Blog Archives

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.

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

Moebius Noodles: A Mathematical Playground for Young and Old

Moebius Noodles book

Contrary to popular belief, mathematics is not an activity that requires textbooks, calculators, and years of training. Because it consists of such fundamental notions as symmetry, classification, counting, and geometric transformations — all concepts that come naturally to even the youngest children — mathematics can truly be studied at any age. If you have picked up a copy of Math From Three to Seven and are wondering whether there is something similar for kids that are younger still, you should take a look at Moebius Noodles.

This book, the work of Yelena McManaman, Maria Droujkova, and Ever Salazar, is a beautifully illustrated collection of activities that engages young kids (even toddlers) in discovering fundamental mathematical principles and abstractions. For example, why wait until middle school or high school to learn about functions when you can think about them in any almost any context? For instance, Moebius Noodles proposes an activity where a child is given the name of a baby animal (like “kitten”) and must identify the corresponding adult animal name (in this case “cat”). The child has just created a baby-to-mother function and there are endless other possible activities that reinforce this idea of mappings between sets. The book covers basic ideas involving numbers, symmetry, functions, and even a little bit of calculus. If you’re a parent or preschool teacher interested in fun activities that involve both playing with and internalizing fundamental mathematical concepts, then Moebius Noodles is worth your time.

Preschool Computer Science: Kids Programming Adults

drtechniko

If you’re now convinced that preschoolers can learn advanced mathematics, you should not be too surprised to learn that preschoolers can learn computer science equally well. That is the idea behind How to Train Your Robot, a lesson designed to help kids ages 5-7 learn basic programming and computer science. Nikos Michalakis, the man behind the idea has a simple proposition: kids use a starter set of simple commands that consist of primitive symbols to program adults who must obey the instructions exactly as they are written. Once kids are comfortable with the basic commands, they can create their own additional commands, and this is what makes the possibilities endless. For those who are ready to put his ideas to use, Nikos offers a post on how to teach one of his classes based on his own experience. One of the advantages of his approach is that it does not require computers or knowledge of any programming languages and that makes it easy for adults with no programming backgrounds to try it out. If you like this computer-free, running around type of learning, Computer Science Unplugged is a good followup to “How to Train Your Robot” and it introduces more computer science theory to older students.

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.