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Engaging Students in Geometry: Addressing Misconceptions and Fostering Classroom Discussions

On July 6, engage in a thoughtful discussion about a geometry article related to misconceptions and students’ understanding of exponents. Following a TIMSS clip review, contemplate strategies to initiate lessons effectively and activate prior knowledge in students. Given the trapezoid OABC with specified dimensions, determine the areas of triangle MBC and rectangle MNPO, exploring when triangle areas might exceed rectangle areas. Collaborate with peers to identify key solutions worth sharing, discuss potential student misconceptions, and outline how to ensure these misconceptions are addressed in future lessons.

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Engaging Students in Geometry: Addressing Misconceptions and Fostering Classroom Discussions

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  1. Week 2 Day 7 Tuesday, July 6

  2. Discuss at your table what you learned from the article • Is there anything that relates to what you have learned so far?

  3. After showing TIMMS clip from yesterday again. • Think for two minutes on your own about how to start the lesson to address the students’ misconceptions and make sure they are ready to move on and how to activate the knowledge kids should have had about exponents.

  4. Given a trapezoid OABC where OA = 4 cm AB = 2 cm OC = 6 cm AO perpendicular to OC M is a point moving on AO Triangle MBC and rectangle MNPO are such that N is on segment BC and P is on segment OC. • Find the areaof the triangle MBC and the areaof the rectangle MNPO. • What is the maximum area for the triangle MBC and the rectangle MNPO? • When, if ever, will the area of the triangle be larger than the area of the rectangle?

  5. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why?

  6. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why? • What important mathematical points or points about mathematical reasoning would you like to make about this problem.

  7. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why? • What important mathematical points or points about mathematical reasoning would you like to make about this problem. • What student misconceptions or errors do you think students might have?

  8. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why? • What important mathematical points or points about mathematical reasoning would you like to make about this problem. • What student misconceptions or errors do you think students might have? • Do you think that these misconceptions would be taken care of by having kids share within their table and/or across tables?

  9. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why? • What important mathematical points or points about mathematical reasoning would you like to make about this problem. • What student misconceptions or errors do you think students might have? • Do you think that these misconceptions would be taken care of by having kids share within their table and/or across tables? • How can you make sure these are addressed?

  10. Homework for Wednesday • Read the six pages of the classroom transcripts from Jean Krusi’s chapter: Revoicing: the Good, the Bad, and the Questions in Promoting Purposeful Discussions p. 125 – 131. • Jean Krusi asked her students for ideas of what makes a good discussion. • What elements in the classroom make it possible to have a good discussion? • Write your ideas down in your journal and be prepared to share some of them on Wednesday.”

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