Who would think young students could learn calculus? But here you go, free from “The Mathman” Don Cohen ~ Calculus By and For Young People.
At some point in our homeschool career someone recommended the tiny 3 1/2″ by 5″ spiral-bound book Calculus By and For Young People. We were already familiar with and using Hands-On Equations (a multi-sensory approach to algebra for younger children) and this book seemed like a logical next step.
Trying to divide six cookies fairly among seven people? Third-grader Brad had the right idea: cut each one in half, share out as many as you can; again halve the pieces not shared until there are pieces enough to share, and continue. He quit at sixteenths, amidst lots of crumbs. But he could see that everyone got 1/2 + 1/4 + 0/8 + 1/16 + 1/32 + 0/64 + … of a cookie. The sum is not hard to express in terms of more familiar series, once you notice that the missing portion of unity is itself a geometric series for 1 / (1- (1/8)). Iteration is more powerful and more intuitive than dividing a round cookie into seven equal parts.Calculus By and For Young People (inside cover review by Phylis and Philip Morrison)
Don Cohen was not what we would consider a typical math teacher. That he had a great love of his subject was very obvious.
I was teaching a class of teachers at Webster College in the 60’s; one day Judy Silver, a first-grade teacher, figured out the relationship between the derivative and the integral. I had tears come to my eyes, I was so excited. I said, why couldn’t I have learned math in the way that I was teaching it now! That’s why I want to share this book with young people (and their parents and teachers), so they can get an early start thinking about these ideas, and not have to memorize a lot of formulas and notations without much understanding, as I did in my mathematics courses.Preface, Calculus By and For Young People
Akin to the idea behind using Cuisenaire Rods in the Miquon math series or “The Manipulative Mode” mentioned frequently by Ruth Beechick in An Easy Start in Arithmetic, the idea is to see math using real objects as explained in the first quote above.
So beginning with page one, the student uses fractions of boxes to represent series and determine what happens when we add them up a little at a time. We search for patterns. Does the sum ever get bigger than one? No, because the top number is always less than the bottom number. As you know if you know calculus, it moves toward one.
And this is how a student progresses through the book, learning the fundamentals of calculus as he goes!
Topics investigated include:
- Harmonic series.
- Fibonacci numbers.
- Binomial expansion.
- Derivatives (or rate of change).
- The integral.
- Rise over run.
The bibliography includes books of reference and other items that may be hard to find at this point. But many of the materials suggested are still around (like graphing calculators, Cuisenaire Rods, and Geoboards).
Though the author passed in 2015, his website is still around and contains more help including Sample Problems and free downloadable worksheets (see below).
Make no mistake. The book cannot be termed “easy.” Like most things worth learning, something is required of the student. But what is often considered a difficult topic is explained in an approachable, investigative way.
The current price of our little book still on the shelf is over $100! Great for budding mathematicians! And free!
Don Cohen “The Mathman”
So much more at his site!
An Easy Start in Arithmetic by Dr. Ruth Beechick
Targeting parents of children in grades K–3, this title explains how children learn math — progressing through manipulative, mental image, and abstract modes of thinking — and then provides a course of learning and suggestions for teaching math for each grade. Excellent tutor for the homeschool handy-mom. (Can also be purchased as one of The Three R’s.)