Journal of Mathematics Education Leadership

Summer 2024, Volume 25, Number 1

Articles in this issue

VERTICAL LESSON STUDY VERTICAL LESSON STUDY TO BRING COHERENCE IN PRIORITIZING STUDENT CONTRIBUTION AND VOICE

by: Holly Tate, Jennifer Suh, Amy Christensen, Kaitlin Kaplewicz, Jacqueline Carlson, Jenny Carter

This article tells the story of a team of K-6 teachers who engaged in action research through Lesson Study to build equitable classroom structures through discourse-rich vertical tasks. Founded within the key recommendations of Catalyzing Change (NCTM, 2020), our community explored ways to prioritize student voice and distribute student mathematical contributions across more students within correlated patterning tasks.

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ONE CURRICULUM COMMITTEE’S PERCEPTIONS OF HIGH-QUALITY MATERIALS

by: Erica N. Mason, Camille Griffin, Ga Kyung Jeong

This paper highlights aspects of the curriculum adoption process that may have previously been overlooked—the degree to which the curriculum committee has a shared view with one another of material quality, including committee members’ views about material appropriateness and the alternatives they would recommend for students. We highlight one curriculum committee’s perspectives, which were generally coherent with one another with respect to their views of material quality and appropriateness. In addition to describing details of the project, we share key insights and make recommendations for how other districts might attend to these aspects of a curriculum series adoption that promote more inclusive mathematics experiences for all students.

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Fall 2023, Volume 24, Number 2

Spring 2023, Volume 24, Number 1

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CRITICAL COLLEAGUESHIP DEVELOPMENT AMONGST ELEMENTARY INSTRUCTIONAL LEADERS: A COMPARATIVE ANALYSIS OF PROCESS AND OUTCOMES

by: Sara Donaldson

Mathematics coaches, as school-based instructional leaders, are well situated to promote instructional effectiveness and student learning. This ability is enhanced through ongoing professional learning opportunities that position them alongside other instructional leaders actively developing the skills, knowledge, and dispositions necessary for facilitating change. This study, conducted in an urban school setting, draws on social learning theories to examine the influence of professional learning processes on mathematics instructional leaders’ critical colleagueship development and collaborative inquiry engagement. Findings indicate increasing attention on establishing collaboration agreements, shared transformational learning goals, and consistent meeting structures promotes critical colleagueship and team functioning in support of coaches’ own professional learning and their facilitation of learning for the teachers whom they support.

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HOW UNDERSTANDING MATHEMATICAL DISCOURSES SHAPES PRINCIPAL NOTICING

by: Heidi Rhodes, Kristin Lesseig,David Slavit

Principal leadership is a key factor in student achievement, but we are not yet sure how knowledge of content influences leadership. Teacher evaluation systems assume principals understand the pedagogical content knowledge (PCK) for multiple disciplines, a particularly challenging expectation for secondary leaders. This study presents a noticing frame- work of PCK for leadership that describes a progression through four levels, from content-neutral pedagogy to an interconnection between pedagogy and mathematical discourses. Using the framework, the study provides evidence that principals can learn to notice significant mathematical events but may struggle to respond to teachers about those events. The framework can serve as a tool for leaders to learn to notice the role of mathematics in classrooms during their work with teachers.

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Summer 2022, Volume 23, Number 1

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BEYOND RIGHT OR WRONG: SUPPORTING TEACHERS IN STRENGTHS-BASED APPROACHES TO EXAMINING STUDENT WORK

by: Stacey C. Zimmerman, P. Holt Wilson

Recognizing the strengths of students through their written work takes time, practice, and intentionality. In this article, we detail a set of questions that can be used to purposefully engage with student written work in a strengths-based way. Derived from the exploration of experienced mathematics educators’ mathematical knowledge for teaching quadratic functions, the questions place value on student thinking while providing the opportunity for teachers to enhance and extend their own mathematical knowledge for teaching. Mathematics leaders can use these questions to facilitate meaningful learning experiences for teachers, professional learning communities, and large group professional development activities.

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INFLUENCING ELEMENTARY PRINCIPALS’ LEADERSHIP SELF-EFFICACY FOR MATHEMATICS: A PROFESSIONAL DEVELOPMENT CASE STUDY

by: Kelly Gomez Johnson, Paula Jakopovic

Building principals are uniquely positioned to drive change, however, often find themselves learning alongside teachers. Principals are key in establishing a vision for high-quality instruction and influencing teacher practice. However, professional development (PD) for principals needs to prepare and support their beliefs, knowledge, and skills as instructional leaders in subject-specific areas like mathematics. This article describes a districtwide, mathematics focused PD model to support principal development. This study examined how PD activities, designed around Bandura’s sources of self-efficacy, influenced principal self-efficacy as mathematics instructional leaders. Findings of this qualitative case study include four themes of PD activities that enhanced principal self-efficacy. Implications of this study may serve school district leaders as they support principals’ development as instructional leaders in subject-specific areas.

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Fall / Winter 2021-2022, Volume 22, Number 2

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IMPLEMENTING LESSON STUDY: CHALLENGES IDENTIFIED BY EMERGING TEACHER LEADERS

by: Angela T. Barlow, J. Christopher Willingham, Alyson E. Lischka, D. Christopher Stephens, Kristin S. Hartland

Within the context of a professional development project, we supported emerging teacher leaders as they facilitated teachers’ engagement in the lesson study process. In this paper, we share the self-identified challenges met by this group as as they led lesson study in their school settings. In addition, we share lessons learned in response to these challenges. Implications for mathematics education leaders are included.

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LEADERSHIP FROM WITHIN THE CLASSROOM: OPPORTUNITIES AND CHALLENGES FOR ELEMENTARY MATHEMATICS SPECIALISTS

by: Kimberly A. Conner, Phi Nguyen, Christina Sheffel, Corey Webel

In this article, we describe the leadership opportunities and challenges experienced by eight Elementary Mathematics Specialists (EMS) who had all remained in their primary role as classroom teachers after obtaining their specialist certificates. Drawing on Gigante and Firestone (2008), we categorize the EMS’ leadership tasks in terms of whether they supported colleagues in increasing their knowledge of teaching mathematics. After describing the leadership tasks and how they came about, we describe four challenges at least some participants faced in enacting leadership from their classroom teaching roles. We conclude with recommendations for ways different stakeholders can support EMS in taking on leadership tasks while remaining full time classroom teachers.

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INCLUSION AND INTERVENTION: UNDERSTANDING “DISABILITY” IN THE MATHEMATICS CLASSROOM

by: Lara Jasien, John Hayes

All students’ learning—including students with learning and intellectual disabilities—is deepened when students with multiple ability levels engage in teamwork on high cognitive demand tasks. Yet, we know little about supporting teachers in inclusive mathematics classrooms. This knowledge void presents challenges for mathematics education leaders who wish to foster inclusion. Synthesizing a small but growing body of mathematics education research, this manuscript is a resource for leaders supporting teachers in inclusive standards-based classrooms. In particular, this manuscript articulates (1) why productive struggle is essential for students with disabilities, (2) progressive definitions of disability and inclusion, and (3) conceptual descriptions of pedagogy in inclusive mathematics classrooms. It is followed by an appendix filled with tangible strategies that mathematics education leaders can adopt and adapt in their own contexts.

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Summer 2021, Volume 22, Number 1

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CURRICULAR REFORM IN SCHOOLS: SECONDARY LEADERS’ PERCEPTIONS

by: Amanda Bauer, Erin Lehmann, Kristine Reed, Gwendolyn Zimmermann, Adlai E.

The landscape of PK–12 education is dynamic, constantly adapting to meet the needs and demands for student learning. These changes inspire curricular reforms, and such processes compound the complexity of leadership roles within PK–12 education settings. This study explored the nature and extent of transformational leadership practices and efficacy beliefs exhibited by secondary school leaders as they implement a mathematics curricular reform. In addition, the study examined the barriers of curricular reform processes as perceived by school leaders. This study employed a phenomenological methodology as participants were asked to describe their lived experiences within the context of the mathematics curricular reform. Semi-structured interviews and focus groups were used for data collection, allowing participants to share stories and examples that captured the essence of their lived experiences. The research findings suggest efficacy beliefs related to relationships and experience influence leaders’ transformational leadership practices as they facilitate curricular reforms in their schools. Furthermore, these transformational leadership practices may be used to address and overcome barriers throughout the implementation of curricular reforms.

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DESIGN AND IMPACT OF FLEXIBLE, ASYNCHRONOUS ONLINE VIDEO-BASED MATHEMATICS PROFESSIONAL DEVELOPMENT

by: Nanette Seago, Angela Knotts, Catherine Carroll

In this article, we share the experimental research design and preliminary impact results from the Video in the Middle project, which is adapting existing face-to-face video-based mathematics professional development materials to online two-hour modules that can be used in flexible asynchronous formats: independent, locally facilitated, or developer facilitated. Preliminary research results indicate that teachers appreciated the variety of formats, found the modules useful and engaging, and learned to appreciate and use visual methods for solving problems, including using color to distinguish and highlight the relationship between numeric, algebraic, and geometric models. The benefits of this asynchronous PD became pronounced as the pandemic emerged during the research study and teachers found themselves shifting to remote instruction with little time to prepare.

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AN INTERDISCIPLINARY COACHING APPROACH TO DATA-BASED INDIVIDUALIZATION: A YEAR-LONG PARTNERSHIP BETWEEN MATHEMATICS TEACHERS AND SPECIAL EDUCATION RESEARCHERS

by: William S. Walker III

This article describes a year-long partnership between a group of general education mathematics teachers and their special education researcher-coach counterparts, an experience we call interdisciplinary coaching. The purpose of this work was aimed at supporting teachers in adopting and implementing an evidence-based instructional practice intended to address the needs of students experiencing mathematics difficulty, including students with disabilities. Findings from this investigation indicate teachers had high rates of satisfaction with the coaching model and that, by some specific measures, this model demonstrates promise for improving teachers’ assessment practice within a data-based individualization framework. We describe the unique tensions and affordances that arose from this type of partnership and share recommendations for how others might engage in interdisciplinary coaching work.

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Fall/Winter 2020, Volume 21, Number 2

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EXAMINING POTENTIAL PITFALLS THAT HINDER PRODUCTIVE COACHING CONVERSATIONS

by: Paula Jakopovic

Instructional coaching is a popular approach for providing professional development to classroom teachers that can help to enhance their knowledge and use of effective teaching practices. A growing body of research on mathematics instructional coaching, and mathematics coaching in particular, suggests that coaches can both increase teacher self efficacy and use of research based instructional practices and potentially have a positive impact on student achievement (Campbell & Malkus, 2011; Ellington et al., 2017; Knapp, 2017). To help ensure the effective implementation of coaching initiatives, researchers continue to examine the types of coaching practices that are most effective at creating these shifts. This paper adds to the literature on some of the challenges that coaches face in their planning conversations with classroom teachers and provides insights into how coaches and other mathematics education leaders can engage in productive coaching conversations that can foster reform-oriented shifts in teacher practice.

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MAKING THE “CUT”: ONE DISTRICT’S STRATEGY OR ALGEBRA PLACEMENT

by: Neal Grandgenett, Roberta Jackson

Some of the most discussed issues in mathematics education today involve Algebra and its instruction. These issues include the optimal timeline for when students first take a formal algebra course, the related selection process for getting into that first course and what algebra instruction should generally look like throughout the curriculum. Algebra is being recognized as a key “gate-keeper” course for high school and college success and has even been called an emerging “civil rights issue” by some researchers and authors. When to place students into an algebra class and how to ensure that a student is ready for Algebra are both critical curriculum decisions for a district. In many districts, algebra placement is a process that may be undergoing considerable revision along with how algebra is integrated across the curriculum. This article describes one district’s approach for evaluating and revising their placement strategy for admitting students into their first middle school algebra course.

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Spring 2020, Volume 21, Number 1

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USING ROLE PLAY TO REHEARSE PROBLEMS OF PRACTICE

by: Shannon Larsen, Cheryl Tobey

In this article, we share a professional development tool for use with mathematics coaches. We describe a protocol we created, inspired by research around Rehearsals in pre-service mathematics instruction, that supports coaches to practice addressing challenges they are likely to confront in their work. After introducing the research that has guided our thinking, we describe our Role Play Protocol and share data collected from coaches and administrators with whom we worked about the usefulness of this form of professional learning. We then outline modifications we have made and continue to make to the Role Play Protocol and discuss implications and future work needed to better understand how effective this tool is at supporting coaches’ learning and practice in the field.

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PURPOSEFULLY COACHING MIDDLE SCHOOL TEACHERS: THE CASE OF AN EXEMPLARY MATHEMATICS SPECIALIST

by: Joy W. Whitenack, Aimee J. Ellington

In this paper, we share results from a large-scale, mixed design study that describe the work of mathematics specialists in middle schools and their impact on teacher learning and student achievement. Within the context of the larger study, we highlight the practices of one exemplary mathematics specialist and how her collaborations with teachers in her building contributed to the practices that they engaged in to achieve the common goals of growing as professionals and supporting their students’ learning. We use a coaching moves-heuristics model that is based on West and Staub’s (2003) framework for lesson design and analysis to characterize the types of moves that this specialist made that contributed to and supported the productive and effective community of practice in this school building.

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Fall/Winter 2019, Volume 20, Number 2

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EQUITY-FOCUSED PROFESSIONAL DEVELOPMENT FOR ALGEBRA I TEACHERS IN URBAN DISTRICTS

by: Emily P. Bonner

Student data show that there is a need to develop a more culturally responsive mathematics teaching force. As such, we developed a framework for equity-focused professional development (EFPD) for mathematics teachers through which we hope to improve student access to mathematical knowledge. In this paper we present our EFPD framework, program, and initial results related to culturally responsive mathematics teaching. Further, we describe our process for tracking teacher progress. In this context, we present struggles that we have faced in implementing this framework in an effort to contribute to ongoing discussions about the ways in which the educational system in general and the current political climate in education impact EFPD.

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TRANSITIONING FACE-TO-FACE MATHEMATICS PROFESSIONAL DEVELOPMENT TO SYNCHRONOUS ONLINE IMPLEMENTATION: DESIGN CONSIDERATIONS AND CHALLENGES

by: Julie M. Amador, Cynthia H. Callard, Jeffrey Choppin, Ryan Gillespie, Cynthia Carson

To make professional learning experiences more accessible to teachers, professional development providers redesigned a face-to-face professional learning experience – a Teaching Lab – for an online platform utilizing synchronous modalities. To design the online version of the Teaching Lab, our team employed design principles derived from research on high-quality professional development and from theories of technology use in education. We describe these design principles, the multiple iterations of the Teaching Lab, and the challenges we faced in the design process. We consider the roles of technology as replacement, amplification, transformation, or hindrance with respect to the online model. We conclude with a discussion of the technology framework to offer suggestions and considerations for mathematics education leaders who design professional learning opportunities.

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TEACHER INTERPRETATIONS OF THE GOALS OF MATHEMATICS PROFESSIONAL DEVELOPMENT AND THE INFLUENCE ON CLASSROOM ENACTMENT

by: William S. Walker

This multiple-case study is an investigation of how four high school teachers interpreted the goals of a professional development (PD) program and how these interpretations influenced their instructional practices during observed lessons. The teachers participated in PD that focused on using standards-based pedagogy and mathematical tasks with higher-level demands. Each teacher stated an interpretation of the goals that was consistent with the PD, but concentrated on one of the objectives for each of the goals. The teachers’ interpretations of the goals influenced the lessons they taught and their use of ideas from the PD.

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Spring 2019, Volume 20, Number 1

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POSITIVE & PRODUCTIVE COACHING: AN INTERVIEW PROTOCOL AND SYSTEMATIC APPROACH FOR CREATING COACHING GOALS

by: Theresa E. Wills, Molly Rawding

Mathematics coaches have an immense responsibility to uniquely coach a diverse group of teachers in “areas related to standards, curriculum, assessment, and professional development” (AMTE, 2010, p. 1). Because of the diversity of teacher’s needs and school settings, it is important that a coach establish personalized goals with each teacher. Establishing these goals and making sure they are effective requires a positive and trusting relationship with the teacher based on shared values. This article outlines an interview protocol to guide initial interactions and a systematic approach for identifying a coaching goal. Included is a sample interview, an analysis of the interview questions, and strategies for creating a productive and positive interview. By using this interview protocol, the coach will be able to select purposeful questions, build a positive relationship with the teacher, and obtain the necessary information to help create an effective coaching goal.

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DISCONTINUITY IN ENACTED SCOPE AND SEQUENCE OF MIDDLE GRADES MATHEMATICS CONTENT

by: Lisa Kasmer, Travis Olson, Dawn Teuscher, Shannon Dingman

The 2010 release of the Common Core State Standards for Mathematics (CCSSM) initiated a tremendous effort to align the mathematics curriculum across the United States. However, the work of enacting these standards, including determining the order to teach grade-level standards, was often left to local schools and district experts to determine. These decisions were influenced by several factors and often formalized in scope and sequence documents, which outlined the order in which grade-level standards would be taught and the amount of time devoted to specific mathematical content and skills. In this paper, we report the analysis of eight Grade 8 mathematics teachers’ scope and sequence documents and the underlying factors that influenced their development. Given the discrepancies apparent across these eight documents, we discuss the implications stemming from these curricular decisions and recommend district leadership consider the connections across mathematical content when making decisions regarding the sequencing of topics in any grade level.

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WHAT EDUCATIONAL LEADERS NEED TO KNOW ABOUT EARLY-CAREER MATHEMATICS TEACHERS

by: James A. Martinez, Lisa R. Amick

In response to a national crisis to retain middle and high school teachers in Science, Technology, Engineering and Mathematics (STEM) classrooms, a study was conducted to define factors that affect job satisfaction among early-career mathematics teachers, including perceived support by school administrators. Survey data gathered from 141 early-career mathematics teachers across the United States revealed the degree that administrative and peer support affected teachers’ perceptions of their enthusiasm for teaching mathematics. Results from the study are being used to design targeted professional development involving early-career mathematics teachers with their principals with the overarching goal being to increase retention for these teachers in middle and high schools. Connections are made to promote professional development aimed at developing instructional leadership skills among school leaders.

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Fall 2018, Volume 19, Number 2

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EXPLORING ELEMENTARY CONTENT SPECIALIZATION: BENEFITS AND CAUTIONS, PITFALLS AND FIXES.

by: Kimberly A. Markworth, Joe Brobst, Ed.D., Ruth Parker, Ph.D., Chris Ohana

Teaching elementary mathematics well is a significant challenge for self-contained classroom teachers who are responsible for teaching all content areas. This article reports on research findings regarding elementary content specialization (ECS), in which elementary teachers share classes of students in order to specialize in certain content areas, oftentimes manifested through a team teaching model. The research findings from this study relate to four takeaways: focus, professional development, instructional time, and student support. In addition, potential pitfalls and corresponding fixes with implementing ECS are identified and discussed. Teachers, specialists, and administrators considering ECS through team teaching may use these results, takeaways, and recommendations to weigh the benefits and challenges of ECS, as well as plan for best practice and potential pitfalls.

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CHARACTERIZING HOW EXPERT ALGEBRA TEACHERS PROMOTE PRODUCTIVE STRUGGLE

by: David Glassmeyer, Joel Roth

While frameworks for analyzing teacher actions have been developed, little research describes how expert teachers promote productive struggle in their classrooms In this paper, we report findings from using a productive struggle framework and a cognitive demand framework to characterize how nine National Board Certified algebra teachers promoted productive struggle in a lesson After analyzing videos of their lessons, we found these teachers, whom we label as expert teachers, used a high-cognitive demand task and gave responses that promoted students’ productive struggle, often maintaining the high-cognitive demand of the task This analysis provides mathematics teacher educators and leaders concrete evidence of how expert algebra teachers promote productive struggle in the classroom We also discuss implications useful for educators and administrators who decide on algebra curricula and professional development, including tailored information for how teachers can respond to student struggle in ways that promote the high cognitive demand of algebra tasks.

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Spring 2018, Volume 19, Number 1

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AN EXAMINATION OF THE NATURE OF POST-OBSERVATION FEEDBACK PROVIDED TO MIDDLE SCHOOL MATHEMATICS TEACHERS

by: Christine P. Trinter, Carlson-Jaquez

The feedback mathematics teachers receive following an administrator’s observation of instruction is a critical component of the teachers’ professional development This study examined the nature of feedback middle school mathematics teachers received from administrators who had differing formal mathematics education or experiences Data included teacher evaluations, classroom artifacts, classroom observation field notes, and interviews with teachers and administrators Within the framework of leadership content knowledge and complexity leadership theory, three major themes emerged with regard to how different mathematical backgrounds and/or evaluative roles of observers influenced their feedback These themes focused on the form of the feedback (written and oral), the process for developing feedback (inductive and deductive), and the nature of feedback (content or pedagogical focus) The findings from this study most notably pointed to the difference in the nature of feedback to middle grades mathematics teachers from observers who had formal mathematics education or experience and those who had different subject backgrounds The findings also provide evidence to support several implications for mathematics education leaders, which are discussed

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MATH LABS: TEACHERS, TEACHER EDUCATORS, AND SCHOOL LEADERS LEARNING TOGETHER WITH AND FROM THEIR OWN STUDENTS

by: Elham Kazemi, Lynsey Gibbons, Rebecca Lewis, Alison Fox, Allison Hintz, Megan Kelley-Petersen, Adrian Cunard, Kendra Lomax, Anita Lenges, Ruth Balf

This article describes a structure for embedding professional development within a school day, which we call Math Labs. It enables teachers to come together, with the guidance of a teacher educator, to engage in collective inquiry into the teaching and learning of mathematics with time to experiment with new ideas with their own students. We explain the design principles, reflecting our commitments to equity and social justice, that motivate what occurs during a typical Math Lab. When Math Labs become an integral part of the school’s culture, they allow teachers and school leaders to negotiate (1) how they position and empower students; (2) what opportunities they give students to learn rich mathematics; and (3) what shared professional values guide their inquiry into students’ mathematical learning.

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