Argumentation is an essential practice that is relevant to all STEM-related fields. Encouraging students to formulate and test conjectures supports their ability to critically question claims, which is a critical habit in the 21st century.

Facilitating argumentation in elementary and middle grades mathematics is challenging for many teachers. Teacher education programs have then a great deal of responsibility in preparing prospective teachers to effectively respond to curricular visions about argumentation in mathematics teaching and learning. The objective of this program of research is to examine how middle school prospective teachers’ knowledge of mathematical argumentation develops in a teacher preparation program. Cross-sectional and longitudinal studies of prospective teachers’ models or systems of interpretation of mathematical argumentation are conducted to provide an understanding of the trajectory that captures how prospective teachers develop their knowledge of mathematical argumentation throughout their university mathematics and pedagogy courses, and into their student teaching.

The main issue our project addresses is how students’ reasoning about concepts that are not new to them changes when learning about a new concept, and we call this phenomenon backward transfer. We specifically focus on mathematics, but believe our backward transfer research is highly relevant within and across STEM content domains more broadly. For instance, this research is relevant to how learning about the relationships between position, velocity, and acceleration in physics could influence students’ reasoning about derivatives and integrals in calculus, and vice versa.

One way our project has been innovative is by being the first to use contrasting cases to examine backward transfer (i.e., comparing distinctly different instructional environments). By comparing backward transfer across contrasting cases (e.g., business-as-usual classroom environments, summer math camps), we have gained insights into backward transfer we would not have gained had we examined a single instructional environment alone. Another way our project has been innovative is by being the first to develop and test mathematics activities designed to teach students new concepts, while simultaneously enhancing their reasoning about concepts that are not new to them.

Algebra readiness is recognized as an important gatekeeper to future success in mathematics. However, many U.S. students are ill-prepared for the study of algebra, indicating a great challenge facing elementary teachers in preparing students for their entry into algebra. 

This project aims to help address this issue by identifying necessary AKT that will support teachers to better teach early algebraic concepts, especially those fundamental mathematical ideas. Fundamental ideas such as inverse relations and basic properties are systematically emphasized by the Common Core; however, there is a lack of sufficient guidance on how these fundamentals can be effectively taught to students. Our project contributes to narrowing this gap by identifying an evidence-based approach that can be used to develop students’ algebraic thinking and beyond.

In addition, our project takes the middle ground of two long-debated research assertions: teaching through worked examples and teaching through problem-solving. As indicated by our project lessons, especially those from China, the above two debated assertions can be seamlessly integrated into a lesson to support student learning. By actively engaging students in working out an example task that is situated in a word problem context, students can construct a mental schema to solve subsequent problems.

Despite decades of reform efforts, research indicates that classroom learning for students remains largely procedural, undemanding, and disconnected from the development of substantive scientific ideas. Furthermore, access to high-quality science instruction that promotes such complex thinking is far scarcer for students of color in communities with high concentrations of families living in poverty compared to their white counterparts. Research shows that many students from disadvantaged communities experience instruction geared to promote development of rote skills, working at a low cognitive level on fill-in-the-blank worksheets and test-oriented tasks that are profoundly disconnected from the skills they need to learn to be successful citizens. This is especially alarming in the United States, as students of color are projected to comprise 54 percent of total enrollments in elementary and secondary schools by 2024 (Kena et al., 2015). The purpose of this project is to reduce the learning opportunity gap in secondary science classrooms by building a sustainable research–practice partnership over five years.

This project develops a new way of engaging teachers in professional learning that is situated in their classrooms while they perform the tasks of their paid employment. Traditional professional development structures frequently place financial and professional pressures on teachers, which limits participation. Rural teachers in particular may have fewer opportunities due to barriers of distance, limited resources, and lack of available staff. Further, they are most likely to be underqualified and most likely to spend their entire teaching careers at their first district prospectively teaching multiple generations of students from their community. The state of Hawaii has a high proportion of such rural schools and a shortage of STEM teachers especially in the area of computer science. This project will investigate a professional development model using fading scaffolds (support that is gradually reduced over time) as part of participants’ paid summer school teaching. Through this model, 20 rural teachers will learn to integrate computational thinking, coding, and science content while working with students from their own communities, with 10 becoming master teachers supporting others throughout the state. Improving teachers’ ability to prepare students to benefit from opportunities in STEM and computing will advance students’ opportunities for future prosperity. 

Engineering design projects can provide authentic and relevant contexts for students to learn and engage in mathematics and science. However, many mathematics and science teachers need support to implement engineering design projects and engage students in engineering design practices in classrooms. This project explored the use of a computer-based learning environment (WISEngineering) to support students and teachers to implement engineering design, based on technologies for knowledge integration from the Web-based Inquiry Science Environment (WISE; wise.berkeley.edu). WISEngineering projects explicitly scaffold engineering practices for students and teachers, including tools to help students define problems, generate ideas, and test and revise ideas. WISEngineering also incorporates simulations and visualizations to help students learn underlying scientific and mathematics concepts. To support teachers implementing design projects, the project also explored the use of automated feedback within WISEngineering to teachers to help teachers notice and respond to students’ ideas within design contexts.

The two main issues we’re addressing through this project are (1) how early math language skills impact the development of math skills broadly, and (2) how to test these mechanisms in methods that can be transformed into school-based interventions that are easy to implement for teachers. We’re using picture books with built-in dialogic reading prompts to naturally scaffold instruction across multiple readings. At the completion of the project, we’ll be working to make the books available in multiple formats so they are accessible to a broad range of schools and families.

Scientific activity is driven by the need to manage uncertainty; uncertainty not only about how to explain the world, but how to represent the world in the form of an experiment, what to measure, and how to convince peers to see what the scientist wants them to see. Yet elementary science investigations typically reflect little of the uncertainty that scientists grapple with. This project seeks to develop a conceptual framework and set of tools that allow teachers and elementary students to engage productively with uncertainty in empirical activity⁠—for example, uncertainty about how to represent phenomena in investigations, how to develop measures, and how to make sense of what investigations don’t explain. We use methods drawn from design-based research, co-design, and implementation research to examine existing investigations and students’ experience of them, re-design so that students can grapple with key uncertainties, and understand how to develop learning environments where uncertainty supports conceptual innovation and meaningful engagement in science practices such as investigation, argumentation, and explanation. We partner closely with a local school district and work with district leaders and teachers to develop and implement materials, analyze student engagement and learning, and develop professional learning experiences.

One challenge that students face when learning about integers and integer operations is building on and also modifying their prior understanding of whole numbers. Through our project we seek to clarify how students build upon and revise their whole number knowledge to learn and develop strategies with integers depending on the types of contrasting cases they experience. For example, students who first learn adding two negative integers in contrast with two positive ones (e.g., -3 + -5 vs. 3 + 5) may overlearn that problems with negative integers have negative answers. Therefore, they may be more likely to think that -3 + 5 is -8.  On the other hand, students who first learn adding a positive integer to a negative integer (e.g., -3 + 5) may overlearn that they should always count up in the number sequence. Therefore, they may be more likely to think that -3 + -5 is 2. Through randomly assigning students to experimental conditions where they evaluate different contrasting cases of integer problems, we evaluate the role problem type sequence, with connections among language, operations, and symbols (e.g., + -2, plus negative two, and more negative two), plays in students’ learning of integer addition and subtraction. 

Children from “non-dominant communities” (Gutiérrez & Rogoff, 2003)—including Appalachian communities—are particularly affected by issues of equity and access to early science learning opportunities. Therefore, supporting elementary science teaching is key, as it can either open up or shut down opportunities for children to learn in science. An ultimate goal of this research is to impact science teaching in Appalachian communities in order to open up science learning opportunities for all children.

In this context, this research examines teachers’ noticing of children’s thinking in science and focuses on designing web-based teacher learning materials surrounding this teaching practice. It is grounded in constructivist and situated theories of children’s learning—children draw on rich and varied cultural resources to form ideas about the natural world and these ideas form the basis for science learning. Thus, teachers’ noticing of these rich and varied resources embedded in students’ thinking should be central to the work of teaching science.

This project involves both interpretive participant observational research and design-based research methodologies with a goal of building theory of teacher knowledge and practice surrounding teachers’ noticing that can be leveraged in the design of teacher learning materials and experiences—specific to an Appalachian context.