It is the beginning of winter break and the family is off to a vacation. The car ride ahead is many hours. Ten minutes into the drive, Katie (8 years old) realizes that she forgot her book. In desperation, she asks me, “Mom, can I look at your book?” I check my bag for what I have. There are two books in it: one is definitely not kid friendly (many pages, small font, no pictures) and the other one is “AVOID HARD WORK!…And Other Encouraging Mathematical Problem-Solving Tips For the Young. The Very Young. And the Young at Heart,” which had just arrived in the mail and I was eager to read myself.
I take out the book, with its colorful and intriguing cover, and Katie upon seeing it immediately exclaims, “Yes, that one. I want that one!”
I give the book to her, expecting her to flip through it and give it right back to me. She opens the book to the first picture/problem (one of interlocking gears) and asks me what one is supposed to do.
I ask her a few questions about what she sees in the picture and what she thinks the arrows mean, and soon she is pointing to the gears one by one, saying which direction they’ll turn in. She then moves on to a much bigger problem of the same type on the next page in the book and proceeds to do the same thing.
Meanwhile, Zoe (4 years old) has noticed that Katie is repeating the same two strange words (clockwise and counter-clockwise) over and over, while looking at a fun picture with lots of question marks. She asks Katie to explain what she’s doing, and instead of telling her younger sister to not bother her (like you can imagine sometimes happens), Katie goes on to carefully explain that the spiky circles in the picture are gears (which Zoe is quite familiar with as she’s often played with a construction set that had many of them), that the arrows show in which direction some of them are spinning and that you have to figure out the spinning directions of the rest. She then proceeds to help Zoe work through the problem that she had just done.
I was in awe! Here was a problem that is interesting to me and that my eight year old and my four year old can think about together. And having now read through the whole book myself, I can say that this is very much in the spirit of the book. Many of the problems in it, if not immediately approachable for the little ones, are easily adaptable for them, and a large part of the book describes how to do just that.
But in fact the book contains much more than that. Not only is it filled with wonderful, thought-provoking problems, it also contains discussions of how one may approach the problems, how to deal with children’s (and adults’) anxiety and frustration, as well as the big mathematical ideas behind the problems. Katie and I have since worked on a number of other problems in the book and there hasn’t been a single one that we did not enjoy. I have also successfully used a few in my second and third grade classes. There is something in the book for everyone, from age 4 to 104!