Guest post by math educators Maria Droujkova and Yelena McManaman, authors of the new family math book "Moebius Noodles: Adventurous Math for the Playground Crowd"
Children dream big. They crave exciting and beautiful adventures and they love to pretend-play. Just ask them who they want to be when they grow up. The answers will run the gamut from astronauts to zoologists and from ballerinas to Jedi masters. So how come children don’t dream of becoming mathematicians?
Kids don’t dream of becoming mathematicians because they already are mathematicians. Children have more imagination than it takes to do differential calculus. They are frequently all too literate like logicians and precise like set theorists. They are persistent, fascinated with strange outcomes and are out to explore the “what-if” scenarios. These are the qualities of good mathematicians!
As for mathematics itself, it’s one of the most adventurous endeavors a young child can experience. Mathematics is exotic, even bizarre. It is surprising and unpredictable. And it can be more exciting, scary and dangerous than sailing the high seas!
But most parents and educators don’t present math this way. They just want the children to develop their mathematical skills rather than going for something more nebulous, like the mathematical state of mind. They try to reduce the struggle and danger, not celebrate it - with good intentions, such as safety and security. So they introduce the tame, accessible scraps of math, starting with counting, shapes and simple patterns. In the process, they leave everything else mathematical behind, “for when the kids are ready.” For the vast majority of kids, that readiness never comes. Their math stays simplified, impoverished, and limited. That’s because you can’t get there from here. If you don’t start walking the path of those exotic and dangerous math adventures, you never arrive.
It is as tragic as if parents were to read nothing but the alphabet to children, until they were “ready” for something more complex. Or if kids had to learn “The Itsy-Bitsy Spider” by heart before being allowed to listen to more involved music. Or if they were not allowed on a slide until they, well, learned to slide down in a completely safe manner. This would be sad and frustrating, wouldn’t it? Yet that’s exactly what happens with early math. Instead of math adventures - observations, meaningful play and discovery of complex systems - children get primitive, simplistic math. This is boring not only to children, but to adults as well. And boredom leads to frustration. The excitement of an adventure is replaced by the gnawing anxiety of busy work.
We want to create rich, multi-sensory, deeply mathematical experiences for young children. As we show in our new Creative Commons book, Moebius Noodles: Adventurous Math for the Playground Crowd, with a bit of know-how every parent and teacher can stage exciting, meaningful and beautiful early math experiences. It doesn’t take any fancy equipment or software beyond everyday household or outdoor items, and a bit of imagination - which can be borrowed from other parents in our online community. We make rich mathematical properties of everyday objects accessible to young children. Everything around us becomes a learning tool, a prompt full of possibilities for math improvisation, a conversation starter. The everyday world of children turns into a mathematical playground.
Children marvel as snowflakes magically become fractals, inviting explorations of infinity, symmetry and recursion. Cookies offer gameplay in combinatorics and calculus. Paint chips come in beautiful gradients, and floor tiles form tessellations. Bedtime routines turn into children’s first algorithms. Cooking, then mashing potatoes (and not the other way around!) humorously introduces commutative property. Noticing and exploring math becomes a lot more interesting, even addictive. Unlike simplistic math that quickly becomes boring, these deep experiences remain fresh, because they grow together with children’s and parents’ understanding of mathematics.
The most frequently asked question we get is: “How can parents not familiar with advanced math recognize it, point it out to children and create meaningful conversations and activities around it?” Here are some things you can do.
● Play. Relax about learning goals, don’t worry about having correct answers. Fool around, experiment, seek multiple silly ways of doing things. Enthusiastically say “ yes” to all the child’s ideas. Can we make a triangle with four angles? What would you call it? Would this name work for all shapes with four angles? Can we build an upside-down pyramid with blocks? Or play a Make Your Own Grid game with paint chips, sticky notes or rectangular picture cards as tiles. Prepare a certain number of tiles and try to use them all for a full grid. What happens if you have 7, 11 or 13 tiles? What numbers can form a full grid?
● Seek. Use online image and video searches to start chains of discoveries. Search for a math word, such as “patterns,” related to what your child is learning. Now search for this math word but add “in nature”, “art”, “building blocks”, or whatever your child is interested in. It is amazing how many beautiful math pictures come up in for, say, “pattern cat”, “angles in nature”, and “ocean symmetry”. Then poke around sites where these pictures are. Children love to sit in your lap and point at pretty things when you do that. For more ideas, follow our weekly Math Goggles challenge, which offers tips for discovering math in everyday things.
● Ask. Find welcoming places for math adventures. Ask questions online, including on our site, and offline - at museums, puzzle and game stores, parent gatherings. Share even simple experiences of creating a math environment for your children. Early math adventures make for excellent starters of friendly conversations and occasional passionate arguments.
● Make. As math is more than counting, so it is more than writing down numbers and drawing shapes. Art and craft activities are an integral part of mathematical learning and come up in every chapter of our book. For example, the game of Two-Hand Mirror teaches about bilateral symmetry, reflection and chirality. To play, draw a vertical line through the middle of a sheet of paper. Tape the paper to a table because your child will be drawing with both hands, holding a marker in each. Imagine that the middle line is a mirror. Explain to your child that his or her hands must move symmetrically at every moment – they should be the same distance from the line of symmetry, they should move at the same speed and in the same direction relative to the line of symmetry (up, down, in or out). From time to time pause to check the drawing in a real mirror by placing it on the line of symmetry, and compare the reflection to the actual drawing. Then, still holding a real mirror, have the child trace the drawing with her dominant hand and observe what her hand’s reflection does in the mirror What happens to the reflection as the hand moves up, down and around?
Can math be interesting? A lot of it already is. Can your children be strong at advanced math? They are natural geniuses at some aspects of it. Your mission, should you accept it: to join thrilling young math adventures.
About the Authors
Dr. Maria Droujkova is a parent, curriculum developer and mathematics education consultant. Maria brings together leaders in mathematics education, researchers, developers, parents and teachers for projects and discussions of family mathematics, early algebra, individualized instruction, math games and math clubs.
Yelena McManaman is a blogger, education consultant and developer, focusing on young children. Yelena homeschools her son and organizes STEM classes and events for kids. Online, Yelena helps other parents collaborate around advanced math for young children.
The book, Moebius Noodles: Adventurous Math for the Playground Crowd, was released in April, 2013.