Maria Droujkova is the founder of Natural Math, a curriculum developer and a mathematics education consultant.
When asked what she thinks should be the main goals of an elementary school curriculum, Maria answers with a quote from a favorite book, The Diamond Age, “The purpose of education is to have an interesting life.” And then she pauses and adds just one more word to it, “Now.” When educating young children, people think of the interesting lives those kids will have in the future, but for Maria the purpose is to have “the adventures and deep intellectual experiences, to exercise their curiosity and make connections, now, as they go through that education.”
So how should we evaluate a math curriculum and the math education our children are getting? Maria believes there should be three components to the assessment: mastery, adventure, and growth. More specifically, we should evaluate the growth of pattern thinking, as well as mastery of values such as precision, reuse of what works, search for algorithms, things of that nature. “And you evaluate these values by how they are expressed in whatever the child does. And what the child does should be individually owned by the child – their own examples, their own problems, their own adventures.”
And what about memorization? Do certain things in math absolutely need to be memorized? Maria believes that memorization can be joyful and can help understanding if done right. She believes that we need to offer children different ways to memorize, have them work heavily on patterns, problem solving, and projects, and in the context of that, let them do memorization that they find useful. She herself recalls having some issues with memorization and building her own systems to go around it. However, she feels that if someone had forced her to memorize, she would have likely quit the field because it was always about patterns and problem solving for her.
I asked Maria why she thinks there is so much math anxiety these days. The reply, “There is math anxiety and fear because there is violence. Mathematics is a strong influence on your mind that could be good or bad. What happens is that people have no way to limit how much they do it, with whom, and when to stop it, and that is cruel. We, educators and professionals, need to stop that, we can’t be that cruel to people.” She imagines that when we give children the freedom to do as much or as little mathematics as they want, and let them choose when to do it and when to stop, then we will see much less of the anxiety. She sees that happening, for example, in math circles, “when people are there for love, they get together and they do it because they choose to and it’s a celebration and festival of joy. Or at least it’s ok, it doesn’t have to create a wonderful thing, it just has to be fine enough.”
On the bright side, Maria sees progress. She sees many more people, in proportion to the whole population, being mathematically literate. There is much more conversation about gentle and joyful ways of doing mathematics than ever before. There is much more awareness. “And we have a female Fields medalist, yay!”
Maria’s advice for someone designing an elementary school math curriculum? Get children involved in your endeavor. She promises that you’ll see miraculous things. “Have a mechanism for them planning the next lesson,” she says, “Children are such good designers in a group with adults and they have very divergent thinking. Every design team should have a 5 year old on it!”
As for great activities to do with children, Maria singles out one of her all time favorites, The Mirror Book: two mirrors put together at an angle. “It’s so rich, leads into group theory easily because of the wallpaper groups it produces, and it leads to infinity – you can see the infinity, and the symmetries. It is low floor and high ceiling. It has all the aspects that I value in an activity, people like it, and it’s playful.”
People sometimes laugh, and ask what math can you learn from children? “What you learn,” Maria responds to them, “is to change your definition of mathematics, what it is. That is really valuable, and we should keep doing it. We should keep changing our mathematics and we can do it better with children.”