An Interview with Jonathan Cerf (the Author of These Lessons)
by B. Wentworth
Q: What do these lessons teach?
A: They teach young kids the fundamental concepts of arithmetic – that is, what it really means to add two numbers together, what it really means to subtract one number from another, what it means to multiply, and what it means to divide. And they teach kids how to connect those operations to their everyday real-world experiences.
Q: Do kids need to “understand” arithmetic in order to get the right answers in math class and to succeed in school?
A: No, they don’t. It turns out that a kid can do pretty well in school without really understanding much of anything. For instance, kids can learn how to add, subtract, multiply, and divide essentially by rote. But eventually, I think conceptual deficits will limit how far kids can go in math. And in the short run, conceptual deficits will cause kids to have difficulty solving so-called story problems – the sort of problems that start out with something like, “Mary has 6 avocadoes, but the recipe calls for 17.” Lots of kids have trouble with story problems. They have trouble recognizing whether a given story problem calls for adding or multiplying or subtracting or dividing. I think that a kid who has a firm conceptual understanding of subtraction will be unlikely to multiply when subtracting would have been a more appropriate choice.
Q: Why are you self-publishing these lessons now?
A: There’s a lot more teaching going on at home these days than was the case at any time in the recent past. But traditional math schoolbooks weren’t designed to do much teaching. Such books are full of practice exercises that were written with the assumption that most of the actual instruction would take place through activities and demonstrations directed by a trained professional teacher. My lessons are different. I feel that teaching is probably an uncomfortable new role for a lot of parents, so I’ve tried to include in my lessons the teaching that would normally take place in a classroom. I think that parents trying to teach their kids math at home might welcome the sort of help I’m offering – more help than they’re likely to get from their kids’ math books.
Q: Your lessons look more informal, more user-friendly, and more playful than other math books. Was that intentional?
A: Yes. Most math books are chockfull of practice exercises. Practice exercises tend to look joyless, because they ARE joyless. There’s nothing “new” about them – they’re not supposed to be new. They’re all about repetition of something old. And experiences that are “old” tend to look less intriguing than experiences that are “new.” Furthermore, traditional pages are full of numbers. And numbers represent fairly abstract ideas, much more abstract and therefore less visually appealing than, say, a herd of elephants or a pile of bowling balls.
Q: Did you write all of these lessons entirely on your own, or are there people whose guidance or assistance you’d like to acknowledge?
A: Several people were very helpful, but there were three who were absolutely indispensable. The first is Bob Spence, a Harcourt executive who created the model on which most of my lessons are based. Bob wrote a 6-page sequence of lessons for young kids that I found to be revelatory and inspirational. His lessons were about measurement – determining the length of everyday objects. Surprisingly, at least to me, he never exactly told kids how to do anything. Instead he posed a series of relatively easy challenges that gently led up to bigger challenges – asking kids to determine the length of objects that were more and more difficult to measure. What a wonderful way to learn! And what a wonderful way to teach! I set out to see if basic arithmetic could be taught this same way. I also owe a huge debt to Marjorie Stromquist for her early encouragement and expert critical reading. The third person I’d like to thank is Arthur Siegel, who persuaded me to return to this project after I had put it aside to pursue other interests.