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 problem…
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 main…
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 to…
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 Algebra2…
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数学的精髓在于其自由。
— Georg Cantor 德国数学家
K-12 Math Enrichment Courses 