

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Book Review: Designing Learning Environments for Developing Understanding of Geometry and Space

Journal of Educational Computing Research, 2000

Most edited books in mathematics education fall somewhere along the continuum anchored by studies... more Most edited books in mathematics education fall somewhere along the continuum anchored by studies of different topics with a common theoretical framework on the one end, and studies of a common topic from different theoretical frameworks on the other end. Lehrer and Chazan’s new book, Designing Learning Environments for Understanding Geometry and Space can be positioned closer to the latter end of this continuum. All of the chapters, in one way or another, focus on learning environments for studying geometry. However, the perspectives range from largely psychological in focus (e.g., chapters by Koedinger, Dennis and Confrey, Pegg and Davey, and Olive) to more socially-focused (e.g., Lehrer, Jacobson, et al; Clements, et al; Middleton and Corbett; and Renninger, Weimar, and Klotz). Such a diversity opens the field of geometry education to a variety of readers interests. In this review, I address the following questions: 1) How is the book organized? 2) What are some of the major them...

How Can Digital Didactic Objects Be Designed to Support the Learning of Mathematics

Discovering Pascal’s triangle

Documenting the Learning Process from a Constructionist Perspective

Constructivist Foundations, 2015

Book Review: Searching for the Most Amazing Thing Over the Last 20 Years: A Review of Research on Technology and the Teaching and Learning of Mathematics, Volume 1 and Volume 2

Journal for Research in Mathematics Education, 2009

Back in 1988, Tom Snyder (of Tom Snyder Productions, one of the most famous early software publis... more Back in 1988, Tom Snyder (of Tom Snyder Productions, one of the most famous early software publishing companies) and Jane Palmer wrote a prophetic book called In Search of the Most Amazing Thing: Children, Education, and Computers. Their thesis was twofold: First, they pointed out that technology, which was just beginning to be introduced in grade schools, was so compelling that educators were “… more interested in so-called computer literacy than the real thing, literacy” (p. 2). Snyder and Palmer called for stakeholders to determine what their educational priorities were, and then to figure out what technology could do to support them. Second, they emphasized the view that teachers are indispensible components in the teaching and learning process, and that no computer will ever take their place. After 20 years, we believe that Snyder and Palmer would be gratified to read Heid and Blume's newly published two-volume set that contains a thorough anthology of how educators have de...

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

PRIMUS, 2016

Abstract Undergraduate research experiences provide excellent examples of high-impact practices. ... more 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.

Three Perspectives in Research on Functions: Multi-Representational, Quantitative, and Phenomenological

Much research on student understanding of functions has been characterized by a "multi-repre... more Much research on student understanding of functions has been characterized by a "multi-representational" perspective that investigates students' efforts to make connections among conventionally accepted mathematical representations such as graphs, tables, and equations. In contrast, a "quantitative" perspective explores students' efforts to identify the quantities and relationships between quantities in a function, and a "phenomenological" perspective considers the social and experiential aspects inherent in students' learning experiences. Two research studies have demonstrated ways to incorporate the three research perspectives. One studied how seventh graders develop their understandings of linear functions as they interact with software in the social setting of a traditional classroom. The other study investigated how quantitative reasoning affects the nature of students' generalizations about linear functions and rates of change. Des...

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A hypothetical learning trajectory on measurement and flexible arithmetic

Journal for Research in Mathematics Education Monograph

List of Guest Reviewers for Volume 19

Journal of the Learning Sciences, 2010

Article usage statistics combine cumulative total PDF downloads and full-text HTML views from pub... more Article usage statistics combine cumulative total PDF downloads and full-text HTML views from publication date (but no earlier than 25 Jun 2011, launch date of this website) to 10 Feb 2013. Article views are only counted from this site. Although these data are updated every 24 hours, there may be a 48-hour delay before the most recent numbers are available.

Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers

Journal of Mathematics Teacher Education, 2011

... Keywords TPACK 4 Technological knowledge 4 Content knowledge 4 Technology ... The overall hyp... more

Designing Multimedia Case Studies for Preservice Teachers: Pedagogical Questions and Technological Design Solutions

In: Society for Information Technology & Teacher Education International Conference: Proceedings ... more

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142 the Teaching and Learning of Algorithms in School Mathematics

DISCUSSIONS of the role of algorithms in the elementary school curriculum give rise to conflictin... more DISCUSSIONS of the role of algorithms in the elementary school curriculum give rise to conflicting notions of how algorithms should be approached in the classroom. These views range from encouraging students to invent their own algorithms with minimal guidance to teaching students to perform traditional algorithms. In this paper, we will discuss an approach that eschews both these extremes. This approach values students ’ construction of nonstandard algorithms. However, it also emphasizes the es-sential role of the teacher and of instructional activities in supporting the development of students ’ numerical reasoning. In addition, this approach highlights the importance of discussions in which students justify their algorithms. It therefore treats students’ development of increasingly sophisticated algorithms as a means for conceptual learn-ing. In our view, an approach of this type is consistent with reform recommendations, like those of the National Council of Teachers of Mathemat...

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Cognitive and in Theory Perspectives Learning

Designing Applets that Instantiate Effective Mathematics Pedagogy

Journal of Technology and …, 2011

Abstract: This report describes reflections from two cycles of developmental research that involv... more

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Evolution of Inquiry Questions in a Cyclic Professional Development Program

The Canadian Journal of Action Research, 2020

Teachers in professional development (PD) programs need time to adopt, enact and reflect on what ... more Teachers in professional development (PD) programs need time to adopt, enact and reflect on what they are learning in the PD within their own situations. To encourage reflective implementation and adaptation of ideas and practices promoted in the PD studied in this article, participants were asked to engage in several small action research projects over time. To gain insights into how the cyclic process of implementation and reflection effected changes in practice and knowledge, we examined the nature of the research questions asked by a cohort of teacher-researchers (n=31) as they engaged in several cycles of action research over a three-year period. We found the nature of the questions they asked shifted over time from investigating the efficacy of particular interventions in terms of students' performance to exploring how to support students as they reason about mathematics. These results provoke questions about why these particular changes occurred and why others did not.

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49. Pre-Service Teachers’ Interpretations of the Common Core Standards: A Comparative Study Along Three Dimensions

A Mathematics Educator Walks into a Physics Class: Identifying Math Skills in Students’ Physics Problem-Solving Practices

Journal for STEM Education Research, Aug 30, 2023

One of the main goals of lower division "service" mathematics courses is to provide STEM-intendin... more One of the main goals of lower division "service" mathematics courses is to provide STEM-intending students with opportunities to engage in activities and contexts that can support their efforts to apply the mathematical ideas they are learning to successive major courses. The Mathematics Association of America has supported many mathematicians' efforts to ask partner discipline faculty what topics and habits of mind they feel should be covered in mathematics classes to prepare them for their subsequent classes. We add to this work with a twist: Instead of asking physics faculty what they want students to know, we analyzed videos that students in an introductory physics class created so that we could ask ourselves what mathematical practices were most and least prevalent in the students' physics problem-solving efforts. A qualitative analysis of the results, which we present here, indicated that most students were proficient in math practices involving problem setup and that the majority were able to apply mathematical concepts such as trigonometry and the solving of algebraic equations. However, only 44% of the student groups concluded their explanations by discussing answer reasonability and only 18% conducted a unit analysis to determine if their answers were applicable to the context of the problems assigned, even though both of these elements are important components of the overall sensemaking process. This report presents examples that illustrate these results and concludes with implications for teaching both entry-level mathematics and physics courses by modeling productive problem-solving and sensemaking practices.

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The Roles and Benefits of Using Undergraduate Student Leaders to Support the Work of SUMMIT-P

The article by Poole, Turner, and Maher-Boulis (2020) describes one way in which undergraduates h... more The article by Poole, Turner, and Maher-Boulis (2020) describes one way in which undergraduates have been used to support the SUMMIT-P goal of investigating examples of how mathematics and statistics are applied in partner discipline courses. Two other universities in the SUMMIT-P consortium, San Diego State University and Oregon State University, also use undergraduates in different ways to support the work of integrating science applications into math classes. In this article, we compare and contrast these three uses to further highlight this somewhat untapped resource.

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