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?
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
Thank you Joy for your summary, stops and including interesting visuals and thought provoking questions! I have not personally taught students who are visually impaired but have co-taught in a class with a student who was visually impaired (but just for one lesson). I've also encountered colour blind students who find the Cuisenaire Rods difficult to use for this reason. I am really not sure how to best support these students but wonder if there are some concepts in math that lend themselves to understanding by touch (or by doing, like paper folding). In the classroom where I did teach one lesson, I had given the materials ahead of time to the teacher and they were adapted for the student but I wasn't a part of this.
回复删除Question 2 is a bit easier for me in that I do incorporate the use of colour, body movement, drawing, and imagery (and sometimes taste when we do 'food math') when teaching math. I think the more senses we can include in learning, the better, especially for some learners who really struggle with the abstract nature in math. I'd like to learn more about other senses but I can't imagine how to include smell or taste - other than eating food we do math with first!
As for question 3, yes, I do use mental imagery in math and believe strongly in multi-modal math teaching (this exactly what I'm learning more about during my PhD course work). An example, is when I use the analogy of wrapping up a gift and I lead students through a mental imagery session where they've "bought" a gift, wrapped it up in tissue paper, put it in a box, wrap it in wrapping paper, finish with a bow and a card and then ask them to continue the image for how that person will unwrap the gift. This is for solving an equation. The gift is the variable and this imagery shows why we solve equations by reversing the order of operations. Things like this really seem to help some students.
Such an interesting read! I like how all of our articles provide a different lens into the conversation of gesture and embodied math. To answer your first question about inclusive teaching, Joy, I like the idea of including diverse learners in the math classroom in the sense that it can teach students empathy and taking on different perspectives. However, in order for inclusive teaching to be successful, the right kinds of resources - both human resources and teaching resources - need to be put in place. Without the proper planning, training or resources, it would be pretty unreasonable to expect the teacher to meet the unique needs of that student. I have struggled with this tensionality myself. I have taught a student on the spectrum, who was non-verbal. It was easy enough to include him in the classroom, but I found the tasks I gave him to participate in a group were often "menial". His learning goals in these contexts were along the lines of making eye-contact, sitting in the circle or keeping his hands to himself. However, his own academic goals of literacy and numeracy were often pushed to the wayside. There has to be a consideration of both aspects - how can we build empathetic, inclusive classrooms AND meet the unique learning needs of all of our learners. Whoever said teaching was easy, had no idea what they were talking about.
回复删除So interesting to think about mental imagery, and how it can be created through multimodality and the senses! Nikki, your example about wrapping and unwrapping a gift as a metaphor for doing and undoing in algebra is thought provoking. As we begin to gain experiences in working with learners with different sensory abilities, I think the challenge is to think of multiple abilities as resources, rather than deficiencies -- and we can talk a bit about that in class. It takes time and lots of observation, research and listening to learn how others perceive the world though, and that is complex.
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