Projects & Collaborators

Current projects:

Fractions & Algebra Project

Algebra is a critical point in school mathematics that often leads to failure for many students. There is growing evidence that fractions may help prepare students for success in algebra. Studies across mathematics education and psychology have shown this fractions-algebra link, but it is not clear why this connection exists. The FracAlg project aims to investigate which aspects of fractions may be related to/support which aspects of algebra by bringing together measures from mathematics education and psychology that have not yet been used with the same students.

In Phase 1, we investigated these questions with students in 7th, 8th, and 9th grade. Students took part in 3 online sessions and completed fractions and algebra tasks as well as covariate measures (e.g., working memory, math fluency, math anxiety).

Now we are in Phase 2 of the project. Phase 2 is a longitudinal project that involves meeting with a new sample of students seven times across 6th, 7th, and 8th grade. Using measures refined in Phase 1, this longitudinal study allows us to answer questions about how the fractions-algebra relationship evolves and changes over time.

You can read more about our project on the FracAlg website.

Biogames

In the early elementary grades, children are expected to learn about the diversity of life on Earth, including the remarkable variability among individuals of the same kind. An appreciation of biodiversity, including both random and systematic variability within species, and systematic changes that organisms undergo over their lifetimes, sets the stage for understanding the process of evolution by natural selection. Yet, children and adults greatly underestimate the amount of variability that exists within species across individuals, over the lifespan, and across generations. At its core, understanding biodiversity involves relational reasoning: discerning relevant relationships within and among biological kinds.

The goal of the Biogames Project is to explore children’s understanding of biological concepts and relational reasoning through play using simple card games. In this study, we work with elementary-aged students and their caregivers. RAs on this team are involved in running participant sessions, transcribing, and coding video and data with opportunities for weekly team meetings, design, and mentoring if interested.

In collaboration with: University of Rochester, College of the Holy Cross, and Worcester State University.

Substitutive Equivalence Project

Algebra is a critical point in school mathematics that often leads to failure for many students. Prior research has shown that having a strong understanding of the equal sign is associated with success solving algebraic equations and that earlier equal sign knowledge predicts later success in algebra. A “strong understanding” has generally meant viewing the equal sign as a relational symbol indicating the sameness of two expressions or values. This is in contrast to an operational view of the equal sign. An operational view of the equal sign is a misconception that the equal sign means “write the answer.” This misconception leads students to write “10” in the blank given 6 + 4 = ___ + 3.

More recent research suggests that there is more to a relational view of the equal sign than just the sameness understanding. Researchers posit that another conception of the equal sign—the substitutive conception—is also important for success in algebra, and a small number of studies support this claim. Students with a substitutive view of the equal sign understand that if we know a = b, then a can be substituted for b and vice versa. For example, if we are given 14 = 2x + 7, then 14 can be substituted for 2x + 7 and vice versa. If we know 98 = 90 + 8, then 90 + 8 can be substituted for 98 and vice versa.

The SubEq project is concerned with further investigating links between students’ equal sign understanding and success with algebraic tasks as well as investigating potential relations with “precursor skills” such as understanding of arithmetic properties, flexibly representing numerical quantities, and mental arithmetic.

Sensory, Neurodiversity, and Learning Group

The sensory, neurodiversity, and learning sub-group in the CD&C lab investigates the relationship between sensory experiences and math concepts. We are motivated by children’s different sensory profiles and needs across all children, including blind and low vision and neurodivergent kids. We want to explore how math instruction could offer new forms of sensory stimulation that could help more kids learn key math concepts, such as using the bodily sense of balance or haptics. Through design-based research, we build new things we think will help students learn based on learning theory, then study what happens, then revise the design based on what we learn, then study what happens again, in an iterative cycle. RAs on this team are involved in collecting, transcribing, and coding video and pre/post data with opportunities for quantitative, design, and writing work if interested.

To read about ongoing projects, check out: https://sofiatancredi.com/balance-board-math/ and https://sofiatancredi.com/teletangibles/

Past work:
Computer-generated woman pointing to a graph. Diagram of the life cycle of a ladybug.

Fostering conceptual understanding and skill with an intelligent tutoring system for equation solving

Collaborators: Vincent Aleven, Carnegie Mellon University
This project will develop a new intelligent tutoring system for algebra equation solving that will foster learners’ acquisition of integrated conceptual and procedural knowledge. The new system will incorporate a range of conceptually-oriented activities, including self-explanations, visual representations, and “warm-up” to activate relevant prior knowledge.
Funded by the National Science Foundation, 6/1/18 – 5/31/21

Cultivating Knowledge of Mathematical Equivalence

Collaborators: Percival Matthews, University of Wisconsin; Ana Stephens, University of Wisconsin
This project investigates the effectiveness of spaced, conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking.
Funded by the National Science Foundation, 9/1/18 – 8/31/21

The role of visual representations in children’s learning about biological variability

Collaborators: Karl Rosengren, University of Wisconsin; Chuck Kalish, University of Wisconsin
The broad aim of the current proposal is to investigate the role of visual representations in promoting (or interfering with) learning and transfer about biological variability. We will focus on two types of visual representations: lifecycle diagrams and genetic diagrams.
Funded by the National Science Foundation, 9/1/18 – 8/31/21

Connecting Mathematical Ideas through Multimodal Instruction

Collaborators: Mitchell Nathan, University of Wisconsin; Jee-Seon Kim, University of Wisconsin; Voicu Popescu, Purdue University; Nicoletta Adamo-Villani, Purdue University; Susan Wagner Cook, University of Iowa
This project developed and tested an animated teacher avatar that gestures. Current studies are investigating the role of the teacher’s gestures in helping students attend to key features of problems and to links between representations.
Funded by the Institute for Education Sciences, 6/1/13 – 12/31/18

Relations between Gesture, Action and Thinking

Collaborators: Autumn Hostetter, Kalamazoo; Sotaro Kita, University of Birmingham (UK)

Cartoon of children discussing how to solve 9 + 7 + 5 = __ + 9.