Week 3

Reading Reflection on "Sustainability Education's Gift: Learning Patterns and Relationships" 

by Dilafruz Williams

This article deals with the pressing challenges of sustainability. It has been seen that traditional schooling methods, their mechanistic and technocratic systems are away from a sustainable approach. We need a shift from these methods and systems by integrating principles of systems thinking and holistic learning. David Orr and Fritjof Capra are the most important people who have postulated systems thinking and holistic learning as a means to shift our modern culture to new models and metaphors for a more sustainable world. Sustainability education would need to include the following three understandings embedded in such thinking and learning:

1. Wholeness Principle: Living systems exhibit unique properties as a whole, emerging from interactions among their parts. Understanding individual components requires grasping the entire system, and emphasizing the importance of contextual thinking in systems.

2. Network Dynamics: Life operates as interconnected networks at all levels. Nature lacks hierarchies, relying instead on networks nested within networks, forming a complex web of life.

3. Nonlinear Ecology: Relationships within ecological communities involve nonlinear dynamics and multiple interdependent feedback loops. To understand life's essence, focus on processes and relationships among living organism components.

 For this sustainability, the author presents a case study from Poland, Oregon, where the Learning Gardens model is sowing the seeds of "change". This study is based on students from kindergarten to eighth grade, where they are not just learning from textbooks but actively engaging in the process of growing, harvesting and cooking food. Additionally, the Learning Gardens program utilized two pieces of land where students, including those from diverse and low-income backgrounds, learned about growing, harvesting, and cooking food while integrating various subjects. Both locations foster students' appreciation for the environment, enhance their knowledge of the cultivation and applications of edible and medicinal plants, and provide education on nutrition and the advantages of adopting healthy eating habits. It also helps them to understand multicultural values, learn through interdisciplinary approaches, promote connections between different generations and embrace multisensory learning. Furthermore, students gain a sense of connection and empathy by participating in service-learning projects, such as working at a shelter for the homeless, encouraging them to think critically about the importance of local food production amid global challenges in energy and transportation.

Stop 1

"As I was walking down by the creek at JEAN’s farm, I noticed my good spider friend looking worried. I asked what was the matter and Spidey (the spider) told me that everywhere he tried to make his web someone would accidentally or purposely knock it down. This was bad because spiders’ webs are not only their homes, but also help them catch their food, which are nasty bugs like mosquitoes, aphids and other bugs that are bad for our gardens."(page 47).

When I went through these lines, it was really striking because as teachers when we teach something to our students, they connect it with their own life experiences. Children are curious about nature and they see everything like insects and plants as their friends. When a spider got into a problem, he identified it and connected it with his previous knowledge and grasped patterns and relationships within the ecosystem. It shows a holistic understanding of nature and the interconnectedness of components.

Stop 2

"They are clearly in need of a good meal, and if they could afford it, they wouldn’t be there…. When we serve, we show people that we care about them. When people know that someone cares about them, they are generally happier and it gives them hope."(page 47)

These lines are filled with emotions and empathy of the students towards everyone around them. I think when students see and realise the issues around their surroundings they become more empathetic and ready to help. This line might evoke a pause because it captures a significant moment of realization for the students. It signifies a transformative understanding that goes beyond academic knowledge, touching on the emotional and social aspects of learning. The awareness of societal issues seems to have triggered a sense of responsibility and a willingness to make a positive impact on them.

These pictures are from my school in India where students grow their own food for their noon meal. They use the school garden for cultivating vegetables and different herbal plants.

Question

How can educators create effective strategies to instil empathy, foster social interconnectedness, and nurture a sense of responsibility among children?

Reference

Williams, D. (2008). Sustainability Education’s Gift: Learning Patterns and Relationships. Descriptive Reports.

WEEK 2 Reading reflection on  

"TACTILE CONSTRUCTION OF MATHEMATICAL MEANING: 

BENEFITS FOR VISUALLY IMPAIRED AND SIGHTED PUPILS" by 

Angeliki Stylianidou, Elena Nardi 

Summary

This reading discusses a study focused on integrating tactile mathematics into a grade 5 classroom and promotes inclusivity for visually impaired and sighted pupils. The study is based on drawing theoretical frameworks including Vygotskian sociocultural theory and the theory of embodied cognition. The mathematical task highlighted in this paper involves the teacher asking the class to close their eyes and describe two shapes, one of which is referred to as "Shape X." These shapes were constructed using Wikki Stix, a flexible teaching tool made of wax and yarn suitable for VI pupils' learning. The focus is on Shape X, and during the task, the teacher also provides circles of various colors and sizes, prompting the class to identify differences between Shape X and the circles. This study records the contribution of two students in 2 episodes, Zak and Luke, one is visually impaired, and the other one is a sighted pupil. 

Episode 1: Zak's Tactile Exploration: 

Zak, a sighted pupil, explores Shape X through touch and vision. He constructs different meanings of Shape X through touch and vision. While he confidently states the existence of a straight-line segment when he feels the shape with his hands, he does not see a straight-line segment when he sees the shape with his eyes. His tactile experience reveals a straight-line segment, contrasting with uncertainty when visually inspecting the shape. The study interprets this through Vygotskii's theory of mediation, emphasizing the impact of different sensory tools on mathematical constructions. Zak's positive response to tactile exploration highlights potential benefits for all students. In the evaluation form of the lesson, Zak wrote that he liked “the hidden facts on the shapes” 

 Episode 2: Luke's Practical Insight: 

Luke, a visually impaired pupil, differentiates between Shape X and a circle through touch. He makes different meanings of the circle and of Shape X. He feels that the circle is going to roll more – while Shape X is not; it is instead going to “bob up and down. The study attributes Luke's varied constructions to different material tools, emphasizing the interplay of sensory and material factors in mathematical understanding. By inviting the entire class to experience mathematics through touch, the study challenges ableism, fostering a more inclusive and diverse mathematical environment. It sets the stage for a future where tactile learning is not just an accommodation but a fundamental approach to teaching mathematics. 

Stop 1 

"The hidden facts on the shapes"(Stylianidou, A., & Nardi, E. 2019, p.348) .

In this study, Zak mentioned this in his evaluation form. As a math teacher, this statement is a thought-provoking one. In Geometry, there are different shapes which involve different hidden properties which we cannot see directly. As a math teacher, this might resonate as an encouragement for students to go beyond surface-level observations and engage in deeper analysis of shapes. It prompts students to think beyond what they see initially. 

Stop 2 

"Luke makes different meanings of the circle and of Shape X through touch. He feels that the circle is going to roll more – while Shape X is not; it is instead going to “bob up and down."(Stylianidou, A., & Nardi, E. 2019, p.348). 

Luke's description of the circle as feeling like it will "roll more" indicates an understanding of spatial properties. As a math teacher, this observation aligns with concepts related to shape dynamics and spatial relationships, providing insights into how students intuitively grasp these ideas through touch. His words like "roll" and "bob up and down" suggest a kinesthetic understanding of shapes. This emphasizes the value of kinesthetic learning in mathematics, where students physically interact with shapes to enhance their understanding. Math teachers might reflect on incorporating more hands-on, movement-based activities to reinforce geometric concepts. 

Questions

1. How might including tactile mathematics tasks benefit all students in your math classroom, including those with visual impairments? 

2. How can you encourage your students to explore mathematical concepts through touch, like Luke's, to enhance their understanding? 

Reference 

Stylianidou, A., & Nardi, E. (2019). Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils. Journal of Inclusive Education in Mathematics. 

Activity

Hexaflexagon

Making a hexaflexagon was a cool math activity that helped me understand shapes better. Watching videos gave me the basic idea, but actually folding and flipping the hexaflexagon with my hands made it more real. Even though I struggled at first, every attempt taught me something new. Creating the hexaflexagon changed it from something in my head to a real thing I could play with.

This hands-on experience made geometry more fun and easier to understand. It wasn't just about learning angles and folds; it was like playing with a math toy. Now, I'm thinking about how this kind of activity could help other students too. Touching and moving real shapes might be a better way for everyone to learn, especially students who can't see or hear well. It could make math class more fun and fair for everyone. Moreover, we can make the students understand math concepts more clearly. When I was teaching in India, students loved to do paper crafts and 3D shapes like pyramids, cones, rectangular prism and cubes. These hands-on activities make them engage in math class.

 

 

 

 

 

 

 

 

 

 

 

 

 

Reflection on the Research Report “Gesturing Gives Children New Ideas About Math”

by Susan Goldin-Meadow, Susan Wagner Cook, and Zachary A. Mitchell

 

Mathematics is often considered as a difficult subject for most students I have seen. As a math teacher, I have witnessed this situation where students have difficulty in solving problems and analyzing math concepts. This research “Gesturing Gives Children New Ideas About Math” is based on the significance of gestures in math teaching and learning. The study mainly focused on fourth-grade students, and they were provided with a set of problems. Researchers studied students' responses, hand movements, gestures, and ways of solving problems by placing their fingers. Some of the students used different correct gestures for solving the problem and they got the correct answers, some of the students were not showing the correct gestures and even if they got answers, the others did not show any gestures and did not get the answers. Students who showed correct gestures learned more than others in the class. Moreover, these experimenters state that gestures are not only useful for communication but also beneficial for mathematical learning. The study's implications extend beyond the traditional learning methods, and it proposes that by instructing learners on how to move their hands, educators may lay the foundations for new knowledge.

Stop 1

“Can the children’s hand movements really be considered gestures? Gestures tend to be meaningful movements produced along with speech” (Goldin-Meadow, 2003; McNeill, 1992,p.271).

When I read the article, I was struck with this question. Sometimes it is difficult to consider students' gestures as we do not know the nature of gestures. Traditionally, it is strongly connected to the spoken language. In this part, we as math teachers need more clarification about the nature of gestures.

Stop 2

“When comprehending an action word that is semantically related to a body part (e.g., lick,pick, kick), the motor area in the brain that is associated with that part (the face, hand, or leg area, respectively) is routinely activated (Pulvermuller, 2005; see also Pulvermuller, Hauk, Nikulin,& Ilmoniemi, 2005; Pulvermuller, Shtyrov, Ilmoniemi,2005). (Goldin-Meadow et al., 2009, p. 271).

 

When I read about this, it had some connection with my life as a math teacher. One of my students in grade 6 was always active in class and always solving problems by shaking legs and hands. In the first week of the class, I was quietly surprised by his actions. But he found correct answers. As I previously learned in my BEd class, learning always involves different bits of intelligence like spatial intelligence, musical intelligence, kinesthetic intelligence and so on. When I read this article, the learning involves gestures that can connect with kinesthetic intelligence, and it is especially useful for mathematics learning. However, as a math teacher, we face difficulties in implementing and teaching math with useful gestures. Only a small percentage of the class effectively uses gestures while others see math as just an abstract subject which does not involve any movements, gestures and so on.

 My questions are:

·       How might the findings of this study be incorporated into our mathematics teaching to enhance every student's engagement, promote a deeper understanding of math concepts, and contribute to a positive learning environment for every student?

·       Can you recall any instances in your classroom where gestures played a significant role in your understanding of the lesson?

Reference

Goldin‐Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272. https://doi.org/10.1111/j.1467-9280.2009.02297.x