I LOVE this Ignite talk from Annie Fetter of The Math Forum. Here's why:
"[My mom] didn't think of herself as someone who did math ... Why is it that intelligent people who are good at sense making and good at problem solving feel no affinity for school mathematics? If our students could do the things my mom could do we would be ecstatic. As math educators we need to make sure students and grown ups understand that doing math means a lot of different things including making incredible, beautiful art."
I especially love this because in her talk Annie points out all the math doing and making in which her mother engaged.
So...how would you fill in the blank here?
Doing math means a lot of different things including...
Hello and welcome to what will likely be a sporadic series called Step Dance Saturday! Our inaugural video is of one of my favorite step dancers, Melody Cameron, her sister, and a few of her sister's kids! They live and dance on Cape Breton Island, which is part of Nova Scotia, Canada.
The dancing starts in the traditional way, with a Strathspey which transitions to a reel. The Melody and her sister have choreographed their steps for this part.
When the two girls come on stage, they position themselves for the reel portion of the Scotch Four, a very old figure dance. Both the figure and the step dancing itself originated in Scotland. From this point in the video all the dancing is improvised, each dancer putting steps to the music as they wish.
As you watch, you can look for patterns of footwork performed on one side of the body and then repeated on the other side. It may take more than one viewing to be able to see those patterns. If you want an added challenge, see if you can figure out the pathways the dancers are taking during the Scotch Four!
There's a cool new international math education project on the interwebs. It's called Mathagogy: Two Minute Math Education. Peps McCrea, the instigator of this project, says on the site: "Our aim is to slowly gather a diverse collection of short ‘approaches to
teaching mathematics’ videos from practitioners around the world."
He asked for submissions. Fueled by John Golden's support, I complied, and now my just-under-three-minute video is up and running on the Mathagogy site along with some other rather fantastic videos. (Although, now I need to give John himself a little nudge!)
This has been the year of videos for me, but I think this one is the best quick, visual description and reasoning of my work out there right now. (However, stay tuned for a new article from me, to be published in the Teaching Artist Journal in October, which pushes forward on what it really means to teach and learn in this kind of interdisciplinary setting. Much of my thinking in this video includes excerpts from that piece of writing.)
Feedback and questions on this video are welcome and encouraged!
If you'd like to leave a comment but don't see a way to do it, chances are my blog template is getting in the way. Try going back to the home page and refreshing your browser. If that doesn't work and if you still want to get in touch, feel free to e-mail me or contact me via the Math in Your Feet website.
Okay, so they say you're your own worst critic, yes? Well, after watching this video a couple times it's clear to me I said most of what I'd planned to say, which is actually quite a victory. There's no way to practice the special kind of adrenaline surge that you get when, not only are you in front of large audience, but you know that your work will be archived online in perpetuity. No pressure. Really.
The hilarious thing is that my almost eight-year-old daughter, who coined the phrase "math mommy" as spoken in a derisive tone (don't worry, she likes math more than she lets on) was actually quite generous with her critique. She overheard my husband and I talking about my reaction to seeing and hearing myself in this format and she said:
"Are you kidding?!? It came out great. It was actually a little interesting for a change."
Oh my gosh, life as a parent is never dull.
Anyhow, I was thrilled to present at TEDxBloomington. It was an amazing day with an array of talks on many different subjects all connected to the theme Jump IN. This meant there were a lot of doers and solution finders sharing their ideas that day, from a doctor whose efforts have literally saved thousands of AIDS patients in Kenya, to a variety of realistic solutions for re framing our views on mental health issues, to frank and hopeful discussions about race and poverty. I was in fine company and it was an honor to share my work in this way.
One important thing that did not come out in the video editing is a really important slide that correlates with my description of the Jump Patterns tool (starting at about 3:48 in the video). I've put a version of the slide below the video. Speaking of which...enjoy!
More information about the Math in Your Feet program can be found at www.mathinyourfeet.com.
Or, you might really dig the Math by Design page. It's the place where the Math in Your Feet approach is translated to all the best making supplies: straws, pipe cleaners, paper, glue and tape. There's also the extension of this blog on Facebook where I share the amazing, cool, creative math that people make, in all different forms. I'd be pleased to see you on Twitter, too!.
I am looking for as many examples as I can find of contextually rich math and math art learning in elementary education. I put the idea out on Twitter, but I'm hoping readers of this blog will be able to contribute any and all ideas you may have.
What is not yet clear to me is how and where math learning and math art learning overlap. Math Art, to my mind, can include all artistic media including dance, music and visual forms. If you are able to help me with links or thoughts of your own, even including specific examples from your own teaching, I would be most grateful.
This is only the beginning of my inquiry to make sense of how math learning can happen in multiple contexts, including artistic and design settings, with all roads leading to real comprehension and mastery of mathematics heading into middle and high school.
So...who likes bedtime? I, for one, am not generally enamored with detours from the normal bedtime routine.
But when my kid said, "Hey Mama! Want to hear this song I made up that helps you with your three times table?!" I decided to give her a little leeway so I could capture the moment. What can I say, I'm a sucker for math!
The song starts: "There were three ice cream trucks at the corner of Circle Drive..."
My favorite part is 'on the corner of Circle Drive' since, of course, circles have no corners! But, I'm pretty sure this was not intentional on her part.
I'm happy to have this unexpected piece of evidence that she is thinking about and internalizing these concepts. I'm also pleased to report a happy conclusion to bedtime!
My new website is up in its temporary home waiting to have the Math in Your Feet address pointed to it. In the mean time, I thought you might like taking a look. It's got a ton of new features including an interactive News page and the brand new Math by Design section. But the best thing of all is...
...a new two-minute Math in Your Feet video!!
I'm about to swoon, truly. I've had the footage for a year or more, but only recently found the golden key that unlocked its riches.
While you're there and if you're so inclined, I'd love to hear any feedback or comments you might have. You can leave your thoughts here or in the comments of the News page.
Listen as my seven year old shares her discoveries about our lunch table, one fine October afternoon:
This moment brought to you by our Paul Salomon-inspired star inquiry. I love the whole sequence because it captures the essence of hundreds of other math conversations and discoveries she and I have had together over the last year. They're small moments of inspiration, identification, conversation and observation that are being layered, pieced and added together into something incredible -- comprehension.
I was in Kansas last week working with 38 physical education teachers (both elementary and middle school). Yes, I know it was massive, but it was a lot of fun! The mostly hands-on, active morning was full of the core Math in Your Feet lessons: creating patterns and rhythm in our feet using my Jump Patterns tool and then combining and transforming those patterns.
PE teachers are used to organizing moving bodies (their own and those of their students) but they are not as familiar with math curriculum, especially in relation to movement work. It was gratifying to see them open up to the experience of both a new movement/art form and the idea of math outside the context of a textbook or a checkbook. This program is truly mathematical 'activity'!
Here is a quick video clip of some of the the teachers' creative work. Just like the kids do, they paired up to work through the Jump Patterns movement variables until they had created a four-beat pattern they could repeat, dance in unison (congruently) with their partner and, most importantly, be happy about.
It's a little hard to hear but the teacher in orange is saying "We combined and we reflected...alternating the reflection... [I think that's what she said -- I didn't hear her at the time either, and I guess I was expecting that the two folks on the inside would be the original pattern, and the two on the outside would reflect that pattern. That's why I was sort of confused on tape!] Here's what they did -- remember it's two individual four beat patterns that have been combined to make eight beats:
What was also surprising and interesting about this pattern is that the second four beats could not be reflected because it already was a reflection and congruent at the same time. Regardless, the team wanted to make it different somehow, so that's why when the original pattern jumps forward, the 'reflection' jumps back. After I turned off the camera we had a good laugh about how they had used the math to inform their creative work but, ultimately, it's a choreographic process and you absolutely have to stay true to the dance aesthetic as well.
That, and sometimes ignoring your students (as long as they're working on something) produces the most wonderful results!
p.s. And, if you want more footage, it might be a while, but I have finally (!) accessed footage of students in Math in Your Feet that I've been collecting for the last couple years. A short video summary of the program and a longer curriculum guide with an accompanying video is in the works. It's a massive project, but I am super excited about finally being able to share the program this way. In the meantime you can read about the program in detail by going here.
p.p.s. We've been have a whole bunch of fun over at the Math in Your Feet Facebook page. Why not join us?
Perhaps you'll remember the kitty census that happened at our house last fall. I just re-read the post and nearly fell out of my chair. Not only is it touching and hilarious (at least to me) it was a completely different activity last year than what happened this morning.
Last year the kid was a newish six. This year she's a newish seven.
Last year it was my idea; that morning, the kid just wanted to take her cats to the vet. When I suggested we could do both she agreed, but only so she could take care of her kitties. She had no interest in data whatsoever.
This year it was all her idea. I ventured a suggestion about how to sort and classify all the cats, but it was clearly her gig and so I backed off. I would have preferred to sort by material (stuffed, ceramic, plastic, flesh and blood, etc.) and then sort into sub categories from there, but the kid had other plans, as you'll see:
It may look straight forward, but the sorting process was actually quite involved. I mean, really, what's the difference between a multi-colored cat and a spotted one? How come the otherwise solid grey kitties with the white paws didn't get put in the multi-colored pile? The point is, she had to figure out what the parameters were to make those groupings; any one of us could come up with multiple variations on the same theme and we'd all be right as long as we were being consistent with the rules. I'd say that's real math right there.
One more difference: Last year she was always performing, but unselfconsciously. For this year's census she was intent on presenting her process and results in a formal way, specifically on video. She's the one who decided what to say. As always, I am just the faithful assistant who just happens to ask a few clarifying questions from time to time.
Yep, you heard right. Our cat Lucy and my daughter have been added to the final kitty census tally. 72 cats! Good thing only two of them need to be fed.
p.s. I've got a new Facebook page
where I'm sharing links to cool math activities I find and some
other things I'm doing with math, making, dance and rhythm. Hope to see
you there!
I'm in the middle of summer programming. It's Math in Your Feet in a lot of ways but also not completely like the program I do in schools. It's more like a whirlwind of percussive choreography, rhythm, and patterns of all kinds. There's also a lot of math in there as well, just not explicitly.
My reasoning for this that kids need as much exposure as possible to patterns in multiple, diverse contexts. These kids I've been working with, for example, are a perfect case in point. When asked on the first day to find patterns in the room in which we were working, they were at a loss. In all the groups, color patterns were found first. Then somebody would notice a sequence of objects, but it didn't repeat. A potential pattern unit, but not a pattern in itself. Even the three examples of simple tilings in the room (floor, ceiling and walls) escaped notice, even when I pointed them out.
Patterns are more than sequences of colors. They are more than two dimensional shapes. They are sounds, movements, expressions, order. They are long and short. They repeat. They change. They're everywhere. So, when I say we're not talking about math explicitly I mean we don't need to talk about it because we're doing it. Calling it 'math' interrupts the flow we've created -- sometimes just doing and experiencing is enough. This doing time is a chance to get swept up in the creating, to be fully engaged and amazed and delighted in your own abilities. I believe this because, simply put, that is what I find best about learning something new.
On top of the sheer fun of watching kids engage in new pursuits like percussive dance, one of the reasons I'm enjoying doing the summer version of Math in Your Feet is that I have leeway to experiment with how I deliver the program, engage my young dancers (right now ages eight to eleven) and how I set up the space.
In the videos, below, you can see what I'm trying out right now. This big grid isn't the normal setup for Math in Your Feet but I was really excited to tape out the space this way. Normally, when kids start making up their own dance patterns they usually get their own personal square dance spaces taped out in individual groups of two, each pair slightly separated from the other groups. I'll be very interested in how the new set up works out (or doesn't).
This new set up came about because the floor really lent itself to a large grid format. 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:
Their movement is a natural kid reaction to squares -- Hop Scotch! But in this second little clip you can see how they started exploring rows as well as columns.
Later, during our class time, when we were talking again about other kinds of patterns they could find, other than the ones we were making with our hands and feet, they noticed that each square of the large blue grid was made up of four smaller tile squares. Given that on the first day they never even noticed how the floor was designed when I asked them about patterns in the room (before I put down this grid), this was a huge step forward at identifying and describing the structure of their environment.
I'm excited to share one of my daughter's math discoveries via video, for the first time ever! I just caught up to this technology last week and am thrilled that I can put my new phone to immediate use.
Yesterday she called me over to the keyboard to share something she had discovered. We have always left all kinds of musical instruments around the house for her explore as she will. She has not yet had any formal music lessons (except for three or four penny whistle lessons from her dad) but her current piano style can be loosely categorized as jazz improv and/or piano bar; she really listens to the rhythms and melodies she creates and, even without 'technique', she is making real music to my ears.
Anyhow, on this particular occasion, she had been noodling around and suddenly yelled to me from the piano, "Mama! I discovered how I can use the piano to count up by threes!" As you watch you might notice how her hand movement shows her understanding of groupings. I've been especially tuned into children's gestures since I read this study on how children show what they know mathematically through their gestures. Here's what she did:
After she showed me what she had discovered about threes, she realized she could do the same thing with fives. In this video I love her excitement about finding other, unexpected patterns in the black keys:
None of this is really earth shattering, but any time a child moves her understanding of a math concept into a new mode or realm, it is cause for celebration. I think it shows that real learning is happening.
Nic Gareiss at Dance is Music continues to be my source for all manner of percussive dance inspiration!
Despite all my more recognizable math postings lately, and my never-ending enjoyment of accompanying my 6yo on her math journey, this kind of dance (not tap dance, actually, but related forms) is really where my interest in math all started.
Over time, performing and, especially, teaching percussive dance made me wonder if there was math in what I did. I simply asked the question and now kids get to learn math topics and exhibit their mathematical thinking and choreographic prowess through their bodies and foot-based dance patterns. Here's the whole story, if you're interested.
I'll wager that each one of us looks into a mirror at least once a day. Surprisingly, what we see in the mirror is up for some debate; at least that's been my experience when talking with fourth graders about the subject of reflection. The result of these conversations is that I now firmly believe that when we use movement to explore the concepts of transformation and reflection, we gain a truly three-dimensional understanding of the subject. Here's a little peek into how it all goes down:
Me: "What do you see when you look in the mirror?"
4th Grader: "Myself."
Me: "But is it really you? There's only one of you! There's no one else like you in all the world. You are an original!"
Different 4th grader: "It's your reflection!"
Later, after my 'magic wand of transformation' has turned the entire class into multiple reflections of me and they've had a chance to experience what it's like to exist on the other side of the mirror, I ask:
Me: "How many of you think it would it be fair to say that your reflection is doing the same thing as you?"
Half the class raises their hands.
Me: "Or, is your reflection doing the opposite of you?"
One third of the class raises their hands.
Me: "Or, how many of you think it might be both, the same and the opposite?"
One or two hands shoot up, other hands raise and lower tentatively.
We work through answering this question in class using our creative dance work. In lieu of this experience here is a video clip for you from the Marx Brothers movie 'Duck Soup' (below). I find this video to be simultaneously fun, highly entertaining, and instructive about the process of reflection. Remember that transformation is essentially about change, and I assert that movement is a particularly effective way to make the process of change visible.
A few things to consider before watching the video, below:
Most of the time we are looking into a mirror straight-on. We brush our teeth, wash our faces, or comb our hair, all while looking at our faces and the fronts of our bodies. In this orientation is easy to think that the reflection is doing the same thing as us.
But remember, the mirror can reflect all sides of our bodies. As you watch this video you will see Groucho and Harpo directly facing the "mirror" but also walking along the length of the mirror (shoulders to the mirror line) and turning toward and away from the mirror. There's even a fun bit where their bottoms are closer to the mirror than their heads!
In Math in Your Feet, children reflect their dance patterns by deciding who will dance the original pattern and who will reflect that pattern; the reflection changes the original pattern in small but very important ways. Based on the narrative arc in this particular video, Groucho is the homeowner (original) and Harpo an interloper (reflection). As you watch, ask yourself:
When is the reflection doing the same thing as the original?
When is the reflection doing the opposite of the original?
I'll give you a couple examples to get you started. When Groucho first sees his 'reflection' in the 'mirror' they both move in toward the mirror and then away from the mirror. In this case they are doing the same thing. Then, still facing each other, Groucho's right hand goes to his chin, but it is his reflection's left hand that goes up. Both hands go up to the chins, but they are using opposite hands.
One more example: At 0:35 Groucho turns away from the mirror over his right shoulder, for a total distance of 180°. Harpo also turns 180°, but over his left shoulder.
How many examples of same and opposite can you find? Can you find any mistakes? I had a hard time tracking if they were using opposite rights and lefts in their footwork, for example. Have fun and don't forget to try out some of the activities listed below when you're done watching!
How'd you do? Ready for a little application of the concepts?
Try this at home:
Put a line of tape on the floor. This is your mirror, otherwise known as a line of reflection.
Decide who will be the original and who will be the reflection.
To start, the reflection has to be the same distance from the mirror line as the original.
Move slowly at first so the reflection has a better chance of accuracy.
Most important: don't forget to experiment with having different sides of your body be 'reflected' in the mirror.
Extra challenge:
Make up a short piece of choreography with a variety of moves and levels (high, medium and low). In Math in Your Feet, the foot based patterns are units of four steady beats. See if you can make a four- or eight-beat combination of moves using your whole body.
Both people practice doing this choreography congruently (everything the same).
Then, do the choreography with the line between you. The original needs to move slowly while the reflection figures out what parts of the choreography needs to change (hint: everything is the same except the reflection uses opposite rights and lefts).
When you're well-practiced and have it a tempo that both people can do comfortably, show off your work!
Extra, extra challenge:
Perform your choreography with your partner first congruently (everything the same) and then reflected (opposite rights and lefts).
If you want a triple challenge, change roles and have the other person become the reflection.
Melody Cameron is one of my favorite dancers, and a former teacher of mine. She is from Cape Breton Island, Nova Scotia, Canada and has her own particular, fluid, musical style of Cape Breton step dance.
Here she is improvising to a piece of 'mouth music' sung in Scots Gaelic by Joy Dunlop.
