Knitting Math
I have a long list of things I’d love to learn in life, like knitting. I have an even longer list of things I’d love to teach my son. Yes, knitting is on that list too. Or crocheting, whatever is more to his liking.
I’m not going to go over all the benefits of teaching a child (or self) to knit. Sharpened fine motor skills and improved concentration are just two of the more obvious outcomes.
The no-less important benefit is that knitting and crocheting produce tangible outcomes. And these tangible outcomes can be re-used as beautiful math toys or math art that will teach advanced math concepts.
If you are too busy and your children are too young to pick up yarn arts, you can browse knitted math-y objects on Etsy, like this dodecahedron. I showed it to my son and asked him what he thought of it. He said that he thought it was an emblem, possibly for a robot. He also pointed out all the triangles he saw.
Next I showed him this fractions afghan. We tried figuring out the pattern – rectangles divided into 1, 2, 3, 4 and more parts. We also counted to see how in some rectangles there was the same number of yellow and green elements while in others there were more green elements.
But don’t get too hard on yourself for not creating something just as beautiful for your child. Instead, stick around to find out how you can create no less stunning geometric shapes for and with your child. Hint – you’ll need to stock up on paper plates.
Posted in Make
Mathematical Faces 06/24/2011
It is often said that mathematical values, mastery and flow transform people who practice math. The transformations are reflected in children’s faces. Look at mathematical faces for inspiration, and share them with your kids. This is what it’s all about!
Submit your photos of mathematical faces for future posts.
This blog post starts a series showing kids and teens doing mathematics. We would like to thank Alexandre Borovik for the idea.
The task requires precision, and the boy’s face shows quiet, prolonged concentration, while his motions are fluid, confident and exact.
Natural Math club, Cary, NC, Spring 2011
The girl has found a mathematical idea in a shell, and now touches it to appreciate the beauty even more. She often draws and diagrams shells mathematically, and she looks inspired and happy.
Natural Math club, Cary, NC, Spring 2011
This kid is in the state of flow – her hands and shoulders are relaxed enough for precise, smooth movements… And her the face looks peaceful and meditative.
Natural Math club, Cary, NC, Spring 2011
The task is tough, and kids look serious and powerful. They managed it!
Natural Math club, Cary, NC, Spring 2011
Posted in Grow
Is our thinking of numbers fundamentally spatial?
Exegesis
Our deepest sense of number is probably not a number line.Flow
We can offer very fun ways to answer math questions. Kids can report higher numbers with louder sounds, higher pitches, stronger claps in high-fives, or more vigorous jumping.Mastery
As children develop their number sense, they can consciously watch out, and avoid the human tendency to squish large numbers together: “Millions, billions, it’s all up there somewhere!”
All over the world, people think of numbers as points on a line. Illiterate people and young kids readily represent approximate numbers by lengths. Schooled kids seemingly lose this ability to the image of whole numbers only, as beads-on-a-string. A handful return to the continuum image of the line later to discuss if there are more real numbers than rational numbers and other sophisticated number line questions. All the same, the number line image seems to be a human universal! But is it?
Núñez, Doan, and Nikoulina asked themselves if the line is a fundamental representation of number. While referring to toddlers and illiterates in their literature review, they focused on the educated population, asking people to report numbers they see in several different ways: by squeezing a handle harder, striking a bell stronger, yelling louder or dragging the cursor more to the right for higher numbers.
To understand what happened next, the extremely cool Weber-Fechner Law is helpful. In math terms, it says our perception of the world of strong stimuli is logarithmic. In practice, it means that when estimating distances, weights, color, pitch, and loudness, humans feel that 5 and 10 are next to one another in the same way 1 and 2 are next to one another, since both pairs represent doubles. Large numbers squish together in our perception. Good thing they do – or we would constantly experience the tortures of the Total Perspective Vortex from the “Hitchhiker’s Guide,” clearly seeing and fully understanding our insignificance within the universe!
If our number sense is fundamentally spatial, Núñez and friends argue, effects like Weber-Fechner Law would manifest themselves at all times, independent on whether numbers are shown as words or dots, and how their estimations are reported. Strikingly, they find it’s not true!
Unlike reporting with the number line, people did squeeze or hit just a bit harder or yell just a bit louder for 10 dots, compared to 5 dots – but not when numbers were presented symbolically, as words. In the symbolic world made of words, people’s minds steeled themselves to deal with the existential dread of large numbers, and did not need the protection Weber-Fechner Law provides.
If we always referred to our inner number line to measure magnitudes, there would be no such differences. The authors believe we have some deep sense of magnitude that is not based on number lines. In the picture below, seeing larger numbers for what they are corresponds to straight lines (and black graphs), and squishing them together corresponds to logarithmic curves.
R. Núñez, D. Doan, and A. Nikoulina, “Squeezing, striking, and vocalizing: Is number representation fundamentally spatial?,” Cognition 120, no. 2 (August 2011): 225-235.
Squeezing, Striking, Vocalizing full article
Posted in Grow
Can Board Games Help Learn Math?
If you are looking for a simple and fun way of bringing more math into your child’s life, then here’s a solution for you. It costs little, takes no time to set up and is a great way to engage the whole family. I’m talking about playing a round or two of a board game.
If you read (or listened to) “Judy Moody Goes to College, you know what I’m talking about. The story revolves around Judy’s problems with math and how she overcomes them. Hint – her tutor, Chloe, starts off playing a round of “Life” with Judy.
Turns out, board games do help children acquire numerical knowledge. So if your child (and yourself) are bored to tears with worksheets and rote learning, board games such as Chutes and Ladders, the Candy Land, and the Ladybugs Game offer a great alternative.
After playing a few rounds of the Ladybug Game with my son I found out another unexpected benefit. If your child, like my son, has small motor difficulties that make work with manipulatives frustrating, board games offer a stress-free and enjoyable alternative.
But the benefits of board games go beyond simple counting (or addition and multiplication). There are games – board games, card games, computer games – that teach children mathematical thinking, including geometric, logical and probabilistic thinking. Here’s a great list, broken down by particular math skills, to get you started.
While right now our stack of board games is small – the Ladybug Game, Candy Land and Four-in-a-Row (which proved the most amazingly flexible so far), I am slowly adding more titles to my wish list.
As for Judy Moody, playing “Life” changes her attitude towards math. She learns that math is everywhere, that life is full of math and, as a result, acquires a new “mathtitude”.
Do you play board games with your child?
Posted in Make
