Secondary Mathematics Professional Development Center
Dr. Agida Manizade, Dr. Laura Jacobsen, Christine Belcher, Robert Thien, Jamey Lovin, Stephanie Brady, Dee Baker
The Secondary Mathematics Professional Development Center (SMPDC) has been funded by multiple Math and Science Partnership grants through the Virginia Department of Education (VDOE) since 2010 through the present. The SMPDC serves high school mathematics teachers as well as middle school teachers teaching high-school-level mathematics classes. The main goal of the Center is to provide a professional development program to teachers interested in improving their mathematical knowledge and pedagogical content knowledge (PCK). Our research has shown that teachers who participate in these programs have significantly improved their subject matter knowledge as well as their PCK in algebra, statistics, probability, geometry, and Algebra Functions and Data Analysis. The SMPDC has partnered with public school systems across the Commonwealth, several institutes of higher education in Virginia, the Virginia Math and Science Coalition and NASA. The SMPDC has served 352 mathematics teachers since its original funding in 2010, providing over 700 contact hours of graduate-level professional development coursework to the teachers. The participants have created several hundred products available to teachers across the commonwealth, including lesson plans, unit plans, performance-based assessments, and classroom videos. SMPDC faculty have produced 39 publications and presentations based on work related to our projects in state, national, and international professional outlets. The purpose of this paper is to present materials developed by secondary mathematics teachers, for secondary mathematics teachers.
The SMPDC was originally funded in 2010 by a Math and Science Partnership grant from the VDOE and has received six consecutive years of funding through MSP grants. The individual projects’ foci varied each year, based on the goals as identified by VDOE, however, they shared the common themes of: 1. Improving teachers’ mathematical knowledge and pedagogical content knowledge; 2. Developing and improving an online PD model; and 3. Developing resources for mathematics classrooms in critical areas identified by the VDOE. In addition, the project Principal Investigators (PIs) published dozens of research papers (e.g., Corey, D.et. al., 2016; Manizade & Jacobsen, 2013; Manizade, & Martinovic, 2016) in national, international, and state outlets. Our purpose for this paper is not to focus on the research findings, but instead the outcomes most relevant and useful for practicing mathematics teachers. We intend to use this paper to disseminate the knowledge gained by teachers during these projects and provide an opportunity to use the materials produced by their peers. These include, but are not limited to hundreds of unit and lesson plans, problem based assessments, classroom videos, and teacher interviews. All of these products are published on the project website and are freely available for use by teachers across the Commonwealth. Several examples will be discussed later in this paper.
The online PD model for secondary teachers was developed through a collaborative effort with public schools, state universities, and other institutions across the Commonwealth such as Virginia Commonwealth University, the College of William and Mary, Longwood University; the Virginia Math and Science Coalition; and NASA’s Langley research facility. Courses are transferable between partnering institutions. Online classes were designed to be hands-on and interactive, see an example at http://lecture-play.radford.edu/Mediasite/Play/84c88e2983c44e4eb35189c4f6e4ee911d . The focus of the model was to improve secondary mathematics teachers’ subject matter knowledge in Algebra 1, Algebra 2, AFDA, Geometry, Modeling, and Probability and Statistics. Since 2010, six grant projects have been conducted, serving 352 teachers, and providing more than 700 hours of instruction. The number of partners each grant year varied between 25 and 52. The complete list of partners and details on each project are available on our website at http://www.radford.edu/rumath-smpdc/PartnersMap.html.
Figure 1. Sample performance-based assessment task
Literature Review and Research Overview
Teachers’ subject matter knowledge and pedagogical content knowledge have long been widely acknowledged as essential components of teaching expertise (e.g., Shulman, 1986). The Mathematical Education of Teachers II (AMS/CBMS, 2012) report recommended continual improvement of mathematical knowledge and teaching skills, with such improvement promoted by regular interactions between teachers, mathematicians, and mathematics educators in the creation and analysis of mathematics lessons, texts, and curriculum materials as well as examinations of the underlying mathematics. The SMPDC provides mathematics teachers with extensive opportunities such as online graduate level courses in mathematics designed for secondary teachers, summer institutes at NASA, and classroom observations and feedback. These programs help develop teachers’ knowledge bases and ultimately increase students’ mathematics achievement.
Teachers’ mathematical knowledge for teaching contributes significantly to gains in students’ mathematics achievement (e.g., Hill, Rowan, & Ball, 2005; Sample McMeeking, Orsi, & Cobb, 2012; Telese, 2012). The Mathematical Education of Teachers II (2012) co-publication by the American Mathematical Society (AMS) and the Conference Board of the Mathematical Sciences (CBMS) indicated, “Although high school mathematics teachers frequently major in mathematics, too often the mathematics courses they take emphasize preparation for graduate study or careers in business rather than advanced perspectives on the mathematics that is taught in high school” (p. 5). The high school curriculum prepares students for sophisticated and often abstract understandings, but may not prepare teachers to see the mathematics through students’ eyes (McCrory, Floden, Ferrini-Mundy, Reckase, & Senk, 2012). Teachers need both advanced mathematical knowledge and an understanding of how that advanced mathematical knowledge relates to the high school curriculum (AMS & CBMS, 2012; McCrory et al., 2012). Our primary underlying assumption is that by providing teachers with quality educational experiences, the corresponding increase in their subject and pedagogical content knowledge will translate into changes in classroom practices that ultimately have a positive impact on students’ learning
The SMPDC’s research examines the Center’s impact on measuring: (1) gains in teacher content knowledge, (2) impact on student achievement, and (3) progress towards meeting the assessed needs of partnering school divisions. Toward these ends, assessment measures include pre- and post-assessments of teachers’ mathematical content knowledge and mathematical knowledge for teaching Algebra I, Algebra II, and AFDA; multiple classroom observations of selected participating teachers using Instructional Quality Assessment (IQA) rubrics (Junker et al., 2006); teacher surveys addressing content or pedagogical content knowledge; assessments of gains in high school students’ understanding and knowledge of Algebra I, Algebra II, and AFDA; surveys of participating school administrators; participating teacher surveys to evaluate the strengths and to offer suggestions for the SMPDC; and course fidelity assessments to evaluate whether courses are designed and taught in ways that correspond with identified needs of partnering school divisions. Based on the SMPDC project evaluation reports from the past six years, teachers have shown a significant gain in their knowledge of algebra, geometry, and probability and statistics as well their ability to implement new educational technologies in their classrooms. Readers who wish to engage with the data and analysis portions of the projects can find full evaluation reports for each of the six projects at the SMPDC website. (http://www.radford.edu/~amanizade/projects)
One of the main outcomes of the MSP projects are the hundreds of products generated and shared by the participating teachers. These include lesson plans, unit plans, and performance-based assessments and have been made available in the Teacher Resources section of our project’s website, http://www.radford.edu/rumath-smpdc/.
These products then went through two to three rounds of blinded peer-review with external reviewers, and are currently available for use by teachers across the Commonwealth. The products implement best practices for teaching mathematics, and feature hands-on, interactive activities with various STEM applications. In this paper we will share two example products including a unit plan and a performance-based assessment.
Our first example is a performance-based learning and assessment task that was designed by teachers Dee Baker, Jamey Lovin and Robert Thien (http://www.radford.edu/rumath-smpdc/Performance/src/Dee%20Baker%20-%20Building%20a%20Recreation%20Center.pdf ). In this task, learners were prompted to explore constructions of triangle centers to determine the best location for a recreation center with respect to three communities in a geographic area (Figure 1).
To solve the task, students used applications such as GeoGebra, Google Maps, as well as standard construction tools. The task included two assessment components and rubrics which assess students’ understanding of the content (Figure 2). Students were expected to select a site and justify their selection using credible research, geometric principles, and constructing triangles (Figure 3).
Figure 2. Rubric for student evaluations
Our next example is a unit plan by Christine Belcher and Stephanie Brady (http://www.radford.edu/rumath-smpdc/Units/src/A%20Change%20in%20the%20Weather.pdf). This unit, “A change in the weather”, guides students through data analysis, finding equations of the curve of best fit, mathematical modeling that includes polynomial, exponential, and logarithmic functions, and making predictions, as well as teaching them about climate as one of the real world applications of mathematics.
Figure 3. Sample of student work
Students create charts and models using provided data of 17 different locations across the world (Figure 4, Figure 5), and make scatterplots and trend lines of the data (Figure 5), as well as other indicators of climate change such as global mean sea level and temperature.
We also have samples of classroom videos of our participants implementing different approaches to teaching mathematics. These approaches include the Structuralist, Integrated-Environmentalist, and Formative approaches. They also feature the teachers’ educational knowledge and insights gained from the program. They can be watched at the SMPDC website http://www.radford.edu/rumath-smpdc/VideoCourse.html (see Figure 6). Our project website includes hundreds of more products like the examples included in our papers. We encourage readers to examine and utilize these free resources.
Figure 4. Example worksheet
Figure 5. Provided temperature data
Implications and Recommendations
Providing teachers with an online, ongoing professional development program that involves partnerships between multiple institutions of higher education, and which utilizes the strengths of these institutions, allows the creation of an effective, statewide program for the continuing improvement of mathematics education. An important element of this model is simple and easy credit transfers between partner institutions, allowing teachers flexibility in taking graduate-level classes. This also allows institutions and their faculty to focus on their strong subject areas, increasing the overall quality of the professional development. An important part of our professional development projects over the past six years has been our presence in participants’ classrooms following the courses. We observed and interviewed teachers and provided them with critical feedback related to the quality of their mathematics instruction. This not only allows us to see if the theoretical knowledge learned during the course has been implemented in the participants’ classrooms, but also provides an opportunity for additional professional development in the field.
We also encourage the continued development of online courses that feature hands-on, interactive instructional practices that allow teachers to engage with the ideas of the content area through exploration and discovery. We recommend the use of all available technological tools such as Adobe Connect, Geogebra, Cinderella, Mathematica, and others to aid in the creation of an interactive online environment. We also recommend providing participants with manipulatives and corresponding explorations to complete as part of their coursework. This helps address the major obstacle of online professional development courses, the lack of interaction and hands-on experiences. Finally, we suggest that all of the teacher-generated products created during the projects be available for use by teachers throughout the Commonwealth, as this is one of the most effective ways of distributing the knowledge generated in each program.
Figure 6. Screenshot of an online video
During the past six years of the MSP projects at Radford University, we were consistently able to show growth in the following areas: 1) Teachers’ content knowledge and pedagogical content knowledge in Algebra, Geometry, and probability and statistics. 2) Students’ mathematical knowledge in the aforementioned areas. We also met the needs of the participating partners, and addressed the goals identified by the Commonwealth. The major challenges of the MSP projects relate to the following: 1) The availability of reliable and valid assessment measures of teachers’ professionally situated knowledge at the high-school level. 2) The rate of turnover of teachers in the partner divisions. 3) The length of the award periods that prevent longitudinal studies. We would also like to invite readers to explore the products and resources created as a result of these projects, which can be found on our website, (http://www.radford.edu/rumath-smpdc/Resources.html).
American Mathematical Society & Conference Board of the Mathematical Sciences (2012). The Mathematical Education of Teachers II. Providence, RI: AMS and CBMS.
Corey, D., Jacobsen, L., Manizade, A., Dove, A., Galeshi, R. & Younes, R. (2016).
Best Practices: Lessons Learned From an Online Statewide Collaborative Master's in Mathematics Education Program. In Proceedings of Society for Information Technology & Teacher Education International Conference 2016 (pp. 2497-2498). Chesapeake, VA: Association for the Advancement of Computing in Education (AACE).
Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
Junker, B., Weisberg, Y., Matsumura, L. C., Crosson, A., Wolf, K., Levinson, A., et al. (2006). Overview of the instructional quality assessment. CSE Report 671, National Center for Research on Evaluation, Standards and Student Testing (CRESST), University of Los Angeles, Los Angeles, CA.
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Manizade, A.G., Martinovic, D. (2016). Developing interactive instrument for measuring teachers’ professionally situated knowledge in geometry and measurement. In P. MoyerPackenham (Eds.), International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives (pp.323-342).Switzerland: Springer Publishers DOI 10.1007/978-3-319- 32718- 1_14
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Sample McMeeking, L. B., Orsi, R., & Cobb, B. R. (2012). Effects of a teacher professional development program on the mathematics achievement of middle school students.Journal for Research in Mathematics Education, 43(2), 159-181.
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