EDCP551 Final project draft 1

Group members: Hsuan-Yu(Sandy) and Natalie

Project name: Appreciation of embodied mathematics through triangular numbers among sport stacking

Grade: 6th

Brief introduction:

    Mathematics has long been considered a subject that is dull and boring, with students frequently questioning its application in daily life (Dietaker, 2015). To enhance students' interest in Mathematics and help them recognize its use in everyday life, particularly in the Grade 6 unit on Numbers and Patterns, two mathematical activities—stacking sports and human pyramid—will be conducted as a continuation of the topic.

    Sport stacking was started in Southern California, USA in 1980. In 2001, the World Sport Stacking Association (WSSA) was founded, which established universal rules and standardized the activity forms of 3-3-3, 3-6-3, and Cycle (Chang, 2020). They not only hold world championship contests but also promote sport stacking activities as part of over 47,000 school and club programs in 54 countries worldwide. Additionally, my graduating class also performed a sport stacking routine with music at the graduation ceremony two years ago, introducing the new idea of its anticipated future development and variations. Therefore, one of our aims is to provide ideas about incorporating this physical activity into mathematics education, helping students explore alternative learning possibilities.

    According to "Math Makes Sense" Grade 6 Unit 1 Lessons 1-2 (Appel et al., 2009), students should have grasped the concept of functions and be able to identify patterns from tables. Furthermore, we aim to introduce triangular numbers, a special number sequence, to students with the strategy toolkit in Lesson 3 by cup stacking. In the mathematics lesson, instead of directly presenting the set of triangular numbers, students are given cups and encouraged to use the stacking sports (cup stacking) to explore triangular numbers by examining the number of cups arranged in each row in groups. After determining triangular numbers through the input-output table they have learned, students are prompted to identify the pattern to quickly ascertain the number of cups needed for a specific row. Having noticed the pattern in triangular numbers, students are then allowed to build their tallest towers with the requested number of cups. In this way, students can apply what they have learned about patterns in Mathematics in practice, and even better, create a giant art piece through cup-stacking. 

    Aiming to enable students to discover the diverse range of artistic expressions that can emerge from the same body of knowledge, students are encouraged to experience embodied mathematics by creating a human pyramid. Unlike cups, which maintain fixed shapes and cannot be bent, humans are flexible and can assume various forms by positioning their bodies at different angles. The human pyramid is an early form of physical activity that embodies the spirit of collaboration, patience, and coordination within a group. A few years ago, I stumbled upon the Department of Physical Education at the National Taipei University of Education, where they incorporate the human pyramid into their department's traditional performance. Through rigorous training, they delivered impressive performances at the annual Academic Year Sports Show. Even though I have never personally participated in this activity I was stunned by its beauty.

    However, due to changes in the era and an increased emphasis on child safety and care, it has become rare to see the human pyramid in contemporary school physical education (PE) programs. This traditional skill has gradually been replaced by sport stacking because of their similar characteristics such as sportiness and entertainment value. Hence, we would like to preserve this traditional art and create a challenge related to the human pyramid, enabling students to explore the wide variety of shapes that can be formed using the same knowledge of mathematical patterns(Mortimer, Krysztofiak, Custard & McKune, 2011). Through this activity, it is hoped that students will not only appreciate the beauty of mathematics and its integration into different disciplines through embodied mathematics but also experience growth in their social, emotional, physical, and cognitive development (Riley et al., 2017).

References:

Correlation between mathematics activities, math interest and skills

Fisher, P. H., Dobbs-Oates, J., Doctoroff, G. L., & Arnold, D. H. (2012). Early math interest and the development of math skills. Journal of educational psychology, 104(3), 673.

 The study investigates the relationship between math interest and skills. The result indicated that with more time spent in mathematics activities, their interest towards mathematics increased , with a result of higher math skills. The reciprocal relationship between math interest and skills will start as early as preschool.

 

  

Advantage of outdoor mathematical experiences

 

Moss, M. (2009). Outdoor mathematical experiences: Constructivism, connections, and health. Tasks in Primary Mathematics Teacher Education: Purpose, Use and Exemplars, 263-273.

Aside from suggesting the definition and reasons of outdoor mathematics, recommendations regarding outdoor mathematical tasks are also provided in this paper, such as Geometer’s scavenger hunt and outdoor graphing.

Riley, N., Lubans, D., Holmes, K., Hansen, V., Gore, J., & Morgan, P. (2017). Movement-based mathematics: Enjoyment and engagement without compromising learning through the easy minds program. EURASIA Journal of Mathematics, Science and Technology Education, 13(6). https://doi.org/10.12973/eurasia.2017.00690a

The results elucidate that both teachers and students experienced increased positive feelings, enjoyment, and enthusiasm for mathematics. Additionally, it enhanced opportunities for students' social, emotional, physical, and cognitive development. An interesting aspect is that students perceive their teachers' positive response to the plan, likely due to trying something different, adopting a new approach to teaching, or experiencing fewer discipline problems. Furthermore, students feel that they are using their bodies to engage with mathematics, attributing their improvements to the diverse presentation of learning materials. They can collect, analyze, and interpret data independently, facilitating their understanding of the subject, especially when oral explanations may be difficult to grasp.

Experience on cup stacking

 

Lloyd, R. J., Whitley, J., & Olsen, S. (2013). Promoting ‘comprehensive school health’in teacher education: From consumers of knowledge to champions of health. Canadian Association of Principals Journal.

 This paper explores the experience of pre-service teachers organizing various health-promoting projects, such as sport stacking cups and health workshops. Feedback from both organizers and participants are included.

Mortimer, J., Krysztofiak, J., Custard, S., & McKune, A. J. (2011). Sport stacking in auditory and visual attention of grade 3 learners. Perceptual and Motor Skills, 113(1), 98–112. https://doi.org/10.2466/05.11.25.pms.113.4.98-112

This study aimed to investigate the effect of sport stacking on visual and auditory attention in Grade 3 learners. The research found that sport stacking improved the participants’ ability to stay on task (consistency), to remember and follow rules under high demand (steadiness), to reduce impulsivity (prudence), and to control fine motor activity. Furthermore, through the different modes of sport stacking, ranging from easy to difficult, participants, when exposed to more complex learning tasks, were likely to perform better compared to their performance following exposure to low-complexity tasks. This finding is particularly interesting given that the school teaching environment typically operates under low-demand conditions. There may be a potential mismatch between the improvements observed following a sport stacking intervention and the low-demand nature of the school environment.

Academic performance on small space psychomotor activities

 

Chang, L.-W. (2020). Effects of Sport Stacking Teaching Program on Attention for The ADHD Students in Elementary School (thesis). Department of Special Education, National Taiwan Normal University, Taipei City. Retrieved 2020, from http://doi.org/10.6345/NTNU202000653.

This study aims to investigate the effect of the sport stacking teaching program on the attention performance of three ADHD students. The results show that the intervention of sport stacking improved at least 6 of the 7 scores of the Tien-Character Attention Test during the acquisition phase. It indicates that a sport stacking teaching program could improve the attention performance of elementary school students with ADHD.

Kalyn, B., Paslawski, T., Wilson, C., Kikcio, T., & MacPhedran, D. (2007). The effect of small space physical activity on school performance. Dr. Sterling McDowell Foundation for Research into Teaching. Project ft, 165.

37 Grade 3 children participated in the study which explores the relationship between academic performance and small space psychomotor activities (Cup stacking, Brain Gym, juggling and rhythmic ribbons). Although there is no significant difference on students’ academic performance through cup-stacking activities, they show improvement in the performance in both activities and academics and negative behaviours are reduced.

 

Cup stacking related activities in learning arithmetic sequence

Domu, I., & Mangelep, N. O. (2020, November). The Development of Students’ Learning Material on Arithmatic Sequence Using PMRI Approach. In International Joint Conference on Science and Engineering (IJCSE 2020) (pp. 426-432). Atlantis Press.

The research suggests using an approach named Pendidikan Matematika Realistik Indonesia (PMRI) to help students learn arithmetic sequence. From arranging the pyramid using matches and ice cream cups, finding patterns of lines from the pyramid, students are asked to find the arithmetic sequence pattern from the arrangement.

The benefit of using instructional materials’ for interdisciplinary learning

Lo, I., & Chen, C. (2023). Timing of instructional materials and types of gameplay for interdisciplinary learning: A comparative experimental study. Research in Science & Technological Education, 1-18. https://doi.org/10.1080/02635143.2023.2209842

The research articulates that instructional materials can play an important role in influencing students’ emotional experiences. Moreover, emotions may impact all forms of memories and contribute to learners’ motivation. Therefore, if the timing of using instructional materials is appropriate, it may help pupils achieve better comprehension, retain academic knowledge, foster a sense of progress and confidence, and serve as a strong strategy for supporting interdisciplinary learning.

Roth McDuffie, A. M., & Mather, M. (2006). Reification of instructional materials as part of the process of developing problem‐based practices in Mathematics Education. Teachers and Teaching, 12(4), 435–459. https://doi.org/10.1080/13450600600644285

The reification of instructional materials was a gradual, incremental process. When problem-based tasks became a regular part of instruction, rather than an occasional insertion, materials were no longer seen as the foundation from which to build a lesson, but rather as tools and raw materials to use for learning. Students consistently experienced mathematics as thinking through problems, reasoning, and figuring out solutions.

The others

楓林, 陳(1938).徒手疊羅漢.天津耀華學校.

The book introduces various types of human pyramids (human stacking) and discusses their significance and values in health and physical education. This sport can enhance participants' courage and cultivate various attitudes such as calmness, collaboration, and patience.

Appel, R., D’ Amour, L., Brown, T., Jeroski, S., & Sui, G. (2009). In Math Makes Sense 6. essay, Pearson.

This is the textbook we are going to take reference from.

Dietiker, L. (2015). What mathematics education can learn from art: The assumptions, values, and vision of mathematics education. Journal of Education, 195(1), 1-10.

This study discusses the benefit of teaching mathematics through storytelling.