**Main Office**

School of Education

UW-Madison

210 Teacher Education Building

225 North Mills Street

Madison, WI 53706

Tel: 608/263.4600

Fax: 608/263.9992

Email: curric@education.wisc.edu

or by contact form

The goals of the NSF-funded project are threefold: (a) investigate the nature of middle school and high school students’, undergraduate students’, and mathematicians’ thinking about the examples they use when developing, exploring, and proving conjectures; (b) investigate ways in which thinking about and analyzing examples may facilitate the development of students’ learning to prove; and (c) develop instructional materials designed to help teachers and university instructors foster the development of their students’ thinking about and use of examples in learning to prove. Principal Investigators: Eric Knuth, Amy Ellis, & Orit Zaslavsky (NYU).

The project consists of three inter-related projects whose overarching goal is to address the impact of early algebra (in elementary school) on students’ readiness for algebra in middle school. In our first NSF-funded project we coordinated research, curricular, and mathematical perspectives to design a grades 3-7 early algebra learning progression (EALP) and associated assessments addressing core algebraic concepts and their progression in children’s thinking. In the second NSF-funded project, we are utilizing the tools developed in the first project to implement a small-scale longitudinal EALP-based intervention in grades 3-5 to examine the effectiveness of a sustained, comprehensive early algebra education. In our most recent IES-funded project, we are scaling up our work (50+ schools) with an experimental, longitudinal study designed to test the hypothesis that children who receive comprehensive, longitudinal early algebra instruction during the elementary grades are better prepared for algebra in middle school than children who have only arithmetic-based experiences during elementary grades. Principal Investigators: Eric Knuth, Ana Stephens, & Maria Blanton (TERC).

This NSF-funded project examines the ways in which reasoning with quantities can also support students’ developing proof skills in algebra. We are investigating how students prove in algebra when they reason with quantities and quantitative situations. We are studying algebra students’ understanding of linear functions, quadratic functions, and exponential functions. Principal Investigator: Amy Ellis.

This NSF-funded project is developing a professional development program to help teachers of 4-year-old kindergarten (4K) develop an understanding of (a) early mathematics development, (b) potential family resources for child learning, and (c) ways to engage home and school to create a culturally relevant, mathematically rich, and developmentally responsive 4K program. Principal Investigators: Anita Wager, Tom Carpenter, & Beth Graue.

This project, with support from the National Academy of Education/Spencer Foundation, investigates the impact of a professional learning model that redesigned the physical, material, and social organization of the learning environment in which pre-service teachers learn to teach mathematics in order to increase the likelihood of carry over from their training to practice. The investigation focuses on the teaching practice of graduates of this model during their initial years of teaching and the factors that shape their use of the high-leverage practices they learned. Principal Investigator: Hala Ghousseini.

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**Completed Mathematics Education Faculty Projects **

The goal is of this NSF-funded project was to extend the cognitive science research into the domain of mathematics education and, more specifically, into the domain of middle school mathematics. The project focused on the strengths and weaknesses of students’ reasoning in and out of mathematics, the connections between their reasoning in different domains, and, their abilities to reason mathematically. Principal Investigators: Eric Knuth, Amy Ellis, & Charles Kalish.

This NSF-funded project investigated how variations in teachers’ communication about mathematical ideas affect students’ learning. Our focus was on variations in teachers’ gestures and language, particularly in their communication about relations among different mathematical representations. Principal Investigators: Martha Alibali, Eric Knuth, Mitchell Nathan, & R. Breckie Church (Northeastern Illinois University).

This IES-funded project investigated how mathematics teachers use visual scaffolding, including pointing, gestures, diagrams, and other methods, and explored whether and how such methods of highlighting visual information influence students’ learning. We addressed these issues in the context of middle school mathematics instruction in the domain of early algebra. Principal Investigators: Martha Alibali, Eric Knuth, & Mitchell Nathan.

This NSF-funded project focused on middle school students’ understanding of what constitutes evidence and justification in mathematics, how such understanding can be extended and refined, and professional development materials designed to support teachers’ efforts in fostering the development of students’ competencies in justifying and proving. Principal Investigator: Eric Knuth.

This IERI-funded project focused on the development of middle school students’ algebraic reasoning, the conditions and pedagogy necessary to facilitate students’ transition from concrete, arithmetic reasoning to abstract, algebraic reasoning, and professional development materials designed to support teachers in fostering the development of students’ algebraic reasoning. Principal Investigators: Eric Knuth, Martha Alibali, & Mitchell Nathan.

The purpose this collaborative NSF-funded study is to develop a multi-tiered profile linking teachers’ subject-matter knowledge of advanced algebra with their instructional treatments, which are then linked to individual students’ mathematical generalizations. Knowledge gained from this profile will aid in the creation of contextualized professional development materials designed to support teachers’ abilities to help students develop more powerful and productive generalizations. Principal Investigator: Amy Ellis.

The DiME Center was one of a network of Centers for Learning and Teaching (CLT) funded by the National Science Foundation. DiME/CLT focused on building an integrated program to develop and enhance the instructional workforce from kindergarten through graduate school. The program consisted of three interrelated components: a doctoral/postdoctoral component; a teacher education component for teachers and instructional leaders; and a comprehensive research agenda. These components were integrated by a strong focus on the ideas of algebra and issues related to learners with diverse cultural, language, and cognitive backgrounds. Principal Investigator: Tom Carpenter.

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**Mathematics Education Affiliate Faculty Projects **

This NSF-funded project focuses on how people learn the mathematics of space and motion. The broad aim of the work is to develop a theory of embodied mathematical cognition. Current foci include: (1) how teachers promote cohesion among representations in classroom geometry and engineering instruction, and (2) the role of action in mathematical thinking, especially in geometry and proof. Principal Investigators: Martha Alibali, Mitchell Nathan, Ricardo Nemirovsky (San Diego State University), Rogers Hall & Kevin Leander (Vanderbilt).

In this research, we will study the effects of instruction that links mathematical ideas in the domain of beginning algebra (i.e., in middle school). We will test several factors that may influence the effectiveness of teachers’ communication about links between ideas: (1) whether links are expressed in speech with linking gestures, gestures that do not link, or no gestures, (2) whether gestured links highlight element-by-element correspondences or more general relationships, and (3) whether links between ideas are expressed using simultaneous or sequential gestures. Principal Investigators: Martha Alibali & Mitchell Nathan.

This project will redesign an existing math curriculum based on cognitive principles and test the new curriculum in a randomized controlled trial. Our focus at UW-Madison is on integration of visual and verbal representations. Principal Investigators: Martha Alibali, Mitchell Nathan, Jim Pellegrino & Susan Goldman (Univeristy of Illinois at Chicago), Ken Koedinger (Carnegie Mellon), Julie Booth (Temple), Neil Heffernan & Cristina Heffernan (Worcester Polytechnic Institute).