This post is the first of a series about favorite resources that we’ve used over the years. In order to qualify as a “favorite,” we must have used the resource in its entirety. Very few seem to retain a favored status all the way until the end.
Elementary Algebra by Harold Jacobs qualifies. This first year algebra text starts out gently, gently enough, in fact, so that the first six or so chapters suffice as a prealgebra course. The text remains gentle, yet rigorous, throughout. Gentle enough so that a gifted fifth grader could thrive using it. And most importantly, gentle enough so that a formerly math-phobic homeschooling mother was able to give her student a solid introduction to algebra using it.
While much is made of the cartoons and mathematical anecdotes that seem to be the book’s trademark, the genius of Harold Jacobs is embodied in his problem sets. They are generally broken into groups, each one developing the concept being taught a little further. By the time the student gets to the final problem in the last group, he has, in a sense, discovered for himself the bridge between his previous knowledge and the new knowledge presented in the lesson. Frequently, concepts from future lessons are foreshadowed as well.
I hesitated to use the word “discovered” in the preceding paragraph. The word “discovery” when used to describe an approach to math education is usually said with a sneer when spoken by folks on one side of the “math wars.” But there is a place for discovery in education, even math education. In fact, if it is done right, a discovery approach can be extremely powerful.
Harold Jacobs provides a structured discovery approach in his algebra text. He begins with a brief explanation of the topic at hand. Then the student moves to the problem set, where the true instruction lies. The problems start out by offering practice on what is already known, either from past arithmetic courses, previous lessons, or the explanation just read. But then they move seamlessly to the heart of the concept, which may not have been explained directly.
The following is an example of this process. In introducing addition and subtraction of algebraic fractions, Jacobs offers some fairly straightforward examples, none of which have a variable in the denominator. Furthermore, none of his examples need to have the solution simplified. However, the corresponding problem set leads the student to both points and clearly illustrates how algebraic fractions directly relate to the arithmetic fractions he has been working with for years.
And so we have structured discovery. Structured in that the process in going from point A to point B is scaffolded on the front end: Jacobs provides carefully crafted problem sets. And structured in that the results of the process can be checked: Did the student manage to get the correct answers? Of course, it is also a good idea to check to be sure that the student is using reasonable methods to solve the problems even if he is getting the right answers, but incorrect answers are a clear sign that more direct instruction needs to take place.
So there it is. Elementary Algebra embodies the genius of Harold Jacobs. Jacobs not only provides a solid foundation for further algebra study, in its pages he also transmits his passion for mathematics. I can’t wait to use it again.