How Dynamic Gesture and Directed Actions Contribute to Mathematical Proof Practices

Principal Investigator (Jul 2016 to Jun 2020)

Funding: U. S. Dept. of Education-Institute of Education Sciences.

Collaborators: Candace Walkington (Southern Methodist University) and Peter Steiner (UW)

We explore how directed actions—body movements that learners are instructed to formulate—combine with language systems to produce co-speech gestures, which reveal abstract and generalizable mathematical thinking. An emerging literature on cognition and mathematics education shows that mathematical ideas can be learned through action-based interventions. In addition to speech, learners’ understandings can be encoded and expressed through physical action, often in the form of gestures. There is value for basic research to inform the design of effective educational innovations, and understand the embodied nature of mathematical cognition and learning. This dual focus drives the current research proposal. Recent research has shown that directed body motions can lead to improvements in geometry theorem proving even though students claim no awareness of the relevance of the actions to the mathematical tasks (Nathan et al., 2014), and that verbal prompts to connect the actions to the mathematical ideas further improve student proof practices. Thus, both directed actions and pedagogical language are plausible malleable factors for influencing mathematical reasoning. Our work is novel in that it extends the consideration of embodied approaches to complex reasoning in a highly conceptual, pre-college mathematics domain—geometric proof production.

Nevada Math Project

Collaborators: Teruni Lamberg (PI; Univ Nevada-Reno), Rebecca Boncoddo (Central Connecticut State College). May 2016 to May 2017.

The Nevada Mathematics Project is a collaborative statewide mathematics initiative to improve math instruction and student achievement in Nevada.  Our goal is to support 140+ teachers from every school in the State of Nevada to improve math instruction and STEM integration, and develop math leaders. Teachers will learn to combine effective uses of instructional gestures with the Next Generation Science Standards: Science & Technology, Physical Science and Personal and Social Perspectives (NGSS) with a special focus on nanotechnology. We are delighted to have partnered up with Northwestern University, and RHK Technology, a business partner. We will also be working with a team from the University of Wisconsin at Madison. Our long-term goal is to transform Nevada and learn from that process.

Connecting Mathematical Ideas through Animated Multimodal Instruction

Co-Principal Investigator (Jun 2013 to May 2017)

Funding: U. S. Dept. of Education-Institute of Education Sciences.

Collaborators: Martha Wagner Alibali (University of Wisconsin-Madison), Voicu Poescu (Purdue), Nicoletta Adamo-Villani (Purdue), and Susan Cook (U Iowa).

We develop avatar-based instruction for experimental studies with middle-school student participants to test hypotheses about how to most effectively link ideas in algebra instruction. 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 among ideas are expressed using simultaneous or sequential gestures. Once we identify the most effective ways of linking ideas in instruction, we will compare avatar-based linking instruction to instruction provided by human teachers. Finally, we will explore whether the avatar can be used to help human teachers improve their instructional communication about links between ideas.

National Center for Cognition and Mathematics Instruction

Principal Investigator (Sep. 2010 – Aug. 2016; sub-award with WestEd)

Funding: U. S. Dept. of Education-Institute of Education Sciences, Education Research and Development Centers Program.

Collaborators: Martha Wagner Alibali (University of Wisconsin-Madison), Jennifer Cooper (University of Wisconsin-Madison), Virginia Clinton (University of Wisconsin-Madison), Steve Schneider (PI, WestEd), James Pellegrino (UIC), Susan Goldman (UIC), Ken Koedinger (Carnegie Mellon), Neil Heffernan (WPI), Julie Booth (Temple), Diane Briars (Pittsburgh Public Schools), and Shandy Hauk (WestEd).

Although cognitive research and theory have explored the nature of competence and its development in multiple areas of the curriculum, this substantial knowledge base has had only a limited influence in shaping the design of most K-12 curricular materials and instructional practices. Through this proposal for the National Center for Cognition and Math Instruction (NCCMI), we propose to rectify this problem by aligning the knowledge base on cognition, instruction, and student learning with a complementary knowledge base explicating important goals and outcomes for the middle school mathematics curriculum. Our proposed Center brings together leading experts with the goal of redesigning components of a widely-adopted middle school mathematics curriculum – Connected Mathematics Project (CMP) – using established, evidence-based principles derived from randomized experimental studies in classrooms and controlled laboratory settings. Our objective is to enhance the conditions of instruction and improve learning outcomes for important and challenging math concepts and skills. We will focus on four primary design principles: (1) combining graphics with verbal descriptions in ways that promote the integration of concepts, (2) structuring practice to interleave worked examples, (3) carefully spacing the learning of critical content and skills over time, and (4) using focused feedback on quizzes and homework to promote student learning.

IES Postdoctoral Training Fellowship Program

Mathematical Thinking, Learning and Instruction

Principal Investigator (Aug. 2010 – Jul. 2017)

Funding: U. S. Dept. of Education-Institute of Education Sciences (IES)

Collaborators: Martha W.  Alibali, Amy Ellis, David Kaplan, Chuck Kalish, Anita Wager & Eric Knuth.

There is a clear and recognized need for well-trained mathematics education researchers who are able to conduct scientifically based qualitative and quantitative research that addresses immediate and long-term questions about the efficacy of educational programs and policies, and who can provide an empirical basis for future designs of curricula, assessments, instruction, and learning environments. The training program emphasizes the interdisciplinary nature of the mathematics education research opportunities at the University of Wisconsin–Madison. It addresses broad research interests, including: Exploratory research, basic processes in learning and instruction, development and innovation, efficacy and replication, and measurement.

Other Current Projects

Gesture and Mental Model Formation

Collaborator: Chelsea V. Johnson Martinez

This line of research investigates the role of body-based resources (hand gestures) in complex cognitive processes. We propose the Gesture as Model Enactment (GAME) theory. Undergraduates (N = 22) who read an illustrated tutorial on the human circulatory system gestured more frequently when answering inference-based questions about the text that drew upon their situation models than when answering questions that drew specifically from information from the passage’s text base. Undergraduates (N = 48) who read a non-illustrated version of the scientific text developed a similarly strong mental model as those reading from the illustrated text, but gestured more frequently, suggesting gestures served a compensatory role during model formation. Undergraduates (N = 79) directed to adhere to a secondary tapping task that continually changed patterns exhibited lower performance on model-based inference questions than participants in two comparison groups--those performing a simpler tapping task, and control participants with no secondary task--suggesting a weaker situation model of the text was formed when interfering with gesture production.  Findings manipulating text and gesture production show that gesture use can reveal aspects of the contents of readers’ mental models and causally influence their construction when learning from text.

Growing the Learning Sciences: Brand or Big Tent?

Collaborators: Nikol Rummel (Ruhr-Universität Bochum) and Ken Hay (Indiana University). Printed in Reflections on the Learning Sciences 2016.

The aims of the learning sciences (LS) are to understand the nature of learning from a broad range of perspectives, and to shape the ways that learning environments and resources are designed and used (Nathan & Alibali, 2010). LS incorporates both systemic and elemental approaches to investigating questions about learning, as a complement to the primarily elemental approach emphasized in cognitive science research. Thus, its greatest potential is in the integration of systemic and elemental perspectives. As the field of LS matures and newly formed graduate programs self-identify as LS, several questions take on importance: Does LS have a common core? Should it? What are the ramifications for LS graduate programs? Participants will review common and varied approaches to LS graduate education from existing programs and explore the tensions within interdisciplinary education and trade-offs between adherence to a common core (maintaining an LS “brand”) or a broadly inclusive model (“big tent”).