In this post we ask: what makes a good math book for children?
Is it more important that a child be left with knowledge that they can understand and retain, or a new awareness that keeps them thinking and wondering? Is mathematics a world that one can enter and join in, or is mathematics a personal journey? Of course both sides are important, but how much weight should be put on one side or the other?
In a recent family conversation someone asked: why do we learn history at school? The standard answers came up: “so that we don’t repeat past mistakes” and “to learn a way of thinking”. Math instruction has similar taglines: “math is everywhere”, and “math is a stepping stone to good jobs”. The underlying idea behind these reasonable sounding slogans is that mandatory education should fundamentally 1) help us understand our world; and 2) teach useful skills to work and function in society.
But there is a third fundamental reason to learn things at school, which people forget to mention. It is learning for learning’s sake. There are people who simply are driven to learn. Who like to turn ideas around in their heads, and who are grateful for avenues to new horizons. When one is lucky enough to have a teacher who encourages curiosity and appreciation, something beyond practical skills is gained. Without this aspect of education, knowledge would not progress, society would stagnate, and, personally speaking, life would be less fun.
Similar questions come up with children’s books. Is the goal to teach skills or to excite wonder and appreciation? Is it possible to do both? Many countries such as Japan, Russia and Hungary have come up with systems for teaching mathematics to children that are highly effective in producing students with strong problem solving skills. Not only that, these methods are fun, and incorporate a nice balance between group learning and competition that works well for a broad range of children and abilities, and lets the top few excel quickly. Lacking wide spread systems like this, US mathematics graduate programs typically see fewer qualified applicants educated in the US compared to those educated in Europe and Asia.
So how is it that some of the greatest mathematicians in the world were born and educated in the United States with little or no extra instruction from family or teachers as children? For some people, it seems that the only encouragement that is needed is the tiniest of childhood triggers. Many successful mathematicians (American and otherwise) were primarily self-taught, before they began studying math more formally at college or university. (Are you one of these people? If so, I encourage you to contribute a comment or blog post explaining how you were introduced to mathematics.)
If there is room in mathematics for people who find their own way to math, then I believe there is also interest in describing the journey in a way that resonates with children. Instead of a single-minded focus on learning a subject and technique properly – that can come from individual hard work once the motivation is there – an alternative approach is to illustrate a few simple but deep ideas in a new and personal way.
Featured Books of the Day
A Moscow Math Circle, by Sergey Dorichenko is a collection of problem sets for eighth graders written by mathematics faculty at the Moscow State University. The problems are organized around weekly lessons at a magnet program called Math Circles run by the University. The program, begun at Moscow State University, is designed to engage students and give them a sense of the continuity between new concepts and ones previously mastered. Since its inception, Math Circles has spread to many mathematics departments around the world, including in the United States. The book contains an explanation by Dorichenko of how the original Moscow Math Circle was run, and includes translations of the problem sets into English.
You can Count on Monsters, by Rich Schwartz is an imaginative depiction of numbers as monsters drawn using fun geometric shapes and colors. The prime numbers are individual monsters, and the composites are made by interactions of the primes that divide them. Thus, the personality of each number is a carefully arranged conglomeration of the personalities of its factors. Meanwhile, a lot of mathematics is suggested by the way the shapes interact, including fundamental concepts from algebra and geometry. For this reason, the book can be appreciated at lots of different levels, and will bring a smile to children of any age.