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.

The Stupidity of the “Math Wars”

we love math tshirt

Unless you’re a professor of education, you may not have noticed that for the last several decades a war has been raging between math education reformers and those from the traditional camp. Their disagreement boils down to one simple question: should students learn traditional computational algorithms (like the division algorithm for two numbers)? Reformers believe that achieving computational fluency is secondary to developing thinking, while traditionalists argue that not only are the basic arithmetic algorithms a fundamental part of mathematics, but that their mastery enables students to progress in the subject.

The historical roots of this conflict are irrelevant to us because like many social policy debates, it is heavily politicized. A more pertinent issue is how does all of this affect parents, teachers, and students. In a recent opinion piece in the New York Times, Alice Crary and W. Stephen Wilson offer an interesting analysis of the false dichotomy created by this ideological battle and come to an obvious conclusion: facility with mechanical mathematical procedures is inseparable from mathematical thinking. A student can’t develop abstract reasoning abilities without being able to easily manipulate the numbers and symbols that represent that reasoning.

Crary and Wilson point out that studying mathematics while de-emphasizing computation is like studying history without the actual historical facts. Even if historians have developed a way of thinking about their subject, they cannot do so without reference to specific facts. Similarly, both professional mathematicians and students of mathematics need to be comfortable with a certain set of basic computation techniques and a body of fundamental facts, before they can either prove new theorems or learn new material.

If you’re a parent or teacher, you need to give your kids an opportunity to practice algebraic and arithmetic computation and at the same time, let them work on challenging non-standard problems that develop their thinking. For a thorough treatment of the computational side of K-8 mathematics we suggest starting with James Milgram’s The Mathematics Pre-Service Teachers Need to Know, and if you need a textbook right away, Singapore Math is a solid choice. For developing problem solving skills and mathematical maturity, we’ve already mentioned a few excellent places to start. The most important takeaway from the “math wars”, is to stay away from standard US math textbooks and to steer clear of anything that has the word reform in it or looks like it was written without any input from well-known professional mathematicians.

Photo Credit: _Untitled-1 A Social Network for Young Engineers and Inventors

Do-it-yourself projects are vital components of a good STEM education, but until recently there have not been good online DIY resources targeting kids., a social network designed for children to share their creations with each other, seeks to change that. The site lets kids learn from each other and from a growing collection of tutorials. is not restricted to purely engineering creations; users can share anything they make, from baked bread to artwork.

Perhaps, the greatest benefit of a site like this is that it allows kids to create a portfolio of their creations. Far too often, the talents and abilities of kids are hidden behind letter grades, numerical scores, and short teacher assessments. We are living, however, in a time when showcasing your work is becoming increasingly more important than bragging about your grades. Instead of aiming solely for perfect test scores, it may make more sense to enjoy the process of working with your hands and your creativity while acquiring useful knowledge and building up your resume. If you’re interested in a more advanced community, Instructables is worth exploring.

NRICH: An Organized Collection of Math Enrichment Problems and Activities


If you liked the expository writing in Plus Magazine, you may enjoy Nrich, a sister project from Cambridge University. The site features hundreds of math problems and activities organized by grade and ability level, as well as by topic. Although Nrich has a section for students, teachers who need to prepare lesson plans may find it more useful. The site content is closely aligned with US and British math curriculum standards, which should make it particularly appealing to educators.

An outstanding feature of the site is it’s emphasis on math enrichment topics that are usually outside a standard school curriculum, yet close enough to it to be relevant in a regular math class that needs to follow strict education guidelines. Another welcome aspect of Nrich is that professional mathematicians, not just math educators oversee the project, making sure that it is both mathematically sound and relevant. There is even a forum for those who need math help. Nrich may not be the easiest site to navigate, but it does contain a convenient topic directory that organizes all of the content. This project is worth exploring and should contain something useful for anyone teaching or learning math.

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

The Seasons Simply Explained

The fact that certain months are hot and others are cold is so deeply ingrained in our brains that we take it for granted. Fortunately, it doesn’t take advanced science to explain the basics behind this phenomenon. In the “Reasons for Seasons” animation below, Rebecca Kaplan talks about the science of seasons as if she is reading a fairy tale, not giving a serious lecture. This makes for wonderful bedtime learning even if you’re already a serious adult.

K-12 Science and Engineering Workshops at MIT

Edgerton outreach logo

One problem that online learning, with all of its obvious advantages, cannot currently solve is how to bring hands-on learning to students. Luckily, quite a few colleges and universities offer out of school STEM programs that complement videos and textbooks, and MIT is no exception. If you’re anywhere near the Greater Boston area you can schedule a free group workshop at the Edgerton Center at MIT, which runs a variety of science and engineering programs for kids of all ages. The activities, which are run by MIT undergraduate and graduate students, include working with electrical circuitry and exploring chemical reactions. For those who want more time to learn and build, longer summer programs are available, but you need to sign up early as they are quite popular. Below is a video that captures some of the spirit of the Edgerton Center.

Mindstorms: Children, Computers, And Powerful Ideas

mind storms book

Some of the most crucial steps in mental growth are based not simply on acquiring new skills, but on acquiring new administrative ways to use what one already knows.

If you’re only going to read one book on learning Mindstorms: Children, Computers, and Powerful Ideas has to be it. On the surface, this may seem like an outdated book about computer science education, but it is really a profound study of how people learn anything from math and physics to juggling and skiing. Written by Seymour Papert, one of the pioneers of artificial intelligence and the creator of what would become the MIT Media Lab, Mindstorms illustrates the idea that children can use their own “objects-to-think-with,” intellectual structures of their own making, to acquire, and more importantly, to work with increasingly complex and abstract knowledge. The book is filled with concrete examples of students learning something completely new or even fear-inducing (like math) using knowledge and intuition that they already have. Logo, the programming language that Papert co-created, serves as the primary example of a tool that helps students reason about new ideas (not just in math) in a perfectly rigorous yet comfortably intuitive way. Whether you’re interested in math and computer science education at the K-12 level or want a deeper understanding of how people learn without all the education jargon than this book will be indispensable.

A Mathematician’s Lament


There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract

Much ink has been spilled on the subject of why K-12 mathematics education needs improving, but rarely has anyone made the point in such an eloquent manner as to make it mandatory reading for teachers, parents, and students of mathematics education. This is exactly what former research mathematician and current math teacher Paul Lockhart has done in his impassioned essay “A Mathematician’s Lament” [PDF].

This is not another dry statistics-filled analysis comparing competing education reforms, but a powerful cry for teaching thinking over mindless procedure following. As an added bonus, Lockhart includes two beautiful geometry problems that capture the essence of mathematical reasoning and that you can start playing with right away. Yes, playing — we need more of that in our math classes.

(Photo by Mikey Angels)