Yu's Math Tent

Doolittle, E. (2018). Off the grid. In Gerofsky, S. (Ed.), Geometries of liberation. Palgrave.  https://doi.org/10.1007/978-3-319-72523-9_7 Summary “We must acknowledge that any grid, straight or curved, is an imposition of our own invention for our own custom or convenience” (p. 111) . The article exemplifies various examples of how human beings use grids to develop civilization in hegemonic ways, and we can also discover, through scenes of everyday life, how the grids reflect changes imposed on indigenous people and the environment by colonialists. This is achieved by equalizing, subordinating, and imposing a uniform grid geometry on the unique life, quality, and character of specific places. In contrast, if grids represent a human's sense of mastery, non-Euclidean geometry provides an alternative approach to the problem. Riemannian geometry offers a perspective, suggesting that none of those grids is inherently better than the others. Additionally, following the Copernican Princ...

The sketch depicts the scenery visible from the window of my room. Actually, before the sketching, I almost imagine the strict straight lines, right angles, and different strict geometry that relate to artificial things. I guess because these structures and patterns are easier for architects to build buildings, and also present humans' inherent inner part of following norms and rules. While in the process of sketching, I can clearly feel the inclination to use a ruler (but I didn't use it) to draw straight lines and ensure the accuracy of every right angle for the artificial elements on the paper. However, when depicting biological elements such as trees, seagulls, or grass, I allow myself to draw them freely and flexibly. I understand that regardless of whether they grow in unusual angles or directions, they all appear natural and make sense.  

Although I have read the article by Angelika Stylianodou & Elena Nardi (2019), I decided to experiment by slicing an apple, a banana, and two sweet peppers. I cut them from different parts, including the top, middle, and bottom. I wanted to observe if there were any variations in their structures. The results of this activity prompted me to reconsider the relationship between the function and shape of the inside/outside of these plants. I speculate that they grow into different shapes due to varying methods of nutrient absorption and their distinct fruiting types. For instance, the core of an apple resembles its flower, divided into five pieces and resembling a star. In Activity 2, I folded a hexaflexagon, and it took me an hour to figure out the process without using the template. Initially, I folded it into various triangles, including the right triangle and isosceles triangle. After watching a video, I realized that I needed to use an equilateral triangle to complete it.   ...

Angelika Stylianodou & Elena Nardi (2019), Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils Summary The research aims to respect students' learning diversities and create a tolerant and comprehensive learning environment. The researcher designed a small experiment based on Vygotskii’s theory of mediation (1993) involving the creation of Shape X(a circle minus a circular segment). The observation focused on how tactile teaching strategies ensure all students have equal learning opportunities and engage in the class. The study also explores how visually impaired (VI) students and sighted students construct math meanings through the process. The conclusion indicates that VI students and sighted students have different cognition in understanding the shape. However, through the teacher’s attuning, the consequence is that both VI students and sighted students obtain positive influences, highlighting the VI student’s discovery and even ma...

Goldin-Meadow et al (2009). Gesturing gives children new ideas about math. Summary The research aims to explore the mechanism by which gesturing plays a role in learning. The study involves observing differences in problem-solving among 3rd and 4th-grade students through a pretest, math lesson, and posttest. The researchers presented a specific question type to the participants: 3+2+8= __ +8. The participants were divided into three groups, each assigned a specific gesture, and provided with the same verbal instruction: "I want to make one side equal to the other side." This aimed to observe the effectiveness of verbal collaboration with the gesture. The three groups are as follows: 1. Correct gesture indicated with a V-hand and pointing to 3+2 2. Partially correct gesture indicated with a V-hand and pointing to 2+8 3. No gesture The results indicate that children instructed to use a fully correct rendition of a particular problem-solving strategy (grouping) during a math les...