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What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education - Week 7 Summary

The article "What Math Education Can Learn from Art" by Leslie Dietiker explores the potential of applying artistic elements to mathematics education to enhance student engagement and learning experiences. The author begins by highlighting the uninspiring nature of traditional mathematics classrooms, emphasizing the need for a shift towards a more stimulating and creative approach to teaching math. Drawing parallels between mathematics and art, Dietiker suggests that mathematical stories in classrooms can be analyzed similarly to literary narratives. Just as in literature, engaging stories in mathematics should have a point, offer anticipation, and avoid predictability to maintain student interest. By viewing mathematics curriculum through a narrative lens, educators can potentially unlock new artistic tools for teaching and provide students with fresh mathematical opportunities. The author explores the idea that mathematical textbooks can be read as stories , with each stat...

Week 6 Make Music Visible, Play Mathematics-- Summary

This article introduces a workshop based on interdisciplinary and interactive activities. Through these activities, the relationship between mathematics and music becomes visible. This approach encourages music teachers to adopt a geometric approach for their students to learn music theory. I t begins by discussing the historical perspective on this relationship, emphasizing the role of counting, ratios, and mathematics in music theory. The article challenges the notion of connecting the creative art of music with the logical framework of mathematics, asserting that music goes beyond mere notes and beats to encompass the creation process.   By involving students in hands-on, multisensorial activities, educators can demonstrate the parallel application of complementary viewpoints in mathematics and music.   This workshop is based on chromatic scale and chromatic scale circles ( If we put these 12 notes evenly distributed around a circle, we obtain what is called “chromatic circ...

Week 3 Sustainability Education’s Gift: Learning Patterns and Relationships- Summary

This case study focuses on the Learning Gardens model in Portland, Oregon, where students learn to grow, harvest, and cook food using a multicultural, interdisciplinary, intergenerational, and multisensory approach. The program addresses urgent issues such as increasing hunger among children, rising obesity and diabetes rates, academic performance gaps, and urban students' disconnection from nature and food sources.       The Food-based Ecological Education Design (FEED) program operates in eight Portland Public Schools, involving 3,500 students, and includes the Learning Gardens program on two parcels of land. Students from diverse backgrounds participate in growing food, building gardens, and learning various subjects simultaneously.       The article also presents student writings reflecting their learning in patterns and relationships, a critical aspect of sustainability education's gift. The students' writings demonstrate their ability to connect co...

Week 2 Tactile Construction of Mathematical Meaning: A Study with Visually Impaired and Sighted Pupils——Summary

This research  explores the benefits of tactile construction of mathematical meaning for both visually impaired (VI) and sighted pupils in mainstream primary mathematics classrooms. The study is grounded in a sociocultural theoretical framework drawing upon Vygotskian sociocultural theory of learning , Sfard’s discursive perspective , the social model of disability , and the theory of embodied cognition . The authors aim to address the affective and social limitations frequently experienced by VI pupils through problematic accommodations and to enrich the mathematical opportunities for sighted pupils through multimodal tasks. The study was conducted in four UK mainstream primary mathematics classrooms, involving pupils aged 6-10, and included VI pupils, teaching staff, and sighted pupils. Data collection methods included observations of mathematics lessons , individual and group interviews with pupils and teaching staff, transcripts of teaching staff contributions, photographs ...

Week 1 Seeing the graph vs. being the graph——Summary

  In this chapter, the author presents the findings from the first two years of a multi-year study into the diverse expressions of secondary students' gestures while tasked with describing mathematical graphs. Existing studies have shown that abstract mathematical concepts are necessarily grounded in our physical, embodied experiences of the world – and that, in fact, the historical origins of these abstract concepts always emerge from empirical, sensory observations (Radford 2009, Arzarello et al. 2009, Nemirovsky & Ferrara 2009, Tall 2004). Thus, as a linguistic researcher in mathematics education, the author is interested in students’ use of gestures in communicating about mathematical graphs. Based on the authors' informal observations, how students describe graphs through gestures in the classroom is very different. After experiencing an exploratory study with colleagues and family members as study participants, t he researcher conducted the study in schools and aske...