An approach using symmetric polynomials to prove that the medians of a triangle intersect at a single point reveals underlying structure and generalization to higher dimensions.
Ryota Matsuura and Sarah Sword
Ryota Matsuura, Sarah Sword and Tatyana Finkelstein
Designing a lesson that uses routine exercises, creates space for language use, and provides a storyline will go far toward supporting mathematical structure.
Richard Askey, Ryota Matsuura and Sarah Sword
The inequality of arithmetic and geometric means in three variables is developed through algebra, geometry, and calculus.
June Mark, Al Cuoco, E. Paul Goldenberg and Sarah Sword
Mathematical habits of mind include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work (Cuoco, Goldenberg, and Mark 1996; Goldenberg 1996). Current recommendations emphasize the critical nature of developing these habits of mind: “Once this kind of thinking is established, students can apply it in the context of geometry, trigonometry, calculus, data and statistics, or other advanced courses” (Achieve 2008, p. 4).
Sarah Sword, Ryota Matsuura, Al Cuoco, Jane Kang and Miriam Gates
Two high school classroom situations illustrate how routinely promoting the two practices of experimenting and describing in increasingly precise language can support students' modeling.