The Cognitive and Intellectual Aspects of Dance (and math)

Dance Magazine recently published an interesting article titled: Don’t get It Twisted: Dance Is An Intellectual Pursuit and parts of the article really resonated with my approach to combining math and dance. Below are some excerpts from that article interspersed with related #movingmath posts from this blog (bolding mine).

People have a tendency to think of dance as purely physical and not intellectual. But when we separate movement from intellect, we are limit what dance can do for the world. It’s not hard to see that dance is thought of as less than other so-called “intellectual pursuits.” How many dancers have been told they should pursue something “more serious”? How many college dance departments don’t receive funding on par with theater or music departments, much less science departments? Perhaps that’s because dance only leaves behind traces. The words and decisions that go into making dances have a hard time being accounted for, and choreographic notes and videos cannot fully capture a dance work.

Dance depends on the presence of the body. Unfortunately, it’s difficult to explain to non-dancers how corporal movement is a means of thinking and engaging with complex ideas. That’s why it’s so important that dancers can talk or write about their work, translating the corporal knowledge into language.

When we acknowledge that our bodies think, move, translate, react—often in conjunction with linguistic thought or prior to itwe can use dance as a tool. 

Related: When the Movement IS the Reasoning Tool | What does it look and sound like when kids use their whole bodies during a math lesson? What happens prior to, during, and after the activity? Luckily Deb Torrance and Lana Pavolova have provided us with some stellar documentation so we can get a closer look at what happens when we give kids a mathematical challenge to explore with their whole bodies.

Linguistic Intelligence Has Its Place in Dance, Too
That’s not to say that language isn’t part of dance. Choreographers craft dancers’ intentions and movements with words, images and metaphors. Even in improvisation, a director dictates a score, and dancers translate the imagery into corporal form. When choreographers layer dance and words, it engages the audience in new ways. As Bill T. Jones explains, “You see one thing and you hear another thing, and then the audience puts together what they mean.”

Related: Learning Math by Ear: The Role of Language in a #movingmath classroom  | “Comprehension of a word’s meaning involves not only the ‘classic’ language brain centres but also the cortical regions responsible for the control of body muscles, such as hand movements.” To me this study explains part of why a “moving math” approach that includes a focus on math language used in context can open up new pathways for our learners.”

Dance Can Help Us Better Understand Our World
Many choreographers use dance to shed light on today’s most pressing topics. Some use dance in conjunction with social activism, like Ananya Dance Theatre’s Ananya Chatterjea, who recently created Shyamali as a tribute to women across the world who have stood up against oppression. Others explore the nuances of science: Michelle Dorrance’s Myelination, for example, translates the biological process of a myelin sheath forming around a nerve into tap dance. Not to mention artists who use their dance practice as research, focusing on the process of dance making to explore a question or subject…

Related: Leaving Room for Question Asking | “It’s these questions, arising in the moments when they’re needed, born of collaboration, that help learners notice structure and pattern and purpose in what they’re doing. From there we can move to the more formal learning. But… I think kids in general are most motivated when they are provided agency by the adults in their lives. Their work may not be technically perfect, but they are in the best part of learning (to me, anyhow): inside the flow of an investigation filled with their wonderings.”

Dancers Connect Multiple Parts of Ourselves
Dance intertwines the cerebral, physical and emotional; science tries to unravel the connections between these. Dance uses these inherent connections to delve deeper into our humanity, and create new ways of reflecting on the world. In that way, dance is a crucial tool in intellectual pursuits.

Related: Learning Without a Body |”The body is not simply a vehicle toward realizing the perceived pinnacle of abstracted knowledge housed in the mind.  The body is where learning originates. Living in a body is also the way children learn personal agency as they make decisions about how their bodies will move and act and how that power can influence and shape their world. And, in the process, learning that there are obvious consequences and responses in relation to their actions. This is literally and viscerally democracy in action.”


Malke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math Malke Rosenfeld Croppedexplorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

“What I’ve Learned (so far) About Teaching and Learning (Mathematics) in Dance Class”

“It’s hard to put your finger on the cause of a slow-burning problem. One day, you feel lucky to be paid to do something you love and the next, you’ve forgotten why you loved it in the first place. It can be even harder to put your finger on a solution. I turned to dance.”
–Ilona Vashchyshyn in her post “This one’s about dance (and burn out)”

Among many other things, Ilona is a secondary teacher in Saskatoon, Saskatchewan, and co-editor of the Saskatchewan Mathematics Teachers’ Society’s monthly periodical, The Variable. I have had the honor being interviewed by Ilona in which she heard all about my work. She posted a gorgeous, forthright story on her blog recently where I got to know more about her. In particular, I want to share her reflection on what she learned about teaching, learning, and mathematics during dance class (bolding mine)but I also encourage you to read her entire post.

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What I’ve learned (so far) about teaching and learning (mathematics) in dance class, by Ilona Vashchyshyn:

Don’t underestimate the importance of routine.

Almost without fail, dance instructors begin class with a warm-up routine that engage dancers’ bodies and minds in preparation for the work ahead. At HDC (Harbour Dance Centre), most instructors kept the warm-up routine more-or-less similar from one day to the next, although new movements might be added (and some left behind) as the class gained proficiency. E.g., in ballet, a barre exercise might be repeated but with new arm movements, or with a relevé balance to finish. Of course, warm-ups are particularly important in dance because they help to prevent injury, but I found that having a common thread from class to class was valuable in other ways: notably, it gave me repeated opportunities to learn and improve the movements / pathways / exercises which, in turn, gave me the opportunity to develop my confidence as a dancer. Seeing my improvement from day to day encouraged me to continue, and experiencing small successes at the start of class offset the occasional frustration of learning new movements and combinations later on in the lesson. Not to mention, slowing down to practice movements in isolation meant that I could perform them with more ease and fluidity when it came to using them in choreography or in improvisation.

Dance is not about [learning] the choreography.

Early in the week, one of my instructors at HDC cut the music just before we began our routine to say: “Stop. Why are you here? If music is playing in dance class, you dance.” And he insisted that we did, even if it felt awkward at first. Later, referring to a complicated move: “Listen, I’m not gonna teach you that shit. You can learn it on the internet. This is dance class.”

More than any dance instructor I’ve ever had, he emphasized that dance isn’t about the choreography. Choreography, which is a sequence of memorized movements, will be quickly forgotten. A more valuable outcome of dance class is increased confidence and joy in responding with movement to music. Of course, an additional benefit of dance lessons is picking up new steps or pathways, but the value of these is not that you can perform them in a specific sequence, but rather that you can go on to combine and remix them in endless ways, in addition to creating your own. In fact, most of the dance instructors regularly set aside time during class for improvisation – even in ballet, which is generally regarded as the most rigid of the dance styles.

The connection to math class, I think, almost goes without saying: formulas, procedures, algorithms are our version of choreography. Of course, it can be fun to learn and execute the moves. There’s a great sense of accomplishment in accurately performing a complicated routine. But the main outcome of math class shouldn’t be a memorized sequence of steps; more important, I think, is increased confidence and persistence when facing new problems (the analogue of improvisation, or developing your own routine), maybe with a few more tools to tackle them.

Note that I don’t feel that there is a clash between routine (c.f. above), choreography, and improvisation – all have their place and their value. All parts of the elephant, as they say. Lest I stretch the metaphor past its usefulness, I will stop here, but the idea of dancing as problem solving (and problem solving as dancing) is something I’d really like to keep exploring.

A teacher learns.

A dance studio can be a prime location to study how great teachers differentiate and adapt instruction to meet their students’ needs. Especially in adult beginner dance classes, students tend to be very diverse in their abilities and previous experiences. While some really are starting from scratch, many are dancers returning after a long break, and still others are trying a new style but have extensive experience in another. At HDC it was instructive to watch how teachers adapted their plans for the week as they learned more about their students, as well as how they provided options in the moment for dancers with different levels of experience (“for now, just focus on the feet,” or “try lifting your hands off the bar if you’d like a challenge”).

On the flip side, the experience of being a student again was also invaluable. As teachers, we know that the struggle of learning something for the first time can be quickly forgotten, replaced by the illusion that it was easy all along. Forgetting is all the more likely when you teach the same course semester after semester, year after year. And maybe the quickest way to dismantle this illusion is to put on a pair of ballet slippers and a leotard and step into a mirrored room full of strangers who all seem to know what they’re doing while you’re still struggling to remember the difference between a frappé and a fondu and to balance with both feet on the ground. Even with the most encouraging of teachers, I sometimes found myself afraid to ask for help, hiding in the back when I felt lost, and even fighting the urge to escape to the bathroom when I started to get overwhelmed. Pushing through the frustration of just not getting it and the fear that I just never will, especially when it feels like everyone else does, can take tremendous effort. And a teacher who – in addition to providing focused feedback – takes time to remind the class that it’s okay to feel lost sometimes, that being on the verge of this is too hard is just where you’re supposed to be, can make all the difference between choosing to stay home tomorrow and showing up to try again.

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Malke here again. More than anything I’d like to encourage you to think about whole- body #movingmath (whether dance or non-dance based) as a process of coming to understand not just the math but the process by which we come to know math, a topic that to many people, seems foreign and inaccessible.  Using the whole body in math class teaches us to persevere. Engaging our learners’ bodies in math class can help this process and as well as help build a community of learners. There are lots of resources on this blog for getting started. Please don’t hesitate to get in touch if you have questions!


Malke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math Malke Rosenfeld Croppedexplorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Prepare to be Inspired! New Math & Dance Resources from a Canadian School Board to Help Guide Your Way

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During the fall and winter of the 2017-18 school year teachers and students in the Kawartha Pine Ridge District School Board (KPRDSB), Ontario, Canada took the plunge. Using Math on the Move: Engaging Students in Whole Body Learning they bravely began the process of bringing math and dance together into the same learning context. Mary Walker Hope, who spearheaded the process, invited me to observe and celebrate the final presentations of children in grades one through eight. During my video chat observations I was incredibly inspired to see how the process laid out in Chapters 4 & 5 of Math on the Move had supported both children and teachers alike.

At the very end of their math and dance project Mary created three individual e-books recounting their work, with a special emphasis on the process. She writes:

Through integrating math and the arts, we engaged our students as inquirers, collaborators, creators, problem solvers, artists, dancers and mathematicians.

We began our journey from a creatively curious stance and with humility. We inquired, persevered, and solved. We learned how to teach math through dance and dance through math. We discovered through our collaborative inquiry that math, dance, language, music, and art are as interconnected as the processes we use to understand, solve, and create.

These three e-books are divided by grade band and FULL of documentation of their math/dance making process from start to finish including:

  • Introductory activities
  • Insights and encouragement for teachers around negotiating math and dance in the classroom at the same time
  • Details about what each step of the process looks like in each grade band
  • Lots of videos illustrating a variety of student work
  • Step-by-step examples of the making process
  • Examples of what they did to apply, extend, reflect, and assess the math/dance work
  • Finally, these e-books provide an overall positive and encouraging message for teachers who might be ready to jump in to #movingmath!

These are real kids and real teachers making gorgeous math and dance.  YOU CAN TOO!

The books are linked below. You might also be interested in another post on this blog inspired by the Canadian crew called “Why Math in your FEET?” which provides an explanation of percussive dance and the different kinds of sounds you can make with your feet while dancing.


Malke Rosenfeld CroppedMalke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Why Math in Your FEET?

In Chapter One of Math on the Move: Engaging Students in Whole Body Learning I share a little of the history of how I developed Math in Your Feet and also describe how, in the years before making the connection between my dance style of percussive dance and mathematics, I worked to support children in becoming dance makers using the elements of this not-quite mainstream dance form. So what is this percussive dance and how does it connect to math and, most puzzling, why do we need to use our feet?

This question about feet came up a lot during almost weekly Skype sessions with the amazing Mary Walker Hope in Ontario, Canada. In January 2018 I was lucky enough to get a peek at the awesome Math in Your Feet patterns and footwork resulting from a 2nd through 8th grade exploration in her school board. I figure that  others may ask this “Why are we using our feet?” question from time to time so in this post I’d like to elucidate the “feet” aspect of the math and dance that we make while creating patterns with our feet in Math in Your Feet.

First of all, there many, many (MANY!) different dance styles in this world. Some of them are percussive (rhythm based) and some of them are not. Sometimes they’re a combination of both. Percussive dance is probably best known through the international performance phenomenon called Riverdance which features Irish step dancing. You might also be familiar with percussive dance through all those tap classes either you or your kid took at some point.

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The main focus of percussive dance styles is to be a rhythm maker using different parts of your feet. The Pattern Properties I created lay out the basic elements of this kind of dance, similar to what creative movement is to modern dance. To answer “why feet” look at the Movement category of the Math in Your Feet Pattern Properties chart on the left. Each movement has a clear sound associated with the movement. Making sure you produce that sound is one aspect that makes this kind of dance so satisfying. In the chart below I’ve provided some information about how these sounds are made.

Pattern Properties description FINAL
So, there you have it! Making patterns and sounds with your feet is fun and satisfying, not to mention mathematical!


Malke Rosenfeld Cropped.jpgMalke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Slow-Paced Book Study of Math on the Move [June 1 – November 30, 2018]

ANNOUNCEMENT: The slow book study of Math on the Move has been cancelled due to lack of participation. However, I wrote the book as an in-depth resource for teachers and created the associated Facebook group as a place of conversation, support and resources for bringing whole-body math learning into the classroom. The group was created to support YOU in getting started with this new modality for teaching and learning. PLEASE feel free to ask us anything! Speaking of resources, I update this document on a semi-regular basis.

Format graphic

BOOK STUDY SECTION HASHTAGS (Updated July 3, 2018) 
#Foreword #movingmath
#Introduction #movingmath
#CH1pp1thru8 #movingmath
#CH1pp8thru15 #movingmath
#CH2pp16thru28 #movingmath
#CH2pp28thru35


OVERVIEW
Based on the tenet that learning takes time I am starting a slow-paced investigation and discussion of the ideas and activities in my book Math on the Move: Engaging Students in Whole Body Learning. The book study opens June 1, 2018 and wraps up November 30, 2018 on both Twitter and in our book group on Facebook. If you have a FB account you can join the group by clicking here.  When requesting to join (if you aren’t yet a member) please make sure to answer the question so I know you’re not a robot or whatever. And, just to be clear, You can progress through the book as quickly or slowly as you like.

This post will serve as an introduction and reminder of the processes by which we will be making meaning together around the topic of whole-body math learning and teaching. Our book study format is a combination of individual public reflection on the reading and conversations in community focused on the ideas and questions we have while reading.

MATERIALS NEEDED
If you do not yet have a copy of Math on the Move you can download the free sample chapter which includes the Foreword, Introduction and first chapter. This will begin your book study journey. Download this chapter and/or buy the book at the Heinemann website. If you are outside the U.S. please check a Book Depository website in your part of the world.

FORMAT
This book study includes small sections of reading followed by responses to four standard questions for each section. This format is adapted from the Reflective Review Protocol from the Artful Tools resource. Artful tools create a descriptive setting in which learners are supported in perceiving deeply, thinking critically, and making meaning, and asks:

  • How do we create a safe space for all voices to come forward?
  • How do we honor all perspectives and encourage critical thought and questions?
  • What is the value of deferring judgment in a learning setting?

KEEPING TRACK 
Each section of text will be denoted and searchable with the same hashtags used on both Facebook and Twitter. For example, we will start by reading the Foreword by Max Ray-Riek; the hashtags for this first section of reading will be #forward and #movingmath. From there we will use a #CHpp format (ex: #CH1pp1thru8) and #movingmath. As we move (ha!) through our reading You will be able to return to the discussions in any section using the specific hashtags, all of which will be updated and archived in this Google doc.

PROCESS FOR RESPONDING TO EACH SECTION OF TEXT
Book study participants respond to each section by answering the following four questions:

  1. What do you notice? Describe what you read without judgment. If judgment emerges, please provide evidence on which the judgment is based: What did you read that makes you say that? How did this section feel to you as a learner? As a teacher? Answer using descriptive terms, without making judgments about the quality of the work or offering personal preferences: “I notice that . . .”
  2. What questions does it raise? What  questions does the text trigger? Raise any questions about the work with “I wonder…”
  3. Speculate about what the text helps you understand: What do you think is the author’s intent? What do you think are the intended understandings? What is the author trying to help readers understand? Respond with what meaning you take away using the phrase: “I speculate that . . .”
  4. Respond/Open Dialogue/Reflect: Participate in an open dialogue with other book study participants about the section in question. This is time for participants to share new ideas for next steps and respond to one another directly about what they read, what they still wonder about, etc.

FINAL THOUGHTS
I am very much looking forward to learning and thinking with you! However, I can also imagine that once things get started there may be some hiccups or little things to be worked out in our process. If this happens I will communicate any changes/adjustments on Twitter and Facebook and record any changes I make to the process as edits to this post. Please don’t hesitate to get in touch with me if you have any questions or concerns along the way.

Let’s get started!


Malke Rosenfeld is a percussive dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

ISO Participants for the Moving Patterns Game Summer Pilot!

Do you have plans for summer programming? Do you want your participants to have an experience with math that is off the page, creative, and highly physical? If so, please consider joining the Moving Patterns Game by Math in Your Feet™ summer pilot! Help us further develop this interactive, moving, and mathematical game!

Overview

The first pilot of the Moving Patterns Game by Math in Your Feetwas with 3rd and 4th graders during school hours. It has also been played at family math nights and at last year’s Math on a Stick exhibit at the Minnesota State Fair. We know that it works but there are additional questions we want to explore.

The game combines the Math in Your Feet  school-based program with the best of informal, kid-initiated playground activity. The overall vision is to get kids moving and thinking mathematically at the same time, and as a creative free play option for recess (inside or out) and/or after-school enrichment.

About the Pilot

Pilot sites will be chosen based on a variety of factors including duration of summer programming, demographics of participating children, and level of commitment. If chosen you will receive all the materials necessary to run this activity and guidelines for getting started with the game including:

  • The original pattern cards AND a set of larger laminated cards that promote creative collaboration between dancers
  • A poster of Pattern Properties to help make sense of the pattern cards
  • Copies of the game when it has been professionally designed and released
  • An opportunity to contribute to the development of the game

If interested please fill out this survey no later than May 20, 2018. The survey includes more information about this pilot and a section for any unanswered questions you might have before committing. I’m looking forward to hearing from you!


Malke Rosenfeld is a percussive dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Leaving Room for Question Asking

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NOTE: This post was originally published at my other blog  April 15, 2017.

How much of the math you do in your classroom is based on someone else’s questions? Someone far away from your classroom? Someone other than your students? Even with specter of standardized tests looming like dark, heavy clouds, how can we leave room for the most important part of learning: question asking?

“So many of the things that we do in math education — and maybe more generally in education — are giving students answers to questions that they would never think of asking. By definition, that’s what it is to be boring. If you’re sitting at a bar and someone’s telling you stuff that you’re not interested in and you would never think of asking about — what is more boring than that? That seems to be the model of our educational system: ‘Here’s the formula for the cosine of the double angle.’ ‘Well, I don’t care about that.’” —Steven Strogatz

The first time I experimented with building scaled-up geometric forms I was homeschooling my then-seven-year-old. At the time she was a “resistant” learner which basically meant she was happiest exploring her own questions, and, over a couple years of homeschooling I realized my best strategy was to influence the child by way of my own curiosities and the way I structured the environment, leaving out provocations to be discovered and, if of interest, investigated.  This was also a time when I was deep into finding answers for my own question “What is math?” and I was heavy into an investigation into Platonic Solids. I had never been a builder as a child, but I had a question and it needed to be answered.

Back in April, on Twitter, I had a conversation with Lana, a third grade teacher who is reading Math on the Move and who has been wondering about how how to “scale up” her students’ mathematical activity.  Specifically she’s been curious about my recent work with building body-scale polyhedra.  Body- or moving-scale means that the whole body/person is engaged in problem solving and mathematical thinking to investigate a mathematical challenge or project of some kind. I think Telanna’s question could be anybody’s question who is wondering how we can do math off the page.

My answer focused on how I structure a making activity and the learning environment in a way that motivates learners to collaborate and ask new questions in response to the activity in an intrinsic way.

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It’s in the process of making something with the freedom to try things out and see where it gets you that creates new questions.

It’s these questions, arising in the moments when they’re needed, born of collaboration,   that help learners notice structure and pattern and purpose in what they’re doing. From there we can move to the more formal learning. But, like my daughter, I think kids in general are most motivated when they are provided agency by the adults in their lives. Their work may not be technically perfect, but they are in the best part of learning (to me, anyhow): inside the flow of an investigation filled with their wonderings.

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To bring kids to math we need to leave room for their own questions.

What happens next? There are more questions to be asked about this kind of approach. I have  my answers and am happy to share them. But I’d love to hear your questions first!


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

When “The Movement IS the Reasoning Tool”

 

ch3p26What does it look and sound like when kids use their whole bodies during a math lesson? What happens prior to, during, and after the activity? Luckily Deb Torrance and Lana Pavolova have provided us with some stellar documentation so we can get a closer look at what happens when we give kids a mathematical challenge to explore with their whole bodies.

Let’s start with this video in which children work collaboratively to explore a body scale 25-cell ladder-like structure in pursuit of proving how they know they’ve found its center. Although teams may solve the initial challenge rather quickly, the core mathematical experience is in using space, structure, and their bodies as tools for making sense of the challenge as they work to prove that they have found the right location.

These are first graders; Deb Torrance, their wellness teacher, and their classroom teacher have teamed up to run the lesson.

What do you notice about what the children are doing?



Here is the first key aspect of a moving math activity — it moves, but in a very focused manner and it also inspires on-topic conversations. Deb reported that “During four minutes of ‘free explore’ time with the ladders I was amazed at the different ways children were attempting to cross the structure! As the wellness teacher, it always excites me to see students moving and they were certainly doing that; hopping patterns, cartwheels, keeping hands in boxes, crawling… Students were then pulled to the center of the gym to discuss their thoughts and ideas about the ladders. The math vocabulary that was already being discussed [with peers in the context of the physical exploration] was amazing (symmetrical, middle. center, odd/even…).”

The role of the adults during the exploration phase of a moving math lesson is to keep tabs on the activity and check in occasionally with the learners about what they’re thinking or wondering. Teachers also play a role when it’s time for teams share out to the whole class; in this lesson the sharing would be focused on the strategies teams used and how they knew they had found the center of the space.

Lana Pavlova did the same Proving Center lesson with a group of kindergarten students and an 11-cell ladder. She reports that “proving was where the fun started. Many students could find the middle and count five squares on each side but weren’t sure how to explain why five and five was the middle but four and six squares was not. So, a lot of conversations revolved around trying to prove it and showing with their bodies what’s going on.”

Although the kindergarten kids were in groups, they mostly worked individually. Some of their reasoning included “because five is the same as five”, “because these two sides are equal”, “because it is exactly the half”. Some students were convinced that the middle was on the line, so they counted both lines and squares; if you stand in the middle “there will be six lines on each side”. One student said that “not all numbers have the middle, six doesn’t. One has the middle and it’s one.”

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When the kindergarten students went back to their classroom they used whiteboards to explain what they did during the moving portion of the lesson. Lana says, “The physical activity helped [most of] them to remember that there were five squares on each side. One student drew a “9 frame” and wrote the number five on each side. As he was explaining it to me, he noticed he had counted it incorrectly and went back to change his number to four on each side. He shared how he was in the middle because there was the “same on both sides.” 


Lana’s final thoughts after running this lesson get right to the core of what what #movingmath is and can do. “I was very impressed by the kids’ reasoning. I also want to highlight how important the initial ‘explore’ stage is; the movement IS the reasoning tool.”

No math concept can be understood completely in one representation or modality. Similarly, not all math can be explored with the body. Whole-body math may be a novel approach but it’s also clear that it can be a powerful tool for both learners and teachers.

You can find the Proving Center lesson plan as well as three other moving math lessons for K-12 learners here.  When you try it out please consider sharing  a picture, video, or blog post to Twitter or Facebook with the hashtag #movingmath.


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She also delights in creating rich environments for math art making in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.

Move with Math in May: Four #movingmath Lessons

UPDATE, September 2017: This post was originally celebrating a special nearing-the-end-of-the-school-year event titled “Move with Math in May. The event featured four math-and-movement lesson plans to chose from. The goal was an opportunity to try out whole-body math in a low-key way to get a sense of what it’s all about…but you can use these lesson plans any time you want! Below you’ll find overviews of and links to each lesson. If you have any questions, feel free to get in touch on Twitter or via the contact form. Most importantly, HAVE FUN!!

 

MOTM Proving Center Lesson 1 HeaderIn this activity, children work collaboratively in teams of three to five (four being an optimal number) to determine the center of a taped ladder-like structure on the floor. Although teams may solve the initial challenge rather quickly, the core mathematical experience is in using space and their bodies as tools for making sense of the challenge as they work to prove that they have found the right location. GO TO THE LESSON


MOTM Rope Polygons Lesson 2 HeaderIn this activity, created in collaboration with Max Ray-Riek from the Math Forum at NCTM, students work collaboratively in teams of three to five to investigate and construct polygons with their bodies and a twelve-foot knotted rope. Although this lesson attends to regular polygons, the activity has been extended to address learning goals for middle and high school students.  GO TO THE LESSON


MOTM Clap Hands Lesson 3 HeaderClapping games are a part of the natural mathematics of childhood; they are also filled with pattern, spatial reasoning, and rhythm.  This activity, which can be different every time you play, was developed by John Golden (@mathhombre) with a class of preservice teachers.  GO TO THE LESSON


MOTM MIYF Lesson 4 HeaderHave you ever wondered what Math in Your Feet would look and sound like in your classroom? Here is a game-based version of this work, developed in collaboration with wellness teacher Deb Torrance (@Mrs_Torrance), as a way for you to see what math and dance can look like when both are happening at the same time. GO TO THE LESSON.

I’m looking forward to seeing and hearing how things go!


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.

 

 

Learning Math by Ear: The Role of Language in a Moving Classroom

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At first glance, this article about the value of reading aloud to older kids would not seem to connect to math learning. But, to me it does.  Here’s the piece that really stood out:

“The first reason to read aloud to older kids is to consider the fact that a child’s reading level doesn’t catch up to his listening level until about the eighth grade,” said Trelease [a Boston-based journalist, who turned his passion for reading aloud to his children into The Read-Aloud Handbook in 1979], referring to a 1984 study performed by Dr. Thomas G. Sticht showing that kids can understand books that are too hard to decode themselves if they are read aloud. “You have to hear it before you can speak it, and you have to speak it before you can read it. Reading at this level happens through the ear.”

Did you catch that? “You have to hear it before you can speak it, and you have to speak it before you can read it.”

I made a similar point while working with teachers and teaching artists in Minnesota in 2013 when participants noticed how the math language was woven naturally and seamlessly into our dance work. This vocabulary development, I said, was initially an attempt to help kids pay closer attention to the details of what they were doing while they created their dance patterns. I noticed that they became much better creators when they had the right words to help them identify their movement choices.

recent brain study focused on how the motor cortex contributes to language comprehension:
“Comprehension of a word’s meaning involves not only the ‘classic’ language brain centres but also the cortical regions responsible for the control of body muscles, such as hand movements.”
To me this study explains part of why a “moving math” approach that includes a focus on math language used in context can open up new pathways for our learners [bolding emphasis mine]:

“An alternative is offered by an embodied or distributed view suggesting that the brain areas encoding the meaning of a word include both the areas specialised for representing linguistic information, such as the word’s acoustic form, but also those brain areas that are responsible for the control of the corresponding perception or action. On this account, in order to fully comprehend the meaning of the word ‘throw’, the brain needs to activate the cortical areas related to hand movement control. The representation of the word’s meaning is, therefore, ‘distributed’ across several brain areas, some of which reflect experiential or physical aspects of its meaning.”

 My take away from the study overview is this:

  1. Our whole bodies are just that: whole systems working in an fascinating and astoundingly connected ways.
  2. “Knowing” something, especially the ideas and concepts on the action side of math (transform, rotate, reflect, compose,  sequence, combine, etc) is strengthened by the partnership between mathematical language and physical experience.

In Math in Your Feet we start by moving to get a sense of the new (non-verbal) movement vocabulary in our bodies. At the same time we say together, as a group and out loud, the words that best match our movement. Sometimes we also pay attention to the words’  written forms on the board so all three modalities of the idea are clear to us.  When learners are more confident with their dancing they are asked to observe others’ work and choose the the specific  words that describe the attributes/properties of the moving patterns. There are over 40 video examples of this in action in Math on the Move.

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In addition to being able to parse our patterns, we use tons of other math terminology while we choreograph in conversations with our teammates and in whole group discussions.  This approach allows learners to fully grasp the real meaning and application of these ideas which, ultimately, allows them to write and talk confidently about their experiences making math and dance at the same time. Teachers consistently notice an increase of ‘math talk’ in their classrooms when children get up to explore math ideas with their whole bodies. As in, “I couldn’t believe how much math vocabulary they were using!”

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Math is a language but it’s not just about terminology, it’s about what those words MEAN.  To do this, learners need to play with mathematical ideas, notice and talk about patterns and structure, sort and compare, and share reasoning about and understanding of mathematical relationships.

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As such, language, in partnership with the body is our tool for thinking mathematically when we are up out of our seats and moving during math time.  Ideally, this language is facilitated by an adult through conversation, play and exploration, all before bringing it to the page to explore the ideas in a different modes and contexts.


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.