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.
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.
“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…”
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:
“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)
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.
The benefits of bilingualism continue to be supported by recent studies indicating that speaking two languages not only can delay or prevent the onset and severity of Alzheimer’s and dementia, but also can improve brain efficiency at certain types of problem solving and the ability to perform some mentally demanding tasks. While I would never say that bilingualism makes you “smarter,” perhaps the more rigorous mental exercise demanded by constantly switching between different languages and the multiplication of neural connections that must be established among thousands of words and word groups keep the brain primed to operate at a higher level of efficiency.