Summary: Nathan points out that our current educational practices are developed from a poor evidence-base of how learning works. He argues that choices for instructional design should return to the roots of how we actually learn, which is through embodiment. His book presents an evidence-based framework of this; I have included a table of his examples of embodied math learning below. The idea is that learning activities maximize first-order experiences that live out the world (playing store), as opposed to the second-order experiences that dominate traditional teaching today, which describe the world (word problems.) Action schemas (I gave you $5 to pay for a $2 item and got $3 back) intuitively build mathematical reasoning (5 take away 2 leaves 3 leftover.) These types of embodied experiences develop grounding metaphors (object operation of removing to arithmetic operation of subtraction.) To these simple foundations, we can then link to more complex topics (like the taking away of negative numbers.) Grounding metaphors are often learned through culture by playing games at home or doing everyday family tasks, but where they are not, teachers must explicitly teach them in order to create the foundations to link more complex topics.
Examples:
Make a collection of things - Idea of quantity (what is 5) [this reminds me of hundreds day collections!]
Using a balance scale - Equated quantities (2+3=5)
Playing games where pieces are moved a number of spaces along a path - Number lines and directionality of operations
Making angles with arms - Magnitude of angles
Stop 1: “Educational institutions are not guided by a coherent, evidence-based theory of learning” (p. 3) and “we regularly make educational choices and implement educational programs with a poor understanding of how people learn.” (p. 4) These statements had me feeling a bit defensive, thinking that all the work we put into designing quality learning experiences and programming isn’t effective and lacks evidence-base. Can this be true? But, then I remembered a discussion in an earlier course about John Hattie’s work in ranking teaching practices effect, and how he started this project due to lack of evidence-base. It is interesting that in scanning the list of the visual representation, I could not find any discrete mention of embodied practices (other than broad “music programs” or “drama/arts programs.”) It would be interesting to see where some of the practices Nathan mentions would fall in.
Stop 2: Nathan mentions children often coming to school with lived experiences, like games played or measuring to prepare home meals, but “when it is not learned culturally, it must be taught explicitly.” (p. 148) This makes sense, but caused me pause to reconcile with my current teaching experience. It seems that some of the basic, grounding metaphors Nathan mentions are not as foundational for students as they used to be, at the start of my career. (For example, my grade 9s really struggled with ordering rational numbers on number lines and thinking about directionality with integers.) Is this because home life is changing? Families are busier or the activities that they do together are different? Or maybe the foundations are there, but we (teaching at the middle/secondary years) are not linking to the foundations well enough for the new concepts to attach on? I would like to explore how to “teach” the linking aspect better.
Questions:
- Nathan remarks that “education is basically about engineering learning experiences,” (p.3) is embodied learning kinda the same thing as experiential learning?
- Nathan mentions our current educational culture tends to steer “away from concrete, hands-on thinking about mathematics” and that restriction of “students’ physical and social interactions…only increase with students’ age.” (p.4) If any, what embodied practices do you already use when teaching math? What challenges do you see in trying to bring in more first-order experiences and embodiment into your classroom?
References:
Nathan, M. (2021). Foundations of embodied learning: A paradigm for education. Routledge.
Waack, S. (2018). Hattie Ranking: 252 influences and effect sizes related to student achievement. Visible-Learning.org. https://visible-learning.org/hattie-ranking-influences-effect-sizes-learning-achievement/
Hi Nichola,
ReplyDeleteI appreciate your thoughts and comments regarding this work. Your first stop where you experienced some defensiveness is such an honest reaction to reading something that challenges your own beliefs or view of the hard work that is being done in classrooms now. The statement that, “Educational institutions are not guided by a coherent, evidence-based theory of learning”, is also one that gives me pause. As a follow-up to that statement, I wonder about what our educational institutions are guided by if not the theory of learning.
Is suspect if we were to critically analyze curriculum from across the various provinces in Canada and then even into other countries, we would notice a different amount of value placed on certain pedagogical practices. Additionally, I would be very curious to see how BC is doing in contrast with others while also seeking ways to continue shifting towards more holistic ways of learning.
Thanks so much for your thoughts and giving me some ideas to ponder.
Hi Nichola, Your summary captures Nathan’s central argument well, particularly his claim that much of schooling is built on second‑order, symbolic representations of mathematics rather than the embodied, first‑order experiences from which mathematical ideas originally emerge. I found myself resonating with the tension you noted in Stop 1: when Nathan asserts that educational practices lack a strong evidence base, it can feel dismissive of the careful work teachers do. Yet, like you, I was reminded of Hattie’s project beginning precisely because research evidence was (and often still is) uneven, inconsistent, or overly narrow. What stands out to me is that many practices we intuitively believe are helpful—such as hands‑on, movement‑based, or socially collaborative learning—are not always elevated in formal ranking systems or meta-analyses, even though embodied cognition research strongly supports them. This raises interesting questions about what kinds of evidence are counted as legitimate and whether current evaluation tools recognize the full range of learning processes.
ReplyDeleteYour reflection in Stop 2 about students’ weakening grounding metaphors also resonates with my experience. Many middle-years learners struggle with number lines, magnitude, directionality, or operations with integers—ideas that should grow naturally out of everyday embodied experiences. I agree that shifts in family life, technology use, and changes in childhood play may contribute; children may have fewer opportunities to physically manipulate objects, measure ingredients, or play games that involve counting, turn-taking, or spatial reasoning. But your second hypothesis, that teachers at upper grades may not explicitly reconnect new abstractions to early embodied foundations, is equally plausible. Even when those foundations exist, they often remain tacit unless instruction deliberately activates them. Nathan’s point that embodiment must sometimes be “taught explicitly” suggests that part of our work is not just building grounding metaphors in early years but continually resurfacing them as mathematical concepts become more abstract.
Regarding your first question, I see embodied learning and experiential learning as overlapping but not synonymous. Both emphasize active participation, but embodied learning specifically foregrounds the role of the body—gesture, movement, perception, spatial action schemas—in shaping conceptual understanding. Experiential learning can include reflection, inquiry, or real-world applications without necessarily engaging the body as a cognitive tool. In Nathan’s framework, embodiment is not just “doing something hands-on,” but using bodily action to structure mathematical reasoning. That distinction feels important.
Your second question about bringing more embodiment into math classes is one I wrestle with as well. I already use some practices that align with Nathan’s examples—such as number-line walks, angle-making with arms, physical grouping/distributing activities, ratio “human bar models,” or using gesture while modelling problem-solving. These help students anchor abstract ideas in lived action. But challenges definitely arise: older students may feel self-conscious moving their bodies; class time is tight; and secondary curriculum is often paced to privilege symbolic fluency over conceptual grounding. There is also a cultural expectation—especially in higher grades—that “real math” looks quiet, still, and pencil‑and‑paper based.
Despite these pressures, I think your insight points to a powerful opportunity: if we can design even brief embodied entry points before transitioning to symbolic work, we may strengthen students’ ability to make sense of mathematics rather than memorize it. And, as Nathan argues, these first‑order experiences don’t replace abstractions, they prepare students to understand them.
Fiona, I like how you have articulated the distinction you find between embodied learning and experiential learning. It has helped me make sense of it! I had not thought of experiences that don't involve the body - but reflection is a great example.
ReplyDeleteThanks Nichola, Amanda and Fiona. Great discussion of the differences meant by embodied and experiential learning, though there are many overlaps. I especially like Fiona's statement about 'using bodily action to structure mathematical reasoning'. Embodied learning IS about learning (not just wiggling or moving about), and it does involve an oscillation between bodily doing (at many scales) and reflecting/ notating/ symbolizing/ drawing, then going back to bodily doing and movement to test and explore new hypotheses, then back to reflection and notation, etc. I've certainly done this kind of work with secondary and post-secondary learners, and I've found that older learners are just as enthusiastic to engage in embodied learning as young ones, as long as their instructors are not cueing them to think that it will be embarrassing!
ReplyDelete