Martha W. Alibali, Ph.D. - US grants

This is a collaborative research project between three universities. The project is a comprehensive, systemic research and development program addressing three inter-related tiers of study: student learning and development; teacher beliefs, knowledge, and practice; and professional development. The project is grounded in both sound theory of how students develop algebraic reasoning and acquire domain knowledge and skills and in the beliefs and existing practices of teachers. In the student tier a detailed developmental model of students' evolving algebraic reasoning and skill acquisition will be constructed concentrating on the transition from arithmetic to algebraic reasoning. In the teaching tier a promising pedagogical approach, Bridging Instruction, will be tested. In the professional development tier a teacher professional development prototype will be implemented. The prototypeT extends an existing technology based approach. It enables the evaluation of a scalable model of teacher professional development. Technology is a central aspect of this project. The findings of this research will be implemented into a coherent educational program for students and teachers using Algebra Cognitive Tutors and the STEP web teacher professional development environments.

Mathematical reasoning requires understanding connections between different representations of mathematical information. The way mathematical representations are linked in the classroom may determine whether students come to understand important mathematical principles and procedures. Our past research showed that teachers use various forms of visual scaffolding to link different mathematical representations. The purpose of this project is to understand how variations in teachers' visual scaffolding affect students' learning. Our specific focus is on the nonverbal supports that teachers produce in instructional episodes that link related representations of mathematical information. In particular, we examine those nonverbal supports that serve to ground ideas in the physical environment or in familiar actions, experiences or representations. The research has three aims: (1) to investigate whether students' learning is facilitated if teachers ground the to-be-linked ideas with hand gestures (as opposed to using speech alone); (2) to examine whether certain types of nonverbal supports are especially beneficial for learning (specifically, redundant vs. complementary gestures, and pointing vs. representational gestures); and (3) to examine whether gestures offer a "special" way to visually scaffold ideas, in the sense that they are more effective at doing so than other, non-gestural methods of visual scaffolding. We will address these aims in experiments with middle school students learning about linear equations. The experiments will involve video lessons that vary the teachers' gestures or the medium used to highlight aspects of the linked representations (hand gestures or digital icons). We will assess students' conceptual and procedural knowledge of linear equations before and after the lessons, so that we can evaluate how variations in teachers' visual scaffolding affect students' learning. We will also conduct a pilot study to prepare us to extend this line of inquiry to college students learning about statistics. This pilot study will investigate how teachers link representations using speech and gesture in instruction about confidence intervals.

This work will contribute to our scientific understanding of learning and instruction from an embodied cognition perspective. By experimentally manipulating the ways in which relations between mathematical ideas are conveyed, and exploring the consequences for learning, we will gain a deeper understanding of the cognitive processes involved in acquiring mathematical understanding. This work will provide an empirical basis for recommendations about how teachers can use visual scaffolding effectively.

NRT DESE: Learning, understanding, cognition, intelligence, and data science (LUCID)

In modern life there are many situations requiring people to interact with computers, either so that they may learn from the machine or so that the machine may learn from them. The applications in education, industry, health, robotics, and national security hint at the enormous societal and economic benefits arising from research into the technologies that promote learning in both people and computers. Yet the potential has been difficult to realize because such research requires scientists with expertise in quite different fields of study. While computer scientists receive training in complex computational ideas and methods, they know little about how people learn and behave. This National Science Foundation Research Traineeship (NRT) award to the University of Wisconsin-Madison will prepare trainees with data-enabled science and engineering training to simultaneously understand computational theory and methods, the mechanisms that support human learning and behavior, and the ways these mechanisms behave in complex real-world situations. The traineeship anticipates equipping forty (40) doctoral students with the skills and expertise necessary to advance our understanding of human and machine learning and teaching, through a new training program that focuses on learning, understanding, cognition, intelligence, and data science.

This project will train doctoral students from computer science, engineering, cognitive psychology, and education sciences, with the goal of promoting a common knowledge base that allows these scientists to work productively across traditional boundaries on both basic research questions and practical, real-world problems. The traineeship will include several graduate training innovations: (1) a project-focused "prof-and-peer" mentoring system where scientists work in cross-disciplinary teams to address a shared research problem, (2) close involvement of partners in industry, government, and non-profit sectors to develop research problems with real-world application, (3) an information outreach effort that trains scientists to communicate with the public, industry, and policy-makers through traditional and new media outlets, (4) a flexible development plan that allows each trainee to garner the cross-disciplinary expertise needed to advance a particular research focus, and (5) new mechanisms for recruiting and retaining under-represented groups in STEM research. This training will prepare US scientists to compete globally at the highest levels for positions in science, industry, and government, in a growth sector of the 21st century knowledge economy.

The NSF Research Traineeship (NRT) Program is designed to encourage the development and implementation of bold, new, potentially transformative, and scalable models for STEM graduate education training. The Traineeship Track is dedicated to effective training of STEM graduate students in high priority interdisciplinary research areas, through the comprehensive traineeship model that is innovative, evidence-based, and aligned with changing workforce and research needs.

This award is supported, in part, by the EHR Core Research (ECR) program, specifically the ECR Research in Disabilities Education (RDE) area of special interest. ECR emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.

This project will develop and test the effectiveness of a semester-long conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Participants in the research will be elementary- and middle- school students. Although many brief, single-session laboratory studies have suggested effective ways to promote equal sign knowledge in the short term, these studies have generally failed to produce practical guidelines for use by regular classroom teachers. This project will apply findings from laboratory studies over a longer time period with the goal of packaging a practical approach to developing students' knowledge of the equal sign for classroom teachers. The hypothesis is that improved equal sign knowledge will lead to improved access to algebra, an important pathway into higher mathematics and science that provides access to Science, Technology, Engineering, and Mathematics (STEM) fields that help power modern society.

This project will explore the effectiveness of spaced, conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Multiple experimental studies have shown that brief, conceptually-based instructional interventions can lead to improvements in children's equal sign knowledge. The proposed research will test whether spacing such interventions over time can lead to more substantial and long-term gains in equal sign knowledge, and whether such knowledge, in turn, fosters algebraic reasoning. One component of the research will aim to optimize the conceptually based intervention. The other component will be a study that investigates the effects of the intervention over time, using a crossover design. The research will employ a measure of equal sign knowledge that is more sensitive than most commonly used measures, allowing for detection of relatively fine-grained gains in response to the instructional intervention. In total, the work will contribute to the field's understanding of how to improve equal sign knowledge and understanding of the causal impact of equal sign instruction on student competence in algebra.

This project is co-funded by the Discovery Research preK-12 program (DRK-12) that seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.