Elementary School Mathematics
[Reviewed by Maria Droujkova, on 01/08/2013]
Learning math through the arts… Moby Snoodles approves! So I was happy to review two books from Marcia Daft’s Moving Through Math project. (The other is Meadow Count.) They are read-aloud books for kids under five and their grown-ups. Both books are illustrated in a distinctive, memorable manner that reminded me of early Japanese watercolors. Of math education aspects, I found notes to parents to be most distinctive and memorable. After a strong book, you can graduate from “What?” (what entities and actions were in the book) – to “So what?” (your new understanding of the world).
Clap, Drum and Shake It
What? Use iconic symbols, such as clapping hands or shaking maracas, to form pattern units, such as “clap, clap, shake.” Then repeat the unit to form the pattern. Perform each movement as you get to that symbol in the sequence.
So what?Unitizing is the foundation of multiplicative and proportional reasoning. For example, 5*3 can mean a unit of five repeated three times, or a unit of three repeated five times. Kids need to work and play with units a lot, such as repeating parts of songs and dances. A kid who thinks of any unit as a single building block is well on the way to the idea of variables.
The book uses iconic symbols – that is, pictures that show what to do. Iconic symbols help kids transition toward abstract symbols. Iconic symbols are accessible even to babies. You can move the baby in your lap as you play through the book and point out its symbols.
The relatively advanced idea of pattern units is introduced qualitatively (without numbers) first. This helps learners to form strong, grounded foundation for the idea. Qualitative intros work for learners of any age, but are absolutely necessary for young kids
“Look for patterns in the air, look for patterns on the ground.” For example, walking feet: left, right, left, right… Or flying wings: up, down, up, down… Inviting kids on scavenger hunts after introducing a new math topic? Yes!!! Scavenger hunts help to notice many aspects and details of a topic; they make the topic stick in memory; and they integrate math with the everyday world of learners.
Building on it
Do more multiplication. In particular, invite kids to multiply within pattern units. For example, how do you double the pattern unit “clap, clap, shake”? That is, how do you show 3×2 in the language of the book? “Clap, clap, shake; clap, clap, shake” is what the book does. You can also do “clap, clap, clap, clap, shake, shake”!
Make the idea of variables explicit. Give your pattern units names. For young kids, the traditional X and Y are too short and abstract for variable names. Invite kids to create and name several pattern units. Kids often name things after themselves, their favorite heroes, or their pets. Let’s say we have these names for pattern units: Alice = “clap, clap, shake” Bob = “drum, clap” Then kids can make patterns out of Alice and Bob! Bob, Bob, Alice = “drum, clap, drum, clap, clap, clap, shake”
Provide even more support so kids can make their own patterns by transformations of old pattern units. The book suggests two transformations. Reflection turns “clap, clap, shake” into “shake, clap, clap.” Swap between moves turns “clap, clap, shake” into “shake, shake, clap.” Invite kids to make up their own transformations. Or catch their mistakes in repeating patterns, and turn mistakes into transformations!