DRK-12 CAREER Awards

Decades of reform efforts in mathematics education continue to fail Black and Latinx children, in part, because parents are excluded from decisions about school mathematics. Nonetheless, Black and Latinx families often persist in supporting their individual children, but a shift toward collective organizing among parents as change agents in school mathematics is necessary for meeting the needs of every student. This project explores possibilities for localized change lead by parents. By making explicit how to foster and increase Black and Latinx parents’ engagement in solidarity with community organizations and teachers, this project could provide a model for other communities and schools seeking to advance racial justice in mathematics education. Through critical community-engaged scholarship and in collaboration with ten Black and Latinx families, ten teachers, and two community organizations, the research team will co-design and co-study two educational programs aimed at advancing racial justice in elementary mathematics. The first program seeks to build parents’ capacity to catalyze change across classrooms and schools within their local communities; and the second program will provide teacher professional development that supports elementary teachers of mathematics to learn with and from Black and Latinx families.

Although there is significant evidence that sense-making through discourse is an essential part of learning, student talk typically makes up a small percentage of classroom time. Further, scholars are calling for the need to re-imagine classrooms for science discourse, away from ‘school science’ to hybrid spaces where students’ experiential ways of knowing, home languages, and cultural practices are viewed as resources for advancing their understanding of science phenomena (Emdin, 2011;  Gutiérrez et al., 1999; Rosebery et al., 2016).

This project is working towards this vision for equitable science discourse. Middle school science teachers serving in urban classrooms attend summer professional development and work in same grade lesson study teams throughout the academic year to plan a lesson around a science talk goal, observe one another’s classrooms, and reflect on how their students’ funds of knowledge serve as assets in science discourse activities (Calabrese Barton & Tan, 2009; Lewis et al., 2006; Moje et al. 2004). This project is based on the premise that when we center students and the contexts that are relevant to them, student engagement in science talk, and ultimately deeper understanding of science ideas and practices will be achieved.

Secondary students often associate their experiences in STEM disciplines, especially in mathematics, with negative emotions (e.g., dull and boring). Recently the Common Core State Standards of Mathematical Practice, such as making sense of problems and persevere in solving them, challenge teachers to design lessons that encourage students to persevere as they engage with complex mathematical concepts. To address this challenge, the MCLE Project draws on the affordances of narratives to explore how high school mathematics teachers can design mathematical stories, which interprets the unfolding mathematical ideas across a lesson as a narrative. To show how the mathematical content unfolds in a sequence of activities within their mathematical stories, the teachers created representations of the mathematical plots, such as storyboards. Each of the six participating teachers designed and enacted three MCLEs to offer different types of aesthetic experiences, such as surprise or wonder. The lesson topics for each MCLE were selected by the teachers so that it can fit within the curriculum of their courses. Using post-lesson surveys and selected student interviews, the student aesthetic experiences with MCLEs were compared with their experiences in lessons that were not designed using the mathematical story framework.

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.

Students with disabilities often experience educational disparities caused by opportunity gaps rooted in instruction that works to remediate students as opposed to creating spaces for students to access their own ways of reasoning from which to build understanding. This project documented initial or informal understandings of students with learning disabilities within targeted mathematical areas (e.g., fractions, ratio, whole numbers) and provided new understandings of how growth occurs and could be nurtured through the learning process. This project also designed, developed, and tested a new math intervention program that educators can use to support students with math difficulty and disability to advance their fractional reasoning.

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.

The project addresses three fundamental problems in professional development.  One problem is the lack of a centralized curriculum that affects teachers’ discussions pedagogical issues around specific content. The animations anchor teachers’ discussions of pedagogical issues by showing examples of problem-based lessons and promoting teachers’ development of an inquiry stance for understanding student thinking during problem-solving. A second problem involves teachers’ difficulties focusing their observations on student thinking. The video clubs allow for showcasing examples from various classrooms and provide opportunities for a deep analysis of student thinking when solving complex tasks. A third problem is that of providing opportunities for practice-based professional development. By having all teachers teach the lesson in their classrooms, the adaptation to lesson study supported teachers in applying what they learned in professional development sessions. Overall, the project enhances lesson study implementation in the U.S. by producing a viable model that engages teachers across school districts who teach the same content area, thus helping to overcome teachers’ sense of isolation by building a professional community.

Data models of variability inform inferences within STEM communities across disciplines. Making inferences that are informed by models of variability is an increasingly important learning goal for both science and mathematics education. For STEM professionals, though, these inferences involve interdisciplinary networks of ideas and practices that emerge from local questions and problems. But institutional boundaries in schools separate mathematics and science disciplines in ways that undermine interdisciplinarity, and students are rarely supported to develop a coherent image of how ideas and practices from different disciplinary communities inform one another.

Our project aims to support middle grades students to create, revise, and use models of variability to make inferences about ecological systems. We are developing innovative curricular infrastructures to help mathematics and science teachers coordinate their instruction and support students to use interdisciplinary networks of ideas as they make inferences about organisms in local ecological systems. We are using a design-based research approach in partnership with middle grades math and science teachers to iteratively design, implement, and study these curricular infrastructures. This project is designed to generate new knowledge about how to conceptualize and support interdisciplinary learning goals related to making inferences with data.

Science learning is often conceived in terms of knowledge and skills. This research draws on theories that recognize students’ identities and agencies as critical aspects of learning. From this perspective, we consider students’ linguistic and cultural differences as fundamental to learning and work on transforming science learning ecologies accordingly.

This program is based on an intervention called social positioning. Social positioning is a two-pronged construct: it encompasses both the learner’s perception of who they are and their ability to engage in science and how others in their immediate environment recognize these performances. We hypothesize that when students’ cultural and linguistic backgrounds are positioned as assets in their learning, this is likely to have a positive impact on their developing science identity. In contrast, when students’ backgrounds are positioned as a deficit, this impacts their self-perceptions and learning negatively. To test this hypothesis, we partnered with local schools, families, and university STEM faculty to design a two-week summer program, called STEAM Your Way To College. Close to 100 middle school students, who were identified as English language learners, will participate in this program for the next three years. 

When students perceive that their experiences are not relevant to their science and mathematics learning, they may view these fields as inaccessible to them. This in turn creates an obstacle to their engagement, which becomes particularly consequential for students from traditionally underrepresented populations. There is a pressing need, then, to prepare STEM teachers to be open and responsive to students’ diverse ideas and  experiences—including their linguistic, emotional, and cultural knowledge—and to leverage them as instructional resources. To address this need, this project aims to cultivate teachers’ “epistemic empathy” to promote an asset-based orientation towards all students as sense-makers, an orientation that may support teachers to be more responsive to students’ ideas and experiences. Using a design-based approach, the team designs and implements educative experiences for teachers aimed at fostering their attunement to and ways of leveraging learners’ ideas and emotions in science and mathematics. Further, the project explores how epistemic empathy shapes teachers’ views of their roles, goals, and priorities and how it influences their enactment of responsive teaching that pursues the productive beginnings in student work. Lastly, the project will investigate how teachers’ empathy shapes students’ engagement and responsiveness to each other’s experiences in the classroom.

This project supports ELs in STEM through making classroom discussions more accessible. We know from prior research that when students engage in classroom discussions, they can learn important mathematical concepts and develop a positive identity as a mathematics student. At the same time, we also know that many bilingual students who are classified as English learners, especially at the high school level, experience mathematics classes characterized by low-level mathematical and linguistic demands. Our goal is to transform this reality through a program of design research, done in collaboration with local teachers at a linguistically diverse school and student researchers from San Diego State University.

Our specific strategy is to research and develop design principles for high school classroom learning environments in which ELs participate in robust discussions. We started by observing mathematics classes during a "business as usual" phase and interviewing a linguistically diverse group of students about mathematics and about their experiences in school mathematics. We have taken what we learned from those observations and we are working with teachers to redesign the classroom learning environment to ensure all students can participate in classroom discussions. Three specific foci of our work are: 1) maintaining a consistent conceptual focus across the units we design, 2) integrating mathematical and language-related goals in each lesson, and 3) incorporating language supports in each lesson to make discussions available and fruitful for all students.

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.

Students’ success in algebra is a key factor for college admission and the potential access that a college degree offers for the future (Moses, 1995). Unfortunately, many students are not succeeding in algebra classes. Research over the past decade has shown that not only can young children think algebraically, but encouraging them to do so is beneficial to future learning of formal algebra.

In order to capitalize on this emergent algebraic thinking, however, grade 6-8 teachers of pre-algebra and algebra courses need to be able to recognize opportunities to elicit the algebraic character of arithmetic and pre-algebraic thinking during instruction. Work in this area has begun. Blanton and Kaput (2003) discuss developing teachers “algebra eyes and ears,” and in prior work I discuss developing teachers’ attention to children’s algebraic thinking. However, this work has primarily focused on children’s ideas as expressed verbally or in writing. Focusing only on verbal and written expression of ideas has limitations, especially for English learners and students who are neurodiverse.

In this project, I will investigate teachers’ attention to multimodal student algebraic thinking and design and investigate a video club PD that uses novel video annotation tools to help support teachers’ multimodal noticing.

The project idea originated from the misconception that it is inappropriate to provide challenging mathematics tasks such as word problems to EBs due to their lack of English proficiency. If EBs receive only easy tasks, such as simple computation worksheets, EBs are denied opportunities to engage in high-level cognitive demand tasks like problem-solving or reasoning tasks that cultivate a more profound understanding in mathematics. More importantly, providing rigorous learning opportunities to all students, including EBs, is crucial for equity in education. Although teaching EBs is becoming an unavoidable challenge for mathematics teachers as the EB population grows in the U.S., almost half of surveyed teachers believe helping EBs adapt to the school culture is not their responsibility; in fact, approximately 20% of the teachers refuse to modify their instruction for EBs. While the student population in the U.S. is becoming culturally and linguistically diverse, many teachers feel unprepared to teach EBs effectively, and as mentioned above, the research found teachers tend to position EBs as low performers in mathematics. Based on the belief that teacher perspectives are related to teaching practices, this study will examine how teachers position EBs and what quality of instruction they provide by implementing modeling tasks and situated PD.

Today’s middle school mathematics classrooms are marked by increasing diversity (National Center of Educational Statistics, 2018; U.S. Census Bureau, 2015). Traditional responses to diversity are tracked classes that contribute to opportunity gaps (Flores, 2007) and can result in achievement gaps. Differentiating instruction (DI) is a pedagogical approach to manage classroom diversity in which teachers proactively plan to adapt curricula, teaching methods, and products of learning to address individual students’ needs in an effort to maximize learning for all (Heacox, 2002; Tomlinson, 2005). Thus, DI involves systematic forethought rather than only reactive adaptation.

In addition, broadly speaking, students enter middle school at three different levels of multiplicative reasoning that have significant implications for how they build mathematical knowledge in middle school, including their fractions knowledge (e.g., Hackenberg & Tillema, 2009; Steffe & Olive, 2010), integers (Ulrich, 2012), and aspects of their algebraic reasoning (Hackenberg, 2013; Hackenberg & Lee, 2015; Olive & Caglayan, 2008). Teaching students at all of these levels is a significant challenge and requires research into student thinking at these levels.

In our project, we are using iterative design experiment methodology to study these issues with middle school students in after school settings and classrooms. We are also creating a community of teachers engaged in these issues through a teacher study group.

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.

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. 

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.

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. 

Middle school students need to understand complex scientific systems through language-intensive science practices, such as developing models and analyzing data. While many students struggle with science practices, the challenges are amplified for ELs who are simultaneously developing proficiency in English.

To support all students in linguistically diverse science classrooms, we partner with eighth-grade science and ESL teachers to develop, test, and refine inquiry-based science materials featuring interactive, dynamic visualizations in physical and life sciences.

Our visualizations explicitly depict unobservable processes, such as relationships between energy, matter, and physical states, while providing students with multiple representations of content (e.g., molecular and macro animations, text, dynamic graphs, and symbols) to help reduce linguistic barriers to science learning.

Our visualizations are supported by scaffolding approaches, such as automated feedback and prediction-reflection prompts, to engage ELs in discourse-rich science practices. For example, students design virtual experiments exploring photosynthesis and cellular respiration by using simulations to explore content, analyze data, and reflect on their work to develop written explanations. Students also use modeling tools to develop visual models of abstract phenomena, such as how water molecules move during a phase change. Automated feedback helps students revise their models and link macro to micro changes.

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.

An important barrier to persistence in STEM fields for marginalized groups, including women and ethnic minorities, relates to cultures in many STEM organizations, such as academic institutions, that foster discrimination, harassment and prejudicial treatment. This research will contribute to understanding the STEM educational climates in high schools and will help to identify factors that promote resilience in STEM contexts, documenting how K-12 educators can structure their classrooms to foster success of all students in STEM classes. We are examining inclusive STEM classes with attention both to college preparatory STEM classes as well as specialized STEM programs that are preparing youth for immediate entry into the STEM workforce upon graduation. Further, this work will explore how to create schools where students stand-up for each other and support each other so that any interested student will feel welcome in STEM classes and programs. This work is innovative in bringing a bystander intervention lens to classroom-based exclusionary experiences. Research on aggression demonstrates how powerful bystanders can be in interrupting unacceptable behavior, but no prior work has examined whether students can be empowered to serve as active bystanders in STEM classrooms to help create inclusive spaces for all students.

Despite that fact that proof is considered a central mathematical process, and policy documents have consistently recommended that proof be taught in school mathematics, success with proof remains elusive. A preponderance of evidence suggests that proof is challenging for teachers to teach (e.g., Cirillo, 2011; Knuth, 2002) and for students to learn (e.g., Chazan, 1993; Senk, 1985). Factors identified as contributing to these challenges include: impoverished curricula (Otten et al., 2014); teachers’ content and pedagogical knowledge (Knuth, 2002); and the lack of recommendations about how to scaffold proof so that students can be successful (Cirillo et al, 2017).

PISC draws on pilot study data and findings that suggest a promising approach to scaffolding the introduction to proof in geometry. Based on these findings, we developed the Geometry Proof Scaffold (GPS)⁠—a pedagogical framework that outlines eight sub-goals and corresponding competencies that can be taught one at a time. For example, prior to being asked to work on a proof, students learn to draw valid conclusions from given information or assumptions. The eight sub-goals in the GPS are: Understanding Geometric Concepts, Defining, Coordinating Geometric Modalities, Conjecturing, Drawing Conclusions, Using Common Sub-Arguments, Understanding Theorems, and Understanding the Nature of Proof.       

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 project broadens participation in computer science and computational thinking by preparing all preservice teachers at Georgia State University to integrate computing activities into their courses. The impact of preparing all teachers to use computing activities is that students receive exposure to multiple computing activities throughout preK-12 and understand how computing is used in all disciplines. Even if students do not pursue a job in computer science, they are better prepared to use computing solutions in their chosen profession and in their personal lives. Integrating computing activities also gives teachers new tools to teach within their discipline, and the computing activities are co-designed with teacher preparation faculty to ensure that they are authentic to the primary discipline. This project is unique because it is integrating computing activities across disciplines and grade bands simultaneously. In this context, researchers can explore which computing concepts and practices are universal and should be considered part of a general computational literacy, a topic that is debated on computing education researchers.

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.

The UJIMA project expands our understanding of the mathematical development of Black youth as a demographic, as well as the curricular supports that can move a mathematics identity from a private, neutral, and implicit space into a public, political, explicit space of learning.