Teacher resources and professional development across the curriculum

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RepresentationSession 05 Overviewtab atab btab ctab dTab eReference
Part E

Evaluating Representation
  Make a Lesson Plan | Summing Up the Session | Final Journal

 
 

Rich mathematical tasks should incorporate the use of representations to help students show their thinking, using both non-traditional and traditional methods. Very young children will use physical gestures, drawings, and invented symbols. As students begin formal writing, the use of words and symbols can accompany these early representations. A good lesson will include opportunities for students to use various forms of representation as they complete a task. We want students to be able to translate among various types of representations, including models, diagrams, tables, charts, and graphs, as well as written representations, including numerical and symbolic forms -- moving from a concrete model to a written representation. Finally, representations should be imbedded in student discussions and class presentations to support students in communicating their mathematical thinking.


An effective lesson should include several stages. In the lessons you have viewed, you saw the teacher introduce a problem by first asking questions to help students understand the problem and make choices about possible tools and strategies to use. Students then worked with partners to solve the problem. A key component of an effective lesson is giving students opportunities to share their approaches, strategies, and solutions. The representations we have talked about in this session are the means by which young students think through and solve a problem, and then demonstrate their understanding of what the problem means. As discussed in previous sessions, the teacher must carefully craft the direction of this summary.


You will now use the information you learned in this session to plan a lesson for one of your classes. Plan an activity around a topic that will focus on the use of representations to demonstrate student thinking. Students' work should include representations of their ideas and solutions. You may want to choose an activity that relates to a concept we have introduced and explored in this session and can now be extended. Alternatively, you may use a problem you teach in your subject area, or select one of the samples from the Learning Math courses.

After you have created your lesson plan, use the Classroom Checklist (an Adobe PDF document) to evaluate it.

Next  Finish the session

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