A in Math

Price = $10

This math book teaches Integers, a topic that is neglected to some mention of “there are positive and negative numbers” and then discussion of the rules in operations with integers.

But an “Integer” is a very important concept. It is significantly different than a whole positive number. An integer number has a new idea compared to whole (positive) number. The problem is that those differences between integer numbers (Integers) and whole numbers are not discussed in class or in math books for kids. The mathematical concept is only discussed in mathematics books for college, not even high school. Teachers (and math books) tell kids that “integers are just both positive and negative numbers”, explain the Operations rules (the “negative times negative is positive), which don’t really make sense to the poor students who were not taught what integers really are. It is only taught “by the way” in 6or 7 grade usually, or in math books for these grades.

Then comes Algebra, with its extensive need for understanding Integers. Without understanding the idea of Integers, how they work, and how to use them, students have no chance in understanding Algebra well, and of solving Word Problems that require those ideas. Later, when students study calculus, which introduces real numbers, it is even more critical to understand Integers fully and deeply.

This book teaches EVERYTHING to know about Integers. It does so simply. It explains what Integers are; the meaning of operations with integers; and how to use integers. Those “negative times negative is positive” rules become logical and easy to remember because students understand why they are so.

Fact: There is a sudden drop in grades for a large number of kids when they start studying Algebra. Then there is another similar drop when they start studying Calculus. Students who were 'A' students, and always got top scores, suddenly, unexplainably, don't do well in Algebra, and then another portion of 'A' students, who survived Algebra, stop doing well when they start Calculus.

The common explanation: Algebra is conceptually hard (nonesense), and Calculus is conceptually hard (not as much nonesense, but not true either) and most students are just not naturally inclined to math.

The real explanation: Algebra and Calculus (more so even) require understanding of numbers, operations, and our place value system. Not in a superficial, operational (can use only) way, but at a deeper level. Those are the topics that are least taught in terms of "why" - the underlying ideas, yet they are the foundation to what happens later.

STORY #2

You study with this book according to the “how to use this book” on the next page.

You understand Integers. You understand why the operations work as they do. You understand lots of other things about numbers and operations.

It takes time to study with this book but at least you can do the practice questions quickly, easily, and well.

Then, you study other things.

You understand those other things because you understand numbers and Integers.

You do well on the tests.

You like math and think you are good at it. Your teacher thinks so too.

End of Story #2

Which story do you want to live?