One conclusion stands out as having the most impact - the choice of problem: discussion was deeper and more productive when practicing-with-the model instead of going-over-homework. Colleen Megowan.
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Tools (diagrams, graphs, models) must be useful and used for multiple reasons.
Practice the model problems are a funnel that opens rather than closes.
Models are necessary to figure what its possible to know.
Diagrams and graphs are necessary to link equations to models and to organize thinking.
The plug and chug strategy utterly fails.Dwayne Desbian
Breaking the problem into parts can destroy the value of open-ended investigation.
Students don't authentically need the models as a tool until they have to solve a complex problem that requires multiple models for its solution.
Students see all the parts, rather than the models.Challenges with Implementation in High School Classes
The other half are re-written as practice-the-model problems and students see them for the first time in their small groups during class.
Solutions go onto the whiteboards first.
Everyone solves the same problem and solutions are compared in board meetings.Split Worksheets
Start with a carefully-designed scaffold and then quickly remove it.
Early introduction helps them handle more complex problems later.Matched Modeling Problems
Space is limited so that they must decide what is important to include.
Must fit on one whiteboard without being cluttered.
Must include multiple representations.
Must have everything necessary to solve any problem to which this model applies.Model Summary Boards
They have to recognize the modes as distinct pieces.
The metaphor of the web site rather than the single fact-filled page.Concept Maps