Final project draft 2 (Slides): Rabia & Renu

https://ubcca-my.sharepoint.com/:p:/r/personal/renu1502_student_ubc_ca/Documents/Presentation9.pptx?d=w0fbd310956fa43b2b9585d50e62346d7&csf=1&web=1&e=RQrgQG

Week 10: Activity Reflection

 

Curricular Work with Coast Salish Weaving and Mathematics

This week, I engaged in the practice of Coast Salish weaving and successfully crafted a pouch by using ropes. I created a slanted design with parallel lines and then digitized it by uploading on to the DESMOS computer program and explored the slope and equations of the slanted lines and their relation with each other. 

Week10: Reading Andrea Hawksley (Bridges 2015) Exploring ratios and sequences with mathematically layered beverages

 

Summary:

The given paper was a part of Bridges 2015 where the author Andrea Johanna Hawksley describes the workshop which explores the mathematical concepts of ratios, fractions, and integer sequences through the creation of layered beverages. By varying the ratios of ingredients like sugar, flavorings, and water in each layer, participants can visually and experientially understand mathematical principles. The workshop is divided into two main parts: exploring ratios with simple two-layered beverages and delving into integer sequences with more complex, multi-layered drinks.

In the first part, participants learn about ratios and fractions by creating beverages with different sweetness levels in each layer. This involves understanding how changing the relative unit volumes between layers affects the overall density and sweetness ratio of the beverage. The workshop encourages hands-on calculations and taste testing to reinforce learning.

The second part focuses on exploring integer sequences through layered beverages with many layers. Participants use sequences like arithmetic progressions or the Fibonacci sequence to determine the proportions of ingredients in each layer, creating drinks with increasing or decreasing sweetness levels. By experimenting with different sequences, participants can observe how the mathematical relationships translate into flavor experiences.

The construction of layered beverages involves following specific steps to ensure each layer is poured correctly onto the ice to maintain separation and visual appeal. The workshop provides examples, such as Fibonacci lemonade, with precise ingredient proportions for each layer. Participants can also explore other sequences like Lucas's numbers. In all such sequences, the ratio between adjacent numbers approaches the golden ratio. The workshop demonstrated how mathematical concepts are inherent in everyday activities and it can inspire others by the basic ideas of teaching math through layered drinks and try creating other mathematical foods.  

Stops:

1. When a large number of layers are used, the proportion of flavorings can increase according to various monotonic integer sequences, for example, the Fibonacci sequence. (p.519)

The above quote expands the possibility of trying different learning activities like using the Fibonacci sequence in baking by using the chocolate proportion in the proportion of the Fibonacci sequence. Using the Fibonacci sequence in this way can lead to an interesting progression of flavors, as the amount of flavoring increases more rapidly with each layer. This concept demonstrates how mathematical sequences can be applied creatively in cooking to achieve different taste experiences based on the number of layers or servings. Students can work with different recipes and not only engage in the hands-on learning experience but can learn the skill of cooking and baking too. 

2. Fractions can seem illogical and hard to conceptualize. This workshop gives a fun way for students to practice calculating fractions in an unorthodox setting using a sense seldom used in mathematics classrooms. (p. 523)

I agree with the statement that fractions sometimes feel illogical and hard to conceptualize. One interesting exercise I used to do with the students is where I used to ask students to bring their favorite flavored drinks and determine the amount of sugar in each. Students used to be tasked with determining the amount of sugar in one serving of their drink and then figuring out the total grams of sugar in the entire bottle. Initially, let's say they found that one serving contains 28 grams of sugar. To determine the total sugar content in the bottle, students must first recognize that the bottle contains 14 ounces, approximately equivalent to 414 mL, with "about 2" servings per container. Students may employ various methods such as doubling the serving amount, calculating sugar per ounce, or using ratios to scale up the sugar content from one serving to the entire bottle. By working independently or in groups and sharing their approaches, students engage in critical thinking and mathematical problem-solving skills while understanding the importance of accurately interpreting nutritional labels and serving sizes. 

in the future, I am eager to use beverage activities with my students to explore and teach integer sequences and ratios to my students.

Question: 

Could you share any hands-on activities you've employed in teaching or experienced as a student that relate to ratios and sequences? 

Week 9 Reading: Radakovic, Jagger & Zhao: Writing and reading multiplicity in the uni-verse

 

2024-03-09

Reading Reflection

Summary:

The article "Writing and Reading Multiplicity in the Uni-verse: Engagements with Mathematics through Poetry" discusses the intersection of mathematics and poetry through the analysis of two poems, "A Love Letter” by Nanao Sakaki and "My Universe" by the author Nenad, and the subsequent engagement with mathematical poetry by students.

 The poem “A Love Letter” beautifully encapsulates various circles of existence, from the intimate to the cosmic. For instance:

·       Within a circle of one meter, you sit, pray, and sing.

·       Within a circle ten thousand kilometers large, you walk somewhere on Earth.

·       Within a circle a million kilometers large, you embrace galaxies and the whole universe

Inspired by Sakaki’s poem, Nenad penned his poetic reflection, titled “My Universe.” In this response, he weaves mathematical themes into his personal experiences:

·       Within a circle of one meter, he sits alone, listening to classical music.

·       Within a ten-kilometer circle, he visits friends and their daughter.

·       Within a circle 100 thousand kilometers large, he waves goodbye to the satellites.

·       Within a circle a million light years large, he embraces galaxies and the entire universe.

 Simultaneously, Susan was teaching an elementary mathematics teaching methods course. She sought ways to engage her anxious teacher education students with mathematics. Together with Nenad, they explored mathematical poetry, discussing its themes and structures. Their experiences led them to incorporate mathematical poetry into their teaching practices. They explore the personal, authentic, and emotive nature of poetry in expressing mathematical concepts. The article reflects on the interpretation and meaning-making of poetry, challenging the formalist approach and advocating for the multiplicity of meanings in mathematical poetry.

Stops:

1.  According to Derrida, meanings are not stable but are instead caught up in the endless play of relations and differences between signifiers (words) and signified (concepts). This play is dependent on the reader and the reader’s prior uses and understandings of and experiences with those signifiers and signified. (P.4) 

In poetry, meaning is not fixed but is constantly shifting due to the interplay between words and concepts, influenced by the reader's subjective interpretations and past experiences. Mathematical poetry can benefit school children by illustrating the fluid nature of meaning in both mathematics and language. By engaging with mathematical concepts through poetic expression, children can develop a deeper understanding of abstract ideas. This approach encourages creativity and critical thinking, allowing students to explore mathematical concepts from multiple perspectives, thereby enriching their learning experience.

Question

 My question is what are some ways of incorporating problem-solving through poetry and How prepared are you as a teacher to integrate poetry and mathematical models to foster recognition of patterns, creative problem-solving, strategic thinking, and time-saving methods across subjects?

Week 9 Activity Reflection

 

Fib poems:

A poem of 6 lines whose syllable line count follows the first 6 numbers of Fibonacci sequences: 1, 1, 2, 3, 5, 8.

Susan

Math

Muse

Susan

Passion craft,

numbers, dance, and play

in her hands, learning finds its way

Guiding minds, motivates, inspires us through each bright day.

 Home

Love

joy

shared time

climbed trees high

echoes of laughter

in my home, where memories lie.

 

Stargazing Symmetry

in

dark

the night's

vast canvas

stars twinkle in sync,

forming constellations divine,

a polynomial of stars in the sky align.

 

Week 8: Activity Reflection

 Activity: Malke Rosenfeld's Math on the Move

Clap Hands: A Body-Rhythm Pattern Game

I and Renu tried the activity with kids and other people. it was an engaging activity, where children could design the rhyme or dance pattern during the game.  To adapt the rhythmic clap hands activity to fit my math curriculum, I would integrate it into a lesson focused on patterns, sequences, and mathematical reasoning. First, I would connect the rhythmic patterns to mathematical sequences, discussing how sequences are formed and identifying patterns in nature and around them. Then, I would encourage students to create rhythmic patterns using clapping, snapping, or other dance movements, emphasizing the mathematical structure behind their creations by using this activity. Students could also explore how changing the tempo or adding/subtracting elements alters the pattern, reinforcing mathematical operations and transformation concepts. Additionally, I would incorporate discussions on spatial reasoning by having students visualize and map out their patterns on grids or through movement in physical space. Throughout the lesson, students would engage in hands-on activities, collaborative exploration, and reflective discussions to deepen their understanding of mathematical patterns and sequences creatively and experientially.

Week 8 Reading: Sarah - Marie Belcastro & Karl Shaffer (2011) Dancing Mathematics and the Mathematics of Dance.

 

2024-02-29

Reading Reflection

Summary:

The article "Dancing Mathematics and the Mathematics of Dances" explores the intriguing intersection between mathematics and dance, highlighting how mathematical concepts influence and are embodied in various aspects of dance choreography. The authors, Sarah-Marie Belcastro and Karl Schaffer, both mathematicians and dancers, delve into the various connections between these seemingly disparate disciplines. It discusses how dancers intuitively apply mathematical principles like symmetry and pattern to create aesthetically pleasing movements and formations. Hence in the given paper authors have given examples of the interplay between mathematics and choreography.

The work of Rudolf Laban in modern dance is cited as an example of explicit mathematical theory applied to choreography. Furthermore, the article describes how choreographers draw inspiration from mathematical ideas to create dances, often blurring the boundaries between mathematics and artistic expression.

It also discusses the role of rhythm and sound in dance, showcasing how mathematical patterns contribute to the complexity of dance compositions. Additionally, the article touches upon the practical applications of mathematics in choreography, such as organizing movements and spatial arrangements. It emphasizes the interdisciplinary nature of dance and mathematics, enriching both fields through creative exploration and collaboration.

Activities "TO TRY"

I have tried a few of the activities outlined in the paper. 

1. How can a "hexastar" be folded at the vertices to form a cube? an octahedron? two tetrahedra?

I used some toothpicks and Play-Doh to make the structure of the hexastar and then tried to make a cube, an octahedron, and two tetrahedra by folding the vertices and connecting them with the Play-Doh.

2. Try to make a cube with a partner, each person using the thumb and first two fingers of each hand. 

3. Walk the borders of a square forward and backward turning through the internal angle how many rotations will you perform.

 To walk the borders of a square forward and backward, turning through the internal angles, I performed a total of 8 '90-degree' rotations. 

Stops: 

1. Each dance tradition has its own characteristic way of using mathematical concepts. (pg. 80)

The diverse ways dance traditions incorporate mathematical concepts illustrate the universal language of mathematics and its profound influence on human expression and creativity. Like in Indian classical dance forms Bharatanatyam uses mathematical structures, such as Fibonacci sequences or geometric progressions, enhancing the aesthetic appeal and symmetry of the performance. whereas in African dance tradition, dancers convey mathematical concepts of symmetry, balance, and harmony through rhythmic patterns and spatial arrangements, reflecting the interconnectedness of their community and environment.

Questions:

How can educators in Asian culture, where dance holds significant cultural and artistic value, incorporate dance as a medium for teaching mathematical concepts? Furthermore, how can parents be actively involved in recognizing the mathematical language inherent in dance and its potential to enhance their children's mathematical understanding?

Another question is how might we assess student learning and understanding when incorporating dance into math lessons. What types of assessments would be appropriate for evaluating both dance skills and mathematical comprehension?