Final Project DRAFT

 Still a work in progress, click here to view my final project. 

Week 9: Mathematics & traditional and contemporary practices of making and doing

 Weekly Reading

This week I read a short newspaper article titled “The Spirit of the Medicine Will Lead Us Back - How Avis O’Brien is Guiding Elders to Weave Their First Cedar Hats" written by Anna McKenzie. The article explains how Avis O’Brien who is Haida and Kwakwa̱ka̱ʼwakw was disconnected from her culture and living in a place that wasn’t her territory. Through participating in learning about cedar in Vancouver Avis was able to reconnect with her culture and feel inspired to want to share the experience of weaving with her elders on her territory. Now Avis runs weekly weaving classes where individuals get to come together to share stories and food while learning about their ancestry through weaving.  

My first stop was connected to how the experience of the weaving class was described. It sounds like the workshop is structured to have time to connect on a personal level and not just about weaving. I wonder what the k-12 system can learn from this style and structure of learning. As a primary teacher I start most days with a soft start that allows students to connect and settle into school. I wonder what this looks like in upper elementary and in high school.

My second stop was connected to this quote “Weaving was one of those practices that went to sleep — it had to,” she says. “Our spiritual and cultural practices were targeted, specifically because that’s where our strength comes from.” As educators it is important for us to learn about Indigenous ways of knowing and being so we can help students understand. There is however a difference between a settler teaching about Indigenous ways of knowing versus an Indigenous person teaching about their way of living and being. I think it is important for Districts to make connections with local Indigenous groups as an act of reconciliation. Furthermore, this connection can lead to authentic learning experiences being brought into the classroom like weaving or language lessons.

Introduction, Videos, and Activity 

I found the videos interesting to watch and noticed that I felt calm as I was watching. I experienced a similar sensation when I went to make my own rope. This was something I had never done before yet the experience was calming. I think this provides a great opportunity to integrate activities like this with students as it can also assist with self-regulation. 

Last year my school had Red Cedar Women visit and teach all students how to weave a small cedar mat. Primary classes were paired with intermediate buddy classes to assist in the weaving. Students felt proud of what they made and had the opportunity to connect with different members of the school community. I am hopeful that this will be a tradition that my school continues for years to come!

Week 8 - Mathematics & Fibre Arts, Fashion Arts and Culinary Arts

 Weekly Reading

This week I read Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving by Gwen L. Fisher. The article explores the progression of the impossible triangle, from its origin by Oscar Reutersvärd to popularization by Roger Penrose and M.C. Escher. Gwen introduces an inventive method using beaded sculptures and cubic right-angle weave to represent impossible figures in three dimensions. Specifically, the focus is on creating a "highly unlikely triangle" through beadwork with quarter twists, resolving optical illusions while maintaining flexibility. This technique is extended to construct highly unlikely squares, frames, and tetrahedra, demonstrating a unique approach to beading structures with unexpected twists and color variations. The author emphasizes the artistic complexity introduced by these methods, providing a creative reinterpretation of traditionally two-dimensional impossible figures in a three-dimensional space.

My first stop was making a connection to present day pop culture and the main idea of this article, seeing the mathematics involved in beading. The pop culture trend I thought of was how concert goers and fans are creating friendship bracelets that they wear to Taylor Swift concerts and exchange with other fans. This led me to thinking about how connecting current pop culture trends might lead to greater interest from students. Students could be introduced to using beading as a way of showing mathematical knowledge. Then students could be involved in creating a representation of a mathematical idea (patterning and shapes) by using beading.

My second stop was related to how beautiful the shapes are that Gwen created. It is a challenging task to help students see the beauty in mathematics if they have already built-up barriers or a negative mindset. This article shows ways educators can integrate different ways of thinking about shapes and mathematics in a way that might shift students thinking about beauty of mathematics.

 

 Introduction, Videos, and Activities

The introduction had me thinking about my own ability to notice mathematics in different and sometimes non-traditional ways. I think this is in part due to the K- 12 education system I experienced as a leaner. Now, as we work on shifting the idea of what mathematics is and how it looks in schools, I am still learning to notice the math around me. “Learning involves patience and time” is one of the First People Principles of Learning here in BC. I think it serves as a good reminder for us doing this work that no matter the age of the learner it takes time and to not feel pressure to integrate all ideas at once. It takes trying and experimenting and adjusting to integrate new ideas into ones teaching practice.

I was drawn to watch Making Mathematics with Needle and Thread: Quilts as Mathematical Objects. It was interesting to understand the basics of quilting as it is a hobby my mother has recently taken up. After watching the video, I got the idea to discuss quilting with my mom and ask her to describe her process and if she has ever viewed steps in her quilting process as math. I noticed a connection to last week’s activity as the audience member are brainstorming ways in which mathematics is involved in quilting and the Fibonacci sequence is discussed.

For my activity I choose to watch “What is the best way to lace your shoes? Dream Proof”. I was experimenting with my own lace tying abilities as I was watching. I was drawn to this video as I am an early primary teacher and most of my students cannot tie their own shoes. That does not mean they will not come to school daily wearing shoes with laces! This video had me thinking about how I could use this with my students and not only help them build an understanding of the math involved in tying shoes but also help them build a life skill of tying their own shoes! I have lots of wonderings around how we involve parents and caregivers in this “new” way of doing math. This video could also be used to share with them to help shift their perspective of what is math.

Week 7 Mathematics & Poetry and Novels

 Weekly Reading

 

This week I read Can Zombies Write Mathematical Poetry? Mathematical Poetry as a Model for Humanistic Mathematics written by Gizem Karaali. The author reflects on the intersection of mathematics, poetry, and human experience. The narrative delves into the author's personal journey of rediscovering poetry and its connection to creativity, consciousness, and cognition—qualities fundamental to humanity. The author explores the analogy between mathematics and poetry, asserting that both disciplines encapsulate the essence of what makes us human. The text also introduces the concept of "humanistic mathematics," emphasizing the human aspect of mathematical endeavours. Furthermore, the author shares insights into their own poetry, discussing the influence of language and the unique relationship between mathematical and poetic language. The narrative concludes by highlighting the incorporation of mathematical poetry in teaching, showcasing its potential to bridge the gap between those disinterested in mathematics and the profound beauty inherent in the subject.

My first stop was related to this quote, “I claim that mathematical poetry can be the ideal ambassador for our efforts to humanize mathematics in the eyes of those who mostly care little for mathematics” (Karaali, 2014). This had me thinking about my first-year teaching when I utilized a picture book related to playing with making simple mathematical equations related to life, for example, leaves + hot soup = fall. The book is called This Plus That: Life’s Little Equations by Amy Krouse Rosenthal. To engage my students in thinking about this idea I took them for a walk to the local meadow and read the story. Students were then paired up to come up with different equations inspired by the book. This simple activity helped humanize mathematics for my Grade 1 learners in a profound way. As students are just starting their journey with addition and subtraction in grade 1, it is important to provide them with opportunities to play with math to develop confidence.

 

My second stop was connected to the quote “Even in adult conversations, I oftentimes feel more at ease in English. But with poetry, I could only hear my voice in Turkish”(Karaali, 2014). This had me thinking about the diversity of classes in British Columbia. In my current class 14 out of 22 students are ELL, with many of those students moving to Canada in the past year. This article was written by an adult, and they still feel more comfortable to do certain tasks in one of their specific languages. I think these serves as a good reminder to let students show what they know in different languages. Asking newcomers to Canada to produce work in English is an unrealistic ask. There is beauty in students being given the agency to decide they way and the language in which they show their thinking. Furthermore, this celebrates students who have more than one language, contributing to building a community of respect for different strengths that all individuals bring forward.

Introduction, Videos, and Activities

 I appreciated the introduction this week to give me some context into the idea of combining mathematics with poetry. As I teach at the early primary level, I do not teach poetry and haven’t thought about it since I was in high school. I appreciated the section around three possible ways that mathematics inspires poetry. I was able to make a connection that sometimes I use literary works about mathematics with my students.

 

It was interesting to move from reading about poetry and math to viewing it in action through Mike Naylor’s video. I almost found it more engaging the way he read Run, Hero, Run! First using zero and one. This poem had me thinking about how I would help students make the connection between poems and mathematics. I wonder if the connection is less abstract if the poem involves mathematical terms/language?

 

I was interested in exploring Fibonacci’s sequence and how it can be used in poetry. I appreciated the explanation from Sarah Glaz. Here is my experimentation with Fib poems.

 

Rural

Urban

Snow covered

Adventure activities await

The mountains are calling me

 

Sand

Water

Driftwood chairs

Seagulls chirp overhead

Waves go in and out

 

Works Cited

Karaali, G. (2014). Can Zombies Write Mathematical Poetry? Mathematical Poetry as a Model for Humanistic Mathematics. Journal of Mathematics and the Arts , 38-45.

Week 6: Mathematics & Dance, Movement, Drama and Film

 Week 6: Mathematics & Dance, Movement, Drama and Film

 

Weekly Reading

This week I read Learning to Love Math Through the Exploration of Maypole Patterns written by Julianna Campbell and Christine von Renesse. This article focuses on how a university teacher and their students explored the mathematics in dance through an inquiry lens. Students started with questions regarding what they were curious about. The course was structured differently as it focused on meta-goals not content goals (Campbell & von Renesse, 2019). The article goes on to incorporate the perspective of one of the students in the class, a student who saw math as a formal, numeric, and logic-based subject (Campbell & von Renesse, 2019). Through the delivery and structure of the course this student began wanting to share their work with the class because they were proud that they got to think of a problem in a way that made sense to them (Campbell & von Renesse, 2019).

My first stop was related to student ownership in learning. As mentioned, the student that this article zoomed in on developed confidence as they wanted to share because the teacher allowed for choice and creativity as to how students shared their learning. This is an important takeaway for us as educators to see how creating choice in the ways students can show their learning increase student commitment to the leaning task and overall enhances their ownership to their learning journey. I wonder what this looks like at a primary level. During the primary years students are still learning about themselves as learners and often need explicit teaching about strategies related to ways to show what they know.

My second stop was around the quote “choosing a topic from the arts can give students that feel negatively about mathematics a chance to start new and meet mathematics in a different way” (Campbell & von Renesse, 2019). This is a statement in the article that is based on the experience of one student. I wonder if this student had a previous passion or interest in dance before they took this course. From other research I have read there is often a connection between student interest and engagement. If the educator can find a way to relate the learning to the interests of the students there will be more of a “buy in” from students. I wonder if choosing a topic from the arts can help increase student engagement if the arts is not an area of interest for the learner?

 

Introduction, Videos, and Activities

I found the videos this week interesting, specifically the TED talk with Erik Stern and Karl Schaffer. In the other course that I am currently taking, EPSE 526, I recently read an article that was about students commenting on what makes an effective teacher. “Students recognise that humour often serves as bridges across many potential divides-including frustration on both sides” (Connor & Cavendish, 2020). I think that is something that both Erik and Karl do well in the TED talk, and I imagine is their approach when they engage with students. This had me thinking about the whole educator rather than just their ability to incorporate teaching through the arts. As I strive to build an inclusive classroom, there are many contributing factors to what can help all learners be part of the learning, one of them involves bringing the right amount of humour into the learning.

I noticed that the source of some of the videos form this week was the Julia Robinson Math Festival. This caught my attention as in my last staff meeting, I was told that this festival will be coming to my school in March. My school is currently focusing on a 3-year FESL (framework for enhancing student learning) around increasing students’ ownership in mathematics. I am interested to see how my students engage with the festival and how it builds a collective commitment to seeing different ways of doing and playing with math at my school.

This week I tried the activity Clap Hands: A Body-Rhythm Pattern Game, click here to see lesson plan. I started by having students at the carpet sitting in a circle and explaining that we were going to use our bodies to make a repeating pattern. Once students got the idea of how it worked, we stood up to use different body parts. Students got to create patterns with 3-6 beats. When this learning was taking place, I tried to highlight the learning that was taking place with comments like “we are doing math right now” and “we can make patterns with movements not just shapes”. After doing some full group work, I split students into small groups, and I went between groups. I noticed that some students struggled with the activity, they were not able to recall the pattern that the leader set. As I noticed this, I changed groups criteria to focus on patterns with fewer beats/movements for all learners to be successful.

 

Works Cited

Campbell, J., & von Renesse, C. (2019). Learning to Love Math Through the Exploration of Maypole Patterns. Journal of Mathematics and the Arts , 131-151.

Connor, D. J., & Cavendish, W. (2020). Sit in my seat: perspectives of students with learning disabilities about teacher effectiveness in high school inclusive classrooms. International Journal of Inclusive Education , 288-309.

Final Project Outline

EDCP 553 Draft Outline

 

Prepared by Amanda Pasternak

o   I will be working on this independently

 

Living with the Seasons: Outdoor Mathematics Explorations for Primary Students

 

Grade Level

o   The resource I will be creating is geared towards primary students in Southern British Columbia.

Outline for Mathematical Topic

o   I will be creating a resource to help inspire educators to take students outside to learn math. I will primarily be creating lesson ideas that connect to the BC Curriculum. These lessons will act as a guide to get educators started and provide enough freedom to be easily adapted to better fit the needs of diverse classes in different geographical locations. There will be math lessons that connect with the seasons to help students see the holistic connection between nature and learning. To honour multiple ways of knowing and learning I plan to include some Indigenous ideas related to mathematics as well as suggestions as to how educators can integrate embodied mathematics. I plan to touch on a range of skills as a key idea behind creating this resources is to help educators understand ways of integrating outdoor and embodied lessons in all subject areas rather than one niche area. I plan to highlight lessons related to shapes, number, graphing, and measurement.

 

Annotated Bibliography

McLennan, D. P. (2020). Joyful Math: Invitation to Play and Explore in the Early Childhood Classroom . Taylor & Francis Group.

This book looks at various ways early childhood educators can integrate joy, art, and the outdoors in to learning activities. The learning activities are interesting and engaging and involve practical advice. Furthermore, this book helps bridge a connection to math being in everyday life rather than an idea that is only explored in school.

 

Louv, R. (2008). Last Child in the Woods. North Carolina : Algonquin Books of Chapel Hill .

In the book Last Child in the Woods Richard Louv helps readers understand the urgency needed to help individuals, specifically children experience nature. This urgency is made clear as Richard discuss the challenges that face children included the rise in obesity and reliance on technology. Richard identifies this challenge as nature deficit disorder. Richard spends time helping readers understand the value in time outdoors.

 

Judson, G. (2017). A Walking Curriculum .

Gillian Judson’s A Walking Curriculum is the perfect resource to help educators start an outdoor education program. This book is written in a way that appreciates the lack of time most teachers have. The book has 8 chapters and focuses on different walks educators can take their students on. This makes the book very practical as an educator can read the details of a walk in a brief amount of time and be inspired to get outside with their students.

Davidson, S. F., Davidson, R., & Archibald, J.-A. (2018). Ptlatch as Pedagogy . Portage & Main Press .

Commitment to truth and reconciliation means making space for Indigenous ways of knowing in all subject areas. This book touches on many important ideas to consider when designing lessons and learning tasks including relationships and honouring the past.

 

Chahine, I. C. (2013). The impact of using multiple modalities on students’ acquisition of fractional knowledge: An international study in embodied mathematics across semiotic cultures. The Journal of Mathematical Behavior, 434-449.

This research study looks at comparing students who used a multimodal curriculum to those who were taught using monomodal curriculum. the author helps describe terms such as modes, modality, and representation which may be valuable information for educators trying to understand this way of teaching and learning.

Week 5: Developing mathematics pedagogies that integrate embodied, multisensory, outdoors and arts-based modalitie

 Weekly Reading

This week I read What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vison of Mathematics Education written by Leslie Dietiker. The focus of this article was trying to help educators imagine a way of teaching and learning math through stories and moving away from “doing the same old thing” (Dietiker, 2015). The idea of mathematical adventures, defined as adventures that are often sparked by a student’s questions or unexpected results is suggested as a way forward in math education (Dietiker, 2015). The key drive behind moving from doing math the same old way to math adventures is related to wanting students to see mathematics as something that is exhilarating, surprising, and full of wonder (Dietiker, 2015).

One of my first stops was when the author mentioned that if they were teaching today in the USA they do not feel they would have the curricular space and freedom to play with the aesthetics of math lessons (Dietiker, 2015).  In British Columbia the curriculum was revamped in 2016, as I am a newer teacher, this is the only curriculum I know. The curriculum is organized by Big Ideas for each subject area. This style of curriculum gives educators agency to decide how the lesson will be delivered. However, there are still many educators who use traditional means of teaching lessons, specifically in mathematics. This led me to a question - What are the primary factors deterring teachers from integrating multimodal and arts-based lessons in other curricular areas?

The author discusses the importance of story and how story is used to teach and inspire curiosity in literacy. This immediately had me thinking about integrating math workshop with primary students. Story workshop involves students using loose parts to create and share stories. The same idea can be used for math to help students understand numbers. Provocations could be used such as how might 3, 4, and 7 all be in a math story together? Or perhaps something more open ended like a few numbers less than 20 are in a math story together, how does the story go? Incorporating math workshop into primary teaching allows students to experience joy, wonder, and creativity while building their number sense.

 

Introduction, Videos, and Activity

I appreciated the video this week for the introduction. I found that ideas stood out to me more easily then when reading the text introductions. I am passionate about taking students outside to learn and have been developing this part of my practice for the past four years. I agree that integration of different ways of teaching and learning need to be integrated and not forced into classrooms. I think it is okay for educators to start increasing their comfort with new ways of doing things by taking traditional math worksheets outside. This provides a base and a starting point for teachers to build on. Expecting teachers to just start integrating planned lessons that evoke curiosity and wonder right away is a stretch, just as learning is a journey that takes patience and time the same can be said for teaching.

 Another point that resonated with me was the importance of not having diverse lessons coming across as orphaned ideas. If we want the education system and students to see the value in this approach to teaching and learning consistent adventures need to be provided to students. I think administrators play an important role in encouraging teachers to develop weekly schedules that allow for outdoor and arts-based lessons. This could be a conversation at a staff meeting at the start of the year to reiterate the importance of having this form of learning not just a one off.

 I appreciated the connection to notation as a follow up from an arts-based or outdoor lessons. I think this is an important part for all students but especially primary students. In primary teaching connections between ideas and concepts need to be made explicit. This had me thinking about integrating a reflection journal where students reflect on the learning and record some information based around notation of the concept explored.

 After watching the videos, I spent some time thinking about how these ideas related to my area of practice as a primary teacher. Teaching about time comes into the curriculum at grade 3 and I thought that body movements could be used to help students grasp the idea of the hands on a clock. As a subtopic of time students learn about recognizing time of year and seasons. This could be paired with an outdoor lesson to the beach to create sundials.

Works Cited

Dietiker, L. (2015). What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education. Journal of Education , 1 - 10.