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.

fairhill-ladder.jpg

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.”

whiteboards5

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

WELCOME!

This is a special nearing-the-end-of-the-school-year event featuring four math-and-movement lesson plans to chose from. The goal? An opportunity to try out whole-body math in a low-key way to get a sense of what it’s all about. Here’s how to play:

A LITTLE OR A LOT:
The lessons are presented in full but you are free to do as little or as much of the plan as you like. The most important thing is that the moving is the math as much as anything else so just getting your learners moving in a mathematical setting is a GREAT start.

SHARE YOUR EXPERIENCE BY MAY 31, 2017 to enter the random drawing to win a copy of Math on the Move: Engaging Students in Whole Body Learning. Share your experience via blog post or video on Twitter or Facebook with #movingmath and, just to make sure, share the link with me

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!!

Header Proving Center 1 FINAL

In 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


Header Rope Polygons 2 FINAL

In 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


Header Clap Hands 3 FINAL

Clapping 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


 

Header MiYFeet 4 FINAL

Have 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.

 

 

A Quick Example of Body-Based Cognition: Spinning

library-poster

Yesterday I was at the library for my now monthly #makingmath sessions for kids and their parents. The ages for this event seem to trend 8 and under, probably because parents with young children are often looking for something to do on Sunday afternoons. Our youngest participant yesterday was two and a little more, and this little story is about her.

I’ve written previously on this blog about what it looks like when children think and learn mathematically with their bodies. Yesterday my new friend was there with her mom and her brother. Her brother made this delightful “Dr. Seuss house with smoke coming out of the chimney” while she made a crown and earrings for herself out of the same materials.

Another activity we had going on was playing around with these cool hexagon building blocks that I found in a big box dollar bin a couple summers ago.  A boy made an object that was just begging to be spun…

…after which my little two year old friend started rotating around in one spot exclaiming to me: “I’m spinning!”

This is just one more example of how children think and learn with their bodies. She was entranced by the toy and it’s gorgeousness.  She spent a quick moment spinning exactly like the top and then went back to making earrings for her mother.

The body is where learning originates. Children use their bodies to show us every day what they know and think and wonder. This non-verbal, physical manifestation of cognition is present every day in some way. I invite you to put on your #movingmath glasses and, when you notice something tell us about it! Here’s a few places where you can share:

In the comments to this post
On Twitter with the hashtag #movingmath
-or-
On Facebook with privacy set to public with the hashtag #movingmath

I can’t wait to hear about (or see) what you notice!


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.

 

“Children think and learn through their bodies”

NOTE: I was thrilled to be invited by Table Talk Math to write a short piece for their weekly newsletter, and they have graciously allowed me to cross post a slightly expanded version here. Check out their resources for supporting math talk at home around the dinner table or any time!


cosmo-heightWhen my daughter was six she was prone to spontaneous bursts of body-based mathematical exploration.  That summer we had two flower plants in our garden that she had nurtured from seed.  By mid-August they had refused to blossom but were still gaining height and had become a daily source of measurement.  She’d compare the plant to her own height, “The cosmo is taller than me!”  As we turned toward autumn she was ecstatic to pronounce, “It’s up to Papa’s chin now!”

That same summer we read the book Sir Circumference the first Round Table a number of times.  She developed a game where she would leap  toward her blow-up wading pool in what she called the “diameter jump.” I held my breath every time as she leaped, finger tips to toes stretched out in one long line to touch the front and back of the pool at the same time, literally flying, flopping almost on the other side of the pool.

straight-lineA year later she was still learning to ride a bike. I took her to the playground which had a big open basketball court. She talked herself through the process: “Okay, all I have to do is think like a straight line in geometry…” and rode back and forth across the basketball courts chanting her new her mantra.

“Think like a straight line, think like a straight line, think like a straight line in geometry.”

When she’d get to the end of the court, she’d get off the bike and turn it around.  Then she figured she could make the turn without getting off. “All I have to do when I get to the end is think like a circle….”

 

Perhaps you’ve also noticed your children or students using their bodies to measure, make size comparisons with other objects, or track growth.  Or maybe you’ve noticed them:

  • walking a pathway along the painted lines on a basketball court
  • crossing a tiled floor on the diagonal by stepping on all the corners, or
  • stepping deliberately over every other floor tile in the grocery store

What can we make of this kind of activity?

Children naturally use their bodies as “thinking tools” to explore and make sense of the world. Studies have emphasized the importance of self-produced movement in the development spatial reasoning which is strongly linked to robust mathematical thinking and problem solving. Both spatial thinking and embodied learning — non-verbal, body-based modes of knowing and reasoning — are especially relevant to the development of mathematical intuition and sense making.

You can support the development of sturdy spatial and math skills in children by:

  1. Having conversations. Use spatial and relational words in the context of talking about everyday activities: over, under, around, through, around, above, below, etc.
  2. Pay attention to how children are using their bodies to interact with the environment, especially in new spaces. The more you notice the more you’ll see (and enjoy) their body-based thinking!
  3. Watch their gestures as they talk about math ideas. Many studies have shown, including the one on which this post’s title is based, that gestures paired with speech can show you a lot about a child’s geometric and spatial knowledge for which they may not yet have words.
  4. Play around! During a visit from a VERY tall Uncle Arlen my six-year-old noticed that he was exactly the same length as the couch! They ended up measuring the sunroom in a hilarious series of units called “Arlens.” The room was almost exactly four Arlens long. They also noticed that one “Arlen” was equivalent to two “Isobel’s” and five lengths of our unamused cat Lucy!

Interested in learning more?

This article on the Mind/Shift blog titled Why Kids Need to Move, Touch and Experience to Learn is an excellent overview of embodied learning.

For some succinct and helpful information about spatial reasoning and how to support and develop students’ spatial thinking in the classroom during math time download this free PDF.


Malke Rosenfeld is a dance teaching artist, author, 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 is titled: Math on the Move: Engaging Students in Whole Body Learning (Heinemann 2016)

 

Moving Scale Math on the Hundred Chart

Chapter Three in Math on the Move is titled “Beyond Mnemonics: Getting Starting with Moving-Scale Math.” The chapter is designed as a “zero entry” pool of sorts for whole-body math learning.  You can start at the shallow end and get your feet wet by incorporating students’ whole bodies into familiar math activities you might already be doing at hand or desk scale. Or, if you feel ready, you can jump into the deep end and facilitate a more organized activity.

This chapter is not about replacing an entire math unit with moving-scale, body-based learning or changing your teaching approach overnight. Instead, this is a chance to get a sense of what it feels, looks, and sounds like to engage your students in mathematical sense making by engaging their whole, moving bodies in collaboration with other learners.

The chapter opens with stories from Jenn Kranenburg’s classroom, many of them centered on the large hundred chart she has taped to the floor of her classroom. Today on Twitter she shared a short video of that shows student activity on the “moving scale” hundred chart.  Notice the way this familiar but scaled-up tool opens up whole-class collaboration and conversation, and allows students to fully engage with the spatial nature of the chart.

Updated 10/7, another video from Jenn!

If you’re interested in joining the Facebook discussion group forming around the book please do!  We are learning together and growing a community of practice around meaningful whole-body learning.


Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in October 2016.

TEDx Talk: Jump into math!

My upcoming book reminds us that the body is best positioned as a thinking tool, that math is about more than memorization, and that amazing things can happen when the body and math come together in both dance and non-dance settings.

I gave a TEDx talk in 2013 (before I had even thought to write a book!) which gives a great overview of what Math in Your Feet and whole-body math learning is all about. Math on the Move: Engaging Students in Whole Body Learning will be available in late October and is ready for pre-order.


Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

The foundation of Mathematical thinking

 

“Spatial thinking is integral to everyday life. People, natural objects, human-made objects, and human-made structures exist somewhere in space, and the interactions of people and things must be understood in terms of locations, distances, directions, shapes, and patterns.”
-National Research Council

For an overview about how to help students make – and sustain – gains in their learning and understanding of mathematics check out the short but mighty Paying Attention to Spatial Reasoning from the Ontario Ministry of Education. Resting on a rigorous research base, this publication outlines seven foundational principles for focusing on spatial reasoning in the classroom. It also provides useful examples of what paying attention to spatial reasoning can look like in K-12 math classrooms.


Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

 

Some thoughts on “hands-on” math learning

IMG_7144

Note: This is a re posting of some thoughts I wrote down at my old blog on April 1, 2015, shared here in its entirety.  

Last night on Twitter Michael Pershan asked me to weigh in on hands-on math learning. The request stemmed from a conversation/debate about the various merits of different ways to learn math.

The minute I read the question I knew that my answer was going to be more detailed than a response on Twitter would allow. Here are some of my thoughts on the matter.

Continue reading “Some thoughts on “hands-on” math learning”