How To Learn Math

Stanford professor Jo Boaler’s invaluable website has tools and resources for students, teachers, and parents. This applies to you! I cannot recommend the mindset approach enough, articulated by Carole Dweck, and along with Jo Boaler and thousands of math teachers around the world, is quietly bringing a revolution to the world of math education.

You can learn more about this approach to learning here.

You can take an amazing online course in how to learn mathematics here.

About Growth Mindsets

Growth Mindset Online Class

Thanks, Jo, for all your hard work and tireless encouragement of substantive and beneficial changes to the math education establishment.

The Five Principles of Extraordinary Math Teaching by Dan Finkel

In this perspective-expanding and enjoyable talk, Dan Finkel invites us to approach learning and teaching math with courage, curiosity, and a sense of play.

Dan Finkel wants everyone to have fun with math. After completing his Ph.D. in algebraic geometry at the University of Washington, he decided that teaching math was the most important contribution he could make to the world. He has devoted much of his life to understanding and teaching the motivation, history, aesthetics, and deep structure of mathematics.

Principle Number One: Start with a question.

Watch now to find out the rest:

How To Learn Better

I just noticed this really fantastic short video on learning at the The Atlantic.

  • Anyone really can learn anything.
  • You must be comfortable with not knowing, with not having answers, with being wrong.
  • Knowing what the rules are and knowing how success is defined means there is no discovery.
  • Be curious: ask questions, build the discipline of curiosity.
  • Sleep encodes memories; practice before sleeping and sleep well.
  • When you believe in yourself, your brain behaves differently; if you believe in yourself, when you make a mistake, your brain “spark and fires” because you know you are learning.
  • Education today force feeds problems; we don’t teach how to ask questions.
  • Any type of creative process usually begins with a good question, one that reframes a problem or challenges a process.
  • Stories help us to understand the world and the people around us while at the same time enhancing our attention spans and developing our imaginations.

Positive Norms to Encourage in the Classroom

More great stuff from Jo Boaler at I’ve been following Jo avidly since taking her amazing online class “How to Learn Math” from Stanford University. The class is free.

Recently they added a poster listing seven positive messages and norms for the math classroom. If you’d like to put it up in yours, you can download it in PDF here.

1. Everyone Can Learn Math to the Highest Levels.
Encourage students to believe in themselves. There is no such thing as a “math” person. Everyone can reach the highest levels they want to, with hard work.

2. Mistakes are Valuable
Mistakes grow your brain! It is good to struggle and make mistakes.

3. Questions are Really Important
Always ask questions, always answer ques- tions. Ask yourself: why does that make sense?

4. Math is about Creativity and Making Sense
Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss and critique.

5. Math is about Connections and Communicating
Math is a connected subject, and a form of communication. Represent math in different forms eg words, a picture, a graph, an equation, and link them. Color code!

6. Depth is much more Important than Speed
Top mathematicians, such as Laurent Schwartz, think slowly and deeply.

7. Math Class is about Learning not Performing
Math is a growth subject, it takes time to learn and it is all about effort.

How to Save Your Neurons

A blast from the past March 2009 Scientific American article by Tracy Shors provides a rebuttal to the somewhat common misconception that the brain does not create new neurons. It does – thousands every day. Don’t get too excited, though. If you don’t cognitively exercise these baby neurons, they will disappear within just a few weeks. Article is linked above, but unfortunately there’s a pay wall. I recommend springing for the subscription. It could be your first step in raising a whole new batch of thinker cells.

How to Save Neurons
How to Save Neurons

“Fresh neurons arise in the brain every day… Recent work, albeit mostly in rats, indicates that learning enhances the survival of new neurons in the adult brain. And the more engaging and challenging the problem, the greater the number of neurons that stick around. These neurons are then presumably available to aid in situations that tax the mind. It seems, then, that a mental workout can buff up the brain, much as physical exercise builds up the body…”

The Precise Relationship between Intelligence and Speed: There is none

Being a Southerner in New York City, I always suspected this. There is no relationship between intelligence and speed. What is important is to deeply understand things and to think about their relations to each other. In math education emphases on speed simply create math anxiety and phobia, rather than great mathematical thinkers. From Fields Medalist Laurent Schwartz:

Laurent Schwartz
Laurent Schwartz

“I was always deeply uncertain about my own intellectual capacity. I thought I was unintelligent. And it’s true that I was, and I still am, rather slow. I need time to seize things because I always need to understand them fully. Even when I was the first to answer the teacher’s questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who weren’t as good as I was answered before me and towards the end of the 11th grade I secretly thought of myself as stupid and I worried about this for a long time. I never talked about this to anyone but I always felt convinced that my imposture would someday be revealed. The whole world and myself would see that what looked like intelligence was really just an illusion Now that never happened. Apparently no one ever noticed it, and I’m still just as slow. At the end of the eleventh grade I took the measure of the situation and came to the conclusion that rapidity doesn’t have a precise relationship to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant. Naturally, it’s helpful to be quick, like it is to have a good memory. But it’s neither necessary nor sufficient for intellectual success.”

Laurent Schwartz, Fields Medal earner, as quoted by Dr. Jo Boaler in EDUC115N How to Learn Math (MOOC)


The Key to Success: Grit

In this excellent Ted Talk, Angela Lee Duckworth bluntly relays where we are in the science of education with regard to the single most important factor that determines success and achievement. At this point, all we know for sure is that a growth mindset can play an important role in helping children develop the stick-to-it-iveness they need to reach high levels of achievement.

Comments welcome.

Open thread on the definition of success at

Suggestions for Making Math Real for your Elementary and Middle Schoolers

Praise the Effort
Praise the Effort

Here are some suggestions for things you can do to help your child with math outside of school.

Every night during dinner or after, have a math minute: ask your child what they learned in math class that day. Was it fun? Give your child a mental math problem based on what they learned that day.

Make sure the mental math problems aren’t too hard. If necessary, make the problems easier – but never be negative or display disappointment. Just be excited when they get one right. Always praise the effort, regardless of the results.

Additional suggestions:

    • Make a point to praise your child’s effort in math, regardless of the results
    • Ask if class was fun today, was the test fun?
    • If you cook, have your child help you with the measurements, especially if you have to adjust the recipe.
    • If you don’t know the meaning of a word on the homework, don’t be afraid to look it up, but don’t use yahoo answers, wikipedia is fine, or a math website.
    • Have your child re-teach you what she learned in class today
    • Take your child shopping and compare prices in differently sized bottles. On your smart phone show her how to check the price per ounce (before you show her that it is often written on the shelf) to decide which one to buy.
    • Shopping: if something is on sale, have her figure out the discount and the price.


Carol Dweck and the Growth Mindset


In the past five years no book or thinker has had a greater impact on my life than Mindset, The New Psychology of Success by psychologist Carol Dweck. The approach to learning and growth she describes in her book and videos has affected me not only in my pursuits of hobbies and interests, but professionally, as an educator, as well. I have found new passion and joy in my own musical and artistic endeavors, and also have, I hope, become a better teacher in cultivating in my students a lifelong love of continual learning and determined practice on the road to discovery and success.