Research Opportunities

This ongoing project seeks to increase the field’s understanding about how students learn to do mathematical modeling, and then use that information to improve the teaching of mathematical modeling. Learning to do mathematical modeling means that students know (i.e., can justify) that their models align with real world conditions and with their mathematical schema This project uses qualitative, quantitative, and mixed methods to study the interactions among modeling problems, student reasoning, and teachers’ attempts to draw out or change student reasoning patterns.  The goal is to draw conclusions about what scaffolding (support) moves a teacher might make to progress the student’s reasoning. (this project is funded by an NSF IUSE, 8/12/2018-8/31/2025). 

Knowledge of differential equations and/or dynamical systems is required. Basic knowledge of quantitative and qualitative methodologies is required. Interest in learning more about individual, social, and distributed cognition are a plus.

J. Czocher

An important aspect of mathematics teaching and learning is the provision of timely and targeted feedback to students and teachers on the teaching and learning processes. However, many of the tools and resources focused on providing such feedback (e.g., formative assessment) are aimed at helping students. Formative assessment of teaching can be equally transformative for teachers and school leaders and is a key component of improved teacher practice. This project will refine, expand and validate a formative assessment tool called Math Habits Tool (MHT) for Kindergarten through 8th grade classrooms. The MHT is intended to capture and understand patterns of in-the-moment teacher-student and student-student classroom interactions in ways that can promote more equitable access to high quality math learning experiences for all students. The tablet or computer-based tool is intended for use with teacher leaders, principals, coaches, and others interested in assessing teacher practice in a formative way.  The tool will be used to code a large database of classroom levels to quantitatively establish productive mathematical interactions amongst teachers and students.

Ability to qualitatively code mathematics classroom interactions required.

Melhuish, K.
Sorto, M.A.
Strickland, S.

Students interested in studying aspects of proving and activity in advanced mathematics classes can reach out to one of the faculty members in this group. We collectively research elements of proof-based mathematics from a number of lenses including linguistics (Lew), logic (Dawkins), and conceptual understanding (Melhuish). Our research projects span Introduction to Proof, Abstract Algebra, and Real Analysis. Grant projects include Orchestrating Discussions Around Proof, (Melhuish, Dawkins, Lew, 11/01/2018 - 10/31/2022), Developing and Validating Proof Comprehension Tests in Real Analysis, (Lew, Melhuish, 10/01/2018 - 09/30/2022), Comprehending conditional Claims' Proofs Organically (Dawkins, 10/01/2020 - 09/30/2023), and Generating a Research-Informed Transition to a Mathematical Proof Curriculum (Dawkins, Lew, Melhuish, 07/01/2022 - 06/30/2025)

Knowledge of abstract algebra required.

Dawkins, P.
Lew, K.
Melhuish, K.

The overarching goals of this project are to (a) advance knowledge of middle school students’ developing understandings of graphs “from the ground up” with attention to underlying coordinate systems and frames of reference that comprise the coordinate systems and (b) iteratively design and test tasks that can enhance students’ graph literacy, and thus provide a foundation for their future STEM coursework and careers. MS-GGU uses a design-based methodology in which we will engage in cycles of intervention and revision to develop, test, and refine cognitive models, constructive itineraries, and instructional tasks. Through several iterations of clinical interviews and small-scale teaching experiments in racially, ethnically, and socioeconomically diverse schools, we intend to produce a theory that explains students’ developing graph understandings and accounts for their varied ways of thinking. Through this process, we will iteratively design instructional tasks and task sequences that support students developing understandings for frames of reference, coordinate systems, and graphs in the widely used Desmos platform.

Knowledge of the teaching experiment methodology, dedication, and enthusiasm towards understanding students’ mathematical thinking is required.

Lee, H.
Hardison, H.

This project is situated within efforts to overhaul the introductory mathematics experience for biology and life science majors by introducing them to mathematical modeling. TAILOR investigates conditions under which university mathematics departments adopt and adapt evidence-based instructional materials for improving STEM education. The focal curriculum Modeling Life, has successfully replaced the calculus sequence at UCLA, and is currently being disseminated across the nation. TAILOR’s project aims are to (i) identify and understand the contextual features that facilitate or impede successful implementation the Modeling Life, (ii) advance understanding of how ongoing, dynamic institutional conditions shape the adaptation of a modeling curriculum in response to local needs, and (iii) lay the groundwork for a multi-site impact study by developing assessment tools to measure broader learning outcomes. The project draws on qualitative methodologies to document stakeholders’ perceptions of the impact of the instructional materials, including the experiences of mathematics and science faculty, teaching assistants and tutors, and students. The project will develop local causal models that explain how and why aspects of the curricular materials are adapted to suit the instructional context. (This project is funded by an NSF IUSE, 08/15/2024-08/14/2027).

Knowledge of calculus and/or dynamical systems is required. Experience working with teachers and curriculum is highly desired. All other methodological skills will be learned along the way.

J. Czocher

The overarching goal of CAREER: Reframing Students’ Graph Literacy with a Focus on Students’ Thinking (GLi-ST) is to construct a new, research-based framework that theorizes students’ graph literacy from an asset-based perspective, modeling students’ constructive resources that could be used to support continued development of graph literacy. Iterations of clinical interviews with middle school students are in progress and we are continuing with our data analysis.

Knowledge of the clinical interview methodology, dedication, and enthusiasm towards understanding students’ mathematical thinking is required.

Lee, H.