I wrote recently about options for math after Singapore 6B that we’ve tried or at least considered. While some of those resources found their way into my older son’s schedule while he was finishing Singapore, he felt strongly about immediately moving on to “real” algebra. He was nine and sick of arithmetic. He was also fascinated with the algebra I used to solve some of the more perplexing parts of Challenging Word Problems 6, Singapore’s last book in their honestly named supplement series. When I couldn’t make those bar diagrams work, I’d resort to methods more familiar to me. He wanted in on those methods.
After a moderate amount of research and consideration, I went with an old-standby, Elementary Algebra by Harold R. Jacobs (ISBN 0-7167-1047-1). Written in 1979, this black-and-white text is written with humor and interest without the distracting color splashes and sidebars that grace more modern textbooks. Perhaps those brighter, busier features and are a draw for some learners, but for my son (with ADHD), the less chaos on the page, the better. The cartoon at the start of most lessons held up well over those decades and grabbed my distractable child onto the page while giving us both a chuckle. A bit of a laugh is a fine way to start a math lesson.
There’s plenty of substance after that laugh. In seventeen chapters with four to nine lessons each, Jacobs takes a learner directly into the use of variables while teaching order of operations, graphing, exponents, radicals, and other pre-algebra topics not covered in Singapore’s first six books. For a mathematically geared child, this seamlessly integrates those missed topics into algebra, obviating the need for a separate pre-algebra course. For my older son who is highly mathematically intuitive, this was fine.
In Elementary Algebra, Jacobs does far more than teach the procedural goings-on of algebra. He explains why it works. This is not a text of algorithms to memorize and practice, practice, practice. Rather this is a book that encourages deeper understanding of the math it contains and that connects math to the greater world. This creates a rather lengthy book, and my son did take a year and a half to move through it. At then end, however, he had a fine grasp of algebra and could easily relate and apply it to other studies.
The structure of the book makes for easy teaching, and the supplemental teacher’s guide (A Teacher’s Guide to Elementary Algebra ISBN 0-7167-1075-7) provides additional ideas for teaching if that’s desired. This is, however, not a scripted program. For the parent whose algebra is more than a bit rusty, this text could be a challenge. Or, perhaps, it could be an opportunity to polish those rusty skills and dress them up with deeper understanding. Even if one doesn’t require the additional teaching tips in the guide, this book contains the answers to three of the four sets of problems in each chapter. (One set has its answers in the back of the textbook.) For this, it was worth its price several times over.
Each lesson takes a mathematical idea and develops it in two or three pages of text, diagrams, and examples. I’m a believer in interactive math lessons, since I think there’s much to be learned from discussion about mathematics. My son and I would sit together, with me reading the chapter aloud and discussing examples along the way, generally with scrap paper or a white board by our sides. Each lesson concludes with four problem sets: one review, two sections to practice the ideas from the current lesson, and a fourth presenting a challenging problem or two often with a historical bent or mathematical twist. We generally omitted the review and did the second set (first set of practice problems) together. He’d then do the third set (second set of practice problems) and fourth set (challenge problems) on his own. The following day, we’d review his mistakes and move on to the next lesson.
Each chapter ends with two sets of review problems, of which I’d assign one. One review could be used for a test, but we used tests from the accompanying Test Masters for Elementary Algebra (ISBN 0-7167-1077-3), which offers four tests for each chapter, additional exercises on a host of topics, four multiple-choice midterms and two multiple-choice final exams. We’d have been fine without this supplement, but this was in my more obsessive “afraid we’ll miss something” homeschooling days. It’s definitely an optional supplement.
Algebra was more than a math class for my son. It was a jump in organization, textbook use, and test taking. Up until algebra, he’d done most of his mathematical work in his head. Dysgraphia and impatience with process had led to me scribing most of his work until this point, and while I’d modeled showing work, algebra was the first time I insisted he show his work every time. It was a painful first many months. The math came easily. Writing down steps did not. A second challenge presented when working through problem sets. Writing answers on paper while referring to a page in a book proved difficult. Often the writing issues, visual tracking work, and organized step-writing proved more challenging than the math. Test taking was also new to him. I don’t test my boys much — generally I can tell what they know and what they don’t. Test taking increased his accuracy and gave him a reason to show his work, since even a wrong answer with a clear and largely correct trail could earn partial credit.
Jacobs’ Elementary Algebra prepared my older well for the math that followed: Algebra II, Geometry, Trigonometry, and Precalculus flowed fairly easily from the lessons learned in that first algebra text. I enjoyed teaching from it, and he enjoyed learning from it. My understanding of some concepts deepened along the way. While it’s hardly the only algebra choice for the homeschooling family, Jacobs’ Elementary Algebra is a strong text based on sound pedagogy that prepares mathematical thinkers well for higher math.