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Student-Adaptive Mathematics Pedagogy (NSF-funded)

Empowering Upper-Elementary Teachers to Transform Mathematics Education by Tailoring Instruction to Students’ Powers


The NSF-funded, Student-Adaptive Mathematics Pedagogy project focuses on empowering teachers with the awareness, understandings and skills to meet the individual needs of their students and to foster students’ reasoning, conceptual understanding and productive participation in communities of learners through professional development (PD), coaching and reflection.

Project Objectives

Promote and study teachers’ professional development of ways to recognize their students’ conceptual understanding, so the teacher can adapt her or his teaching methods to the learners in a way that fosters student mathematical reasoning. Through professional development, team teaching, coaching and reflection, teachers will move toward student-adaptive practices. Specifically, this project focuses on students’ understanding of and teachers’ growth towards practices pertaining to multiplicative and fractional reasoning in grades 3-5. The methods learned by the teachers can be transferred to other contents, subjects and grade levels. ​​

Primary Investigator (PI) Ron Tzur, professor, provides project leadership and mathematics education expertise, based on prior projects funded by National Science Foundation (NSF). He earned a BS at Haifa University and a MS at the Technion (both in Israel), and PhD at the University of Georgia (Athens). [More]

Co-PI Heather Johnson, associate professor, provides mathematics education expertise. She earned her BS, MEd, and PhD at Penn State. [More]

Co-PI Alan Davis, professor, provides research methodology expertise, based on his work as PI on projects that employed Hierarchical Linear Modeling and qualitative methods. He earned his BA at Pomona College, MAT at Harvard, MA at Western Michigan University, and PhD at CU Denver. [More]

Co-PI Sally Nathenson-Mejia, associate professor, provides expertise in educational and research work at urban schools, based on over 30 years of work as a bilingual educator. She earned her BS at Mankato State University, and MS & PhD at Ohio State University. [More]

Co-PI Maria Uribe, senior instructor, provides expertise in educational work at urban schools, based on over 20 years of service as a bilingual educator—15 years as teacher, five as principal at Goldrick Elementary School in Denver Public Schools and nine years as a coach and liaison with the CU Denver. She earned her BS in Colombia (South America), MS at CU Boulder, and PhD at CU Denver. [More]​

Co-PI Michael Ferrara, associate professor in Mathematical and Statistical Sciences, provides expertise in ensuring rigorous and comprehensive use of mathematics as well as in teaching Math Content Knowledge (MKT) to teachers. He earned his BS at Stevens Institute of Technology and PhD (mathematics) at Emory University. [More]

Co-PI Xin Wang, provides psychometrics expertise in designing reliable and valid quantitative measures. She earned her BA at Ocean University (China) and MA/PhD (educational psychology) at University of Illinois (Urbana-Champaign).

Graduate Research Assistants (GRA)

Nicola Hodkowski, project manager, GRA, is a doctoral (PhD) candidate in mathematics education at the University of Colorado Denver. She instructs courses at the university for pre-service and existing teachers on their mathematics as way to enhance their pedagogy with elementary students. She has seven years of classroom experience and three years of experience coaching teachers of elementary mathematics. She earned her BA at the University of Colorado-Boulder and her MA at the University of Colorado Denver.

Peter Hornbein, GRA, is a doctoral (PhDstudent in mathematics education at the University of Colorado Denver with 27 years of experience in the classroom. He earned BAs at the University of Colorado-Boulder and at San Jose State University, San Jose, California. He earned his MSEd (mathematics education) at the University of Colorado Denver.

Amber Gardner, GRA, is a doctoral (PhDstudent in mathematics education at the University of Colorado Denver with 15 years of classroom, counseling and administrative experience in preschool, elementary and middle school environments in rural Colorado. She earned her BS at Colorado Mesa University and MA at Adams State University.

Cody Jorgensen, GRA, is is a doctoral (PhDstudent in mathematics education at the University of Colorado Denver with 10 years of classroom experience teaching 3rd grade at Mapleton Public Schools. She earned her BS and MA at the University of Colorado Denver.

Bingqian Wei, GRA, is a doctoral (PhDstudent in mathematics education at the University of Colorado Denver. She has three years of experience in the classroom, teaching high school mathematics in China. She earned her BS and MA at Beijing Normal University, China.


The Student-Adaptive Pedagogy for Elementary Teachers: Promoting Multiplicative and Fractional Reasoning to Improve Students’ Preparedness for Middle School Mathematics is a full design and development project within the DRK-12 learning strand. The project aims to implement and study a professional development (PD) intervention designed to shift upper-elementary teachers’ mathematics teaching toward a constructivist approach, called student-adaptive pedagogy (AdPed), which adapts teaching goals and activities based on students’ conceptions and experiences. The project focuses on multiplicative and fractional reasoning--critical for students’ success in key areas of middle school mathematics (e.g., ratio, proportion, and function). Its design is rooted in an innovative, cohesive framework that integrates four research-based components:

  1. A model of mathematics learning and knowing
  2. Models of progressions in students’ multiplicative and fractional reasoning
  3. A model of teaching (AdPed) to promote such learning
  4. A mathematics teacher development continuum.

Capitalizing on successful preliminary efforts in the Denver Metro area to refine a PD intervention and student-adaptive resources, models and tools (RMTs) that challenge and transform current practices, the project will first validate and test instruments to measure: (a) teacher growth toward adaptive pedagogy (b) students’ growth in multiplicative reasoning. Using these new instruments, along with available measures, the project will then promote school-wide teacher PD (grades 3 - 5) in multiple schools in an urban district with large underserved student populations and study the PD benefits for teacher practices and student outcomes.

In the project’s first year (field-testing), the team will study how to measure teachers’ growth toward adaptive pedagogy and students’ multiplicative reasoning (Study A and Study B, respectively), developing and validating instruments in ~8 classrooms per grade level at schools 1 & 2. In year two (PD), grade 3 - 5 teachers (~50) in four other schools in the Aurora Public Schools district (see eager-to-participate letters) will receive a five-day Summer Institute, be involved in learning through co-teaching and receive a second, five-day Summer Institute PD to promote rigorous infusion of the RMTs into their regular lessons. Using available data collection tools, and the validated teacher and student measures, the team will study (a) how teachers develop and implement student-adaptive pedagogy and (b) initial benefits of intervention for participating students’ (~1100) outcomes as compared to the Year-1 baseline. In Year-3 (Pilot), participating teachers (~50) will independently implement the RMTs while the team studies (a) their growth toward adaptive teaching (Study C) and (b) student outcomes (Study D; ~1100 in intervention schools). In Year-4 (findings), the team will analyze data and disseminate materials, instruments and findings.


The proposed project advances knowledge of teachers’ development of student-adaptive teaching practices and the benefits of these practices to students’ development of multiplicative and fractional reasoning, which is imperative for success in middle school mathematics. It also provides research instruments sensitive to measuring teacher PD and student growth in those specific areas, and insights into co-developing with teachers and infusing materials into regular Common Core State Standards-informed curricula.

The project provides resources, models and tools (RMTs) for capitalizing on successful, school-based empirical work for promoting teachers’ buy-in, adoption and sustaining of student-adaptive pedagogy. Conducted in low SES schools, it focuses on students from urban, underserved populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics. An extensive dissemination plan of a professional deveopment intervention for teachers/coaches (scalable to district/state levels), of RMTs, and of research instruments and findings, will promote sharing project outcomes with a wide community of stakeholders (teachers, administrators, researchers, parents and policy makers) responsible for students’ growth, while fostering development of novice STEM researchers (five to eight graduate research assistants).​

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