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Teaching Math Without Words, A Visual Approach to Learning Math
Could it really be as simple as applying this visual approach?
This video intrigued me as does the question if the visual approach enough. My first instinct in answering the issue is that one should never rely on using only one strategy for teaching. It would be silly to use only the visual approach to learning math, wouldn't it? Or would it? Arguably, math teaching needs reformation. Just like the video pointed out, math class has operated the same way for years. One method used religiously, is the talk, talk, talk manner of communicating. For the majority of students, that doesn't work. This strategy may be the revolution math education needs. I am waiting with great anticipation to read how my fellow aspiring teachers feel about this matter. I appreciate the idea, understand the effort, and feel it is an investment that will reap untold rewards for the students for the rest of their lives.
I decided to look further into the topic. In this linked paper SEEING AS UNDERSTANDING: The Importance of Visual Mathematicsfor our Brain and Learning. written by Jo Boaler, Professor of Mathematics Education with Lang Chen, Stanford Cognitive and Systems Neuroscience Lab, Cathy Williams & Montserrat Cordero, youcubed Stanford University, the authors called for what they deemed an "urgent need for change in the ways mathematics is offered to learners" (Boaler, Chen, Williams, & Cordero, 2017) . They shared results from important brain studies.
When we work on mathematics, in particular, brain activity is distributed between many
different networks, which include two visual pathways: the ventral and dorsal visual pathways
(see fg 1). Neuroimaging has shown that even when people work on a numerical calculation,
such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing
(Boaler, Chen, Williams, & Cordero, 2017) .
Figure 1.
This information tells me that whether we want to acknowledge the research that shows we think visually in mathematics or not the fact remains that we do. The faster we get on board with the research and start making the necessary changes the more quickly our students will benefit.
Extend
Indigenous Teaching and Learning
Consider the ways of knowing, learning and teaching of indigenous people.
What similarities and differences do find between this perspective and those of the Western perspectives that you've studied thus far?
Although many Westerners might claim to be lifelong learners, present company included, our society doesn't emphasize a need to learn beyond secondary school or college. The Indigenous people see four stages throughout one's life. These cycles include childhood, adolescence, adulthood, and maturity. Western learning takes place in the rigid structures called schools and is quite formal. There are segments of the educational realm that focus on the environmental impact and social interactions on learning. However, the Indigenous people use their interactions with each other, animals, and the natural world as their arena for learning. They feel that everyone and everything is interconnected. That belief sounds spiritual and at the same time scientific. Aren't you and I made from the same star stuff? Probably. Aren't we breathing in the same molecules breathed at one time by Ceasar, Harrison Ford, and Margaret Thatcher? Don't we all look at the same moon, sun, and stars? Can we admit that we are all in the same family called "Earthlings?"
Another notable difference between the Western way of knowing and learning and the Indigenous people's way of learning is the attitude of sharing knowledge as we grow older. For Westerners, in general, we feel that when we're done, we're done! No more pencils, no more books, no more teachers' dirty looks! Sayonara, baby! We might indulge Grandpa's stories at Thanksgiving, but we don't honor oral traditions of passing down knowledge or learning skills from our elders anymore. The Indigenous people expect to impart their wisdom as they age. I found it fascinating to hear that they believe that we have individual knowledge that we share in a collective knowledge. They say, "We come to one mind." This resonated with me. I mentioned in a previous week's entry that I am a huge Star Trek fan. When I hear collective knowledge, The Borg immediately come to mind.
The Borg Collective
The goal of learning to the Indigenous people is to achieve wholeness with the universe. Children are respected in the Indigenous communities and they follow the ethics of non-interference. There is also an emphasis on learning through self-reflection. I'm not seeing that very often in Western circles. We've also moved away from the extended family model. I feel like there are educational movements that are trying to capture the essence of the Indigenous way of knowing and learning- specifically, the observation and experience aspects of it. It is heartbreaking to know that Indigenous people lost their ways and were forced to conform to the Western way. A gentle sharing of knowledge would have benefitted both.
https://www.taleas.com/memes/this-just-in-3-out-of-2-people-have-trouble-with-fractions.html
References
Boaler, J., Chen, L., Williams, C., & Cordero, M. (2017, March). Seeing as understanding: The importance of visual
mathematics for our brain and learning. Retrieved from https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna
ssl.com/wp-content/uploads/2017/03/VisualMath-Paper-vF.pdf
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