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.

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.

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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.

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.

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.”

Fairhill MiYF

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.

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.

5 Articles that Answer: “How can they learn math if they’re moving?”

Or, more succinctly, “How is this math?” There is an entire chapter in Math on the Move that answers this question in great detail, but here are some research-based articles, as well as bonus perspectives from mathematicians, that I hope will provide a strong rationale for you when explaining to others the benefits of whole-body math learning.

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1. A recent study in Denmark has concluded “Math is learned best when children move…and it  helps to use the whole body.”

Participation in math lessons focusing on integrating gross motor activity can positively contribute to mathematical achievements in preadolescent children. In normal math performers, gross motor enrichment led to larger improvements than fine motor enrichment and conventional teaching. Across all children gross motor enrichment resulted in greater mathematical achievement compared to fine motor enrichment. From a practical perspective, teachers and related personnel should consider integrating gross motor activity in learning activities relevant to the academic curriculum as a promising way to engage children and improve academic achievement.

This is great news but we need to keep our eye on what it means to do this in a meaningful way in the classroom!

2. Spatial Reasoning IS mathematics: “It is almost as if they are one and the same thing.”

Even though spatial reasoning includes the body (see information in #3, below), there has been little research on whole-body-based spatial reasoning. Nevertheless, spatial reasoning is a foundational skill for learning math and Math on the Move is, in part, about illustrating in great detail how we can harness and develop whole-body spatial reasoning during math time.

“The relation between spatial ability and mathematics is so well established that it no longer makes sense to ask whether they are related” (p. 206). Researchers have underlined that the link between spatial reasoning and math is so strong that it is “almost as if they are one and the same thing” (Dehaene, 1997, p. 125). Reflecting on the strength of this relationship, others have noted that “spatial instruction will have a two-for-one effect” that yields benefits in mathematics as well as the spatial domain…”

 3. Paying Attention to Spatial Reasoning

A succinct document targeted to educators that explains the importance of spatial reasoning in mathematics and what it looks like when it’s integrated into math class in grades K-8.

Students need to be explicitly taught and given opportunities to practice using executive functions to organize, prioritize, compare, contrast, connect to prior knowledge, give new examples of a concept, participate in open-ended discussions, synthesize new learning into concise summaries, and symbolize new learning into new mental constructs, such as through the arts or writing across the curriculum.

4. Developing Executive Function

Math is more than facts and being in control of your own body while focusing on a specific body-based task is an opportunity for students to develop Executive Function as well as apply and deepen their learning.

Creative opportunities — the arts, debate, general P.E., collaborative work, and inquiry — are sacrificed at the altar of more predigested facts to be passively memorized. These students have fewer opportunities to discover the connections between isolated facts and to build neural networks of concepts that are needed to transfer learning to applications beyond the contexts in which the information is learned and practiced … When you provide students with opportunities to apply learning, especially through authentic, personally meaningful activities with formative assessments and corrective feedback throughout a unit, facts move from rote memory to become consolidated into related memory bank, instead of being pruned away from disuse.

5. Children think and learn through their bodies

We conclude that children think and learn through their bodies. Our study suggests to educators that conventional images of knowledge as being static and abstract in nature need to be rethought so that it not only takes into account verbal and written languages and text but also recognizes the necessary ways in which children’s knowledge is embodied in and expressed through their bodies.

BONUS: Mathematicians can recognize the whole-body activity as “doing math”

“Its [the second part of[Math on the Move] that is the most mathematical, from my perspective as a pure mathematician. The dance moves within the tiny square space are an abstract mathematical idea that is explored in a mathematical way. We ask how the steps are the same or different from each other, identifying various properties that distinguish them. We investigate how these new objects can be combined and ordered and transformed. We try out terminology and notation to make our investigations more precise and to communicate both current state and how we got there. These are all the things we pure mathematicians do with all our functions, graphs, groups, spaces, rings and categories. The similarity of this to pure mathematical investigation is striking.”

 David Butler, University of Adelaide, Australia [Read full review]

“The movement activities described [by Malke] naturally link to the notions of transformational geometry and the subtle questions of sameness and difference that are explored. Enabling people to find the links between that physical understanding and the mathematical abstractions is a wonderful way to make mathematics open up. Overall this is a wonderful book on the power and importance of mathematical thinking to explore all sorts of surprising topics, and conversely the importance of physical movement and dance to explore mathematics.”

—Edmund Harriss, Clinical Assistant Professor, Department of Mathematical Sciences, University of Arkansas [Read full review]


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.

New Year, New Tools for Making Sense of Math!

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Happy 2017!! This year harness the original “thinking tool” to help your learners make sense of math! What is this tool, you ask? Why, your students’ own bodies and creative spirits of course!

Math on the Move: Engaging Students in Whole Body Learning is now available from Heinemann. Included in the book are specific, actionable ideas for including your students’ moving bodies in the math you are already doing in your classroom!

Here is your first tip in the New Year for a simple first step in bringing Math in Your Feet and other #movingmath activities into your classroom in a low key way.  All the best to you for a new year filled with enthusiastic math making!

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You can download the Movement Variables from the Classroom Materials page.

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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. Her new book Math on the Move: Engaging Students in Whole Body Learning was recently published by Heinemann (2016). Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.

A Framework for Whole-Body Math Teaching & Learning

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What is whole-body math learning? How can we be doing math if it’s not written down? What are our expectations for student work and learning math out of their seats?

My focus in Math on the Move is on how we can harness our students’ inherent “body knowledge” to help them develop new understanding and facility with mathematical ideas that often seem remote and impenetrable as presented in their textbooks. This is not to say that math is this way, but for many people, myself included, the symbolic side of math creates a barrier, at least initially, to understanding. This is why approaches like Numberless Word Problems  (“They just add all the numbers. It doesn’t matter what the problem says.”) and Notice and Wonder  were created: to help kids make sense of math.

The phrase “body knowledge” was coined by the late Seymour Papert, a protégée of Jean Piaget. In the 1980s Papert’s work at MIT focused on developing “objects to think with,” including the Logo computer programming system for children. Here are a few images of children engaged in self-initiated, body-based exploration of a math idea as they investigate the spatial aspects and physical structure of their environment.

Papert’s intention was to harness a child’s own lived experiences and natural, self-intiated explorations in the world as a way to investigate more formal mathematics via the programming of a little metal object called the “Turtle.” Much of what we do in Math in Your Feet is similar to what children do with the LOGO turtle – working independently or in teams within a specific system/constraint, investigating and creating units of commands or patterns in a spatial and geometric language and, along the way, fine tuning our intentions and results.

Similar to Papert’s work, Math on the Move is about math, but it is also about the nature of learning by actually making something and the need to develop strong pedagogy for what might be seen as a non-traditional approach. For me this means a meaningful  interdisciplinary, movement-based approach beyond the preschool years. In the first chapter I provide an overview of what meaningful whole-body math learning looks like in my own and others’ moving math classrooms. I clarify the body’s role as a thinking tool and its use within a purposeful making and learning context. I also provide a conceptual framework and pedagogical base for any educator wishing to do similar work with his/her own students at body- or moving-scale.

Because our encounters with math have been, for the most part, visual and on the page, a whole-body approach to learning math may feel foreign to both teachers and students. To quell the qualms of others who may want to try this approach in their own classroom I have spent years working to define the pedagogical elements that must be present so children can think deeply and engage in mathematical sense making with their whole bodies.  The criteria (which are explained in more detail in the book) include:

  • The lesson explores one or more mathematical ideas off the page and out of the chair.
  • The math-and-movement lesson provides a structure in which students make choices, converse, collaborate, and reflect verbally on what they did and what they noticed while they were engaged in whole-body-based activity.
  • The body activity is focused on mathematical sense making, and  often through efforts to solve a challenge of some kind, not on using the body to illustrate a math ideas as it is typically represented on the page.
  • The teacher is not the expert but acts as the facilitator of the learners’ activity by setting expectations for controlled, intentional movement, and monitoring lesson pacing and classroom discussion.
  • Students reflect on the activity as both doers and observers, learning from their own experiences and the work and thinking of their peers.
  • In partnership with the change of scale, the math-and-movement activity should be explicitly connected with the same math idea as it is experienced in other contexts, scales, or modes. 

    Just like any organized lesson, moving math needs a frame of expectations and learning goals. It may look and feel different from the norm, especially because its kinetic nature, but as long as there is an underlying structure and intent, it’s worth exploring to see what the possibilities might be.  You might be very surprised at how enthusiastically children embrace the opportunity to harness their whole selves, body and mind for a mathematical investigation!


    Malke Rosenfeld is a dance teaching artist, author, 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. Her new book Math on the Move: Engaging Students in Whole Body Learning was recently published by Heinemann (2016). Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.