Week 3: Sustainable mathematics in and with the living world outdoors

Thoughts on Introduction and Video 

This week I appreciated the connection to outdoor learning as a way in which teaching math can happen. I feel lucky that all the school sites that I have worked at have easy access to both beaches and forests. This had me thinking that this is not the reality for all educators. Some educators teach at sites in busy city centres and others in places where natural landscapes are covered by snow for some of the year. I think teaching math using the outdoors becomes powerful when it is a routine and a way of thinking about math and not just an experience that happens occasionally. I wonder how this experience can be brought to areas where nature access is limiting.  

Mathematics outdoors has many possibilities. Including connecting leaners to place and helping build self-confidence with body movements. Just this week The Canadian Paediatric Society published a report stating the benefits of risky play in children’s development (click here to see report). I think this provides a great opportunity for educators to reference research when helping all families understand why this is a meaningful way of learning. 

I was amazed at the talent represented in the Dancing Euclidean Proofs. However, as I am not a dancer, I started to think about myself as a learner and how being asked to create a similar project would be challenging for myself. This made me think about allowing students to represent their knowledge in multiple ways and allowing choice, a key idea in UDL. I think it’s important to build students awareness of movement as a way of showing knowledge, however, I see that this mode of learning will be meaningful for some learners but not all. 

Weekly Reading 

This week I read Dancing Teachers Into being with a Garden, or How to Swing or Parkour the Strict Grid of Schooling written by Susan Gerofsky and Julia Ostertag. This article looked at how intertwined the grid system is into teaching and everyday life. Examples included the Teacher Education building at UBC to checklists used. A connection was made between how the grid system has been used in history as a powerful tool or territoriality and colonialism (Gerofsky  & Ostertag, 2018). The authors suggest that the grid system is used so much as it is familiar, comforting, and powerful. The article moves on to discussing ways to think about teaching more creatively using dance movements and school gardens. 

One of my stops while reading this article was over the idea of the grid system as a way of control. When I was a student the education system was teacher directed now, depending on the educator, schooling can be student-centered. I think one way to move away from the use of grids is to view educators from a student-centered point of view and the educators as an equal learner alongside students. With this change learning becomes organic and open-ended rather than rigid and scripted to check boxes. 

My second stop was related to the author discussing teacher education programs, specifically when the article mentioned conforming to traditional teaching within the grid or imagining other ways teaching could be possible. This made me think about how when I was in the teacher education program there was a core math course that did not encompass any ideas around teaching math outdoors or through movement. As this was within the last 5 years I wonder if much has changed. How can we create change within a system of education, and traditional math approaches to be different when training programs for educators do not expose them to diverse ways of knowing. 

Sit Spot Activity 

Sit spots is an activity I do regularly with my students. I was excited to see what they were drawn to regarding lines. I took my class to the school garden and had them sketch living and human made objects they could see. We then had a discussion regarding lines as angles does not come into the curriculum yet. Most students found numerous examples of straight lines. This made me think back to my weekly reading this week and how grid like the school structure and garden are. 

As for experiencing angles using body movement. I had my class go to the field and form shapes by all holding hands. Students moved into the shapes of a circle, triangle, rectangle, and square. By making shapes students were experiencing what different angles look like. 

References

 Gerofsky, S. & Ostertag, J. (2018). Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling. Australian Journal of Environmental Education, 34/2, 172-188.

Week 2 EDCP 553 – Multisensory Math

Insights from Reading 

This week I read The Six-Cornered Snowflake by Johannes Kepler. The timing of this reading couldn’t have been better as Vancouver experienced its first major snowfall of the winter. The author spends time developing their thoughts on the beauty of nature and the science behind some of the shapes we see in nature. A specific example is a snowflake. The author discusses how water vapor and the release of underground moisture play a role in the geometry of a snowflake. Other examples including beehives and pomegranates are analyzed from geometrical perspective. The shapes of these objects are looked at regarding how combining the shapes (rhombic) with different sides connect to build a whole. The author continues to share their thinking about shapes by thinking of a cubic arrangement and how with pressure a sphere become a cube shape.

My first stop while reading this article was thinking about the objects the author deicide to analyze, being snowflake, pomegranate, and a beehive. This led me to thinking how exploring different shapes with students can connect them to place. For example, if it never snows where students live it might not be the most meaningful learning to look at. However, if students can visit a school garden or orchard and see the shapes occurring in flowers or apples this knowledge can be made visible. 

My second stop was connecting the knowledge that I was learning through the authors descriptions to a trip I had been on. When I was reading about the hexagonal shape of the beehive maximizes space, a memory of visiting various basalt columns in Iceland popped into my mind. When viewing them last spring break I did not think about how the shape of the columns fits together perfectly to make it a whole. However, now after reading this article I am further building my understanding as to why they look the way they do! 

Thoughts on Introduction and Videos 

I really appreciated the introduction this week and the connection to use multisensory mathematics to help diverse learners find success. This term I am taking EPSE 526 with the topic being Learning Disabilities. I am very passionate about developing my practice as classroom teacher to include ways of reaching all students. Involving students in hands on learning experiences and allowing them to show their thinking in multiple ways helps build community within the classroom as all learners are given the opportunity to succeed.  Reading about students with sensory impairments made me make a connection to a beautiful picture book titled 10 Ways to Hear Snow by Cathy Camper. The author tells the story of a snowfall happening in a town and a young girl thinking about the sounds one hears when a city has a snowfall. The girl thinks of the sounds snow makes to help her grandmother understand that there was a snowfall as she cannot see. 

The videos were interesting. I never thought of all the detail and mathematics involved in simply eating Halloween candy or cutting a bagel. The videos did serve as a good reminder to me as I have yet to integrate mathematics through the sense of taste into my class. This led me to thinking about the possibilities to think about the math students experience when they receive hot lunch. Such as looking at the amount of pepperoni pieces they get on their pizza or pineapple or even thinking about the different pizza selected. The class could look at a question like what is the most common pizza choice? 

Activities and Connections to Practice 

With the snowfall this week I took some time to experience looking at the detail of many snowflakes. I also explored snowflakes with my students. We started out by watching a video about the science and learning that a true snowflake has 6 points. As they are in Grade 2 this was a good starting point to start to look at shapes in more depth. Students then built snowflakes with loose parts and by creating oil pastel and watercolour paintings. When doing art, I said that the criteria would be designing a snowflake that has 6 points. I found this to be a meaningful experience for leaners to use different modes to understand the science of a snowflake. 

I decided to apply what I learned in my reading last week with my students also. As I read the article about being the graph, I decided to introduce the idea of graphing with students acting out the data. For example, we focused on the question “do you want it to snow tonight”. Students then moved to an area of the classroom assigned to the response yes and a separate area for the answer no. After counting and recording the data students moved to their table spots to complete a bar graph with the collected data. 

Week 1: Mathematics and the body

This week I read the article Seeing the graph and being the graph by Susan Gerofsky. The article focused on explaining different studies that have been done that look at the use of gesturing when teaching mathematics. The article moves on to highlight a study that was done in 2008 with 22 high school students. The focus of the study was to see if elicited gestures representing the graphs of mathematical functions are meaningful to learners and if gestures influence engagement. The researcher was interested in where students used the gesture in relation to their body (heart, shoulder, nose level). Some students utilized small movements, another group utilized whole body movements, and some students had difficulty producing any gesture. The researcher was able to determine whether students were top, average, or struggling by viewing videos of student’s use of gestures and graphing. It is important to note that one student was rated as the top student by their classroom teacher and appeared in the struggling group based on their use of gestures with graphing (Gerofsky, 2011). 

This was an interesting to study to read and I appreciated that it was locally based (Vancouver). When studies have small sample sizes and results that stand out, I think it is important to think about what further research could be done to draw meaningful conclusions for educators. I was also left wondering about what exactly was meant by elicited gestures. What was the process used to determine the gesture that would be used, was it teacher directed or were the students involved in the decision?

My first stop that came up was thinking about learners that use ASL and how gestures could be meaningful or potentially confusing. In my first year of teaching a student in my class speech was unintelligible. This student was learning ASL with an EA. As I wanted to build a strong classroom community, I would also teach all learners and use ASL in certain situations. In my opinion, integrated gestures in this situation would be confusing for learners as there is a difference between gestures and ASL. I wonder what research has been done to look at the use of gesturing with ASL individuals. 

My second stop was about the idea of elicited gestures. Information regarding the process of choosing and what was elicited didn’t seem to be clear. I wonder how student choice could be involved when deciding to integrate gestures into learning tasks. This stopped me as when I reimagine math education, I think about involving students more in the learning and making the topic related to their interests rather than a teacher explaining something in one way that makes sense to them and may not click with others. 

This week we also thought about using the body as a form of measurement. As I teach Grade 2 and measurement is part of the BC Curriculum, I decided to integrate this idea in a few different ways. With my class I started by discussing standard and non-standard measurement and built to understanding that a non-standard unit could be measured and utilized to reference to the specific standard measurement. For example, students measured a body part using a ruler and recalled what that measurement was when they went outside to measure in the school garden. Some of the conversations I heard were” oh this is bigger than my foot so it must be over 18cm” and “this is exactly the same size as my hand!”. I was amazed to see the engagement and determination students took on with this task. 

Over the last two days Vancouver has been experiencing below average winter temperatures (sorry Pat and Shawn that you must hear me talk about cold temperature when you deal with much worse!). I decided to use the this as an emergent learning opportunity to further look at measurement. Students and I discussed different quantities of water and what would freeze first. We then placed various quantities of water outside and waited to see how long it would take for them to freeze. I noticed many students going over to the window to see what was changing. I heard “I knew it was going to be the one with the small amount of water that froze first!” and “look, you can see ice crystals!”. 

These in class experiences remind me of the importance of involving students in the learning in ways that are meaningful to them. Now when they think of measurement, they may think about their time in the school garden or freezing water!

Works Cited

Gerofsky, S. (2011). Seeing the graph and being the graph . Integrating Gestures, 245-256.

Hello World!

 My name is Amanda Pasternak and this blog will be used to explore ideas connected to teaching and learning mathematics.