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 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.

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.

A Powerful Tool for Both Learners & Teachers

 

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Larry Ferlazzo invited me to answer this question on his Ed Week Teacher blog: “What is an instructional strategy and/or teaching concept that you think is under-used/under-appreciated in the classroom that you think should be practiced more widely?”  I am sharing my response here but do check out the other answers!


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Every day students of all ages come to school with a powerful tool for mathematical reasoning but rarely get the opportunity to harness its full potential. When this tool, our students’ own bodies, are used, the activity is typically relegated to acts of memorization that lead no further than the next test. In contrast, taking math off the page and into the spatial, embodied realm of the whole, moving body has great potential to open up new avenues for understanding. Here are some examples of how a whole body, #movingmath approach can open up new opportunities for learning in a variety of grades and settings:

  1. Changing the scale:  When you change the scale of the math you are already exploring in your classroom you provide learners with the opportunity to get to know math from a completely new and novel perspective. Whether it’s exploring  number patterns on a scaled-up hundred chart, physically experiencing magnitude, scale, distance, and direction on an open body-scale number line, or noticing new things about polygons using lengths of knotted rope, learners collaborate, discuss, evaluate, reflect upon, record their activity, and start to connect it to other experiences in which they encounter and use these ideas. Seeing connections develops intuition,” Dan McQuillan at the University of Norwich tweeted recently. “Proofs are great; just like climbing trees, but the ability to swing from tree to tree is also great.”CH3P26
  2. Reasoning in action: During a Proving Center lesson Kindergarten students were asked to work in teams of four or five to find the center of an 11- cell structure, which looks a bit like a ladder.  Children were able to find the “center” of the object with their bodies rather quickly but their biggest challenge was to justify their physical reasoning. Lana Pavlova, an elementary teacher from Calgary, Canada told me that some of her students’ reasoning included “Because five is the same as five”, “Because these two sides are equal”, “Because it is exactly the half”.  Another student said that “not all numbers have the middle, six doesn’t. One has the middle and it’s one.” Lana told me, “I was very impressed by the kids’ reasoning. I also want to highlight how important the initial ‘explore’ stage is [and that] the movement IS the reasoning tool.”Fairhill ladder
  3. A reason to persevere: Lisa Ormsbee, a P.E. teacher at Fairhill School in Dallas,TX spent three weeks this past June running an enrichment program using movement and rhythm to explore and deepen enjoyment and understanding of math with intermediate students, many of whom exhibited what she called “math reluctance.” One of her main activities was Math in Your Feet  which requires precise physical/spatial reasoning around rotations,  categories of pattern properties, unitzing, complex patterning, equivalence, and perseverance to create original foot-based patterns. Lisa told me, “The kids were ALL so engaged in this activity! It was extremely hard for a couple of students, but because they were working with a partner they were more interested in “sticking in there” where it was uncomfortable until they got it!”rb-5a
  4. Cognition is embodied: “Conceptualising the body, in mathematics, as a dynamic cognitive system enables students and teachers’ physical, visual, verbal, written, mental, and (in)formal activity to be taken not simply as representations  of abstract spatial concepts but…as corporeal and contextually grounded forms of cognition.” [Spatial Reasoning in the Early Years, Davis et al. 2015]

Overall, 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 for many but it’s also clear that it can be a powerful tool for both learners and teachers.


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter coverwhose interests focus on the learning that happens at the intersection of math and the moving body. She also delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Her book Math on the Move: Engaging Students in Whole Body Learning,  was published by Heinemann in 2016.

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.

Notes from a #movingmath Summer Classroom

I am so excited to share the work of Lisa Ormsbee at Fairhill School in Dallas, Texas  who has spent the past two weeks running a math and movement summer enrichment camp using resources from Math on the Move, the Move with Math in May lesson plans, a rhythm-based exercise program called Drumfit, and a lot of other great ideas she pulled together to meet the needs of her students through rhythm and movement. She has ten students with most of the students “learning different” (e.g. dyslexia, dysgraphia, ADHD, mild autism, and selective mutism)  not all of them fans of math, what she described as a “general math reluctance.”

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I was thrilled to get her wonderful email updates on the first and second week of programming which showed just how much of an impact a #movingmath approach can have for all learners. I especially love the progression Lisa created to gently lead reluctant movers (and math-ers) into what has become enthusiastic engagement! Here’s some of what Lisa shared with me:

Monday:  I did a couple of ice breaker activities which involved moving around and were non-threatening (meaning no one HAD to talk in front of the  group).  I started by challenging them to put THEMSELVES into patterns during this warm up time – it was totally spontaneous but it was fun for them. We also got oriented to our class space.  I had removed all the desks and chairs and had the [Math in Your Feet] squares taped on the floor.  They had to adjust to the idea that we weren’t going to sit in desks. I also introduced Drumfit on this day and used that activity time to introduce “follow me” patterns with the drumming rhythms. These kids are fairly reluctant to move around and have pretty low physical literacy and body confidence so I wanted to be sure to take the introduction of the program slowly.  They did extremely well with the movement during the icebreakers!  The drumming is growing on them but took several days for them to feel confident and, some still do not, but I’m not pushing them in that area as it’s a “fun” time. It’s such a good fit with patterns and using your body to make them though! 

Tuesday: We did the pattern game sitting in a circle that you outline in one of your lessons [Clap Hands: A Body-Rhythm Pattern Game].  This was HARD for some of them!  They were all engaged in it though.  We could certainly do this again!  Then we went to our gym space and used the ladders to prove the center [Proving Center lesson] in teams and also to create patterns as a team using bodies and any other items they wanted to use. They were told to be as creative as they wanted with their repeatable pattern. We discussed symmetry here too.  I used my purple circle discs to have them create a game using their ladders also. The game had to have some “math” in it. It was so very, very interesting to watch them do all of this!! We discussed a lot after that and talked about what they had done and how they had thought of their games and patterns.

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After one more day of getting kids used to moving and thinking about math at the same Just turns postertime Lisa introduced the first step in the  Math in Your Feet “pattern/partner/dance process.”  Lisa wrote:

It was slow and I didn’t hurry them.  It took a while to orient them to the squares, talk about sameness (congruence), and review the movement variables. We also took a LONG time talking about the turns. That’s all we got done but I told them we’d be making a pattern with our partner the next day and we’d be concerned with precision and sameness.

On Friday they started working with their partners on creating their 4-beat patterns.

The kids were ALL so engaged in this activity!  I couldn’t believe it.  They had some trouble with cooperation and with identifying sameness. It was extremely hard for a couple of students but because they were working with a partner they were more interested in “sticking in there” where it was uncomfortable until they got it right!  AWESOME!!  I felt like it was a successful day and I can’t wait to do more. 

Next week, I want to have them write a little bit about their patterns and make a drawing etc. like you do in the book.  I also want to let them do this part again then work on combining and transforming.  When we get to the mirroring piece we will have to go pretty slowly I’m guessing. 

During the second week of summer school Lisa did the mirroring/reflection lessons and was also able to extend and connect the physical work by having them having them map their patterns and then read/decode each other’s pattern maps.

Once I added music to the activity they had a blast!  I feel we were all inspired by the Math in Your Feet program to be open to new ways to learn through movement. I was so caught up in our activities I didn’t get any pictures!

But she did eventually get some videos! Here are a couple showing the children’s awesome physical thinking around reflection. One person is keeping their rights and lefts the same as they originally designed the pattern, and the other person is dancing the pattern with opposite lefts and rights. And this is all on top of some tricky rotations. A mighty feat!

Lisa says: I hope [this account] helps others dive into the program because my kids really engaged with it and I am 100% sure that they would not have been so engaged had I chosen a more traditional program for the summer enrichment. I really hope this will help them with their understanding of math and also with their movement confidence and honestly, their joy of moving! I’ll be the P.E. teacher here next year – although I must say this might actually make me a fan of math too. Yay!

Thank you, Lisa, for sharing your work with us!


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.

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.