Week 7 Response on The role of gestures in the mathematical practices of those who do not see with their eyes

Summary:

By exemplifying through three examples of gesture used in participants who have visual disadvantages, the paper discusses the role of human body, the concrete artifacts and signs created to convey math ideas. It argues cognition is embodied and situated in the activities, and comes and been remembered throughout life and learning, especially during semiotic resources, such as spoken and written languages, drawing, gestures and mathematical representation systems. Based on our study of these examples, the authors suggest that movements represent imaginary re-enactions of historically observed events and appear as symbolic abstractions in educational contexts, playing a central role in the sense-making processes associated with the interpretation of conceptual significances.

Stop 1: quality education in inclusive classrooms

I am really curious about the inclusive educational institutions regardless of any special educational needs in Canada. Personally, I see the urgency and necessity of providing education for learners with special learning needs within the regular classrooms. From my teaching experience, I have students with emotional disorder, dyslexia, and ADHD in a grade 4 classroom. I also see the difficulty of classroom management and course preparation from teachers’ point of view. But I don’t have experience learning or teaching in such inclusive classroom before I become a teacher, thus I feel I am not very well-prepared and ready to produce efficient teaching.

Question 1:

Do you have experience teaching students who do not see with their eyes? If yes, could you introduce some strategies you adopt to foster learning? If no, what’s your opinions on inclusive education in math classroom? Do you think it increase the difficulty in instruction?

Stop 2: the role of gestures as instruments for both communication and cognition

I was impressed by how these diverse categories of gesture types relate to mathematics representations. I was amazed by how gestures become tools for creation and communication, and suggest understanding. I felt the sensory experience are critical and inspiring not only for blind students, it could also be associated within regular math classes.

Question 2:

Do you know any resources which promote sensory experience in learning? Do you think sensory experience in special education is worth introducing to student teachers, as they are comparable and transferable in interdisciplinary instruction?

Stop 3: mental imagery and the multimodal cerebral activity

In the article, the third participant Edson, who lost the sight later in life, he seems mentally simulate the process of folding in his description of symmetry. His description indicates a visual sense and some mental imagery with depiction and proposition. It is likely that Edson re-enacts the experience of seeing through his eyes mentally: at the very least he describes having a perceptive state probably consistent with seeing it visually previously.

Question 3:

Do you introduce mental imagery in math teaching? What do you think about the advantages of using multimodal cerebral strength?

Reference:

Healy, L., & Fernandes, S. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies In Mathematics, 77(2-3), 157-174. doi: 10.1007/s10649-010-9290-1 

Week 6: Reading Response on Teaching Mathematics in Two Languages: A Teaching Dilemma of Malaysian Chinese Primary Schools by Chap Sam and Norma Presmeg

Summary

The paper discussed a teaching dilemma in the Malaysia Chinese primary schools after a new language policy launched in 2003 that using English as the language of instruction of mathematics in all schools. Due to the complex sociocultural and linguistic condition, teachers spent considerable amount of time translating and code-switching mathematical terminology between English and Mandarin frequently, especially in the low-performance classes. The paper suggested to test the efficacy of bilingual versus monolingual teaching of mathematics in a Malaysian context.

Stop 1: a national move of switching instructional language

Initially, the language medium of instruction of mathematics was Malay between the diverse ethnic groups. With the concerns of decline of English language proficiency and for the purpose national development, Malaysian government took a brave move of switching instructional language from Malay to English. Although receiving strong oppositions from Chinese communities, Chinese students ended up taken two subjects: Mathematics in English and Mathematics in Mandarin. I understand the starting point was to conserve language and culture, but would extending learning hours become an advantage or a burden on students and teachers? And the learning outcome are necessary optimized?

Question 1:

Do you think language shape people’s angle of perception in acquiring knowledge, especially in the STEM subjects?

Stop 2: code-switching in multi-lingual classroom

Growing up in a Mandarin-speaking family, and moving to Canada at 16 to English-speaking environment. I have experienced similar code-switching period, as to translate all the information around into English, in daily activities and in reading textbooks. I felt I picked up piece-wise information, and consistently added new mathematics registers, replaced unfamiliar notions with other familiar words etc. In a word, the learning journey looks like unfold and wipe up the ambiguity into clear vision. Standing from students’ point of view, I wished I could have such a linguistic practitioner as instructor when faced with new culture.

Question 2:

Do you think inter-changing languages during everyday instruction is helpful for ESL and multi-lingual students, for their math thinking and reasoning? Or would you stick to one language to deepen mathematics perception?

Stop 3:  language habit observed from the feedbacks from teachers and students 

(Lim and Presmeg, 2010)

From the interviews, their daily and formal conversation are also a mixed dialogue between English and Mandarin for teachers and students from Malaysian Chinese primary school. I was amazed that they naturally opted for the more accurate and efficient word and jumped between expression in the two languages and fit in with ongoing grammar in their dialogue. I guess it’s the environment they lived in shaped them reciprocally and thus reflected in their teaching.

Question 3：
Are you familiar with any other counties/cities which has similar multi-lingual language society and learning environment? Do you think students have their own right to choose what language they want to learn with?

Reference:

Lim, C., & Presmeg, N. (2010). TEACHING MATHEMATICS IN TWO LANGUAGES: A TEACHING DILEMMA OF MALAYSIAN CHINESE PRIMARY SCHOOLS. International Journal Of Science And Mathematics Education, 9(1), 137-161. https://doi.org/10.1007/s10763-010-9225-4

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