Reference: Nathan, M. J. (2021). Foundations of embodied learning: A paradigm for education (1st ed.). Routledge. https://doi.org/10.4324/9780429329098
Summary: In the introduction, Nathan argues that education is about engineering learning experiences for children, but we aren't using all the options/possibilities open to us; we could do better by applying evidence-based research into our classroom strategies, particularly around embodiment in the learning process. By tapping into our natural ways of making meaning by using our bodies, and connecting that to prior knowledge, we could maximize lasting changes in our behaviour and understandings. Children intuitively already use their bodies to understand new concepts without being formally taught, but two obstacles hold us back: First, our society does not value embodied forms of knowing (first-order) and instead relies on second-order (descriptions of experiences instead of first-hand) due to, perhaps, ease or simplicity. Second, the sciences behind the study of learning have not made actionable the findings of their research.
Stop 1: "Education is basically about engineering learning experiences." (Nathan, 2021, p. 3). Imagining myself as an experience generator is a very interesting thought experiment - I feel that the way I go about teaching currently doesn't maximize the expectation that I have with this job title. I believe that elementary school teachers are wonderful experience generators due to their classroom bins full of manipulables. This connects really well with first-order (practical hands-on) experiences vs second-order (descriptions of ) experiences. After completing the AI course with Dr. Saville, and witnessing the techno-centric schooling we've developed (in-part due to COVID adaptations of digitizing most learning experiences for safety), I can imagine that students are starved for first-order mathematical experiences. I will double-down on my commitment to providing hands-on math with my students, perhaps they can demonstrate their proficiency by generating first-order learning experiences for others of a younger grade as an extending assignment.
Stop 2: "What makes mathematics difficult for many people is not their inability to understand the ideas, but to learn the meaning of the formal notation and how it describes these basic ideas and their variants" (Nathan, 2012, as cited in Nathan, 2021, p. 147). This idea of understanding the concepts, but not knowing how to explain it occurs quite frequently in my classroom with my students saying just that. They produce calculations without work, and intuitively they know what and how to do it - I ask them to represent their understanding using paragraphs if they cannot write math symbolically as an adaptation.
Stop 3: "Linking metaphors allow people to offload the cognitive operations needed for a new domain, such as negative numbers, onto a previously grounded domain, such as counting numbers" (Nathan, 2021, p.148). This concept is very interesting to me. It's almost like another way of saying scaffolding where learned ideas must be connected relationally to other mental concepts to really grasp its meaning and depth. This idea also really connects to Roger Antonsen's (2016) TEDtalk where he argues that understanding has to do with the ability to change ones perspective. In other words, the better you can scaffold (or attach linking metaphors) to new concepts, the better you understand them.
Wonder: In one of the examples from the article by Nathan (2021), he mentions "when [a math concept] is not learned culturally, it must be taught explicitly." What does it take to maximize the ability to scaffold or cognitively incorporate linking metaphors? If we only teach using second-order (descriptions of) experiences, is it enough for students to generate strong understanding?
Oliver,
ReplyDeleteStop 2 in your reflection strongly resonates with my own experiences as both a learner and an educator. There have been many moments when I knew how to solve a problem procedurally but could not fully explain the mathematical meaning behind it. This also reminds me of students who complete large numbers of similar practice questions successfully, yet struggle to articulate the underlying concept. In these cases, they may be able to carry out calculations almost mechanically, but sometimes fail to explain their reasoning to a peer or represent their thinking in multiple ways.
Your point in Stop 1 about students being starved for first order mathematical experiences also resonates with me. Many students grow tired of learning mathematics through repetitive and traditional approaches that emphasize worksheets and practice questions. When learning is limited to second order experiences, such as symbolic representations or verbal descriptions, students may disengage or fail to build meaningful connections. Incorporating hands-on or embodied learning experiences has the potential to reawaken student interest and support more durable understanding by allowing students to physically and cognitively interact with mathematical ideas.
In response to your question about whether teaching primarily through second order experiences is sufficient, I think students may still achieve a satisfactory level of performance. However, for deeper and more transferable understanding, second order experiences alone are not enough. Knowledge gained in this way is often easier to forget and harder to apply in unfamiliar contexts. In contrast, first order experiences tend to be more memorable and meaningful in supporting the kind of conceptual understanding that allows students to explain and extend their mathematical thinking.
Oliver - your discussion about scaffolding and linking metaphors reminded me of the OECD Skills for the Future paper we read a few courses ago. In there they discussed transfer as a invaluable skill for students. I think that goes well with Nathan's framework of grounding metaphors, cognitive offloading and linking metaphors.
ReplyDeleteI do get the impression that many young people are missing out on first-order direct experiences of the world that used to be taken for granted through free play, messing about outdoors, movement, balancing, climbing, etc. (See Megan Zeni and Mariana Brussoni's work on the benefits of risky play, including their newly-published book!) We might need to offer some of these kinds of experiences during school time, at every age, as sensory, grounding metaphors. For example, how can a person make sense of balancing an equation if they've never played with balancing on a teeter totter, or a log, or while skating, or ...?
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