I am Moby Snoodles, and this is my newsletter. Send me your questions, comments, and stories of math adventures at firstname.lastname@example.org
Have you seen our multiplication models poster? If you have wanted to get one, now is the perfect time! For any number of posters you order in the next two weeks, we will send you twice the number of posters. This is our way of celebrating our Natural Math Multiplication course and the ~600 registered participants. Thank you for all the stories, music, art and craft in virtual and physical media!
To quote Malke Rosenfeld of Math in Your Feet: I mean, just look how many ways we can experience and come to understand multiplication! Stunning. Given this reality, why would we want our students to only understand multiplication as a series of facts?
Staple some paper together into a little book, or use a small notebook. You will make your own counting book of dimensions.
What to do: Draw a point.
Where’s the math: In the world of math, points have no width, height, length, anything – they are zero dimensions. And they belong to the 0-th dimension.
What to do: Make a line out of points. This process is called integration. Is your line straight or curvy? Does it form your favorite letter? Now that I have asked these questions, do you want to integrate more, fancier lines? Have you used many points?
Where’s the math: Mathematical lines use infinitely many points! If you know where you started on the line, and how far to go, and which way (+ or -), you can find one precise destination unambiguously. Think about it: however your line curves in space, if you are a Line-Land citizen, you don’t care. Just knowing one number (positive or negative) gives you all the information about your destination. This means that whatever line you drew, however it curves or angles, it is of the 1st dimension.
What to do: Integrate a flat shape out of lines. Will your lines crisscross or stay parallel? Does your shape resembles anything or is it abstract? Can you still see the lines within it?
Where’s the math: In the world of mathematics, flat shapes are made of infinitely many lines, and belong to the 2nd dimension.
What to do: The second dimension is as far as you can directly model on paper!
You can draw a stack of 2D shapes, faking the 3rd dimension. Or you can make a bookform or a sliceform pop-up of your shapes, and insert it into your book.
Where’s the math: In mathematics, a volume is made up of infinitely many 2-dimensional slices.
Beyond Page 4. You can draw and imagine shapes in higher dimensions! More details at https://naturalmath.com/2014/04/inspired-by-calculus-math-circle-week-5/
Watch a short animated cartoon, The Dot and the Line: A Romance in Lower Mathematics.
Have a math spark from your family or group? Email us so we can share your adventures on the blog!
On Saturday June 7th, we will be at the Maker Faire, celebrating the DIY spirit in mathematics. If you are going, come say Hi at the Natural Math station at the Faire. Email me to volunteer to help us design and lead activities. Even if you are not local, send us ideas for crowd-pleasing, math-making activities!
Dee Harvey shared a fantastic “pattern creature” by Iseult (6), inspired by mirror-drawing activities from the Moebius Noodles book. Check out the attention to detail in reflections, for both shapes and colors!
Our Math Mind Hack about making mistakes on purpose is generating some following – and some objections! Dana Ernst at Math Ed Matters used the method in her study of combinatorics of Coxeter groups: I set myself the task of trying to come up with clever mistakes. I intentionally followed what I expected to be dead ends. An hour later, I had several new insights. I still haven’t cracked the problem, but for the first time in a while I felt like I had made some headway.
Dana asks her readers how to help students develop healthy attitudes and practices around mistakes. In several responses, the topic of play comes up, since mistakes are handled gracefully in many playful contexts. For example, Christopher Hanusa suggests games such as Planarity, where you make a lot of experimental mistakes before figuring out the solution to your graph theory problem.
Play was also a major theme in my Learning Revolution keynote, and in questions people asked.
However, the invitation to make mistakes on purpose raises some red flags during discussions at the Multiplication course forum. You can see my comments there. @cleabs says the very idea can alarm a very anxious, perfectionist child:
Celebrating mistakes is also part of what we do, but she just doesn’t buy it. Like the other day we were making gluten free donuts in our new donut pan, and both batches came out tasty but not donut shaped. She cried! I was like – no, this is fine, it’s our first attempt, we learned this recipe doesn’t work, we learned this other recipe needs tweaking but we’re closer, etc. – and it just didn’t make a difference. She is phobic of making mistakes despite how she has been taught (and I think is partly just genetic hardwiring) in any field, and since there is a “right” and a “wrong” in math, she has a lot of fear here.
And @katying points out two potential conflicts: with applied math, and with standing on the shoulders of the giants:
I homeschool my son. He is only 5 right now. But one reason I like it already is that as his mother I know him so well, I know when he is tired, stressed, over worked, bored and silly and so I know when to push a bit further and when to pull back. We have fun and are silly at times, and he likes to make erroneous math sentences and have me correct them, or he likes when I make the mistake and he corrects them. This is fun because I know in a round about way, it confirms for me what he knows and doesn’t know, which I am always keeping an unwritten log of. But I also think the goal of mathematics is to measure the world. In my homeschooling we have plenty of room for mistakes and practices, but I do intend for him to be a serious student of the world, and to have reverence and respect for teachers and adults and the thinkers who came before him… I guess I am not sure to what extent or in which context I agree with the idea of celebrating mistakes…
Does making mistakes on purpose bother you? How can you use mistake as a tool without building faulty bridges, disrespecting Newton and Kovalevskaya, or triggering your panic attacks? Share your thoughts!
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Talk to you soon! Moby Snoodles, aka Dr. Maria Droujkova