Traditional Math: An effective strategy that teachers feel guilty using

by Barry Garelick, J.R. Wilson

This book provides a glimpse of what explicit instruction looks like in the
classroom for K–8. The book seeks to inform readers of our approaches to
traditionally taught math. This has two purposes: 1) For approaches that
are similar to what you may already practice, it provides some assurance
that you are not alone, and 2) it may give you some new ideas.

Despite experiencing our teaching in different times, we are both oriented to traditional math teaching. It wasn't because we were both taught that way, as some may believe, but because that method worked for us and we have seen it work for our students. It is efficient, effective, non-confusing and helped our students develop mathematical reasoning, understanding, and confidence. Most importantly it helped them to be successful.

460 pages, Paperback

First published November 18, 2022

About the author

Advocate for better math education. Majored in math at U of Michigan. Had career in environment (air quality) and retired from US EPA in 2011. Obtained teaching credential for math and taught 7th and 8th grade math, until 2021.

He has published articles on math education in online Atlantic, Education News, Education Next, Educational Leadership and Non-Partisan Education Review.

Reviews

[Mike Sullivan · Rating 5 out of 5]

Wow - this book was like a breath of fresh air! Usually, education books are written for people who don’t want to teach. They typically give advice on the best way to avoid teaching altogether in the hopes that the kids miraculously figure it out for themselves. (They also usually include a list of excuses why their approach may appear not to work: poverty, parents, funding etc.)

Not this book though. Traditional Math is a book for teachers who actually want to teach, who want students to thoroughly understand Math and to develop a love for its many challenges.

Like many other teachers, I’ve often wondered, “Is there a better way to explain fractions/negative integers/proportions than the way textbook they gave me does?”

Well, there is. And it’s in this book. Also, even the explanations you use that are generally good are improved upon in this book. Just to give one example, the author uses a water tank losing a set amount of water each hour to demonstrate multiplication with negative integers.

The water level in the tank decreases by 2 inches each hour (-2). What will the level be in 4 hours (+4)?

-2 x (+4) = -8. The water level will be 8 inches lower.

Sounds pretty standard, right? BUT, the author adds in a bit about time that they had previously learned to demonstrate why a negative multiplied by a negative is positive.

Same example as above: If the water level in the tank decreases by 2 inches an hour (-2). What was the level 3 hours ago (three hours in the past is -3)?

-2 x -3 = +6. The water level was 6 inches higher.

Can’t wait to use this example with my 7th graders in the Fall. And, there’s plenty more where that came from. In fact, I’ll be using Traditional Math as I plan lessons for this upcoming year and will reread each section before I start each topic in class.

In short, I can’t recommend this book enough. If your students’ fluency, proficiency and deeper understanding of Math is your goal, then this book is for you.

I’d also urge you to ignore the naysayers who think anything “traditional” is regressive or harmful. Far from it. There’s nothing “progressive” about letting students struggle, suffer and surrender while we watch from the sidelines. As teachers we need to demystify the content in order to spark their curiosity for the more challenging content to come. As Professor Kirschner says in the Forward, “Traditional is the New Progressive.” Couldn’t agree more.

[James · Rating 5 out of 5]

Tried and true math teaching is a breath of fresh air. Old is fresh? Old is not bad when it works. The authors are combatting new and unproven methods of teaching math with traditional approaches, which the current educational inner party considers "bad". What actually is bad is the math outcomes over the past decades, so it's really incumbent on those in charge to question their current philosophy and tactics.

What if math knowledge is not constructed? If it is naturally true, emerging from historical discoveries based on the countable real world, then perhaps it isn't constructed in the vein of William James' pragmatism, whereby truth is derived from language. Math likely is an exception, due to its universal truth in the physical world. But I digress.

The foreword by Paul Kirshner includes links to several resources which describe flaws in postmodern math pedagogy, then the authors spell out the content for math up to the 8th grade. If you've ever questioned teaching conceptual understanding instead or in advance of procedural fluency and math facts (a.k.a. putting the cart before the horse), this is the book for you.