Journal of Mathematics Education Leadership

Spring 2018, Volume 19, Number 1

Articles in this issue

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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Fall 2017, Volume 18, Number 2

Articles in this issue

THE TEACHER ACTION Q-SORT: A CARD-SORTING TOOL FOR PROFESSIONAL LEARNING

by: Dana P. Franz, Jane Wilburne, Drew Polly, David A. Wagstaff

Reflection is an essential component of classroom teaching that successful mathematics teachers perform routinely and it is one of the imperatives that the National Council of Supervisors of Mathematics has identified as being integral to the provision of effective instruction that maximizes learning for all students Reflecting on one’s mathematics teaching promotes self-awareness and facilitates the implementation of the desired teaching practices In this article, we report on the use of a Q-sort to promote teachers’ reflection on their teaching as the latter relates specifically to their enactment of teacher actions associated with high-quality teaching practices We share teachers’ reflections on their use of the Teacher Action Q-sort and their views regarding the benefits of using a Q-sort We also address mathematics coaches’ insights on how a Q-sort can be used as a needs assessment and as a professional learning experience for teachers who want to conduct a self-appraisal of the degree to which they implement high-quality classroom teaching practices that provide all students with meaningful mathematics instruction.

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ELEMENTARY MATHEMATICS SPECIALIST PROGRAM: ONE STATE’S STORY OF DEVELOPMENT AND IMPLEMENTATION

by: Stacy Reeder, Juliana Utley

In this paper we present the development and implementation of the Oklahoma Elementary Mathematics Specialist certification pathway. The partnership among mathematics educators from several universities that led to the development and implementation of program requirements and coursework is shared. We also discuss the various challenges we faced throughout this process at the state and local levels. Finally, we provide evidence of the impact of these efforts from interviews of several teachers who completed the program.

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TEACHER TIME OUT: EDUCATORS LEARNING TOGETHER IN AND THROUGH PRACTICE

by: Lynsey Gibbons, Elham Kazemi, Allison Hintz,Bothell Elizabeth Hartmann

In this paper we present the development and implementation of the Oklahoma Elementary Mathematics Specialist certification pathway. The partnership among mathematics educators from several universities that led to the development and implementation of program requirements and coursework is shared. We also discuss the various challenges we faced throughout this process at the state and local levels. Finally, we provide evidence of the impact of these efforts from interviews of several teachers who completed the program.

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Spring 2017, Volume 18, Number 1

Articles in this issue

STRUCTURE VS. PEDAGOGY: THE IMPACT OF A FLIPPED CLASSROOM MODEL OF INSTRUCTION ON FIFTH-GRADE MATHEMATICS STUDENTS

by: Bethann M. Wiley

The Flipped Classroom model of instruction is being implemented at all levels of schooling and academic areas; yet, there is very little research regarding its effectiveness This study attempted to expand this body of research by looking at the Flipped Classroom model as it was implemented in fifth-grade mathematics classrooms As enacted in this study, the model involved students watching a video lecture at home and then completing traditional homework in class the next day The participants were 112 fifth-grade students from four classrooms in a Midwestern suburban school district Qualitative and quantitative data were collected through classroom observations, interviews, and posttests The Mathematics Teaching Practices were used as a framework to analyze the classroom instruction Further, research on students’ conceptual understanding of decimals and fractions formed the basis for understanding student thinking during interviews The data suggested that the Flipped Classroom model, as enacted in this study, strongly supported the use of rules and procedures, not always accurately, to the detriment of developing conceptual understanding Of equal concern was that low-achieving students had less access to the videos at home and more frequently found them frustrating or confusing Implications for mathematics education leaders are provided.

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MEETING THE NEEDS EXPRESSED BY TEACHERS: ADAPTATIONS OF THE TRADITIONAL MODEL FOR DEMONSTRATION LESSONS

by: Jeremy F. Strayer, Angela T. Barlow, Alyson E. Lischka, Natasha E. Gerstenschlager, D. Christopher Stephens, J. Christopher Willingham, Kristin S. Hartland

Demonstration lessons are one means for providing teachers with opportunities to reflect on instruction. Although different models for demonstration lessons are described in the literature, the Implementing Mathematical Practices And Content into Teaching Project, or Project IMPACT, developed two additional models of demonstration lessons in response to the expressed needs of project participants. In this article, we introduce these two models with the goal of supporting mathematics education leaders in enacting these models, or further adapting them, in their own work. Further, we aim to demonstrate how these models were developed in response to project participants’ needs.

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Fall 2016, Volume 17, Number 2

Articles in this issue

TEACHING REFORM-ORIENTED STATISTICS IN THE MIDDLE GRADES: RESULTS FROM A CASE STUDY

by: Natasha E. Gerstenschlager

With the Common Core State Standards for Mathematics, statistics has a more influential role in the middle grades curriculum than in the past However, statistics is generally not a priority in teacher professional development programs leading to teachers’ poor content knowledge in statistics and many teachers feeling unprepared to teach statistics These prove to be barriers to reform-oriented instruction, and some have recommended using lessons created by statistics educators as a way to address these barriers Unfortunately, simply having these lessons is not enough to ensure that students develop a conceptual understanding of the topic In addition, even if teachers have those lessons, there is limited research on how well instruction aligns with curriculum expectations when the lessons are implemented in the classroom and how this implementation is related to teachers’ mathematical perspectives Therefore, this descriptive case study examined the implementation fidelity, including deviations and alignment, of a reform-oriented statistics unit in a sixth-grade classroom and challenges the teacher identified regarding the implementation of the unit Implications of results to the mathematics and statistics education community are included.

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LEVERAGING MODELING WITH MATHEMATICS-FOCUSED INSTRUCTION TO PROMOTE OTHER STANDARDS FOR MATHEMATICAL PRACTICE

by: Jonathan D. Bostic, Gabriel T. Matney

The Standards for Mathematical Practice (SMPs) describe mathematical proficiency in terms of behaviors and habits that every student should develop during mathematics instruction. Modeling with mathematics supports students in gaining facility with multiple representations and making sense of real-world phenomena. We investigated K-10 mathematics teaching for possible associations between mathematics teaching behaviors promoting modeling with mathematics (SMP4) and those identified by the other SMPs, using a classroom observation protocol called the Revised SMPs Look-for Protocol. Data consisted of lessons and videos of mathematics instruction from 70 K-10 mathematics teachers engaged in professional development focused on the SMPs. Results illuminated several associations between modeling with mathematics (SMP4) and other SMPs. A typical instructional case illustrates these associations and suggests potential for further opportunities. Teachers aiming to foster students’ mathematical proficiency might consider instruction promoting SMP4 as a means to promote further connections to other mathematical behaviors and habits described in the SMPs.

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Spring 2016, Volume 17, Number 1

Articles in this issue

EXPLORING THE TECHNOLOGICAL PEDAGOGICAL CONTENT KNOWLEDGE (TPACK) OF HIGH SCHOOL MATHEMATICS TEACHERS: A MULTIPLE CASE STUDY

by: Jessica T. Ivy, Dana P. Franz

The Technology Principle highlights the opportunities offered to enhance instruction through technology integration. With the advent and increased availability of new technologies, access has become less of an issue, yet widespread integration of instructional technologies in ways that support learning are not necessarily observed in classrooms. In this article, the barriers to technology integration are considered, with a particular emphasis on pedagogical content knowledge and its role in development of technological pedagogical content knowledge (TPACK). This interplay of beliefs about student learning and practices when teaching with technology is explored through the cases of two secondary mathematics teachers with common backgrounds but contrasting levels of TPACK.

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MOVING BEYOND ONE-SIZE-FITS-ALL PD: A MODEL FOR DIFFERENTIATING PROFESSIONAL LEARNING FOR TEACHERS

by: Amy R. Brodesky, Emily R. Fagan, Cheryl Rose Tobey, Linda Hirsch

This article describes an innovative model for differentiating professional development to address teachers’ wide range of content knowledge, experiences, and interests. The model has three components: core activities that all participants experience; choice points that allow teachers to choose options to individualize their learning; and self-assessment opportunities to help teachers reflect on their knowledge and identify areas to strengthen. To elucidate the workings of each component and the overall model, we present design principles and examples from a differentiated professional development sequence on fraction multiplication. To support the application of the model, we share implementation findings and offer suggestions to help mathematics education leaders plan and facilitate professional development that is differentiated for their teachers’ needs.

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SEEKING BRIDGES BETWEEN THEORY AND PRACTICE: A REPORT FROM THE SCHOLARLY INQUIRY AND PRACTICES CONFERENCE ON MATHEMATICS METHODS EDUCATION

by: Alyson E. Lischka, Wendy B. Sanchez, Signe Kastberg, Andrew M. Tyminski

This paper reports on the NSF-funded Scholarly Inquiry and Practices Conference on Mathematics Education Methods (Grant No. 1503358), held in Atlanta, Georgia on September 30 through October 2, 2015. Conference participants from three different theoretical perspectives (sociopolitical, cognitive, and situative) discussed the goals and activities of methods courses with a focus toward developing more scholarly inquiry and practices in the work of methods instruction. Conference participants discussed ways of building partnerships between K-12 schools and university teacher education programs. Implications of the conference for mathematics supervisors and leaders are provided.

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Fall 2015, Volume 16, Number 2

Articles in this issue

IS THERE A COMMON PEDAGOGICAL CORE? EXAMINING INSTRUCTIONAL PRACTICES OF COMPETING MODELS OF MATHEMATICS TEACHING

by: Charles Munter, Mary Kay Stein, Margaret S. Smith

Debates concerning which ideas should be included in the K-12 curriculum, how they are learned, and how they should be taught are longstanding Although the adoption of the Common Core State Standards for Mathematics largely resolves content-focused aspects of the debates, pedagogical decisions remain open to interpretation The National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics have attempted to address this issue with recent calls to action, promoting particular instructional practices that represent a shared vision of the goal for every mathematics classroom We examine these practices from the perspectives of two competing approaches to mathematics instruction—dialogic and direct—to ask whether a shared vision is sometimes inaccurately presumed, and to press for a common pedagogical core that includes not only specifications of observable practices, but also their underlying rationales in terms of equitably supporting all students in coming to know and do mathematics.

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FRAMING PROFESSIONAL CONVERSATIONS WITH TEACHERS: DEVELOPING ADMINISTRATORS’ PROFESSIONAL NOTICING OF STUDENTS’ MATHEMATICAL THINKING

by: Cory A. Bennett, Julie M. Amador, Christine Avila

In this paper we share the first phase of an on-going professional development project for administrators aimed at helping them facilitate non-evaluative professional conversations with mathematics teachers. School administrators have the ability to support teachers’ instructional practice, however, administrators’ ability to notice pivotal moments in students’ mathematical thinking greatly influences the quality of support they can provide. Findings indicated that administrators were initially not specific about noticing students’ mathematical thinking when observing lessons, but their ability to notice and plan for conversations about students’ mathematical thinking developed over time.

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THE NEED FOR RESEARCH INTO ELEMENTARY MATHEMATICS SPECIALIST PREPARATION

by: Zandra de Araujo

The continued concern for the mathematical preparation of elementary teachers has kept discussions of elementary mathematics specialists (EMS) a vital part of many mathematical reforms. With over half the states providing or in the process of developing EMS certifications, a closer examination of the ways in which EMS are prepared is needed. In this paper, I explore several types of EMS, the current state of EMS preparation, and literature related to EMS. I then discuss the potential constraints associated with preparing EMS. I close with a discussion of future avenues of research related to EMS preparation and a call for more research in this area.

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LESSONS FROM THE FIELD: CHALLENGES WE FACE WHEN COACHING TEACHERS

by: Joy W. Whitenack, Aimee J. Ellington

In this article, we highlight three of the common challenges that many coaches have experienced in one form or another: seeking administrative support for coaching teachers; working with teachers who are resistant or reluctant; and moving beyond demonstrating lessons. Each challenge has its unique set of circumstances that present possible opportunities for the coach to capitalize on and further support teachers’ daily work. We use these particular examples to provide the reader with opportunities to examine and reflect on situations coaches might encounter.

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Spring 2015, Volume 16, Number 1

Articles in this issue

MATH TEACHERS’ CIRCLES AS A FORM OF PROFESSIONAL DEVELOPMENT: AN IN-DEPTH LOOK AT ONE MODEL

by: Diana White

In this paper, I discuss one chapter of a growing professional development program that aims to improve the quality of mathematics education for students by developing middle level mathematics teachers’ content knowledge and problem-solving skills, as well as their facility with applying the Standards for Mathematical Practice I provide context within the national program, then discuss how the local chapter emerged, describe in detail the summer workshop and associated academic year sessions, discuss outcomes from the program, and provide information regarding how to start a similar program.

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NORMS FOR TEACHERS’ DISCUSSIONS OF STUDENTS’ MATHEMATICS IN PROFESSIONAL DEVELOPMENT SETTINGS

by: Cyndi Edgington, Paola Sztajn, P. Holt Wilson, Marrielle Myers, Jared Webb

In this paper, we share our experiences using student work to engage teachers in learning about students’ mathematical thinking and the need to develop norms for talking about students’ mathematics in professional development settings. In such settings, it can often be challenging to maintain productive perspectives that focus on students’ mathematics. We describe our experiences facilitating a professional learning task designed to support teachers’ participation in discussions about students as mathematics learners. We share discourse norms that can be used by teacher leaders to focus teachers’ discussion on students’ mathematical thinking and a set of questions that teachers may use to reflect on their students’ mathematical thinking as they engage in discussions with colleagues about students’ mathematics.

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THE ESSENCE OF FORMATIVE ASSESSMENT IN PRACTICE: CLASSROOM EXAMPLES

by: Marjorie Petit, MPC Mary Bouck

Formative assessment involves the eliciting of students’ understanding for the purpose of informing instructional decisions In this paper, we present an overview of formative assessment strategies We include classroom examples that capture the essence of formative assessment and conclude with questions intended to engage teachers and teacher leaders in reflecting on the teacher actions necessary to support effective implementation of formative assessment strategies

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ENVISIONING THE ROLE OF THE MATHEMATICS TEACHER

by: Charles Munter

This article presents a tool for identifying and tracking changes in teachers’ (and others’) evolving visions of the role of the mathematics teacher through five levels: motivator, deliverer of knowledge, monitor, facilitator, and more knowledgeable other. It includes a brief account of the rubric’s development and a description of its use in a large-scale, longitudinal study of mathematics instructional reform efforts in four urban school districts, including an examination of relationships between the ways that teachers envision their roles and the quality of their instruction. The article concludes with a discussion of implications for mathematics education leaders, including a description of how the tool was used in a recent professional development effort.

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THE PERSPECTIVES OF TEACHER LEADERS ON MATHEMATICS, LEARNING, AND TEACHING: SUPPORTING REFORM-ORIENTED INSTRUCTION

by: Michelle T. Chamberlin, Melissa L. Troudt, Reshmi Nair, Alisa Breitstein

We conducted a qualitative study investigating the perspectives of mathematics teacher leaders on mathematics, learning, and teaching throughout a mathematics teacher leadership program. Data sources included nine mathematics teacher leaders’ work on three application essays and four assignments across the leadership program. Through a template analysis, we applied a perspectives framework to characterize the views of teacher leaders in transition toward reform-oriented mathematics instruction. Findings revealed all the mathematics teacher leaders entered the program with a view of mathematics as connected and logical with desires to provide active mathematical experiences for students to develop understanding. Approximately half of the teacher leaders enhanced this view to begin to incorporate students’ different views on mathematics into instruction, while the other teacher leaders appeared to continue to view mathematics as an objective discipline, independent of students’ constructions. Implications include ideas for supporting mathematics teacher leaders in enhancing their views of mathematics, learning, and teaching.

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Summer 2014, Volume 15, Number 2

Articles in this issue

ROLE-PLAYING THE STANDARDS FOR MATHEMATICAL PRACTICE: A PROFESSIONAL DEVELOPMENT TOOL

by: Jonathan D. Bostic, Gabriel T. Matney

This article describes a performance assessment to use during Common Core-focused professional development and shares insights from research using this assessment regarding about teachers’ comprehension of the Standards for Mathematical Practice (SMPs). We asked 46 teachers from grades K-10 to read and make sense of the SMPs and then role-play a classroom scenario indicative of one SMP. This performance task is called Unpacking the SMPs. Teachers’ interactions during the role-play activity were intended to help them interpret the SMPs. From this role-play activity, PD providers were more aware of teachers’ initial comprehension of the SMPs.

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THE COMMON CORE STANDARDS FOR MATHEMATICAL PRACTICE: TEACHERS’ INITIAL PERCEPTIONS AND IMPLEMENTATION CONSIDERATIONS.

by: Travis A. Olson, Melfried Olson, Stephanie Capen

Teachers’ responses to surveys involving two prompts after their first in-depth reading of the Standards for Mathematical Practice (SMP) in professional development settings are reported. Specifically addressing calls for research on how teachers are viewing their role in the implementation of the Common Core State Standards for Mathematics, and in particular the SMP, these data highlight what terminology teachers potentially focus on in reading the descriptions of the SMP. Additionally, the data highlight the roles that teachers envision themselves taking as they plan for and implement the SMP in their classrooms. We provide analysis of the teachers’ responses, as well as discussion and suggestions for mathematics education leaders as they engage classroom teachers and other leaders in considering the implications for implementing the SMP with respect to student and teacher classroom roles.

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ANALYZING STUDENTS’ WORK TO REFLECT ON INSTRUCTION: THE INSTRUCTIONAL QUALITY ASSESSMENT AS A TOOL FOR INSTRUCTIONAL LEADERS

by: Melissa D. Boston, Michael D. Steele

In this article, we discuss how instructional leaders can use collections of students’ work and the Instructional Quality Assessment (IQA) Mathematics rubrics to initiate conversations with groups of mathematics teachers and to monitor the success of professional development initiatives and curricular implementation efforts. In our work, collections of students’ work are used to reflect on instructional practice, by considering the nature of instruction that supported students to produce the mathematical work and thinking. We ground the discussion in specific examples from two studies in which collections of students’ work and the IQA rubrics were used to diagnose the effectiveness of professional development and curriculum implementation efforts, engage teachers in reflecting on practice, and inform next steps in the instructional change process.

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THE MATHEMATICS EXCELLENCE PARTNERSHIP: DEVELOPING PROFESSIONAL LEARNING COMMUNITIES

by: Lillie R. Albert, Karen Terrell, Vittoria Macadino

The Mathematics Excellence Partnership project was a professional development project aimed at supporting the development of 22 high school teachers of mathematics, including special education and bilingual teachers. In this paper, we share our school-based, bottom-up, collaborative design that supported the development of professional learning communities.

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USING PARTICIPANT RESPONSES TO VIDEO OF COACHING PRACTICE TO FOCUS MATHEMATICS COACHING PROGRAMS

by: David A. Yopp, Angela T. Barlow, John T. Sutton, Elizabeth A. Burroughs

This article addresses what practices coaching experts and school-based coaches observed and did not observe when watching the practice of another coach. A coach is broadly defined as a person who works collaboratively with a teacher to improve that teacher’s practice and content knowledge, with the ultimate goal of affecting student learning. Definitions of coaching knowledge, coaching texts, and standards for mathematics specialists identify three primary aspects of knowledge for coaching: developing teacher content knowledge, promoting reflection by the teacher, and negotiating professional relationships. When we asked school-based coaches and coaching experts to assess the practice of a novice coach depicted in a video-recorded coaching session, surprisingly few of the respondents commented explicitly on these three areas of coaching practice. This indicates that professional development for mathematics coaches can focus specifically on how these three big ideas for coaching are enacted in practice. We offer recommendations for mathematics programs for focusing professional development with respect to these three practices.

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Winter/Spring 2013, Volume 15, Number 1

Articles in this issue

LEARNING TO LEAD PROFESSIONAL LEARNING COMMUNITIES IN MATHEMATICS

by: Karin Brodie, Nicholas Molefe, Flourencia Lourens

Professional learning communities are increasingly seen as a generative and sustainable method of in-service teacher development in mathematics. Professional learning communities are situated in teachers’ instructional practices and support teachers in using their experience, evidence from their classrooms, their own and their colleagues’ insights, and knowledge from research, to decide what they need to learn and how they can learn it. Leadership of professional learning communities is central to their success and facilitating mathematical conversations in communities is an important part of leading them. Learning to facilitate community conversations takes time and collaborative work among facilitators. In this paper we show how a professional learning community of mathematics facilitators worked together to develop facilitation skills. As part of the community of facilitators, we analysed episodes from teachers’ community conversations, focusing on the role of the facilitators. We show how our analyses supported the facilitators’ learning through a focus on mathematical inquiry, developing teachers’ mathematical knowledge and building community.

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ESTABLISHING A COMMUNITY OF PRACTICE FOR COOPERATING TEACHERS

by: Theresa Gurl

This article reports on a qualitative study examining the establishment of a community of practice among cooperating teachers in secondary mathematics. Data were collected during several semi structured group and individual interviews and analyzed using qualitative coding methods. Results indicated that the cooperating teachers found the community to be helpful and supportive, and revealed what cooperating teachers felt that they needed to be successful, including hard-working student teachers who respond to feedback and clear expectations from the college. This study also found benefits to cooperating teachers, including learning or re-learning innovative approaches, reenergizing their teaching. The study also found that cooperating teachers were more likely to use such approaches when the university supervisor was present, admitting to doing "different things" during observations than on a day-to-day basis. Participants found it difficult to mediate what they referred to as the "idealism" of the college in relation to the realities of the classroom. Implications for the field are shared. 

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PROFESSIONAL DEVELOPMENT MODELS AT SCIENCE, TECHNOLOGY, ENGINEERING, AND MATHEMATICS (STEM) FOCUSED HIGH SCHOOLS

by: Catherine Scott
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TEACHERS’ PERCEPTIONS OF OBSERVING REFORM-ORIENTED DEMONSTRATION LESSONS

by: Angela T. Barlow, Sydney M. Holbert
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DEEPENING TEACHERS’ UNDERSTANDINGS OF MATHEMATICAL AND PEDAGOGICAL CONNECTEDNESS: THE WALK-ACROSS TASK

by: Gabriel Matney

The study here exams ways in which mathematics professional development providers and teachers can examine new forms of mathematics standards to deepen understanding about the subtle differences from prior standards. Teachers engaged in a type of cross-walk activity which focused on making connections. Findings from the study revealed that teachers deepened their knowledge of the connectedness of mathematics and from this quality of mathematics emerged four important pedagogical changes for their teaching:  1. providing students time and opportunity to make their own mathematical connections; 2. providing students with worthwhile mathematics tasks to engage their intellect; 3. establishing a safe and respectful learning environment with an expectation of student sense making; and 4. becoming more adept facilitators of mathematical discourse. Through the Walk-Across discussions, the teachers became more open to their development of adaptiveness to students’ mathematical ideas and emergent teaching scenarios.

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Fall/Winter 2012-13, Volume 14, Number 2

Articles in this issue

STATE-LEVEL ACTIONS FOLLOWING ADOPTION OF COMMON CORE STATE STANDARDS FOR MATHEMATICS.

by: Barbara J. Reys, Amanda Thomas, Dung Tran, Shannon Dingman, Lisa Kasmer, Jill Newton, Dawn Teuscher

The adoption of Common Core State Standards for Mathematics (CCSS-M) by 45 states,1 the District of Columbia, the Northern Mariana Islands, and the U.S. Virgin Islands represents a historic landmark in curriculum governance in the United States. For the first time, a significant majority of K-12 teachers and students will focus on common learning expectations for mathematics. Coupled with common grade-level assessments aligned to CCSS-M currently under development by two state-led consortia—Partnership for Assessment of Readiness for Colleges and Careers (PARCC) and the Smarter Balance Assessment Consortium (SBAC)—this initiative has the potential to impact aspects of educational practice critical to K-12 students’ mathematical learning (e.g., teacher preparation and professional development, curriculum material development, and policies related to K-12 course-taking and graduation requirements).

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STANDARD ALGORITHMS IN THE COMMON CORE STATE STANDARDS

by: Karen C. Fuson, Sybilla Beckmann

This article discusses standard algorithms for multidigit addition, subtraction, multiplication, and division. It clarifies that the Common Core State Standards state that students are to develop, discuss, and use efficient, accurate, and generalizable methods in the first year in which a multidigit computation is introduced so students may use a standard algorithm from that early year. Standard algorithms rely on decomposing numbers written in base-ten notation into base-ten units. The properties of operations then allow any multi-digit computation to be reduced to a collection of single-digit computations. These single-digit computations sometimes require the composition or decomposition of a base-ten unit. There are multiple standard algorithms for any computation; these are just variations in the written method. Criteria for variations that should be taught in classrooms are discussed. The best method for multidigit addition writes the new groups on the line below the problem. The best method for multidigit subtraction does all needed ungrouping first and then subtracts everywhere; this can be done from the left or from the right. Best methods for multidigit multiplication and division are discussed. Common methods that are often taken to be “the standard algorithm” for an operation are described and shown to be problematic because they elicit errors or make it difficult to understand the place values involved. Math drawings that show place value and support student sense making are used throughout the article to enable teachers to use such drawings in the classroom and teach computation meaningfully.  

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CHALLENGING COURSES AND CURRICULA: A MODEL FOR ALL STUDENTS

by: Bernadette Mullins, Patty Lofgren, Ruth Parker, Barry Spieler, Faye Clark, Rachel Cochran, Ann Dominick, Jason Fulmore, John Mayer, Sherry Parrish,

 The Common Core State Standards for Mathematical Practice describe “varieties of expertise that mathematics educators at all levels should seek to develop in their students.” These eight mathematical practices are consistent with the definition for Challenging Courses and Curricula developed by the NSF-supported Greater Birmingham Mathematics Partnership (GBMP). The four main attributes of challenging mathematics courses are that they deepen knowledge of important mathematical ideas, promote inquiry and reflection, develop productive disposition, and foster communication. We describe classroom practice with examples from GBMP classrooms that illustrate our definition of challenging courses and develop the student proficiencies described in the Standards for Mathematical Practice.

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THE IMPORTANCE OF CONTEXT IN PRESENTING FRACTION PROBLEMS TO HELP STUDENTS FORMULATE MODELS AND REPRESENTATIONS AS SOLUTION STRATEGIES

by: Travis A. Olson, Melfried Olson

Drawing on research with middle grades students, and preservice and inservice teachers of mathematics, we provide an analysis and discussion of work related to a particular contextualized mathematical situation involving fractional quantities and proportional relationships. We examine ways in which individuals utilize contextual aspects of the mathematical situation to visually represent solutions within mathematical structures of ratios and proportions. We provide our perceptions of the ways in which district and teacher leaders may engender the importance of contextualizing and decontextualizing within the framework of the Standards for Mathematical Practice.

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EFFECTIVE PROFESSIONAL DEVELOPMENT: DEFINING THE VITAL ROLE OF THE MASTER TEACHER

by: Paul Cruz, Ngozi Kamau, Anne Papakonstantinou, Richard Parr, Susan Troutman, Robin Ward, Carolyn White

Originally conceptualized in 1987 as a bridge between the research mathematicians at Rice University and the precollege mathematics education community, the Rice University School Mathematics Project (RUSMP) has evolved over time, transcending its initial goal, and now serving as a nationally recognized K-12 mathematics education center with a documented ability to improve teacher knowledge and student learning  RUSMP nurtures and prepares mathematics teachers to become a collaborative community of highly-skilled, K-12 mathematics educators capable of providing effective mathematics instruction to all students - regardless of race, gender, socioeconomic status, mathematics aptitude, or prior success in mathematics.  Although RUSMP offers a wide variety of programs and support for the K-12 educational community, the cornerstone of RUSMP is its Summer Campus Program (SCP) initiated through National Science Foundation funding.  A key to the success of SCP are master teachers, who are K-12 classroom teachers who serve as instructors, role models, and mentors for participating teachers. The term “master teacher” can mean many things to many people. Master teachers have always been selected for their abilities as exemplary teachers as identified by Rice University faculty and local district mathematics leaders. The roles of the RUSMP master teachers have evolved over time. This paper is an attempt to further the discussion towards a common understanding of the meaning of the role that is vital to effective teacher professional development and to investigate the selection, development, characteristics, roles, and impact of teacher leaders identified by RUSMP as SCP master teachers. 

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Spring 2012, Volume 14, Number 1

Articles in this issue

SUPPORTING TEACHERS’ EFFECTIVE USE OF CURRICULAR MATERIALS

by: M. Lynn Breyfogle, Kay A. Wohlhuter, Duluth Amy Roth McDuffie

Using “teacher leader” broadly to include anyone in a position to support teachers in their professional development and learning, this article outlines two approaches for teacher leaders to support mathematics teachers in developing their curricular reasoning. These approaches were used effectively and with measurable improvement in classroom instruction. Curricular reasoning is the thinking processes needed to work effectively with curricular materials to plan, implement, and reflect on instruction. The approaches outlined in this article are an observation-conferencing cycle and supporting teacher collaboration. During the observation-conferencing cycle teacher leaders are encouraged to employ deep-listening and suspending personal assumptions to help teachers make decisions based on students’ needs and provide opportunities for focused reflection. Secondly, teacher leaders are also called upon to support teacher collaboration by establishing and supporting teacher learning communities. Across both forms of professional development the teacher leader is most effective by employing powerful questions to prompt critical thinking.

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SUPPORTING TEACHERS’ UNDERSTANDING AND USE OF ALGEBRA TILES

by: Randall E. Groth, Jennifer A. Bergner, Harel Barzilai

One of the most formidable challenges in school mathematics is helping students learn algebra. The construction of algebraic habits of mind is an important milestone in students’ mathematical development (Driscoll, 1999). To reach this milestone, students must learn algebra with understanding rather than simply learning by rote (Kieran, 2007). Although conceptually oriented teaching approaches show promise for building student understanding (Senk & Thompson, 2003), making the shift to a reform-oriented curriculum is a non-trivial matter. Teachers often must re-examine their personal paradigms of athematics instruction while also learning about new content and instructional materials. Mathematics education leaders need to be cognizant of teachers’ specific professional development needs with regard to algebra teaching and learning and determine how to address them.

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CONDITIONS THAT SUPPORT THE CREATION OF MATHEMATICAL COMMUNITIES OF TEACHER LEARNERS

by: Michelle Stephan, Charlotte Didem Akyuz, George McManus, Jennifer Smith

In his seminal work, Richard DuFour argues compellingly that if educational reforms are to be sustained long-term, schools must transform themselves into professional learning communities (DuFour, 1998). Professional learning communities (PLCs) can be distinguished from traditional school cultures in that all personnel from the principal to the classroom teacher are committed to collaboration using data about student learning to make decisions regarding school policy and practice. Supporting a school-wide culture that acts in this way is more difficult than it seems since teachers are accustomed to (and quite comfortable with) working in isolation. Encouraging teachers to make their students’ learning public to other teachers is met with resistance because it exposes our personal teaching practices and beliefs to our peers.

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EARLY NUMERACY INTERVENTION: ONE STATE’S RESPONSE TO IMPROVING MATHEMATICS ACHIEVEMENT

by: Sara Eisenhardt, Jonathan Thomas

A significant number of children struggle with quantitative ideas during the first few years of their academic careers and fail to construct a meaningful sense of number. These early struggles, if not addressed, can limit students’ mathematics performance as they move through the grade levels. If these struggling students are fortunate enough to receive intervention services, most often they are provided too late and are provided by teachers with little knowledge of numeracy development. Duncan et al (2006) identified the predictive power of early mathematics knowledge and found that knowledge of numbers and ordinality were the most powerful predictor of later learning. The study recommends future research to identify “promising early math interventions” (p. 21).

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CHANGING TEACHERS’ CONCEPTION OF MATHEMATICS

by: Eric Hsu, Judy Kysh, Diane Resek, Katherine Ramage

This paper describes the efforts of the authors to work with a group of in-service and pre-service math teachers to change their conception of mathematics. We describe the teachers’ starting conception and our desired re-conception. We then detail our efforts to craft moving experiences that would shift their thinking. We discuss why it is insufficient to “just tell them” and conclude with a cautionary note about the differing experiences of our teacher leaders who did or did not craft similar experiences for their fellow teachers.

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PARTNERSHIPS FOR LEARNING: USING AN INNOVATION CONFIGURATION MAP TO GUIDE SCHOOL, DISTRICT, AND UNIVERSITY PARTNERSHIPS

by: Cathy Kinzer, Lisa Virag, Sara Morales, Ken Korn

There is a pressing need for effective partnerships between government, business, communities, schools, universities, and other stakeholders in education. This need is magnified by the current involvement of foundations, business, and government in educational endeavors such as the Common Core State Standards for Mathematics and research grants funded through the National Science Foundation. These endeavors often require focused collaborative interactions between all stakeholders that ultimately support a learning system and students’ achievement. The purpose of this article is twofold: (a) to report key findings that emerged from our research partnerships, and (b) to offer an instrument that assesses the readiness and measures the effectiveness of educational research partnerships between schools and universities.

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PREPARING TEACHERS TO CULTIVATE PARENT-CHILD COLLABORATION IN MATHEMATICS

by: Regina M. Mistretta

The National Science Foundation, through its funding of curriculum projects such as Everyday Mathematics that include a family component, demonstrates its recognition of the significance of families in mathematics education. This is just one example of several curriculum projects and school initiatives that value collaboration with families. Such efforts respond to the National Council of Teachers of Mathematics’ call to build family understanding of current school mathematics goals and instructional practices so that home and school may support each other (National Council of Teachers of Mathematics, 2000).

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Fall 2011, Volume 13, Number 2

Articles in this issue

IMPROVING STUDENT ACHIEVEMENT BY SYSTEMATICALLY INTEGRATING EFFECTIVE TECHNOLOGY.

by: Jeremy Roschelle, Menlo Park, Steve Leinwand

It is the position of NCSM that in order to develop all students’ mathematics proficiency, leaders and teachers must take responsibility for the systematic classroom integration of effective technologies to enhance curriculum, pedagogy, assessments, and approaches to equity. Using research informed practices, NCSM members need to identify the technologies and make decisions about when and how to use these technologies in ways that strengthen students’ mathematical thinking and learning.

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MATHEMATICS COACHING KNOWLEDGE: DOMAINS AND DEFINITIONS

by: John T. Sutton, Elizabeth A. Burroughs, David A. Yopp

Instructional coaching is a professional development approach where a coach works collaboratively with a teacher to improve that teacher’s practice and content knowledge. We conducted a Delphi study to develop an operational definition of coaching knowledge that capitalizes on the existing knowledge of experts in the field of mathematics coaching. The result is a set of definitions for eight domains of coaching knowledge: assessment, communication, leadership, relationships, student learning, teacher development, teacher learning, and teacher practice.

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STANDARDS FOR COMPUTATIONAL FLUENCY: A COMPARISON OF STATE AND CCSS-M EXPECTATIONS

by: Barbara Reys, Amanda Thomas
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ORGANIZING A FAMILY MATH NIGHT

by: Tim Jacobbe
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REFLECTIONS ON CREATING STRONG MATHEMATICS COACHING PROGRAMS

by: Janet M. Herrelko
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TRANSFORMATIONAL PROFESSIONAL DEVELOPMENT: TEACHER LEARNING THROUGH A BIFOCAL LENS

by: Janet Lynne Tassell, Hope Marchionda, Sandra Baker, Allison Bemiss, Liz Brewer, Kathy Read, Terri Stice, Alice Cantrell, Daryl Woods
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WE NEED ELEMENTARY MATHEMATICS SPECIALISTS NOW, MORE THAN EVER: A HISTORICAL PERSPECTIVE AND CALL TO ACTION

by: Francis (Skip) Fennell

This article noted the need for urgency, response-wise in both understanding and implementing the Common Core State Standards for Mathematics (2010) while recognizing that elementary mathematics specialists are the “go-to” building and school-based leaders for addressing such an initiative. The article summarizes many of the important responsibilities of elementary mathematics specialists (e.g., mentoring/coaching, providing professional development, coordinating interventions) and provides a historical perspective identifying particular milestones in the development and support for mathematics specialists, including the dissemination of important policy-related related manuscripts and decisions. Examples include NCTM recommending state certification endorsement for elementary mathematics specialists (1984); Everybody Counts’ support for specialization in mathematics at the elementary school level (1989); NCTM’s Principles and Standards for School Mathematics suggesting exploration of models for elementary mathematics specialists and teacher leaders (2000); the National Mathematics Advisory Panel’s recommendation regarding elementary mathematics specialists (2008); and the NCTM/NCSM/AMTE/ASSM Joint Position Statement related to the Role of Elementary Mathematics Specialists in the Teaching and Learning of Mathematics. The article also discusses how states have become involved in using the varied policy documents and recommendations discussed to advocate for elementary mathematics specialist certification and the Association of Mathematics Teacher Educators’ (AMTE, 2009) guidelines for specialist accreditation and certification. Finally, the article also noted that many elementary mathematics specialists/coaches/instructional leaders are appointed to such positions without elementary mathematics specialist certification or proper vetting related to their content, pedagogical, and leadership knowledge and skills, and raised concerns about the limited research related to the impact of mathematics specialists/coaches/leaders, recommending research related to aspects of an elementary mathematics specialist’s responsibilities. 

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