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A Book on Modern Mathematics for Elementary School Students

modern math for elementary school

Sadly, professional mathematicians play a mostly decorative role in shaping mathematics education. Research is simply a much more attractive activity than the politics of education reform and curriculum development. There are not enough incentives to lure most mathematicians away from their academic responsibilities and to push them into improving the quality of mathematics instruction, unless of course, those mathematicians are parents concerned with the quality of their children’s education. That is the story of Oleg Gleizer, a mathematician and parent who could not find a suitable mathematics program for his five year old son and decided to take matters into his own hands.

The result of his effort is the book Modern Math for Elementary Schoolers [PDF], which bridges the gap between the requirements of school mathematics and a deeper conceptual understanding of the subject. This is not a replacement for a good textbook because it does not cover all of the standard topics, but it is a vital supplement that opens the doors of high level mathematical thinking to elementary school students. For example, the first chapter introduces number partitions, parity, and other basic properties of numbers using Young diagrams, which are important objects in advanced mathematics. This approach actually makes the topic more visual and easier to understand even though advanced ideas lurk in the background. Other topics that are deeply yet playfully explored in the book include straight line geometry (and its connection to physics), straight edge and compass constructions, modular arithmetic, and algorithms.

In effect, Modern Math for Elementary Schoolers [PDF] is a lively guide and collection of problems for parents and teachers who want to weave a non-superficial mathematics, computer science, and physics narrative into their teaching. Contrary to the title of the book, a significant part of the material in the book will be relevant to students of any age. If you’re looking for something similar to Math from Three to Seven, this book fits the bill perfectly.

Photo Credit: faungg

Stop Mindlessly Memorizing the Order of Operations

Breaking news: the order of operations that elementary schools teach students is not a fundamental law of nature but a convention to make our lives easier. Unfortunately, many students add PEMDAS (as the order of operations is commonly called in the US) to the list of mystical yet unquestionable truths to be memorized and feared. Everyone’s life might be a bit easier if we realized that mathematical expressions are written in a special mathematical language, and that like any language it has its own rules. The English language, for example, has spelling rules that dictate how to spell the word “bite” in the sense of eating and the word “byte” in the sense of data stored in a computer. If it wasn’t for those rules, there would be a great deal more confusion, and different people would read the same sentence in multiple ways. The same is true in mathematics. The notation and rules that we learn in school have developed over centuries to make reading and writing mathematical expressions an unambiguous activity. In the short video below, Henry Reich explores the conventions we use today and reminds us that thinking deeply about even the most basic ideas is more important than memorizing them. If you’re interested in the history of modern mathematical notation Ask Dr. Math has a bit more information.