Recipient of CPM’s Outstanding Dissertation in Mathematics Education Award

September 2023

CPM’s Research Department is pleased to announce the 2023 recipient of CPM’s Outstanding Dissertation in Mathematics Education Award. This competitive $30,000 award is intended to support one doctoral candidate each year to pursue a dissertation that will have a positive impact on both mathematics education research and the practice of mathematics teaching and learning in secondary mathematics classrooms. The request for proposals for funding for the dissertation award is released each year in October with proposals due in February, and the awardee notified in June. All dissertation proposals submitted for the fellowship were reviewed by a panel of highly qualified mathematics education researchers.  

This year’s recipient, Amanda Huffman Hayes, is pursuing her dissertation at Purdue University under the mentorship of Dr. Jill Newton. Her dissertation focuses on the distribution and delegation of mathematical authority in problem-based classrooms. This topic is not only significant in mathematics education research but is also timely for CPM with the CPM 2023 Research Base on Problem-Based Learning focusing on mathematical authority. 

Bio: Amanda Huffman Hayes, Purdue University 

Amanda Huffman Hayes is a Ph.D. Candidate at Purdue University pursuing a Ph.D. in Curriculum and Instruction with a focus in Mathematics Education. Her dissertation developed through her sustained work with pre-service teachers in teaching mathematics methods focused on student-centered practices. Amanda’s work with pre-service teachers began during her career as a high school mathematics teacher at an urban high school in Indianapolis, Indiana. While teaching high school, Amanda simultaneously earned a graduate degree (M.S., Effective Teaching and Leadership, Butler University) with a thesis that examined the relationships formed between a mentor teacher (Amanda) and pre-service teachers during practicum site-based mathematics methods workshops. The thesis focused on dimensions of the mentor-mentee teacher relationship that supported the pre-service teachers to bridge theory and practice. Amanda continued to lead site-based mathematics methods workshops with undergraduates at Butler University after she completed her study, and this model expanded to all content areas and was recognized at the national level through Teach to Lead. 

Amanda also holds a B.S. in Middle/Secondary Education with a double major in Mathematics. In addition to her M.S. from Butler University, Amanda has also earned a graduate certificate in Mathematics from Indiana University. 

Dissertation Abstract: An Exploration into the Development of Students’ Mathematical Authority in a Problem-Based Algebra Classroom

Mathematics education researchers have repeatedly found an undeniable link between classroom practices that foster mathematical authority and more equitable learning opportunities. In particular, advancing students’ mathematical authority repositions them as competent sense makers by shifting the power differential to be more distributed between teachers and students rather than centered within the teacher. 

In her dissertation, Amanda Huffman Hayes is investigating how CPM curricula and teacher moves help develop students’ mathematical authority — defined as students’ engagement in solving mathematical tasks and responsibility to contribute in conversations with others, justifying one’s process and reasoning and establishing mathematical arguments while developing one’s mathematical understanding — in problem-based algebra classes. 

Using a school-based ethnographic case study, Amanda will examine how two expert teachers, curriculum materials (i.e., CPM’s Core Connections Algebra), and students contribute to developing students’ mathematical authority in problem-based learning classrooms. Data will consist of interviews and classroom observations focusing on discourse and mathematical authority. 

This dissertation’s exploratory studies of students’ development of mathematical authority in problem-based algebra classrooms will provide both theoretical and practical contributions to the field of mathematics education. To contribute to theory, this study will increase understanding of the interactions between the curriculum, teacher, and students by re-conceptualizing the curriculum from a static scope and sequence to a more teacher-embedded and student-centered living course of action. To contribute to practice, the new insights developed by this study will be articulated in ways that other researchers and teachers can learn from as they also work towards developing students’ mathematical authority.

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.