We have been fortunate enough to be able to write our own textbook series for our 9th-11th grade courses. This was possible thanks to Park School’s F. Parvin Sharpless Faculty and Curricular Advancement (FACA) program, which supports faculty every summer in major curricular projects. In addition to the support of FACA by the Nathan L. Cohen Faculty Enhancement fund and the Joseph Meyerhoff FACA fund, this project was also funded by grants from the E. E. Ford Foundation, the Benedict Foundation, Josh and Genine Fidler, and an anonymous donor.
In writing the textbooks, we wanted to introduce new material through an exploratory approach, so that students would see mathematics not as handed down from above but as something that makes its own sense. We also wanted students to see mathematics as a subject that was primarily about problem-solving, so that they would develop both the expectation that most problems require some insight to solve and also the confidence that they could, indeed, solve those problems. Our approach to developing problem-solving skills is through targeted practice with specific strategies such as “Tinker,” “Change or Simplify the Problem,” “Visualize,” “Represent Symbolically,” etc. These strategies are mathematical habits of mind.
Though our approach is different from many existing textbooks, both “traditional” and “reform,” we cover a fairly traditional core of mathematical topics. Many of our students choose to enter a calculus class when they have completed the curriculum.
Our textbook series consists of eleven chapters, each chapter consisting of lessons grouped roughly by theme. It is an integrated curriculum: students study algebra, geometry, and trigonometry in each year, often applying the tools of one of those areas when studying another.
Each chapter of our text begins with a “habits of mind” lesson. This lesson consists of puzzle problems in which using a certain habit of mind will be useful. For example, in “Change or Simplify the Problem we ask, “How many squares of any size does an 8×8 checkerboard have?” and “Find two consecutive positive integers where the difference of their squares equals 3747.” Teachers normally begin a chapter in the habits lesson so that the students become familiar with the habit and its application. When they move on to subsequent lessons, they continue to assign problems from the habits lesson over the course of the chapter.
The remaining lessons in a chapter follow this structure:
- An introduction, consisting of a puzzle or some text providing an entry into the topic
- A development section in which students are prompted to discover or create the tools they’ll need for the lesson
- Practice exercises, so students can solidify the skills they’ve learned
- The “Problems “section, a collection of nonroutine problems constituting the core of the lesson. The problems in this section push the topic further and encourage students to make connections between topics. Because these problems require ingenuity, using the habits of mind is often very helpful to students.
- “Exploring in Depth” problems are either more difficult than those in the “Problems” section, or else venture farther afield from the main topic of the lesson.
In the lessons, we highlight opportunities for students to use the habits of mind they are familiar with. We also have problems throughout the lessons reinforcing probability, functions, algebra, and other topics.
Portions of our textbooks are available here. If you are interested in obtaining the entire series, please contact email@example.com .