My course “Geometry after Algebra 1” includes and balances three pillars: geometric computations, geometric proofs and geometric constructions, while the course “Geometry after PreAlgebra” focuses on only geometric computations and omits the other two. In “Geometry after Algebra 1”, students need to understand proofs of theorems and derivations of formulas. They need to know howContinue reading “What Are the Differences between the Two Courses “Geometry after Algebra 1” and “Geometry after PreAlgebra”?”
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Textbooks of Elementary Math Courses
There are a large number of textbooks for each elementary math course. We may easily agree on what a bad textbook reads like but have different opinions about what makes a good textbook. In my humble opinion, a good textbook must explain math clearly in a precise and concise manner, demonstrates a variety of problemContinue reading “Textbooks of Elementary Math Courses”
Prealgebra
Prealgebra serves as a bridge to connect arithmetic and algebra. As its name suggests, Prealgebra is a course to prepare students for algebra, the unifying thread of almost all mathematics. In my Prealgebra course, I cover the following topics. I write my own notes for these topics using the AoPS Prealgebra book as the mainContinue reading “Prealgebra”
Connection of Trigonometric Functions with Real-World Applications
Someone in our class asked “After reviewing the past lessons of trigonometric functions again, I was just wondering if there are any real world instances that would link to such specific functions, and why these applications relate to the ratios and angles in a right triangle. ” I think I should share my answer toContinue reading “Connection of Trigonometric Functions with Real-World Applications”
Algebra 1, 2 and Precalculus
课程内容: 美国初等教育中,Algebra 1 和 Algebra2, 以及以及 Algebra 2 和 Precalculus 这几门课的内容, 无论是从教材还是教学大纲看起来,都有不少重复的部分 (见 Plano Independent School District 的这三门课的内容安排,以及常用的教科书的内容提要, Art of Problem Solving -AoPS 的教材有一些专题内容,与常规教材在编排上不太一样)。 教学内容: 所以在教学内容上,表面看起来好像 Algebra2 上的还是 Algebra1, 或 Precalculus 上的还是 Albegra2。但老师在教学安排上,从 Algebra1 到 Algebra2 到 Precalculus 应该有加深和加广(见以下教学理念),特别从 Algebra1 到 Algebra2。Algebra2 和 Precalculus 的区分度要小些,学完我的整个 Algebra2, 如果学得好, 可以很快地学完 Precalculus (因为大部分内容已被包含)。所以我在教 Precalclulus 时更侧重定理和公式的证明。 教学理念: 在教 Algebra2Continue reading “Algebra 1, 2 and Precalculus”
K-12 Math Enrichment Courses 