Proposal Defense

Representative Mathematics Instruction in Elementary Classrooms

A Mixed Methods Study of Teacher Preparedness, Professional Learning, and Implementation


Iesha Griggs
Doctor of Education in Educational Technology and Leadership
Dissertation Proposal Defense | July 15, 2026
New Jersey City University







A study of representation, teacher learning, and implementation in elementary mathematics

Research Problem

Representative mathematics instruction is inconsistently implemented — or entirely absent — in many elementary mathematics classrooms.

Mathematics as Culture-Neutral

Mathematics is frequently taught as if it exists outside of history and culture — erasing the contributions of diverse peoples and communities from the story of mathematical knowledge.

Policy Without Practice

Representative curriculum policies exist nationally and in New Jersey, including the Amistad Commission. Policy does not automatically guarantee classroom implementation.

Teacher Preparedness Gap

Many teachers lack the preparation, resources, and professional learning needed to implement representative mathematics instruction in elementary classrooms.

Why Elementary Mathematics Matters

Elementary mathematics shapes early mathematical identity, engagement, and participation — making this gap especially consequential.

Core claim: Equity in mathematics includes whose knowledge, histories, and contributions are made visible through representative mathematics instruction.

Problem Statement

"Representative mathematics instruction is inconsistently implemented or entirely absent in many elementary mathematics classrooms, and limited empirical research has examined elementary teachers' perceived preparedness to implement representative mathematics instruction or the professional learning experiences that influence implementation."

01

Policy Expectation

Representative curriculum mandates exist nationally and in New Jersey.

02

Teacher Preparedness

Whether teachers feel prepared to implement representative mathematics instruction remains underexamined.

03

Classroom Implementation

The translation from policy to practice in elementary mathematics is inconsistent and understudied.

Purpose of the Study

The purpose of this explanatory sequential mixed methods study is to examine the relationship among teacher preparedness, professional learning, and the implementation of representative mathematics instruction in elementary classrooms.

Teacher Preparedness

Includes knowledge, confidence, resources, and readiness to implement representative mathematics instruction in elementary classrooms.

Professional Learning

Includes both formal professional development experiences and informal learning through digital communities, social media, podcasts, and online professional networks.

Implementation

Refers to how teachers report incorporating representative mathematics instruction — including but not limited to Black history and Black intellectual contributions — into classroom practice.

The survey shows the pattern. The interviews explain the pattern.

Research Questions

Four research questions guide this explanatory sequential mixed methods study.

RQ1 — Descriptive

To what extent do elementary teachers report their awareness, preparedness, and implementation of representative mathematics instruction?

RQ2 — Perceived Factors

What factors do elementary teachers perceive as contributing to their preparedness to implement representative mathematics instruction (e.g., preservice teacher education, district professional learning, instructional coaching, and instructional resources)?

RQ3 — Correlational

What is the relationship between elementary teachers' preparedness and their implementation of representative mathematics instruction?

RQ4 — Qualitative

How do elementary teachers explain how the implementation or limited implementation of representative mathematics instruction influences their perceptions of students' mathematical experiences and outcomes (e.g., mathematical identity, confidence, engagement, participation, sense of belonging, and academic learning)?

RQ1 describes. RQ2 explores factors. RQ3 correlates. RQ4 explains.

Theoretical Framework

Three interconnected frameworks ground this study's examination of representation, teacher learning, and professional community.

Culturally Relevant Pedagogy

Ladson-Billings (1995)

Why representation matters. CRP centers academic success, cultural competence, and sociopolitical consciousness — connecting curriculum to students' lived experiences and identities.

Andragogy

Knowles (1980)

How teachers learn. Adults learn best through relevant, self-directed, problem-centered experiences — informing how professional learning shapes teacher preparedness.

Communities of Practice

Wenger (1998)

Where teachers learn. Teachers learn through formal and informal professional communities — including digital habitats, social media, and online networks.

CRP explains why. Andragogy explains how. Communities of Practice explains where.

Conceptual Framework

The logic of the study: professional learning shapes preparedness, and preparedness shapes implementation.

Professional Learning Experiences

  • Formal: professional development, workshops, coursework
  • Informal: social media, podcasts, YouTube, online communities

Teacher Preparedness

  • Knowledge, confidence, resources, and readiness

Implementation

  • Representative mathematics instruction in elementary classroom practice

CRP — Why

Andragogy — How

Communities of Practice — Where

The survey examines the relationships. The interviews explain them.

Literature Review Themes

The literature review is organized thematically — synthesizing scholarship that informs the study without simply retelling history.

Representation & Curriculum

Scholarship on the historical exclusion of diverse contributions from mathematics curricula and the case for representative content in elementary mathematics.

Mathematics Identity & Belonging

Research on how curriculum representation shapes students' mathematical identity, sense of belonging, and academic participation.

Culturally Relevant & Sustaining Pedagogy

Frameworks for affirming student identity and connecting curriculum to lived experience — the instructional foundation for representative mathematics instruction.

Teacher Preparedness & Implementation

Research on instructional confidence, readiness, and the factors that support or hinder culturally responsive teaching in mathematics classrooms.

Professional Learning & Digital Communities

How teachers learn through formal professional development and informal digital spaces — including social media, podcasts, and online professional networks.

Research Gap

This study is positioned at a critical and underexamined intersection.

What Exists

Research on culturally relevant pedagogy, mathematics identity, equity-oriented instruction, teacher professional learning, and communities of practice provides a strong foundation for understanding how teachers learn and implement equitable practices.

What Is Limited

Empirical research examining elementary teachers' perceived preparedness to implement representative mathematics instruction as a specific classroom practice remains limited. Few studies connect professional development, informal learning, and policy-to-practice context to instructional implementation in elementary mathematics.

What Is Needed

Teacher-centered evidence on how formal and informal professional learning influence preparedness and implementation of representative mathematics instruction — including the role of digital communities.

The gap is not that representation has never been studied. The gap is that this specific intersection has not been examined enough.

Explanatory Sequential Mixed Methods Design

This design was selected because the study needs both measurable patterns and teacher explanations.

01

Phase 1: Quantitative Survey

An online survey administered to K–5 elementary mathematics teachers measures preparedness, professional learning experiences, and implementation of representative mathematics instruction. Descriptive statistics and correlation analysis identify patterns and relationships.

02

→ Informs

Quantitative results guide the selection of qualitative participants and the focus of interview questions. Survey findings determine who is interviewed and what is explored in depth.

03

Phase 2: Qualitative Interviews

Semi-structured interviews with a purposively selected subset of survey participants explain the quantitative patterns through teacher voice and lived experience.

Why Not Purely Quantitative?

A survey alone cannot explain why patterns exist or how teachers experience the process of implementing representative mathematics instruction.

Why Not Purely Qualitative?

Interviews alone cannot identify the extent of patterns or examine relationships among preparedness, professional learning, and implementation across a broader sample.

The survey shows the pattern. The interviews explain the pattern.

Measurement & Data Collection

Two phases of data collection, three instruments, three core constructs.

Appendix A: Teacher Survey

Online Likert-scale survey measuring teacher preparedness, professional learning experiences, and implementation of representative mathematics instruction. Administered to K–5 elementary mathematics teachers.

Appendix B: Interview Protocol

Semi-structured interviews with a purposively selected subset of survey participants. Explores how professional learning shaped preparedness and implementation.

Appendix F: Alignment Matrix

Connects each research question to its construct, instrument, data source, and analysis procedure.

Phase 1 survey participants → Phase 2 interview subset → Integration of findings.

Data Analysis Procedures

The analysis is intentionally focused — aligned to the research questions and designed to avoid unnecessary statistics.

Quantitative Analysis

  • RQ1: Descriptive statistics — frequencies, percentages, means, standard deviations
  • RQ2: Pearson correlation (if assumptions met) or Spearman's rho (if not)
  • Cronbach's alpha for internal consistency of survey scales

Qualitative Analysis

  • RQ3: Thematic analysis of semi-structured interview transcripts
  • Initial and secondary coding → categories → themes
  • Participant quotations to illustrate themes
  • Member checking may be used if approved by the committee
01

Quantitative Results

Patterns and relationships identified through survey data

02

Qualitative Findings

Themes and explanations from interview data

03

Integration (RQ4)

Qualitative findings explain the quantitative results for a comprehensive understanding

Describe the pattern. Examine the relationship. Explain the meaning.

Significance & Closing Claim

This study contributes to mathematics education, teacher professional learning, and educational technology.

For Students

Representation, belonging, engagement, and mathematical identity. When students see diverse contributions in mathematics, they may see themselves as mathematical thinkers.

For Teachers

Preparedness, confidence, and implementation support. Findings clarify what teachers need to implement representative mathematics instruction and what professional learning supports that readiness.

For School Leaders & PD Providers

Findings may inform the design of targeted, culturally responsive professional development aligned with representative mathematics instruction.

For Educational Technology

The study centers technology as a professional learning environment — digital communities, informal learning, and online networks — contributing to the field of educational technology leadership.

"If representative mathematics instruction is expected, then we need to understand whether teachers are prepared to do it — and what helps them get there."

Selected Anchor References

Theoretical Frameworks

  • Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal.
  • Knowles, M. S. (1980). The modern practice of adult education. Cambridge.
  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge University Press.

Mathematics Identity & Representation

  • Nasir, N. S., & Shah, N. (2011). On defense: African American males making sense of racialized narratives in mathematics education. Journal of African American Males in Education.
  • Aguirre, J., Mayfield-Ingram, K., & Martin, D. B. (2013). The impact of identity in K–8 mathematics: Rethinking equity-based practices. National Council of Teachers of Mathematics.
  • Paris, D. (2012). Culturally sustaining pedagogy. Educational Researcher.

Teacher Learning & Professional Development

  • Gay, G. (2010). Culturally responsive teaching. Teachers College Press.
  • Trust, T., Krutka, D. G., & Carpenter, J. P. (2016). "Together we are better": Professional learning networks for teachers. Computers & Education.

Policy-to-Practice Context

  • New Jersey Department of Education. (2002). Amistad Commission Act. New Jersey Legislature. https://www.nj.gov/education/amistad/
  • New Jersey Department of Education. (2021). Diversity and inclusion curriculum framework. https://www.nj.gov/education/standards/dei/

Methodology

  • Creswell, J. W., & Creswell, J. D. (2022). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE.
  • Patton, M. Q. (2015). Qualitative research and evaluation methods. SAGE.