Mathematics

In our project we design and study opportunities for mathematics and science teachers to coordinate their instruction to support a more coherent approach to teaching statistical model-based inference in middle school. We aim to help more students develop a deeper understanding of ideas and practices related to measurement, data, variability, and inference.

This project examines how instructional activities involving quadratic functions influence students’ prior ways of reasoning about linear functions, and develops and refines instructional products for teaching quadratic functions in ways that influence students’ prior ways of reasoning about linear functions in predictable and productive ways.

This project advances the understanding of teaching and learning of algebra in grades K through 12 by using a methodology that leverages the cumulative power of an analysis of many studies on a topic. This work will synthesize results aggregated from 40 years of research in the field of mathematics education and develop a unified framework to inform parents, students, teachers, other educators, and researchers.

We will share the results of our designed based research project on how to design secondary mathematics lessons which shift the aesthetic opportunities of students. We worked with a group of six high school math teachers and used mathematical story framework to explore how mathematics lessons on topics that are typically described as boring or dull by students can instead be described as surprising or intriguing.

This design-based research project investigates ways to understand and cultivate science and mathematics teachers’ “epistemic empathy”—their capacity for tuning into and valuing students’ intellectual and emotional experiences in constructing, communicating, and critiquing knowledge. The project team develops educative experiences aimed at cultivating teachers’ epistemic empathy, examines the role of such empathy in facilitating responsive teaching, and explores how epistemic empathy can promote more equitable and humanizing learning environments.

Project CARe’s goal is to explore how new technologies create a path into algebra that allows students to build algebraic reasoning and knowledge from their intuitive covariational reasoning, which entails conceiving two quantities changing together. For example, Project CARe explores how students can learn to solve equations by comparing two changing quantities in a dynamic digital depiction of a real-life situation.

In this project, we investigate haptic systems that are readily available for rendering visual STEM content through sight, sound, and touch. We use combinations of visual display, text-to-speech, vibrations, and the movement of one’s hands for interacting with STEM content (such as charts and graphs in math and science-based simulations) multimodally on touchscreens. Our investigations extend into "smart" tangible manipulatives that pair with interactive PhET simulations and enable rich kinesthetic manipulation of on-screen content through touch.

Through critical community-engaged scholarship with ten Black and Latinx families and two community organizations, the PI is co-designing and co-studying an educational program aimed at advancing racial justice in elementary mathematics. Specifically, the program seeks to build parents’ capacity to catalyze change across classrooms and schools within their local communities. I share preliminary findings from the program’s initial year and the development of parent-community-university partnerships that promote a shared vision for racial justice in mathematics.

Over the last five years, the Responsive Math Teaching Project has developed and refined a sustainable model for the development of mathematics instructional leadership through a research-practice partnership with a network of 14 urban under-resourced K-8 schools. Teacher instructional capacity is built through developing new visions of mathematics teaching and learning, practice-based pedagogies of enactment and reflection, and mentored engagement in collaborative lesson design and enactment.

Our work focuses on developing teacher knowledge within a PLC that uses the AIM-TRU learning cycle to support teachers’ engagement with mathematical tasks and video cases. The learning cycle is grounded in the Teaching for Robust Understanding (TRU) framework (Schoenfeld, 2014) and utilizes Charles’s (2005) Big Mathematical Ideas within Formative Assessment Lesson (FAL) content. Teacher conversations were analyzed with respect to congenial and collegial characteristics with the latter resulting in greater alignment with TRU.