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My Little Big Math Book

Lars Rönnbäck
Publication Date: 
Number of Pages: 
[Reviewed by
Geoffrey Dietz
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Before obtaining a copy of this book, please be aware of what this book is and what it is not. This book is not a children’s story in the sense that it is not intended to be read to a child nor is it a story with a plot. Instead the book is meant to be read by an adult, probably a parent but maybe also a teacher of children under the age of eight, who would like to analyze some of the developmental stages young children will proceed through as they become more and more mathematically aware and mature. (The fact that the book is not meant to be read with a child is somewhat a shame given the cute illustrations, which would be great accompaniments for a children’s story.)

The author presents an ordered list of twenty-one mathematical stages that he suggests children pass through between birth and about eight years of age. He starts with a basic philosophical awareness of existence different from other people and things and passes to the notions of sets, sameness, order, and defining characteristics. Eventually the child becomes aware that sets can be combined or altered through ideas that we call union and intersection or by adding and subtracting elements (starting with adding or taking away one). In the latter stages, he suggests that children start to pick up ideas of pattern and the abstraction that comes from identifying numbers and their arithmetic as independent from a specific set or type of object. In general, there is a progression from the concrete and simple to the abstract and increasingly complex.

Each stage runs over a pair of colorfully illustrated pages with a title followed by an explanation that includes references to terms of art in modern mathematics that have some relevance to the stage, even though the child is completely unaware of the connection. As a mathematician (and a parent) I found these associations interesting, but I think many of them potentially serve to exclude the vast majority of adults from taking too much interest in the main text. For example, references to an idempotent operation or Peano’s axioms will be meaningless to most parents without a college degree in mathematics, even if such references are relevant to a certain stage of development. The author states that he included such terms on purpose to encourage readers to seek out more information if they are curious.

At the end of each stage, the author suggests an experiment to try with a child to illustrate a certain concept. Some of these are great. For instance, after a discussion of how one particular pea can be easily lost among a pile of one hundred peas, the author suggests working with a child to find a way to manipulate or organize the peas to make such a discovery of one particular pea easier. Others are a bit of a stretch, such as the one that seeks to find examples of infinite sets where one is countable and one uncountable. Georg Cantor had plenty of trouble convincing his mathematical peers of the nineteenth century that there were different types of infinity, and I have found that attempting the topic with kids aged under eleven does not go very far either. Kid-friendly examples of true infinity (and not just very large quantities) are hard to come by, let alone different orders of infinity.

Overall, the layout of the book is very inviting, and the text is interesting, but the readership pool might be rather shallow.

As a side note, one of the most interesting sentences in the book might be found on its copyright page: “Parts of the book are based on research from Anchor Modeling.” I am curious to know how the author’s research into a novel database model led to writing a story about the mathematical development within young children. The problem mentioned above, about how to retrieve one, specific pea among a large pile of seemingly identical peas, takes on new relevance given the author’s research on databases.

Geoffrey Dietz is an Associate Professor at Gannon University in Erie, PA. He is married and has six children.

The table of contents is not available.