Embodied Learning and Math

Though not necessarily tied to the idea of technology, one excerpt from this week’s readings reminded me of this graphic that’s been floating around my social media feeds:

(MindShift.com, 2018)

Winn writes, “Some recent thinking suggests that it is better to consider students to be tightly coupled to the environment rather than embedded in it. Being embedded suggests the student is passive, carried along as the environment changes. Successful students are anything but passive.” (Winn, 2003).

To be brief, Winn argues that “Artificial environments can use computer technology to create metaphorical representations in order to bring to students’ concepts and principles that normally lie outside the reach of direct experience” (2003). Essentially, technology helps the learning and provides a form of adaptation, in that the learner interacts with their environment significantly more than was possible or realized previously.

In another article, I read about the application of a program on handheld devices called TechPALS to mathematical problem solving. It was a great reminder of how the software of the technology does not have to be entirely about immersive experiences within the specific curriculum area for it to be effective. This article used control classes and classes integrating TechPALS to have students work on “repeated practice, feedback, and cooperative learning”, which creates embedded experiences within the content, and affects the environment in which the students interact with the subject matter. Roschelle et al. write that TechPALS is important because, “technology can socialize learning, encouraging positive behaviors such as asking questions, giving explanations, and discussing disagreements. These social behaviors, in turn, may engage students in connecting conceptual and procedural aspects of mathematics content” (Roschelle et al. 2010). The embodiment of their learning is intrinsically tied to what they refer to as “positive interdependence” and “individual accountability”. As far as setting up a similar scenario in my own practice, a mobile app like Kahoot or something comparable but perhaps less gamified? The students should be able to fit pieces of learning together like a jigsaw this could serve similar aims for embodied learning. From my perspective, reading for its usefulness and engagement, the instructional design of the lessons had everything to do with the embodiment of the content, and little to do with the actual technology.  As the environment changes, the students interact with it in various ways, and the ability to engage in conversation about those observations, question each other respectfully, and have their views challenged goes back to the “adaptive” learning environment Winn was referring to. The point of technology helping to facilitate those goals is outlined in his idea of learning as adaptation, and the possibility of “us[ing] technology to reduce the limits imposed by our sensory [or cognitive] bandwidth” (Winn, 2003), facilitating more spaces for students to interact with the environment as it happens.

Finally, the last article I read was about mental mathematical strategies by Jérôme Proulx. It was a very interesting take on embodied and embedded learning, as it’s a current article linked to the theoretical ideas of John Threlfall (2002), and not necessarily what I would instinctively teach. I think I have some researching to do! Proulx argues that teaching strategies for mental maths is almost unnecessary, and could be readdressed in education. He writes that, “This is at the grass roots of Threlfall’s argument for the futility of classification and choice of strategies, for no mapping of classifications of strategies produced by students appears satisfactory. This said, even if some authors, as Threlfall highlights, recognize the variety in strategies as too great to contain them in categories and that these would need to be broadened enough to encompass them all, he insists that not even broad categories would successfully account for the diversity in strategies from one author to another. Categories or classifications somehow become useful fictions, that can even be seen to serve a question- able purpose, especially when it comes to teaching these strategies” (Proulx, 2013). His article cites perspectives “grounded in enactivism” where students interact with the problem as it happens and use what is comfortable for them to solve it. So my first question to you is based on his writings:

Q1: Is there value in naming strategies (specifically for mental maths) if Proulx has determined “it does not give much justice or credit to the nature of students’ mathematical activity when they engage in these strategies in a mental mathematics context” (2013)?

Q2: How does an educator monitor differentiation in embodied learning?

References:

Roschelle, J., Rafanan, K., Bhanot, R., Estrella, G., Penuel, B., Nussbaum, M. & Claro, S. (2010). Scaffolding group explanation and feedback with handheld technology: impact on students’ mathematics learning. Educational Technology Research and Development, 58 (4) pp. 399-419.

Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educ Stud Math. (84) pp. 309–328.

Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114.