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Module 1, "Teaching Mathematics: Conceptualizing Linear Relationships", was piloted in five different sites in the country. Three different evaluation efforts assessed various aspects of this work. Two efforts were aimed at assessing teacher learning from these materials and one examined facilitation. In addition, the VCMPD project staff conducted a small ethnographic study of four teachers in one of the VCMPD pilots.
Learning Content in the Context of Practice: A Videocase Curriculum Example
Heather C. Hill, University of Michigan, Rachel M. B. Collopy, Winthrop University
Summary
Heather Hill and Rachel Collopy developed an external pre and post assessment that attempted to measure growth in teachers' content knowledge and pedagogical content knowledge. The instrument Hill and Collopy developed is based on their work on the "Study of Instructional Improvement" and "Developing Knowledge for Teaching Mathematics, " studying the professional development institutes supported by the University of California, Office of the President (Hill & Collopy, 2002). They conducted a quasi-experimental study of a pilot and comparison group.
Their analysis suggests tentative optimism regarding the efficacy of the VCMPD approach in improving a teachers' capability in understanding a narrow range of subject matter in teaching linear functions. Teachers in the VCMPD experimental group did improve their ability to algebraically represent at least one problem involving geometric patterns, connect their algebraic representation to the geometric pattern, and in another case, compare and link alternative representations of the same linear function. They were also more able to identify one potential student misunderstanding—using a recursive method for predicting the next term—than the comparison group. Although finding this effect of VCMPD participation, Hill and Collopy do not ascertain the extent to which teachers' growth between the pre/post-tests is statistically significant, given the small sample size. However, equivalent growth did not appear in the small comparison group, which provides some assurance that the improvement did not result from retaking the same items over a relatively small time span.
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Measuring Teacher Knowledge in Mathematics Professional Development Using Embedded Assessments
Daniel J. Heck (Horizon Research, Inc.)
Summary
Horizon Research, under the guidance of Iris Weiss and Dan Heck, developed an embedded assessment to measure the impact of the program on teachers' content knowledge and pedagogical content knowledge. These "embedded" tools are part of the actual work teachers do within sessions. One of the embedded instruments asks participants to solve a mathematics task, reflect on their own approaches to solving the task, and predict approaches students might use to solve it. Near the end of the module they are asked to do a similar process with another mathematics task. There is also a pre and post video analysis task. This assessment was analyzed across four pilot sites and a comparison group of similar teachers to support treatment group-control group comparisons.
In terms of exhibiting mathematical knowledge pertinent to the teaching of mathematics, VCMPD participants were statistically more likely than comparison group teachers to increase in their ability/propensity to connect their work on the Mathematics Tasks back to the pictorial representations in which the task originated. This finding was supported both through identifying the intercept in the pictorial representation and through describing or representing the arrangement of the pictorial representation in their solution. Aiding students in translating from pictures to more abstract representations, such as equations, likely depends on teachers' ability and propensity to make such connections. The increase in attention to the intercept as represented in the pictorial representation may reflect another effect of the program, as VCMPD teachers were more likely than comparison group teachers to attend to this concept in their plans for instruction.
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Lessons Learned from the Pilot Test of Module 1
Pamela Tambe, Mark St. John,Kasi Fuller, Nina Houghton, Joan Mitchell, Tamara Evans
Summary
Inverness Research and Associates conducted a study of the use of the VCMPD materials in five pilot settings located across the country examining how facilitators used the materials, what supports they needed and what teachers seem to be making of their experiences with them. They identified the benefits and challenges of using the materials and the supports required by facilitators to use these materials effectively. To gather data they used multiple interviews with facilitators, interviews with session participants, and observation of different sessions at each of the pilot sites. Their findings indicate that overall the materials were feasible for use by lfacilitators in real settings and that every facilitator judged the materials to be of high quality, thoughtfully designed and coherent. Facilitator training was found to be critical to the level of success of the professional development in these pilot settings, and yet the importance and difficulty of "mining the video" surfaced repeatedly (Tambe, St. John, et al, 2002).
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Examining Teachers' Development in Representing and Conceptualizing Linear Relationships within Teaching Practice
Judith Mumme and Nanette Seago
Summary
Each teacher was observed pre and post project using a classroom observation protocol. Each teacher was also interviewed post project and asked to comment on their participation and was they felt they gained from the experience. Data from the Horizon and the Hill/Collopy assessments were cross-analyzed along with the classroom observation and interview data. This small study appears to demonstrate that teachers who showed increase in content and pedagogical content knowledge also showed growth in classroom practices.
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