I homeschooled my daughter for first and second grades but I did not explicitly employ any kind of kinesthetic approach to learning math or anything else, for that matter. She wouldn't accept anything formal for the first year so we spent a lot of time out of the house -- on walks (with lots of opportunities to talk math), math games, thrifting (always lots of history lessons there), reading books, listening to audio books, library visits, making stuff.
For a while I wasn't completely confident in my approach, but over time I realized she was showing me what she was learning in many different ways: through conversation, through her art work and other creations, and, very often, through her physical movement.
Here are some summaries of and links to blog posts from the past couple years that documented this phenomenon of "the mind needing a body to think with". At the very least this will give you a peek into what I see when as I watch a child physically interact with her world.
I'll start with a potent example in full, and give excerpts for the rest. My daughter was six and seven in these examples.
Think Like a Straight Line (June 14, 2012)
It's been a loooong time since the kid has ridden her bike. So long it seemed like the first time again today.
She felt wobbly. Steering was a challenge. So, she gave herself a pep talk as she worked to reacquaint herself with the activity.
"Okay, all I have to do is think like a straight line in geometry..."
She rode back and forth across the basketball courts chanting her new her mantra.
"Think like a straight line, think like a straight line, think like a straight line in geometry."
When she'd get to the end of the court, she'd get off the bike and turn it around.
Then she figured she could make the turn without getting off.
"All I have to do when I get to the end is think like a circle...."
I'm sure she'll be back in the swing of things in no time. Plus, I love the thought that pathways have specific intentions. She's in the math, man. Totally in it.
"Look Mama! I can do Origami with my body!" | Origami Twirling Bird: Points, Edges, Turns, Poetry and Poses | August 25, 2011
"We've read Sir Circumference the first Round Table a number of times. Now she has a game she made up where she leaps towards her blow-up wading pool in what she calls the "diameter jump' -- I hold my breath every time as she leaps, finger tips to toes stretched out in one long line to touch the front and back of the pool at the same time, literally flying, flopping almost on the other side of the pool." Spontaneous Math / Math All Around | August 19, 2011
This next post relates to body knowing because it is built around the fact that we went on daily walks all over our little city. Many times we would set out and I'd let my daughter navigate us downtown. The map of our city and our experience in the real territory in the map made for a very potent game. | Totally Territorial: Cats, Maps, Area and Multiplication (April 3, 2012)
How we came to understand scale: "If an ant weighed fifty pounds (the weight of a human child) how many pounds could it lift? My girl counted it up on her fingers and immediately sprang up and ran around the living room trying to lift up all the chairs. I nixed that idea, but it was such an immediate reaction that it sparked the idea that this needed to be an interactive experience." | Ten Times Better, Longer, Faster, Farther: Understanding Scale | January 11, 2013
This final example is from some summer work in the city: "The girls in the room were hanging out with me before class while I set up and helped me tape out the floor. Any time I have a chance to let kids help me tape, from preschool to upper elementary, my helpers invariably end up spontaneously exploring their newly taped environment without any prompting. This is actually my favorite time with kids -- manipulating the floor space with tape and then seeing what they do when they first discover it. Here's a peek at the space and the only part of their exploration I could capture on video." | Floor Tape How Do I Love Thee? (Video Edition) | July 15, 2012