Icy (Yunyi) Zhang
University of Wisconsin-Madison

For centuries, philosophers and researchers have argued that our understanding of concepts is grounded in our physical experiences—how we see, touch, and interact with our physical environment (Hume, 1938; Locke, 1948; Quine & Ullian, 1978). Yet, traditional education often does the opposite, prioritizing symbols, equations, and formal knowledge before hands-on experience (Nathan, 2012). While this formalism-first approach works for some learners when they learn certain concepts, it assumes that students can intuitively understand abstract ideas without direct experience, which is often a false assumption (Goldstone et al., 2008; Martin, 2009). In fact, students often memorize facts and procedures without fully grasping how they apply beyond the original learning contexts. This is especially true in complex fields with many abstract concepts, where learners may understand high-level ideas but struggle to connect them to different representations or real-world problems (Lau & Yuen, 2008; Nathan, 2012; West & Ross, 2002).

For instance, in the field of statistics and data science, the concept of randomness is foundational for understanding simulation-based approaches—such as permutation tests—and making statistical inferences based on those simulations. However, because randomness has no tangible or perceptible presence in the real world, students often fail to develop a meaningful understanding of it. Instead, they may resort to rote memorization by memorizing that shuffling breaks the relationship between two variables without really understanding what “breaking the relationship” means, which hinders their ability to interpret randomness-generated distributions or apply the concept of randomness to, for example, compare the sample statistics with the sampling distribution generated from permutation tests). Without these meaningful connections, applying knowledge in new situations becomes difficult (Bransford & Schwartz, 1999; Stigler et al., 2010). Learning through meaningful physical experience may be key to helping students develop a more transferable understanding of abstract concepts in complex domains. Numerous studies have designed and successfully demonstrated the efficacy of various embodied learning strategies that use direct physical movement, observing others perform movements, or mere mental simulation of the movements to improve how we learn and understand new concepts (e.g., Alibali & Nathan, 2018; Congdon, 2024; Zhang et al., 2024).

Why do embodied pedagogies, whether through learners physically performing actions or watching someone else performing the actions, work? Whether called embodied, enactive, ecological, embedded, or extended cognition, these perspectives of cognition suggest that we make sense of concepts through action and perception (Barsalou, 1999, 2008; Borghi & Pecher, 2011; Clark, 2008; Golonka & Wilson, 2012; Lakoff & Johnson, 2008). Interacting with ideas in a tangible way grounds abstract concepts in physical actions, making it easier to connect new concepts to prior knowledge and experience in the world (Barsalou, 1999). This sensorimotor foundation of the knowledge makes the knowledge representation more robust, meaningful and easier to transfer (Nathan & Alibali, 2021). For instance, many students have only a vague understanding of what data collection and a dataset actually is. Simply explaining these concepts abstractly can be challenging. Instead, having students manually collect and document real data—such as their classmates’ ages, heights, and favorite subjects—can make these ideas more concrete. By physically gathering and organizing information, students build a sensorimotor foundation of the concepts. This is true beyond teaching statistical concepts. For example when teaching psychological topics such as implicit bias, instead of simply defining the term, instructors can have students review and rank resumes that are identical in qualifications but differ only in identifying details like names or demographic cues. Working in groups, students can make decisions and then reflect on how subtle differences influenced their choices. In this way, students experience the concept through their own decision-making in a concrete context (that they are familiar with) rather than just memorizing its definition. These embodied experiences ground abstract ideas in real-world interactions, resulting in more robust and transferable knowledge.

In our work, we apply embodied learning theories to improve teaching and learning in the domain of statistics and data science. We chose this domain for two main reasons. First, teaching statistics and data science is notoriously challenging, whether it's helping students grasp specific concepts like probability distributions, sampling distributions, and confidence intervals (Zhang et al., 2025; Chance et al., 2004; Henriques, 2016), or develop intuitive understanding of simulation-based methods such as permutation and bootstrapping (Zhang et al., 2022). Research in this area can yield practical insights for improving instruction. Second, the abstract nature of these concepts makes them an ideal context for testing theoretical questions—specifically, how concrete embodied pedagogies can support the development of abstract understanding.

Our research suggests that grounding abstract concepts—such as randomness—in hands-on interactions with physical datasets can significantly enhance students' comprehension and ability to apply statistical inferences (Zhang et al., 2022, 2024). In one study, we designed an instructional video that introduced the concept of randomness through hands-on manipulations and compared it to a non-embodied instructional video (a control video created by screen-recording an instructor’s live-coding on a laptop), as illustrated in Figure 1 below.

Figure 1

Screenshots of the Two Versions of Instructional Videos

Although both videos covered the same content, the hands-on version featured a unique element: a pair of hands physically cutting and rearranging pieces of paper with data written on them to simulate the shuffle function in R, a widely used statistical programming language. This manual “shuffling” mirrors a familiar real-world action—shuffling a deck of cards to randomize their order—providing students with a sensorimotor grounding for the concept, even when merely observing the actions in the video. Through two lab studies, we found that students who first watched the hands-on video—before seeing the same process demonstrated on a larger dataset via computer simulation in a subsequent live-coding video—developed a deeper understanding of randomness compared to those who only watched two computer-simulated videos (Zhang et al., 2022).

These findings have important practical implications: live-coding to conduct computer simulations is an increasingly popular instructional pedagogy. Computer simulations can provide experts with a fast and efficient way to explore various statistical scenarios. However, because such simulations are highly complex perceptual objects, they can be confusing for novices who do not know what they are looking at (e.g., is this a sample or a sampling distribution?) nor where to look during a dynamic simulation (e.g. when the values are moving around during shuffling). Our findings suggest that some level of embodiment is needed to ground abstract computer simulations in more concrete and meaningful actions. For teachers, although developing and effectively implementing a hands-on demonstration in class can cost more instructional time and resources, they might still implement an embodied experience, whether through instructor-performing (Zhang et al., 2022) or student-performing (Congdon et al., 2018) to introduce an abstract concept in the classroom.

The effectiveness of embodied pedagogies have been well-researched in laboratory settings, but mastering complex real-world domains requires more extensive interaction with a broad array of interconnected concepts over longer periods of time than is typically offered in laboratory studies or a single classroom observation (Fries et al., 2021). Although we gain value from comparing an embodied intervention with a non-embodied intervention for all students as a whole, embodied pedagogies and also the learner population are far more heterogeneous than this all-or-none distinction. To provide more actionable insights for teachers,, we recognized the importance of moving beyond the question of whether a particular approach is effective for all learners. Instead, we ask how different types of embodied pedagogies impact learners with different levels of prior knowledge differently. This points to the necessity of a developmental perspective to better understand the role of embodied pedagogies in learning and why some embodied experiences fail to support abstract learning in some situations.

By developmental perspective, we mean that in addition to existing embodied learning theories that operate primarily at a cognitive level, we need theories at a different level: specifically, a learning theory about how different types of embodied pedagogies facilitate knowledge development over time. As educators, we know that students come into the classroom with different levels of prior knowledge. But how does that impact the way they learn best? We proposed and tested a cognitive developmental learning theory, named the Performing First Theory, which offers a simple yet powerful working framework of embodied learning. The Performing First Theory hypothesized that:

• Students with lower prior knowledge will learn better when they actively perform hands-on activities. Since they don’t yet have a strong sensorimotor foundation, engaging in physical actions helps them build understanding from experience.
• Students with higher prior knowledge will benefit more from observing these actions. Because they already have foundational knowledge, watching allows them to focus on making connections and applying knowledge in new ways.

We tested this idea using a longitudinal classroom design in a college-level introductory statistics course, where 227 college students were paired up and randomly assigned to one of two groups: (1) the perform group, in which students actively participated in hands-on activities, and (2) the observe group, in which students observed their partner doing hands-on activities. Take one of the week’s activities with the concept of the confidence interval as an example. Using the setup in Figure 2, the instructor began with a sample where the mean difference (labeled as b1) is 1.2 . Building on students' prior knowledge of sampling distributions, the instructor asked the performer to physically move the sampling distribution (color printed on a transparency paper) on the axis under different assumptions while the observer watched and provided feedback to the whole process. For instance, when β1=0, the performer moved the sampling distribution from its initial position (left of Figure 2) to a new position (right of Figure 2).

Figure 2

The Confidence Interval Part 1

How would you move the sampling distribution below if β1 = 0?

Initial position: the sampling distribution is at the sample b1 (β1 = 1.2) Ending position: the sampling distribution is at β1 = 0

The key idea is then introduced: determining the point where shifting the distribution further would make the observed value of b1=1.2 unlikely. This is visually shown on left of Figure 3, where the performer, figured out by physically interacting with the distribution, that moving the distribution too far left would place b1 in the unlikely green region. That threshold defines the lower bound of the confidence interval. Similarly, as illustrated in the right of Figure 3, the performer identifies the upper bound of the CI. The observer watched the whole process, providing verbal feedback.

Figure 3

The Confidence Interval Part 2

Move the sampling distribution to find the value of β1 such that if you move it any further, the sample b1 is no longer likely to come from this sampling distribution.

Finding the lower bond: if the sampling distribution is moved any further left, b1 will be considered unlikely Finding the upper bond: if the sampling distribution is moved any further right, b1 will be considered unlikely

An analysis of students’ midterm and final exam scores showed a significant interaction between prior knowledge and type of pedagogy in the hypothesized direction. Interestingly, by examining students’ self-rated factors and their performance on the summative assessments, we found that only self-rated prior knowledge—not other factors such as math anxiety or how well they had performed in math in previous classes—significantly moderated the effectiveness of the embodied pedagogies. Multilevel analysis of weekly tests supported the findings from the summative assessments, demonstrating that low-prior knowledge learners benefited more from physically performing the activities, whereas high-prior knowledge learners benefited more from observing the activities. Interestingly, whereas it is typical for students’ performance on a pretest to predict their performance after the learning intervention, it is only true for students in the observe group. For students in the perform group, there was no significant correlation between how they did before and after the intervention.

This study bridges an important gap between research and practices in the classroom: how should teachers implement embodied activities into classroom settings? These findings suggest that one-size-fits-all teaching may not work when we have a classroom with diverse students. Instead, we can tailor embodied instruction based on students' prior knowledge. Although teacher demonstration might be easier and more resource-efficient from the teachers’ perspective, our findings suggest that teachers need to reconsider this assumption based on the knowledge state of their students: if students have low knowledge, active participation in hands-on activities might be the optimal pedagogy for learners to develop a meaningful and robust understanding of the concepts; on the other hand, for learners with high prior knowledge, observing peer or teacher demonstration of the hands-on activities or other less embodied pedagogies might more efficiently facilitate connection-making and transfer. We encourage teachers to assess their students' understanding and adapt their instructional methods accordingly. Providing hands-on experiences when novices first learn a concept may be especially beneficial, because they lack a sensorimotor grounding for abstract concepts.

Additionally, this study offers methodological insights into implementing embodied pedagogies in large classrooms. While the idea of hundreds of students engaging in physical activities may seem daunting, our findings suggest that simple, well-structured interventions—such as distributing hands-on manipulatives (e.g., a printed sampling distribution on transparency paper) with clear instructions—can make the process manageable. Often, students do not require lengthy, immersive experiences; rather, brief yet concrete interactions, such as physically shuffling dataset pieces, can effectively ground abstract concepts like randomness and the confidence interval.

References

Alibali, M. W., & Nathan, M. J. (2018). Embodied cognition in learning and teaching: Action, observation, and imagination. In International handbook of the learning sciences (pp. 75-85). Routledge.

Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22(4), 577-660.

Barsalou, L. W. (2008). Grounded cognition. Annu. Rev. Psychol., 59, 617-645.

Borghi, A. M., & Pecher, D. (2011). Introduction to the special topic embodied and grounded cognition. Frontiers in Psychology, 2, 187.

Bransford, J. D., & Schwartz, D. L. (1999). Chapter 3: Rethinking transfer: A simple proposal with multiple implications. Review of research in education, 24(1), 61-100.

Chance, B., del Mas, R., & Garfield, J. (2004). Reasoning about sampling distributions. In The challenge of developing statistical literacy, reasoning and thinking (pp. 295-323). Dordrecht: Springer Netherlands.

Clark, A. (2008). Supersizing the mind: Embodiment, action, and cognitive extension. OUP USA.

Congdon, E. L., Kwon, M. K., & Levine, S. C. (2018). Learning to measure through action and gesture: Children’s prior knowledge matters. Cognition, 180, 182-190.

Congdon, E. L. (2024). Individual differences in working memory predict the efficacy of experimenter‐manipulated gestures in first‐grade children. Child Development, 95(5), 1494-1507.

Fries, L., Son, J. Y., Givvin, K. B., & Stigler, J. W. (2021). Practicing connections: A framework to guide instructional design for developing understanding in complex domains. Educational Psychology Review, 33(2), 739-762.

Goldstone, R. L., Landy, D., & Son, J. Y. (2008). A well grounded education: The role of perception in science and mathematics. Symbols, embodiment, and meaning, 327-355.

Golonka, S., & Wilson, A. D. (2012). Gibson’s ecological approach. Avant: Trends in Interdisciplinary Studies, 3(2), 40-53.

Henriques, A. (2016). Students’ difficulties in understanding of confidence intervals. The Teaching and Learning of Statistics: International Perspectives, 129-138.

Hume, D. (1938). An Abstract of a Treatise of Human Nature, 1740. CUP Archive.

Lakoff, G., & Johnson, M. (2008). Metaphors we live by. University of Chicago press.

Locke, J. (1948). An essay concerning human understanding, 1690.

Martin, T. (2009). A theory of physically distributed learning: How external environments and internal states interact in mathematics learning. Child Development Perspectives, 3(3), 140-144.

Nathan, M. J., & Alibali, M. W. (2021). An embodied theory of transfer of mathematical learning. Transfer of learning: Progressive perspectives for mathematics education and related fields, 27-58.

Nathan, M. J. (2012). Rethinking formalisms in formal education. Educational Psychologist, 47(2), 125-148.

Quine, W. V. O., & Ullian, J. S. (1978). The web of belief (Vol. 2). New York: Random House.

Stigler, J. W., Givvin, K. B., & Thompson, B. J. (2010). What community college developmental mathematics students understand about mathematics. MathAMATYC Educator, 1(3), 4-16.

West, M., & Ross, S. (2002). Retaining females in computer science: A new look at a persistent problem. JCSC, 17(5), 1-7.

Zhang, I., Guo, X. H., Son, J. Y., Blank, I. A., & Stigler, J. W. (2025). Watching videos of a drawing hand improves students’ understanding of the normal probability distribution. Memory & Cognition, 53(1), 262-281.

Zhang, I., Xu, A., Son, J. Y., & Stigler, J. W. (2024). Exploring the Role of Prior Knowledge During Embodied Learning. In Proceedings of the 18th International Conference of the Learning Sciences-ICLS 2024, pp. 1770-1773. International Society of the Learning Sciences.

Zhang, I. Y., Tucker, M. C., & Stigler, J. W. (2022). Watching a hands-on activity improves students’ understanding of randomness. Computers & Education, 186, 104545.

Zhang, I. Y., Xu, A., Son, J. Y., & Stigler, J. W. (2024). Watching hands move enhances learning from concrete and dynamic visualizations. Journal of Experimental Psychology: General.