Moving Through Math: two book reviews

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ClapDrumAndShakeItCover MeadowCountCover


Learning math through the arts… Moby Snoodles approves! So I was happy to review two books from Marcia Daft’s Moving Through Math project. 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).

Count, 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.

Thumbs up!

  1. 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. If the baby is too young to clap or jump, you can move the baby’s hands in yours, or bounce the baby in your lap as you point out the symbols.
  2. 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.
  3. “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!

Meadow Count


What? A traditional counting book, for numbers from one to ten. Children count by making whole-body movements, such as three giant puddle jumps, seven high reaches to the clouds, or eight jiggles down as you wiggle to the ground.

So what? Fine motor skills use some of the same parts of the brain as mathematics. That’s why activities that require fine motor skills, such as playing musical instruments, crocheting and origami, develop “the math brain.” But you don’t want to overwhelm and overload this math brain. Challenging fine motor skills, on top of challenging new math ideas – that can be too much for one activity! That’s why using gross motor movements helps to introduce new math ideas. Whenever I work with kids, I design whole-body methods for introducing each topic, from equations to infinity. This way, the math brain can devote itself to math, without having to coordinate the fine motor movements too.

Thumbs up!

  • Children in the book look and dress like they come from all different continents, without any cliches. Kudos to the artists on this tasteful presentation!
  • One-to-one correspondence is not challenging as an idea: babies are born understanding it. However, the reliable implementation is hard for young kids. Gross motor movements will definitely help to count more reliably.
  • The descriptions of movements are artistic. There are evocative metaphors, such as “count one leafy spin,” and emotions, such as “two happy hops,” and details that go with the story, such as “nine sharp tugs to create a bouquet” when the kid picks wildflowers. Kids love that rich stuff – and relate to math through it!

Building on it

  •  Use more intrinsic quantities to support the number sense. One example in the book is to hop two times to take off both shoes. You could also sprint to each corner of a room (four sprints) or reach to the sky with each finger on your hand (five stretches).
  • Connect counting to pattern units. For example, count to nine again and again as you create many bouquets for all your friends.

Reviewed by Maria Droujkova

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