Learning Math: Geometry
A course for elementary and middle school teachers, introduces geometric reasoning as a method for problem-solving. In this course, which is organized around the content standards of the National Council of Teachers of Mathematics (NCTM), you will explore the properties of geometric figures; make constructions using pencil and paper, and also using dynamic software; and practice using mathematical language to express ideas and justify your reasoning. Some important geometric ideas, such as symmetry, similarity, and trigonometry, will also be examined.
1. What Is Geometry?—Explore the basics of geometric thinking using rich visualization problems and mathematical language. Use your intuition and visual tools for geometric construction. Reflect on the basic objects of geometry and their representation.
2. Triangles and Quadrilaterals—Learn about the classifications of triangles, their different properties, and relationships between them. Examine concepts such as triangle inequality, triangle rigidity, and side–side–side congruence, and look at the conditions that cause them. Compare how these concepts apply to quadrilaterals.
3. Polygons—Explore the properties of polygons through puzzles and games, then proceed into a more formal classification of polygons. Look at mathematical definitions more formally, and explore how terms can have different but equivalent definitions.
4. Parallel Lines and Circles—Use dynamic geometry software to construct figures with given characteristics, such as segments that are perpendicular, parallel, or of equal length, and to examine the properties of parallel lines and circles.
5. Dissections and Proof—Review and explore transformations such as translation, reflection, and rotation. Apply these ideas to solve more complex geometric problems. Use your knowledge of properties of figures to reason through, solve, and justify your solutions to problems.
6. Pythagorean Theorem—Continue to examine the idea of mathematical proof. Look at several geometric or algebraic proofs of one of the most famous theorems in mathematics: the Pythagorean theorem.
7. Symmetry—Investigate symmetry, one of the most important ideas in mathematics. Explore geometric notions of symmetry by creating designs and examining their properties.
8. Similarity—Examine your intuitive notions of what makes a “good copy” and then progress toward a more formal definition of similarity. Explore similar triangles and look into some applications of similar triangles, including trigonometry.
9. Solids—Explore various aspects of solid geometry. Examine platonic solids and why there are a finite number of them. Investigate nets and cross-sections for solids as a way of establishing the relationships between two–dimensional and three–dimensional geometry.
10. Classroom Case Studies, K-5—Watch this program in the 10th session for K–2 and 3–5 teachers. Explore how the concepts developed in this course can be applied through case studies of K–5 teachers who have adapted their new knowledge to their classrooms.
11. Classroom Case Studies, 6-8, Part 1—Watch Videos 11 and 12 in the 10th session for grade 6–8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6–8 teachers (former course participants) who have adapted their new knowledge to their classrooms.
12. Classroom Case Studies, 6-8, Part 2—Watch Videos 11 and 12 in the 10th session for grade 6–8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6–8 teachers (former course participants) who have adapted their new knowledge to their classrooms.
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