A Cultural Shift Several features of the textbooks, which are typically ignored or de-emphasized in standard U.S. high school curricula, represent a cultural shift in how mathematics is viewed and studied in the U.S., but which are very well-known around the world and have been adopted by many countries for decades, if not centuries.

7.1. Reading Mathematics. Every math problem has “words” – these are concepts expressed in different ways, whether as numbers, standard everyday words, or by visual aids such as diagrams and figures.

Emphasizing the different forms of “words” as a regular part of math language and math communication and learning to read, interpret, and write in “words” is a major part of the new curriculum. The pilot parent’ comments below addresses this and more:

A pilot 6 th grade parent shares, 7 months after the new curriculum was launched:

”*As a teacher and teacher educator, I am familiar with several math programs that have been used throughout the past twenty years in California. The Bulgarian math program is exceptional in the way it supports students’ deep understanding of mathematical concepts, develops students’ ability to transfer skills to new and unfamiliar mathematical situations, and creates a mathematical language for students to express themselves mathematically, using numbers, drawings, and narratives.*

*I can see, and most importantly hear, the way my child interacts with the Bulgarian math program and I am impressed with the strong foundation it is giving him that will surely lead to lifelong competency and the ability to pursue more advanced mathematics.**”*

*– ***Jacqueline Regev , parent and educator**

7.2. Logic and Communication. Learning to know correct from flawed reasoning and being able to explain one’s mathematical ideas smoothly and convincingly to others will represent a gradual move towards a more mature relationship with mathematics.

7.3. Writing Mathematics. “Showing your work” is only the beginning to understanding how math really works. All problems have answers in the back of the textbook. Bringing back just an answer on a homework problem from the textbook will be worth no credit. The explanation that leads to the answer is what counts in our study of high school mathematics. Even harder than learning to correctly interpret problems is learning to consistently write solutions in a correct, complete, and clear way. (See Lesson 5 in 9A textbook.)

7.4. Multiple Solutions. Although there is usually (but not always!) only one correct answer to a math problem, the beauty of mathematics is that there may be different solutions leading to that answer. These are not “subjective opinions”; rather, they are objective mathematical creations that obey the laws of Logic. Students will learn that each solution (and even each incorrect attempt) has its value and usefulness in the long run and that one needs to open up to others’ ideas and ways of thinking as a path to enriching oneself, to becoming more proficient and, ultimately, wiser.

7.5. Efficient Solutions. Yet, among “all the roads [that] lead to Rome,” there might be a shortest or an easiest to follow. The ability to see “the big picture” and pick out the most efficient solution is a skill developed over a lifetime. And we start on it in this very textbook series.