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.