GRADE BAND: 7-8 Domain: Geometry
Why this domain is a priority for professional development sequencing from grade 8 to high school geometry is a shift from previous state standards to the common core – students are asked to understand how to use translation, rotation, tran TRANSFORMATIONAL GEOMETRY IS PERHAPS ONE OF THE BIGGEST DIFFERENCES FROM PREVIOUS STANDARDS/TEACHING TO THE COMMON CORE (CHANGE FOR STUDENTS, TEACHERS, AND TEACHERS OF TEACHERS). CHALLENGES INCLUDE ATTENTION TO PRECISION AND LANGUAGE.
Key standards in this domain that pd should focus on Q: What themes exist across states with respect to pd needs? Q: How do the words on the paper convey the necessary pedagogy? Q: What PD training is needed (for those providing PD to teachers)? Q: What are the experiences to give to teachers to develop foundational knowledge? (progressions, tasks, videos/dynamic illustrations, student work, commentary tying these together) Describe the effects of dilations, translations... attention lengths/angles Transformational approach to similarity – area of huge need across states 8.G.6. Explain a proof of the Pythagorean Theorem and its converse
Existing resources that support these domains and standards Some materials under current field test (Learning and Teaching Geometry videocase materials) Fostering Geometric Thinking (Driscoll)
Domains and standards that are in need of new resources PD needs to establish vision for the math classrooms (videos or other means of seeing it happening) Also, they must experience it themselves. Guidance on what proof (explain, prove, justify) in middle school means (examples) Q: What must teachers understand about geometry that is new? What opportunities do teachers have to think about precision? How do they take the new knowledge back to their classrooms? 8.EE 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane... 8.G angle-angle criterion for similarity of triangles