 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 10, Part A:
Geometry and Reasoning (25 minutes)

The study of geometry in high school is often associated with proof -- usually an axiomatic development with a focus on two-column, statement-reason type proofs. Newer curricula based on the NCTM standards have reduced this emphasis on two-column proof in geometry in favor of a problem-solving approach. Even so, geometry remains an ideal way to approach reasoning and proof, and it can be started earlier than high school. Note 2

When viewing the video segment, keep the following questions in mind:

 a. How does the teacher incorporate geometric reasoning into the lesson? b. Where in the lesson are students learning new geometric content? What is that content? c. Where in the lesson are students drawing logical conclusions and thinking mathematically? How does the reasoning relate to the geometric content? d. Thinking back to the big ideas of this course, what are some geometric ideas these students are likely to encounter through their investigation of this situation?   Video Segment In this video segment, sixth-grade students in Ms. Saenz's class have, through data gathering, conjectured a form of the triangle inequality: Three lengths make a triangle if the sum of any two lengths is greater than the third length. The students, however, are unsure what happens when the sum is equal to the third side. Here, one student tries to explain why he thinks a triangle can't be formed in this case. If you are using a VCR, you can find this segment on the session video approximately 14 minutes and 7 seconds after the Annenberg Media logo.    Problem A1 Answer the questions you reflected on as you watched the video:

 a. How does the teacher incorporate geometric reasoning into the lesson? b. Where in the lesson are students learning new geometric content? What is that content? c. Where in the lesson are students drawing logical conclusions and thinking mathematically? How does the reasoning relate to the geometric content? d. Thinking back to the big ideas of this course, what are some geometric ideas these students are likely to encounter through their investigation of this situation? Problem A2 This lesson is not couched in a "real-world context." Students are thinking about mathematical ideas in the abstract. What are the advantages and disadvantages of this kind of lesson? Are "mathematics only" lessons important in your classroom? What purpose do they, as opposed to contextualized lessons, serve? Note 3  Join the discussion! Post your answer to Problem A2 on Channel Talk; then read and respond to answers posted by others. Problem A3 Ms. Saenz's lesson was based on a lesson from Session 2 of this course. Discuss the ways Ms. Saenz's lesson was similar to and different from the one in this course. What adaptations did she make and why?   Session 10, Grades 6-8: Index | Notes | Solutions | Video