Week 5 - Developing mathematical pedagogies that integrate embodied, multisensory, outdoors and arts-based modalities

Reading - Reconfiguring mathematical settings and activity through multi-party, whole body collaboration - Kelton & Ma

The reading that I chose for this week explains two studies that use different approaches to embodied learning. The first involves a middle school class and a walking scale number line, focusing on integers and then their opposites, but also safe ways to get from one place to the other. They are using the space (gym) that they are very familiar with, but in a different context. The students each represent a different number on their living number line. The second case has elementary students "participate in a ratio-and-proportion activity called whole and half" (Kelton & Ma, 2018). The teacher had the students get up, one student making a space between their two hands, and the other trying to find the middle by placing their hands between their partners. In a specific example, partner A would make the activity harder and harder for partner B, eventually using parts of their classroom in a different context than usual.

For the "stops" to the reading this week, I took notes of whenever I could relate these examples to my own teaching experiences. The first one relates to the walking scale number line. Two years ago during a math intervention session, one of my students had difficulty counting on from a number. When I would prompt her with how far away is 18 from 12, she would always begin with 12, and her answers would be one too many. Without learning subtraction yet, her and I made a walking number line. She made all of the numbers, each on a piece of paper, and laid them down from 1-20. She then started on 12, then lept her way to 18, counting her jumps as she went along. This learning moment made her realize that the answer was six instead of seven, which then laid the foundation for subtraction. She later let me know that she pictures herself doing that activity in her head to help her with her counting. 

My second stop relates to how both of the studies not only de-centered the room, but used the gym and the classroom in a different context than what the students were used to. One of my classes favourite activity is when we turn our class into stations of Non-Permanent Vertical Surfaces. At least once a unit, students are grouped at a different station, where they write on each of the whiteboards, the Smartboard, and their favourite station, the windows of the classroom. They get so excited by this idea, and are always eager to start the problem solving activity. 

My question this week: In your varied experiences, in either your classrooms or through observing or coaching other teachers, have you incorporated any embodied or multi-sensory experiences? If so, what did they look like? 

Part 2 - Videos and activity

Weekly Intro

The intro has me relating to parents who tell me that they don't understand the "new math", and "that's not how I did it when I was in school". I would usually battle this sentiment, but this course seems to accept it as fact. While it's not "new" math, we are trying to evolve our practices to ultimately be more beneficial to the learners. Through a math leadership role in my school, I need to remind both myself and other teachers that, as Susan says, the shift is not from one extreme to the other. We need to teach both ways, in an integrated, meaningful way. Further into the intro video, a statement such as "some students prefer the static, but it's not the majority" does make me want to look deeper into studies that have measured this. Is it true that the majority of students don't prefer the traditional way of learning math? I would think so, but is there evidence?

Video Response

I decided to look more into the Sarah Chase video. Before the video concluded, I had jumped ahead to test a theory that I had. I had wondered if the patterns would work if the numbers weren't prime. I made a sketch of a 4 step repeated pattern vs. a 6 step repeated pattern. As I had assumed, the patterns reset at 12, the lowest common multiple, rather than 24, 4x6. My sketch below is evidence of my experiment. As I continued the video, I laughed to myself as the presenter explained that she sometimes lets people make the mistake of choosing numbers of 6 against 8 and seeing what happens (similar to what I just did). Incorporating dance of movement sequences as Sarah does makes for strong cross-curricular connections between Phys. Ed. (non-locomotor movements) and Math.

Activity

As mentioned, the picture below shows how I extended the video. In grade 6 math, part of our curriculum has a focus on factors and multiples. One of the questions that I made on our last test read: Sammy and Suzie both work at the Riverview Cineplex (the movie theatre in town). They love working together, but Sammy only works every 4th day, while Suzie works every 6th day. If they both work together today, how many days will it be until they work together again? 

The question has real-life context, and students are to find the Lowest Common Multiple between 4 and 6. Students may use whatever strategy they wish to get to their answer. Some sketch out their thinking, while many know to quickly calculate the LCM. The latter group of students more often get the incorrect answer, as they all need to remember that Suzie and Sammy work together today, which would be day one, so they need to add one to their LCM. The question continues with different names (e.g. John works every 9th day. When will he work with Sammy? When will he work with Suzie?) To extend the question gives the students more opportunity to show their understanding of the concept of lowest common multiples. 

References:

Kelton, M. L., & Ma, J. Y. (2018). Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration. Educational Studies in Mathematics, 98(2), 177-196. https://doi.org/10.1007/s10649-018-9805-8

Sarah Chase: Dancing combinatorics, phases and tides (long version 13:35)