Hello, everyone.

In this article, I would like to introduce the content and thoughts regarding a paper discussed in our English Literature Seminar.

• Paper Title: Teaching with embodied learning technologies for mathematics: responsive teaching for embodied learning.

• Journal: ZDM

• Volume and Pages: Vol. 52 (7), 1307-1331

• Authors: Virginia J. Flood, Anna Shvarts & Dor Abrahamson

• Year of Publication: 2020

The following is an overview of this paper. Please read it if you are interested.

In modern educational environments, the use of body-centered technology in learning mathematics is increasing, but how educators specifically utilize these systems is not yet fully understood. This paper utilizes Ethnomethodology and Conversation Analysis (EMCA). EMCA is an approach that analyzes the structure of human interaction and communication in daily life in detail. Through this ethnomethodology and conversation analysis, we have summarized three multimodal approaches to explore how educators react to students’ embodied ideas and transform sensorimotor patterns into mathematically significant perceptions. Specifically, we examine how students express their thoughts through gestures, how to confirm students’ understanding using multimodal methods, and how to collaboratively construct embodied ideas with students. These approaches suggest the potential to create learning opportunities and promote embodied responsive teaching.

Furthermore, based on the methods of responsive teaching (the process of advancing while adjusting learning activities to support students’ individual needs and the growth of their independence) and clinical interviewing (an evaluation procedure used in psychiatric practice to collect information necessary for diagnosis and treatment through personal interaction between the clinician and the client), we clarify strategies for educators to effectively engage with students’ embodied ideas and provide specific examples through a case study using the MIT-P (Mathematics Imagery Trainer for Proportions). The purpose of this study is to understand how educators respond to students’ diverse forms of expression in technology-leveraged embodied learning environments and how those responses promote mathematical discovery.

The study participants were 23 students attending schools in urban California, who engaged in learning activities with four teachers who were researchers in mathematics education design. The students were between 9 and 12 years old, and the classes used the MIT-P, an embodied learning device for mathematics. This device works by operating a remote control to move a cursor on a computer screen, and the screen turns green when a specific ratio is achieved. Each session was conducted in a 70-minute task-based tutorial interview format, during which students learned about ratios and proportions using the MIT-P.

As a specific example of utilizing MIT-P in this study, Student A was operating the remote control to achieve a 1:2 ratio, but it did not go well at first. When the teacher observed, Student A’s remote control movements were inconsistent, and the student did not understand at what height to stop the cursor. At this point, the teacher had Student A reproduce the remote control’s movement through gestures and explain their thoughts in words.

In that process, the teacher noticed that Student A’s gestures and explanation did not match. It was discovered that when Student A lifted the remote control, they were not correctly perceiving the height of the cursor. Therefore, the teacher provided specific feedback again and demonstrated the correct movement. Following this feedback, Student A corrected their gestures when operating the remote control and eventually was able to achieve the 1:2 ratio accurately.

Based on this case, it was shown that by having students express their thoughts through gestures, the learner’s understanding deepens, and by educators providing appropriate feedback on the spot, the learning effect improves. Furthermore, it was found that by using multimodal methods, students’ understanding can be accurately grasped and appropriate support can be provided. Moreover, it was confirmed that by educators and students jointly constructing embodied ideas, students’ mathematical discoveries are promoted and learning outcomes are improved.

The following are my thoughts.

The reason I chose this paper is that it explores the possibilities of embodied learning through the lens of qualitative analysis. Although I rarely use qualitative analysis in my own research, I wanted to understand how qualitative analysis is used in embodied learning and gain new hints. At the same time, the focus of this article is on the practical utilization of embodied learning in the context of mathematics learning, based on specific efforts in educational and learning settings. I think it is beneficial in terms of understanding the potential of embodied learning. While there are many XR technologies that support the utilization of embodied learning, I believe that observing specific utilization in educational settings is the most effective and direct way to make embodied learning truly practicable in the classroom.

However, I believe there are several limitations to this paper. First, the focus of this paper is on the learner’s performance when learning the concepts of ratio and proportion in a classroom mathematics learning situation, in order to explore how learners learn. This is done through video-recorded multimodal analysis. While it is stated that learners are learning through physical actions such as gestures, there is no deep examination of why learners take such actions. Second, the analytical method used here is EMCA, and it can be said that it is limited only to the qualitative analysis of learner performance. This paper states that it analyzes learners’ embodied ideas and thoughts based on their words, gestures, and demonstrations, but because the interpretation utilizes ethnography, I feel a weakness in the objectivity supporting it. Finally, while the use of responsive teaching methods and clinical interviewing methods are mentioned as ways to explore learners’ thoughts in the learning process of mathematical knowledge, they are not sufficiently explained in this paper. At the same time, since this article ultimately intends to present the utilization of embodied learning in mathematical knowledge and the findings obtained therefrom, it is unclear whether it is appropriate to limit it to learners’ ideas.

While I feel these limitations exist, this study is an important step toward deepening the understanding of embodied learning in educational settings, and more research is needed in the future. In particular, exploring learners’ physical actions and the motivations and intentions behind them more deeply may lead to improvements in educational methods. I also hope that a more comprehensive and practical educational strategy will be developed through the fusion of EMCA, responsive teaching, and clinical interviewing. As research in this field progresses, it is expected that insights will be gained for educators to maximize students’ learning effects using technology.

(Written by: Li Tang, 2nd-year Master’s student)