11th and 12th Grade Workbook – Teacher’s Edition: Algebra II, Precalculus, Calculus, Statistics
Making Math Meaningful™ workbooks are specifically designed to lead the students along a path of discovery. The teacher needs to carefully guide the students along this path. The problems contained in these workbooks are NOT randomly ordered or selected. They are chosen to promote the development of mathematical thinking in a very conscious way. As teachers of math, our most important task is to develop mathematical thinking in our students. This thinking needs to be flexible and creative.
Who can use this workbook? Most of the author’s teaching experience is within the Waldorf school system. Yet this workbook can be effectively used by any teacher or homeschooling parent who wishes to teach meaningful, age-appropriate math.
Problem-Solving Exercises! The eleventh grade year in math should be exciting and mind-expanding. Puzzles, games, and problem-solving can be a welcome change from the normal routine; they are also an important component of a math curriculum in order to develop students’ thinking capacities.
This is why we have included an entire unit on problem-solving exercises at the end of this workbook.
Additionally, you can many puzzles and games in our book, Puzzles, Games and More!
Blind procedures vs. discovery and mathematical experiences. As we mention in our High School Source Book, we feel that all too often the standard approach to teaching math is based on “blind procedures”; students simply follow procedures without any understanding of what they are doing. In contrast, we have tried to put together our high school workbooks so that, whenever possible, the students are led down a path of discovery.
We also feel that mainstream mathematics emphasizes procedural skills too much. Often, 90% of classroom time (or more) is spent having the students slog through countless “problems”, all in the name of checking off topics on the LIST, and ensuring ourselves that our students have good “skills” (at solving meaningless problems). In contrast, we believe it is important to have a healthy balance between procedural skills and real “mathematical experiences”.
Main lessons also provide opportunities for the “big picture”, where you can integrate history and philosophy with mathematical topics. This develops wonder and enthusiasm, and shows how math is a human endeavor.
We encourage you to read more about all of this in the introduction of our High School Source Book.
Regarding Skills. While our 9th Grade Workbook focuses largely on skills, the purpose of this 11th/12th Grade Workbook is not just skills. The purpose here is also to experience the beauty of mathematics and to develop mathematical thinking capacities.
Why an eleventh & twelfth grade combined workbook? This workbook is designed to be used by either an advanced or regular math track class. The two calculus units are intended for an advanced class, while the two statistics units are more designed for a regular math class. With the exception of the statistics units, an advanced math class ought to be able to work through most of this workbook over the course of the eleventh grade year and the first half of twelfth grade. A regular math track class in eleventh or twelfth grade can simply pick and choose from the many units in this workbook and from units in the second half of our 10th Grade Workbook (e.g., “Exponential Growth”, “Sequences & Series”, “Math & Music”).
The units covered in this workbook are:
- Cartesian Geometry, Part I
- Trigonometry, Part II
- Complex Numbers, Part I
- Cartesian Geometry, Part II
- Possibility & Probability, Part II
- Trigonometry, Part III
- Cartesian Geometry, Part III
- Logarithms, Part III
- Complex Numbers, Part II
- Trigonometry, Part IV
- Cartesian Geometry, Part IV
- Calculus, Part I
- Calculus, Part II
- Statistics, Part I
- Statistics, Part II
- Problem-Solving Exercises
About the Author
Jamie York’s search for meaningful education led him to Shining Mountain Waldorf School (in Boulder, Colorado), where he started teaching math in 1994. In addition to teaching middle and high school math, Jamie consults at Waldorf schools and teaches math workshops across North America. In the summer, he serves on the faculty at the Center of Anthroposophy (in Wilton, NH) as part of their Waldorf High School Teacher Education Program and adjunct professor of Antioch University, NH.
Andrew Starzynski grew up steeped in Waldorf education as the son of two Waldorf teachers, and as a student at the Chicago Waldorf School, which he attended through high school. Andrew went on to attend Beloit College, graduating in 2001 with a double major in mathematics and philosophy, and a minor in computer science. He taught part-time at the Chicago Waldorf School before spending two years in the computer industry. In 2004, his love of math led him to graduate school where he acquired his master’s degree in applied mathematics. His enthusiasm for Waldorf education and Waldorf math prompted his return to the Chicago Waldorf School where he taught for three years. In 2008, Andrew completed his Waldorf teacher training under the tutelage of Jamie York. Andrew has taught math and computer science at Honolulu Waldorf School and Waldorf Academy in downtown Toronto. He currently lives with his wife and two sons in Richmond Hill, Ontario, Canada where he teaches at the Toronto Waldorf School.