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Parents, Teachers, and Multilingual Children Collaborating on Mathematics Together (NSF 2010417)
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 designbased 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) 
Reasoning Language for Teaching Secondary Algebra
The Reasoning Language for Teaching Secondary Algebra (ReLaTeSA) project proposes to study the teaching and learning of algebra in grades 79, 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 bidirectional relationship between reasoningrich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equationsolving process, and functions. With a focus on the teacher, ReLaTeSA will analyze classroom narratives about algebraic concepts and procedures and provide an 80hour 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. 
The Math Habits Observation Tool Project
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 inthemoment teacherstudent and studentstudent classroom interactions in ways that can promote more equitable access to high quality math learning experiences for all students. The tablet or computerbased 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. 
Mathematical Modeling
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 mixedmethods 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 mixedmethods) research
 Willingness to get creative with task design, interpretive analysis, and quantitative modeling of qualitative data.
Czocher, J.

Undergraduate Modeling Challenge
SIMIODE is a nonprofit 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 selfefficacy 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.

The Teaching and Learning of Proof
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 proofbased 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 ResearchInformed 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. 
Middle School Students' Graphing from the Ground Up
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. MSGGU uses a designbased 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 smallscale 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.