The professional development comes from a sequenced series of eight, three-hour video case sessions designed to enrich teachers' ability to teach linear relationships and deepen their own detailed knowledge of the distinctions and linkages among the various representations. Each session includes three basic elements: doing mathematics, viewing and discussing video, and linking to practice. Over the course of the first five sessions, the 24 participating middle school teachers were very engaged in solving mathematics problems and analyzing classroom video episodes. One new area for many of the teachers was representing various non-simplified methods algebraically. During one session, the teachers worked on the following task in preparation for viewing the video segment of a high school classroom:
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After solving the problem individually, the teachers shared their solution methods with each other in small groups. The facilitator pulled the whole group together to share particular solution methods, asking one teacher to share her method with the whole group. She shared her method without speaking, drawing circles around tiles, using different colors to distinguish chunks in the picture and matching them to the equation:
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After she had finished, the group that had been intently watching her draw and write, collectively responded with "Ahhh!" As the teachers reflected about their learning at the end of the eight sessions, many talked about their increased knowledge of various methods to solve a single problem and how to represent them algebraically, allowing them to look at other problems with new skills for decomposing, representing, and generalizing.
A five-day institute for middle school science teachers focused on the flow of matter and energy in living systems. A central goal of the institute was to deepen teachers' content knowledge of a specific benchmark from Benchmarks for Science Literacy (AAAS, 1993), which states:
Food provides molecules that serve as fuel and building materials for all organisms. Plants use the energy in light to make sugars out of carbon dioxide and water. This food [sugars] can be used immediately for fuel or materials, or it may be stored for later use. Organisms that eat plants break down the plant structures to produce the materials and energy they need to survive. Then they are consumed by other organisms. [5E(6-8)a, p.120].
In working towards a deeper understanding of the ideas within this middle grades benchmark, facilitators addressed the content within the benchmark, related common prior conceptions, and more advanced ideas about the content. Because this benchmark includes multiple abstract ideas, the institute was designed to address each specific component idea situated within the concrete notion of food. Daily focus questions led teachers through explorations of and discussions about these component ideas:
| Daily Focus Questions | |
| Day 1 | What is food? Why do organisms need it? |
| Day 2 | Where does food come from? |
| Day 3 | How is food used for growth? |
| Day 4 | How is food used for energy? |
| Day 5 | What happens to matter/energy after death? |
The process began with teachers developing a diagram (i.e., concept map, energy flow diagram, Venn diagram, or cartoon) depicting their current thinking in answer to these questions. Daily reflections on their content learning resulted in modifying their existing diagrams and/or creating new diagrams. By the end of the week, the teachers had constructed a visual depiction of the entire benchmark, portraying understanding of each of the component ideas and the connections among them, conceptually similar to the diagram below:
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