Research Opportunities

The goal of this project is to develop and study a mathematics partnership that engages multilingual children, their teachers, and their parents in mathematical experiences together. These mathematical experiences are designed to advance equity in mathematics education for multilingual students. The project will design professional learning opportunities for parents, teachers, and students, and study the ways in which the professional learning opportunities influence teacher beliefs, quality of instruction, parent beliefs, and teacher and parent understanding of positioning.

This project uses a design-based implementation research (DBIR) approach, along with principles of Social Design Experiments to engage in iterative cycles of inquiry to develop, implement, and refine the model. Parents, teachers, and students in three states (Arizona, Maryland, and Missouri) will be recruited that represent diverse populations both with respect to demographics and with respect to the policy contexts surrounding multilingual learners.

Bilingual (English/Spanish) preferable

Advisory Board Member: M. Alejandra Sorto
PI: Beatriz Quintos (University of Maryland)
PI: Marta Civil (University of Arizona)
PI: Rachel Pinnow (University of Missouri)

The Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions. With a focus on the teacher, ReLaTe-SA will analyze classroom narratives about algebraic concepts and procedures and provide an 80-hour professional development program designed to support teachers in developing stronger explanations of algebraic objects, their properties, and their relationships.

Patterson, C.
Bonner, E.
Prasad, P.

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.

Maintaining an effective pipeline of students into STEM careers depends upon their ability to learn mathematical modeling. Mathematical modeling involves creating a mathematical representation that can describe a nonmathematical problem. This  funded project has two research goals: 1) to understand how undergraduate STEM students build a mathematical model, including the process by which they define a mathematical strategy to describe a nonmathematical problem; and 2) to identify task features and facilitator scaffolding strategies that best support the growth of students' mathematical modeling abilities. The project will focus on three critical competencies related to mathematical modeling: making assumptions, mathematizing, and validating. Improving student skills in mathematics is important for improving student performance in STEM fields, a national priority. 

The mixed-methods study will enter Phase 2 (design and execution of teaching experiments) in Autumn 2020.

Project participation will provide opportunities for publications.

Requirements: 

• Desire to read widely in the literature
• Familiarity with basics of qualitative and quantitative (or mixed-methods) research
• Willingness to get creative with task design, interpretive analysis, and quantitative modeling of qualitative data.

Czocher, J.

SIMIODE is a non-profit professional development community for learning to teach mathematics from a modeling perspective. SIMIODE hosts an annual modeling challenge, SCUDEM.  Part of the SCUDEM initiative is to get students excited about doing mathematical modeling with complex, authentic problems.

The challenge is for three member teams that work at their home institution for a week developing approaches and solutions to a modeling problem of their choice and preparing an Executive Summary and 10 minute Presentation. The problems are designed so that every team may experience success in modeling, enhance their model building skills, and increase their confidence in modeling with differential equations. Problems are drawn from the physical, social, and life sciences. 

This research project is designed to assess students' growth of modeling skills and mathematics self-efficacy as a result of participating in the challenge.

Requirements:

• Spreadsheets
• SPSS (or willingness to learn)
• Basic knowledge of research design (or willingness to learn)
• Basic qualitative analysis skills.

Czocher, J.

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.