Parents, help, and wishes
Parents often ask how to help kids do math projects without upsetting the kids, taking over, or otherwise breaking the flow.
“Every time I correct my child’s mistake she starts crying.”
“We started to build a model, but as soon as I helped, my son stopped working!”
Our recipe is simple. It is similar to the advice, “Don’t answer questions nobody asked.” Be co-workers, doing separate projects side by side. Do what you want – on your side, on your project. And help kids do what they want, on theirs. Don’t impose your wishes on children’s projects.
Help kids do what they want.
Ask kids to help you do what you want.
Don’t help kids do what you want.
I mean, would you want someone to help you do something that person wants, not you? Exactly!
Posted in Grow
Rachel’s question: What should you do when you’re bored in math class?
Please help Rachel with her question! What should you do when you’re bored in math class?
Posted in Grow
Kids tackle dimensions, mistakes on purpose, Poster*2 sale: Newsletter May 1, 2014
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I am Moby Snoodles, and this is my newsletter. Send me your questions, comments, and stories of math adventures at moby@moebiusnoodles.com
Poster*2 to celebrate multiplication
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?
Math Spark: Point-Line-Shape-Shape-Shape…
Staple some paper together into a little book, or use a small notebook. You will make your own counting book of dimensions.
Page 1
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.
Page 2
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.
Page 3
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.
Page 4
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!
Join us at Maker Faire North Carolina
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!
Book news
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!
Blogs and networks
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!
Sharing
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Talk to you soon! Moby Snoodles, aka Dr. Maria Droujkova
Posted in Newsletter
Inspired by Calculus Math Circle – Week 5
If we don’t teach kids to do actual calculations, what do we teach them in our calculus circle? And can it even be called calculus? Wouldn’t it be better to wait a few years until kids get older? These are the questions we are focusing on as our “Inspired by Calculus” local math circles for 7-11 year olds come to an end. Do try these activities at home by yourself (good), with your child (better), or invite some friends over (the best). If you do, please share your experience with us. As always, we welcome your questions and comments.
Week 1 activities | Week 2 activities | Week 3 activities | Week 4 activities
Week 5 – The Tale of Two Worlds
We started the first meeting of the series with free play. We also wanted to end our last meeting with it. Only this time we wanted the kids to move beyond noticing existing patterns and toward making their own by solving a series of open-ended puzzles. We also wanted them to think about and experiment with pattern-making in the abstract calculus world, not just in the concrete, physical, world.
The kids appeared eager to follow the White Rabbit. As soon as Maria explained that calculus world is the world of imagination, several of them exclaimed: “I want to go to the calculus world!”
Our first puzzle became our starting point on this journey.
Puzzle 1 – Draw a point
Draw a point. Does a point you draw exist in our world (physical world) or in the calculus world?
The points kids drew, however small, had some length and width. But a point in the calculus world does not have either. It has no size.
Imagining something with no size is very hard! Most kids, when asked, said they could not do it. Did they get upset or discouraged? Not at all!
Mathematical Lesson Learned – Difficult Can be Enjoyable
Deep math is difficult, but that does not make or break motivation. When we enjoy doing something, whether it’s yoga, crafting or math, we do so despite the difficulties or even because of them. Children’s joyful reaction to the challenges we presented is a good indicator of their enjoyment of playful, deep mathematics.
Puzzle 2 – Draw a line
Next, we asked the kids to draw a line made out of points: to integrate a line. We got straight lines and curves, lines with points very close together and those with points farther apart. After a brief discussion of the lines, one of the kids said: “Everything has a point in it!” They seem to get the point (pun intended).
Since the individual points that make up a line have no size, the line itself has no width. Can you imagine something infinitely thin? Once again, it’s hard, although perhaps a bit easier because a line does have something – its length.
Puzzle 3 – Draw a shape
Once all the kids drew their lines, they faced something new – the idea of dimensions. Although all them are familiar with the words “2D” and “3D” and use these terms often, they were confused when the concept of dimensions was brought up.
Mathematical Lesson Learned – the Importance of Asking Questions
It seems to raise more questions than answers. Will a line always be one-dimensional? What if it loops? What about a disk? How many dimensions does it have? A quadrilateral has four sides, so how come it only has two dimensions? The confusion happens between the spatial dimensions and abstract dimensions. Seems like another rabbit hole, promising another exciting adventure, just opened up!
Puzzle 4 – Integrate a Circle
The new challenge was to integrate a circle out of lines. It seemed we got as many solutions as there were kids, and then some! This is another great sign of children’s enjoyment of and interest in the topics. Although they worked at different speeds and could easily see each other’s solutions, every child in the circle continued working on the problem. With closed-ended problems that only have one answer, many kids stop working once someone in the group finds that answer.
Mathematical Lesson Learned – True Understanding Happens When You Do Things Your Way
But it is also a good check of children’s understanding. We have talked about integrating a circle, but kids tried it first with the triangles. In exploring and imagining so many other ideas, the kids showed they understood what it means to “integrate” a shape.
Puzzle 5 – Integrate a shape, any shape
Next came an even more challenging task. We asked the kids to draw a shape, any shape, and integrate it. As usual, math activities must be full of meaningful choices. While some kids got started, others said they were confused.
Mathematical Lesson Learned – It’s OK to Get Emotional About Math
Expressing one’s feelings about a problem, reacting to it emotionally, is a necessary step toward a solution. Confusion, irritation, annoyance – it’s okay to feel that way about life’s problems, including math problems. If you do something about it, the negative feeling just might go away. The children worked hard on this task, composing (integrating) shapes out of lines, but also out of small 2D shapes, and out of points. You can build bridges from this activity to different types of formal integration, such as the shell method or double integrals. It was time to kick it up a notch and move to the third dimension.
Puzzle 6 – Turn a Surface into a Body of Revolution
The kids were handed thin wooden disks. What can we integrate out of them? The kids explored different solutions which depended on the sizes of disks they used for stacking as well as on the order in which disks of different sizes were stacked: cylinders, cones, and more complex bodies of rotation.
Sometimes when you put surfaces together, you just get another surface. But sometimes you don’t. The kids played with pieces of craft foam trying to solve this puzzle. What if we roll a piece into a spiral? What if the piece is infinitely long and infinitely thin? Have we just crossed from the physical world to the calculus world? Looks like it!
Puzzle 7 – For the Road
We finished the final math circle with a brief foray into integrating into 4th and 5th dimension. And the kids got to watch the trailer for Flatland. There were no challenges other than our suggestion to “think of it on your own” and “try it at home”.
Posted in Grow
