Week 1: Mathematics and the Body

Hello! 

As I was measuring my body to complete the first part of the activity, I went to visit my Mom who was helping my nephew do a very similar activity. He is in Kindergarten but in a blended program where he does work at home half the week, his math activity for the day was to measure things using his body parts. It was exciting to see what I was doing for this course being used and working with him to see what different things we could measure together, discussing why my measurements were different than his (he needed to use more hands than I did to measure the book size) and how we could still get an accurate measurement. He was so happy to do math together and show me what he was learning! 

Working with him to use his body as a measurement tool showcased the significance of embodied experiences, my nephew was using his body as a resource to connect what he was learning about measurement and connecting these ideas to his next lesson on proportion. While he does the majority of his math work at home, his learning experiences are engineered in a way that supports his natural ways of thinking. 

Activity 

I started the activity by completing the chart with my body measurements, I found through this activity that I was getting caught up on accuracy in my measurements and had to remind myself that the width of my finger doesn't have to be super exact. I measured some things using my measuring scale inside my house (flower pots, desk, couch) and some things outside (width of a chairlift, fence, car). 

Indoor Measurement: I had a new roommate move in with me at the beginning of the month, there is not a ton of storage space so we were trying to figure out if his hockey bag would fit in the tiny storage space we have open. I measured that the space we had was 4.5 of my feet x 5 of my feet and then measured his hockey bag to be 4 of my feet x 3 of my feet. Without finding a measuring tape and trying to make it fit we figured out that the bag will fit in the limited space. 

Extension: We had a lot of visitors at my parents' house over the break and lots of cars in the driveway. Working with my nephew we decided to try and figure out how many cars could fit into the driveway if we parked them all straight ahead. We measured how big the driveway was using paces and then how much a vehicle was using feet. I helped him with the organizing and converting measurements. Using his counting skills he worked with his grandma to figure out how many cars we could fit. (I forgot to take any pictures while we were working on this activity). 

In the TedTalk, Antonsen (2015) explains that understanding has to do with the ability to change your perspective and use your imagination. In changing your perspective you are learning something new. I found that this was true for me as I worked through this activity, I had to remind myself to change my perspective and not measure things super precisely. This activity also changed my perspective on measurement - I think its easy to think of measuring as using a ruler or a 'standard' measurement tool but using your body or other less conventional measurement tools provides the same mathematical skills in a way that embraces the embodiment of math. Antonsen also explains mathematics to be finding patterns, representing patterns, making assumptions and doing cool stuff. I really connected this activity to the 'doing cool stuff' aspect. Being able to use my imagination to measure and think of things to measure allowed me to see how my nephew thinks about math as a five year old and how I can create new math experiences. 

Reading Reflection 

The reading I read this week was an excerpt from Foundations of Embodied Learning (Nathan, 2021). There were a lot of stops for me throughout reading this, I found myself thinking about new terms I haven't heard of before, connecting to my personal experience and nodding my head as I agreed with the author. This reading discusses embodied learning, misguided educational systems and grounding metaphors for math education. 

Nathan (2021) discusses early algebra education and the importance of giving students time to think before teaching them how to solve the problems. The students intuit how to work towards solving the problem and apply a guess-and-test method to see what works, guiding them closer to a correct answer. When students were asked to describe how they used intuition to solve algebra problems many students will say "I cheated" as they view this method not acceptable for school. This section really stood out to me as students are feeling like not using a set method to solve a problem but instead using what they know with trail and error is cheating. In so many ways society has taught students that cheating is wrong so I am curious as to how these scenarios have encouraged these students to continue this method of solving problems. I am interested in knowing more about how this method has worked in classrooms to support students understanding of concepts but also how it has worked with students who struggle to try unless they are given explicit steps. I can see how this method would positively foster a growth mindset towards math but at the same time could be frustrating to students who may take more time to solve problems. 

Grounding metaphors provide the basis for meaning in math and help to link one branch of mathematics to another. These grounding metaphors are good for simple foundational concepts however linking metaphors are used when cognitive offloading is needed to understand a more complex concept. There are examples that outline how these grounding concepts apply to different mathematical concepts. While some of these metaphors may seem intuitive to us as adults who have an understanding of mathematics, they need to be learned. Nathan explains that often these concepts are taught at home or in the community, there are instances where students do not learn these ideas, "when it is

not learned culturally, it must be taught explicitly." (p. 148). Students who are not experiencing these learning at home are missing out when they come to school - this is often seen in underserved communities. I connected to this idea as I work in communities where there is a large mix between privileged and underprivileged students. There is often a clear divide among students who have learned foundational concepts at home and those who haven't. This made me think about how some students who struggle in math at an early age may just need to learn these foundational metaphors and it may be beneficial for early education teachers to learn more about the activities suggested to help teach these concepts. 

Questions

Have you ever given your students time to solve a problem without any prompting or prior instruction? how did it go? If not, do you see this being successful? 

Have you heard of the grounding metaphors before or have you learned ways how to develop these in students who may not have learned them before school?