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An Online Problem Solving Course for Young Kids

logo for young mooc math class

We’ve mentioned the work of James Tanton, Maria Droujkova, and Yelena McManaman before, and now they have teamed up to offer a one month long online math problem solving course. mpsMOOC13: Problem Solving for the Young, the Very Young, and the Young at Heart revolves around a small set of accessible nonstandard math problems that kids and parents solve together. The solutions and discussions are recorded and reported on the course website resulting in a community-generated math education research project.

The course has already started, but you can still do all of the problems and follow the discussions. If you’re homeschooling this course will be especially useful, and you should stay tuned for similar future courses from this team.

Computer Science Unplugged: A Computational Thinking Curriculum Without the Computer

cs unplugged image

The chorus calling for teaching computer science to all children seems to be getting louder by the day. Even the White House seems to think that programming is the new literacy. Programming is clearly an important skill, but the rush to teach programming languages and popular web technologies seems to have eclipsed a much more fundamental aspect of computer science: computational thinking. Billions of lines of code may run today’s infrastructure, helping land airliners and processing billions of dollars in commerce, but behind that code are algorithms and deep mathematical ideas. Unfortunately, most of the theory of computer science is left to either AP or college-level courses, which is too late. Computer Science Unplugged, a free computer science curriculum that features activities, games, and problems, seeks to address that problem. The curriculum comes with a free book that contains engaging activities, some of which are kinesthetic, but which cover topics like binary numbers, information theory, and searching algorithms. Computer Science Unplugged is appropriate for children as young as seven and is a good way to incorporate computer science concepts into regular math classes or enrichment programs. In some ways, the best part of the curriculum is that it does not require a computer and lets students move around.

The Fascinating World of Preschool Mathematics Education and Enrichment

math enrichment and math circles for preschoolers

Teaching math to young kids who don’t know how to read, write, or count is a complicated task. Providing these kids with mathematical enrichment seems like an even more daunting task. Unfortunately, the vast majority of math materials for young kids involve colorful pictures, games, and activities without real mathematical substance. Sure, knowing the names of shapes is important and receiving prizes for this knowledge is fun, but it doesn’t require too much thinking. A more sophisticated but still age appropriate activity would require giving a child three pencils and asking her to place them on a table so that none of the erasers touch the table (the pencils cannot be made to stand vertically). Solving this problem requires the application of three dimensional spatial reasoning, an important long-term skill.

This type of activity has been the cornerstone of elite Eastern European preschool math programs, and until recently was not widely available in the English-speaking world. The recent translation and publication of Alexander Zvonkin’s unique book, Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, changes that. This memoir gives an in-depth view of a two year math circle that Zvonkin, a professional research mathematician, ran for a group of kids ages three to seven. It meticulously describes every session and reveals a world of problems and activities far beyond the confines of the regular preschool curriculum. Perhaps as valuable as the mathematical content of the book, are the observations and insights that Zvonkin shares with the reader. Anyone interested in math education, not just at the preschool level, will learn a great deal from this one-of-a-kind work. Once you read this, you will be prepared to start your own enrichment program.

How to Start Your Own Math Circle or Enrichment Program

math circle session

Traditionally, math enrichment programs are run by professional mathematicians with an interest in education or by teachers with an interest in math competitions, but for most other people the idea of starting their own program seems like a daunting task. Fortunately, a few years ago, Sam Vandervelde and the Mathematical Sciences Research Institute put together Circle in a Box, a definitive guide on starting your own math enrichment program. It includes almost two hundred pages of advice on everything from the logistics of setting up an enrichment program to a fairly large set of suggested math topics and problems. There is even a section on how to apply for funding. Circle in a Box focuses primarily on setting up a math circle as opposed to any other type of enrichment program. Math circles are informal problem solving and discussion groups that were extremely popular for decades in Eastern Europe and which have played a crucial role in the development of several generations of mathematicians. Unlike school math clubs which usually focus on preparing students for specific math competitions, math circles are more flexible and their aim is to introduce a greater range of mathematical ideas (not simply problem solving tricks) and to explore even nontraditional topics in depth.

In our experience, the approach outlined in the book is similar to the one used by The Math Circle, one of the oldest math circles in the United States and by the Gentle Knowledge Math Circle, one of the first free out of school math enrichment programs. The author is the founder of the Stanford Math Circle and is well-known in the world of math outreach. If you’re a teacher, a parent, or simply a math enthusiast who is interested in starting your own program, this book along with Mathematical Circles (Russian Experience) will be an invaluable guide.

Problem Solving Russian Style

math circles book cover
You’ve read about the lack of proper problem solving in schools and you’ve even started thinking about a few recommended nonstandard elementary problems, now what? You could browse the Web looking for puzzles or math olympiad problems, but a much better approach would be to find a source of problems that is structured by topic, ability level, and that has been tested on tens of thousands of students of all backgrounds. Mathematical Circles: Russian Experience is exactly what you need. Most of the topics in this book, including parity, combinatorics, basic number theory, the pigeon hole principle, proof by induction, invariants, and inequalities often appear in math competitions, but the goal of this book is not narrowly focused on competition preparation. In some ways that would be just as bad as “teaching to the test.” The ultimate aim of Mathematical Circles (Russian Experience) is to start with quite simple problems that anyone can solve and then, in bite-size increments, increase the difficulty of the problems until a whole branch of mathematics has been introduced. The selection of the problems, the detailed guide for teachers, and the depth of coverage makes this book stand out among other great problem solving books. It is geared towards middle school and high school teachers who would like to enrich the standard school curriculum, but even regular students who don’t attend math clubs and competitions would benefit. In fact, we would recommend this book as the best form of standardized test preparation. Anyone who can solve at least a few of the problems in each of the sections of the book is, in our experience, ready to tackle the hardest SAT problem. As is typical for Russian math literature there are a few extra fun topics included, such as strategy games, that one rarely encounters in English-language books. If you’re looking for one book that contains a complete problem solving curriculum that has stood the test of time, this is a good place to start.