This 3-year project seeks to build the essential preliminary components necessary to investigate the impact of early algebra education on students’ algebra readiness in the middle grades. In particular, the goals of the project are fourfold: (1) To coordinate (empirical) research, curricular design perspectives, and mathematical perspectives to design a curricular learning progression [CLP] that identifies core algebraic concepts and articulates their progression in children’s thinking across upper elementary and middle grades (grades 3-7); (2) Using the CLP, to design grade-based assessments of students’ algebra understanding for upper elementary and middle grades (grades 3-7); (3) To conduct a preliminary efficacy study concerning the impact of an early algebra intervention based on the CLP and measured by the assessments developed in Goal 2; and (4) To use the CLP and associated tasks to inform the design and implementation of content-based teacher professional development.
Director: Eric Knuth
This longitudinal study seeks to understand how middle school students acquire and develop their understandings of what constitutes evidence and justification in mathematics and how such understandings can be extended and refined, and to develop professional development materials designed both to enhance teachers' understandings of proof and to support them in fostering the development of students' competencies in justifying and proving.
Director: Eric Knuth
This longitudinal study seeks to understand the development of middle school students' algebraic reasoning, to understand the conditions and pedagogy necessary to facilitate students' transition from concrete, arithmetic reasoning to abstract, algebraic reasoning, and to develop professional development materials designed to support teachers in fostering the development of students' algebraic reasoning.
Directors: Eric Knuth & Martha Alibali
The purpose of this collaborative three-year 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.
Director: Amy Ellis
Diversity in Mathematics Education (DiME) is one of a network of Centers for Learning and Teaching (CLT) funded by the National Science Foundation. DiME/CLT is building an integrated program to develop and enhance the instructional workforce from kindergarten through graduate school. The program consists of three interrelated components: a doctoral/postdoctoral component; a teacher education component for teachers and instructional leaders; and a comprehensive research agenda. These components are integrated by a strong focus on the ideas of algebra and issues related to learners with diverse cultural, language, and cognitive backgrounds.
Director: Tom Carpenter
This project investigates how mathematics teachers use visual scaffolding, including pointing, gestures, diagrams, and other methods, and explores whether and how such methods of highlighting visual information influence students’ learning. We will address these issues in the context of middle school mathematics instruction in the domain of early algebra.
Director: Martha Alibali
Mathematics education research paints a bleak picture of students’ abilities to reason
mathematically. In contrast, cognitive science research has revealed surprising
strengths in children’s abilities to reason in non-mathematical contexts, suggesting that
children are capable of developing complex and abstract causal theories, and of using
powerful strategies of inductive inference. Thus, this raises something of a paradox:
Why are children so good at reasoning in non-mathematical contexts, yet so poor at
reasoning in mathematical contexts? The purpose of the proposed research is to
explore this seeming paradox. In particular, we seek to extend the cognitive science
research into the domain of mathematics education and, more specifically, into the
domain of middle school mathematics. We believe, first, it is important to understand
both the strengths and weaknesses of students’ reasoning in and out of mathematics
and, second, that students’ ways of reasoning in non-mathematical contexts may
provide an important bridge to improving their mathematical ways of reasoning.
Directors: Eric Knuth, Amy Ellis, & Charles Kalish