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Vickie Inge, Chair	Loren Pitt, VMSC Liaison
Mathematics Coordinator	President VMSC
Stafford County Schools	Mathematics Professor University of Virginia

Susan Birnie	Patricia Moyer-Packenham
Curriculum Specialist for Mathematics	Assistant Professor Mathematics Education
Alexandria City Schools	George Mason University

Donna Dalton	Patricia Robertson
President VCMS	Mathematics Supervisor
Director of Instruction	Arlington City Schools
Chesterfield County

Jerry Gambino	Yvonne Smith-Jones
Mathematics Coordinator	Director of Mathematics, Science and Technology
Fairfax County Schools	Hopewell City Schools

Jacqueline Getgood	Diane Tomlinson
President VCTM	Science Content Specialist and Virginia Co-director
Mathematics Supervisor	Coalfield Rural Systemic Initiative
Spotsylvania County Schools	Russell County Public Schools

Jenny Groh	Tina Weiner
President VSELA	Mathematics Coordinator
Augusta County Schools	Roanoke City Schools

Vandivere Hodges	Denise Walston
President-Elect VCTM	Mathematics Coordinator
Mathematics Specialist	Norfolk City Schools
Hanover County

Betti Kreye	Jay Wilkens
Mathematics Supervisor	Assistant Professor Mathematics Education
Montgomery County Schools	Virginia Tech

LouAnn Lovin	Susan Wood
Assistant Professor Mathematics Education	Professor of Mathematics
James Madison University	J. Sargeant Reynolds Community College

Marcella McNeil
Mathematics Supervisor
Portsmouth City Schools

Over the last decade several compelling studies and reports have identified the strong connection between student achievement and the quality of teacher knowledge and skills (Wenglinsky, 2002; Public Agenda, 2000; Kain, 1998 ). Furthermore, Sanders and Rivers (1996) as well as Monk and King (1994) found that low-achieving students made significantly greater performance gains when assigned to effective teachers.

The National Research Council’s report, Educating Teachers of Science, Mathematics, and Technology informs us that, “the kind and quality of teachers’ inservice education can make a difference in how their students achieve” (p. 63). Richard Elmore (2002) reports that professional development focused on student learning must be tailored to address the difficulties encountered by real students in real classrooms. School based mathematics specialists will allow elementary and middle level teachers to benefit from site-based and in-depth learning experiences which are close to classroom practice and that are ongoing and reflective. (WestEd, 2000)

Efforts to support Teacher Specialist Programs are taking root across Virginia as school divisions look for ways to raise student achievement by improving mathematics instruction. For the purposes of this report we will define instruction as what teachers do. Instruction consists of the interactions involving teachers, students, and content. To frame our work and to guide our research we asked the question, “What interventions or deliberate efforts to improve instruction will be enhanced by a mathematics teacher specialist and what preparation is necessary take on this role?”

We believe any efforts aimed at improving instruction require a departure in some degree from current practice. Implementation of these efforts requires teachers to learn new knowledge, skills, and practices as well as increasing their capacity to use more effectively what they already know and can do (Cohen & Ball, 2001). Research informs us that teacher knowledge profoundly affects student achievement. Students perform better when they are able to learn from teachers who have a deep understanding of the mathematics they are teaching and who also are knowledgeable about improved ways to teach (National Research Council, 2000). In today’s high stakes education climate students who are not taught by highly qualified teachers may be penalized. For example, they may be held back or not allowed to graduate. We need more highly qualified teachers but instead, what we are faced with is a scarcity of teachers who possess a profound understanding of the mathematics they teach. Today this issue is so critical that the goal of having highly qualified teachers in all classrooms is mandated in the No Child Left Behind (NCLB) Federal education act.

To help teachers improve instruction and become increasingly expert we must recognize teaching as a lifelong journey of learning rather than a final destination of “knowing” how to teach (Darling-Hammond, 2000). We must ensure that teachers have the necessary support as they move through the continual changes encountered on their journey. From our interviews and observations we have learned that a variety of strategies are underway across the Commonwealth to improve instruction in mathematics. The common element among all of these interventions is that classroom teachers must make changes in their instructional programs and practices. In Virginia schools these changes center around implementing new and innovative curricula, increasing teacher learning through professional development opportunities or coursework, restructuring instructional time, and establishing accountability for outcomes.

Effective mathematics teaching is complex, requiring both a broad base and a special content knowledge for successful instruction. The 2000 National Survey of Science and Mathematics Education conducted by Horizon Research Inc. for the National Science Foundation reported that only 60 percent of the elementary teachers in their survey felt qualified to teach mathematics. Based on our surveys and interviews with school division personnel Virginia teachers at the elementary and middle school levels lack profound understanding of the content as well as a comprehensive knowledge of content pedagogy. In elementary schools teachers are typically generalists, with minimal course work in mathematics. Often these teachers have only one or two mathematics courses in college. While Virginia has raised the requirements in mathematics coursework for those seeking middle school certification, many middle school mathematics teachers do not have the equivalent of a mathematics major or minor in college. In many cases middle school teachers are former elementary teachers who have moved to middle school.

Virginia , just as many other states, has many teachers entering the classroom through alternative licensure routes. School divisions are finding that while these teachers may have the content knowledge for the workforce, they lack the specialized content knowledge and the content pedagogy for effective teaching. Subject matter knowledge is not sufficient for effective teaching to take place (Wilson, Floden & Ferrini-Mundy, 2002). In their government commissioned report they also state, “[Without training in pedagogy] it appears that prospective teachers my have mastered basic skills but lack deeper conceptual understanding necessary when responding to student questions and extending lessons beyond the basics.” (p. 192)

To address these issues, the Virginia Department of Education as well as school divisions in Virginia have provided staff development and course work for teachers in both content and in pedagogy. School divisions have implemented mentoring programs for new teachers. Informal observations and interviews reveal that these interventions have not been sufficient for various reasons. Often it is not possible to scale up staff development learning opportunities to reach all of the teachers in a school. Most of these learning opportunities as well as the mentoring programs are not sustained over time; thus the impact on teachers’ beliefs and behaviors is marginal. Virginia teachers and administrators reported to the Task Force that ongoing site-based assistance is necessary to adequately support teachers in the change process. One way to provide this sustained support is to develop and maintain a cadre of mathematics teacher specialists who can offer site-based consistent and meaningful guidance to their colleagues.

Evolution of the Lead Teacher Program in Virginia

The concept of a content teacher specialist is not a new concept in Virginia but it is an evolution of the lead teacher model established in Virginia more than ten years ago. In 1992 the Virginia Mathematics Coalition, now the Virginia Mathematics and Science Coalition, joined with the Virginia Department of Education, the Virginia Council of Teachers of Mathematics and others in a National Science Foundation (NSF) funded project, V-QUEST, to prepare elementary and middle school teachers to serve as “Math Leaders” or “Science Leaders” in their schools. Over the three years of funding, participating K-8 mathematics and science teachers increased their knowledge in mathematics and science content and in content pedagogy during intensive and focused summer institutes. These teacher leaders returned to their schools to lead efforts toward improving teaching and learning in mathematics and science.

A 1997 report by Pitt and Critchfield documented the variety and effectiveness of lead teacher programs in nine representative Virginia school divisions three years after V-QUEST ended. Among other indicators these school divisions reported the lead teachers served as curriculum leaders and resources for teachers as well as providing staff development for teachers. Several divisions attributed the rise in test scores to the work of the lead teachers. The report also illuminated the significant variations across the state in how the lead teacher program evolved and was sustained. The greatest differences were seen in the preparation and support for the lead teachers. In some divisions there had been no additional training beyond the V-QUEST training. In other divisions there was modest unfocused and inconsistent training. Some divisions were able to secure grant funding to support continued preparation for teacher leaders. One division secured an ExxonMobil teacher leadership grant in mathematics. Several divisions participated in SCHEV Eisenhower grants focused on preparing teacher leaders. However, it was clear from this report that without a statewide infrastructure to prepare specialists these nine divisions had difficulty maintaining a pool of highly qualified mathematics specialists.

In March 2002 a survey of 43 Virginia school divisions conducted at a meeting of the Virginia Council of Mathematics Supervisors indicated that the teacher leader concept lives on in schools across the state. However, there is no stability in the programs because there is no statewide agenda to continually prepare content-based teacher leaders or content specialists. In addition, there is presently no license to validate the teacher leader or to recognize teachers who have participated in learning opportunities that might prepare them to be specialists.

Further analysis of the surveys revealed that twenty-three different titles are used to designate the state's mathematics lead teachers. The primary responsibility of these leaders was to serve as liaisons between the school boards’ central offices and the school sites. The surveys indicated a critical need for the mathematics teacher leaders to take a more active role in providing staff development for teachers and leadership for the building level mathematics program. However, from these surveys we learned that a number of barriers stand in the way. Teacher leaders need a deeper understanding of the mathematics content being taught. In addition, teacher leaders need more knowledge about mathematics content pedagogy (how both students and adults learn to make sense of mathematics) and they need to develop leadership skills as well as skills to facilitate adult learners.

On May 20, 2002 the Virginia Mathematics and Science Coalition, the Virginia Council of Mathematics Supervisors, and the Virginia Council of Teachers of Mathematics with support from ExxonMobil Education Foundation hosted a forum, “Moving from Teacher Leaders to Mathematics Teacher Specialists”, in Fredericksburg, Virginia. At this time representatives from school divisions across Virginia indicated their commitment to providing high quality mathematics and science programs for all students. As school divisions continue to move forward to strengthen their instructional programs so that no child is left behind, what support will classroom teachers need? The participants in this forum agreed that a well-prepared mathematics teacher specialist could be an effective support for classroom teachers.

Virginia educators and politicians have set forward an agenda to ensure that every student has the opportunity to study a high quality mathematics program that prepares them for further study in mathematics as well as to be productive members of society. Expectations for student learnings have been defined in the nationally recognized framework, The Virginia Standards of Learning. A state assessment system has been implemented to monitor student progress toward meeting the Virginia Standards of Learning in Mathematics. In grades K-8 Virginia students are assessed in mathematics at the end of grades 3, 5, and 8. Under the No Child Left Behind act additional assessments in mathematics will be implemented at grades 4, 6, and 7. At the secondary level students enrolled in Algebra I, Geometry, and Algebra II must take end-of-course assessments.

Accountability weighs in, as students must pass prescribed numbers of end-of-course tests depending upon the type of diploma they are seeking. Each year greater numbers of students are passing the Virginia Standards of Learning (SOL) assessments. However, many children across the Commonwealth are still not passing these assessments and are at risk of not graduating from high school. Most troubling are the results of tests at the elementary and middle school level. An examination of the 2002 SOL test results posted on the Virginia Department of Education web site reveals that 20% of the state’s third graders, 29% of the state’s fifth graders, and 29% of the state’s eighth graders did not pass the 2002 SOL grade level tests in mathematics.

The disaggregated data from the 2002 SOL reveal that across the state there are gaps between the percent of white students passing the tests and the percent of the subpopulations who passed the tests. This can be illustrated by looking at a few of the smallest gaps. In mathematics at grade three there is a 22 point gap between the white and black populations and a 29 point gap between the white population and the disabled population. We see similar differences between the white population and the LEP population as well as the Hispanic population.

While concerned with the numbers of students not passing and with the gaps between populations, we are just as concerned that more students are not passing at the advanced proficient level. It is important to note these tests set forth minimal expectations for students.

Teacher learning is a catalyst for school reform and improvement in teaching and learning. As shown in this report, staff development efforts are unlikely to be either effective or enduring without carefully considering provisions to support the growth of teachers’ understanding of their practices. Improvement in student learning is not as simple as teaching teachers how to teach differently but requires actually working in classrooms in such a way that teachers in the process of changing their practice are continuously supported. Teachers, with support from a building level content specialist, can develop strong expertise in the teaching and the learning of mathematics and science (Elmore, 2002). A specialist is a teacher whose interest and special preparation in mathematics content and pedagogy are matched with special teaching or leadership assignments to support teaching and learning (Reys & Fennell, 2003, p. 280).

Building level administrators seldom have the time or the expertise in mathematics to lead the changes to improve instruction in this area. The NCTM Principles and Standards of School Mathematics states (2000, p.375): “There is an urgent and growing need for mathematics teacher leaders – specialists positioned between classroom teachers and administrators who can assist with the improvement of mathematics education.” Teacher specialists in Virginia ’s middle and elementary schools will be first-hand observers and participants in the school culture. These specialists will be aware of the needs of the school, provide solutions that address those needs, and help ensure that every child becomes proficient in mathematics.

Adam Gamoran and colleagues (2002) used information from a multiyear study conducted by the National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA) to examine what successful schools and school divisions are doing to transform teaching in mathematics and science. The teachers in this study reported that the most important resources of the change process were time spent planning and learning with other teachers and in collaboration with experts inside the school.

Franke, Kazemi, Shih, and Biagetti (1998) found that professional development was more effective in helping teachers make significant changes in their practice if teachers were able to reflect on their own students and practice rather than hypothetical students and situations. Furthermore, Fennema, Carpenter, Franke, Levi, Jacobs, and Empson (1996) in their work with teachers implementing Cognitively Guided Instruction found that site-based support was paramount in facilitating changes in teachers’ beliefs, knowledge, and instructional practice - changes that were found to ultimately enhance student achievement. The Task Force believes that school based specialists in mathematics teaching and learning can fill the role of experts in teaching and learning and that their work can be distributed within a number of different models.

We have learned through interviews and surveys that within the past two years several school divisions in Virginia have implemented building level “mathematics specialist” type positions. Each division or in some cases each school has defined the role of that “specialist” type position to meet their individual needs, some have full release time while others do not. Since there is no state sanctioned definition of “math specialist” there is no common language and school divisions have chosen to use different titles for the position. Not having state licensure creates an even more problematic issue in terms of preparation for the job. There is no confirmation of who is highly qualified to fill the role. The Virginia stories below will illuminate both the benefits of school based “mathematics specialist” as well as the difficulties created without state licensure and institutionalized preparation programs.

In Stafford County full time mathematics specialists have been placed in five elementary schools to co-teach classes, to provide site-based and job-embedded professional development to teachers and paraprofessionals, to coach first and second year teachers, to analyze student assessment data to inform instructional planning, and to provide parent education programs. Stafford is using a grant from the ExxonMobil foundation to provide staff development to provide the skills and knowledge to meet the requirements of the job, however this preparation is not recognized outside of Stafford County .

In Dinwiddie County schools full time mathematics resource teachers in each elementary school are doing a “push-in” program where they work with small groups of students in teachers classrooms and model lessons for teachers. They also collaborate with teachers in analyzing assessment data and in planning mathematics instruction. Without state licensure there is little recognition of their work outside of Dinwiddie County .

In 1988 Alexandria City schools began participating in the Chicago Math Project for math specialists training. Two sets of math specialists were trained during the grant period. However once the grant ended the initiative lost energy, the concept of mathematics specialist was not recognized by the state and therefore was not self-sustaining. The project is underway once again with an ExxonMobil grant.

For the past eleven years Hanover County schools have participated in an ExxonMobil grant to prepare teacher leaders. In fact these teachers have become strong and capable leaders within their schools and these teachers are ready to assume staff positions with release time to assist their peers. However, since there is no statewide designation for mathematics specialist their preparation and expertise is not validated or readily identified.

Eleven Title I schools and one targeted assistance Title I school in Prince William County added a full time mathematics specialists position in 2002-2003. Without state licensure or state sanctioned competencies principals did not have immediate evidence of which applicants were most qualified for the job.

Norfolk City schools have maintained Project Math Lead that was begun during the V-QUEST project. Significant staff development funds are dedicated to the ongoing training and support for these teachers. However, the qualifications of the specialists varies greatly. In addition, there are thirteen Title I schools with Title I math teachers and 4 additional schools with math resource teachers. Principals choose the teachers for these positions with no state licensure or identified competencies to guide their decisions. Statewide infrastructure for preparing specialists and for licensing specialists would enhance the Norfolk program and increase the effectiveness of the teachers serving in the roles described above.

As shown in the examples above consensus continues to grow across Virginia that mathematics teacher specialists can facilitate teacher learning leading to improvement in student learning. Based on our research and from information gathered during interviews and surveys in Virginia schools, The Task Force recommends that school based mathematics specialists be prepared to assume any or all of the following responsibilities.

Recommended School-based Mathematics Specialist Responsibilities:

Teachers in a program leading to an endorsement as a mathematics specialist need to be in an environment where they can work collaboratively, feel free to make mistakes and learn from them; and they need challenging mathematics content, which at the same time is related to school mathematics. Typically, higher education mathematics departments do not offer the kinds of courses that would be appropriate for these teachers. It is crucial that the faculty in the college of arts and sciences and the faculty in the education department collaborate with school divisions to plan and deliver programs to prepare school based mathematics specialists. Schools of education should look for ways to “reinforce and integrate learning, rather than maintaining artificial barriers between courses in content and pedagogy (National Research Council, 2000).

The Task Force believes it is important that specialists develop a broad range of vision about the mathematics curriculum, student learning, and teaching. Mathematics specialists need to learn significant mathematics in situations where good mathematical content pedagogy is modeled. They must increase their content knowledge as well as deepening their knowledge of both school mathematics content and content pedagogical issues based on current research in mathematics teaching and learning. School based specialists will provide leadership in a variety of ways and must have the opportunity to strengthen their own leadership skills, to develop facilitation skills for adult learning, and to become effective change agents. The Task Force recommends that mathematics specialists demonstrate the following competencies.

Recommended Competencies for Mathematics Specialists:

Support a commitment to all children learning mathematics.
Possess a deep understanding of the mathematics that teachers teach including a core knowledge base of concepts and procedures within the discipline of mathematics, incorporating the following strands: number systems and operations; geometry and measurement; statistics and probability; and functions and algebra.
Focus on a thorough development of basic mathematical ideas and skills with an emphasis on understanding the sequential nature of mathematics and the mathematical structures inherent in the content strands.
Display careful reasoning and an understanding of the connections among mathematical concepts and procedures in solving problems.
Possess an understanding of and the ability to use the five processes: becoming a mathematical problem solver; reasoning mathematically; communicating mathematically; making mathematical connections; and using mathematical representations.
Possess the ability to use meaningful measures of students’ skills and understandings in mathematics.
Evaluate student’s work and student’s thinking and use this to inform instruction.
Support the use of technology to improve teaching and learning mathematics.
Demonstrate ability to collaborate with teachers through coteaching, mentoring, and coaching.
Demonstrate the ability to identify teachers’ individual professional development needs and individualize staff development efforts to include both formal and job-embedded professional learning experiences.
Demonstrate the leadership skills necessary to facilitate staff development in mathematics content, mathematics pedagogy, and assessment of student learning.

The Task Force reviewed the possible role and responsibilities that a specialist in Virginia ’s school might take on and the competencies necessary to carry out these responsibilities. Based on our review of research at the national level as well as information gathered from school divisions in Virginia we recommend that a candidate seeking an endorsement as a mathematics specialist have completed at least three years of successful classroom teaching experience in which the teaching of mathematics was an important responsibility. In addition the mathematics specialist should have graduated from an approved mathematics specialists preparation program (master’s level); or completed a master’s level program in mathematics, mathematics education, or related education field with at least 30 semester hours of graduate course work in the competencies described above, including at least 21 hours of coursework in undergraduate or graduate-level mathematics.

Not only must mathematics specialist have mathematics content knowledge but also a conceptual understanding of the principles underlying its topics, rules, and definitions (National Research Council, 2000). In addition, they must have pedagogical content knowledge to include but is not limited to useful representations, unifying ideas, clarifying examples and counter examples, helpful analogies, important relationships, and connections among ideas. Pedagogical content knowledge is a subset of content knowledge that has particular utility for planning and conducting lessons that facilitate student learning (Shulman, 1986).

Teachers preparing to be mathematics specialists must have the opportunity to take classes that include content in number and operations, functions and algebra, geometry and measurement, and data analysis, statistics, and probability. Technology as a tool for teaching and learning should be integrated into coursework as appropriate. Furthermore, these classes should incorporate the five processes: becoming mathematical problem solvers, reasoning mathematically, communicating mathematically, making mathematical connections, and using mathematical representations. Classes must be relevant to the work of mathematics specialists, allowing them to develop a deep understanding of the mathematics content. Instructors must model effective content pedagogy and allow specialists the opportunity to demonstrate their ability to implement effective teaching practices in their school. The key aspect is to verify that teachers can transfer what they have learned in the college setting to their work as a specialist.

To build leadership skills courses must be offered that will enable candidates to build a deep understanding of how students learn mathematics and of pedagogical knowledge specific to mathematics teaching and learning. Candidates will learn to develop curriculum based on current research including national and state standards for mathematics and will design instruction that meets the needs of diverse learners.

Coursework will enable candidates for a mathematics specialist endorsement to develop skills in analyzing individual student performance on a variety of assessment protocols and in analyzing and interpreting individual as well as collective test data. They will use the results from this analysis to inform instructional decisions. In addition, candidates will learn to gather and interpret relevant data about instructional strategies and instructional programs to facilitate improvements in student learning.

Programs preparing mathematics specialists will include the opportunity for candidates to develop skills in planning, implementing, and evaluating job-embedded support and staff development for all teachers including the mentoring of new teachers. This preparation will also help teachers develop effective communication skills to share researched based knowledge and skills with administrators, parents, and the greater community.

Recommendation for Mathematics Teacher Specialist Licensure

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Preparation for the Mathematics Teacher Specialist