contributed by Dr. Peter Meyerhoff, CEO of 10storymath
Imagine if the folks who make our phones and TVs had stopped paying attention to scientific research. We’d still be fiddling with antennas and turning rotary dials, instead of watching movies on supercomputers we carry in our pockets! Fortunately, discoveries in fields such as communications and transportation have moved quickly from research into everyday life.
In education, we haven’t been as lucky. Scientific investigation of cognition and learning has come a long way, but despite calls for ‘research-based’ educational practice, the latest discoveries haven’t yet made their way into the classroom.
The problem is not a lack of technology: many American schools are fully loaded with the latest gadgets and software. The problem is that educational publishers program these devices using ideas about learning that are more than three decades old. Science moved on, but publishers didn’t keep up.
The learning theories of the last century made important contributions to our knowledge and inspired some excellent software. But improving classroom instruction, especially elementary math, depends on translating current research findings into our schools. It’s time for math leaders to bring instruction in line with modern-day ideas about cognition.
The Facets Of 4E Cognition
So, what does that research tell us? Many cognitive and learning scientists now explore how the mind, body and environment work together as people think and learn. This perspective—called 4E cognition (1)—gives us a framework to think about learning in 4 ways:
• Embodied in our senses and in our lived, physical reality
• Embedded in a cultural and social context
• Enacted through experiential problem-solving
• Extended across tools, devices, and collaborators
4E cognition has important implications for curriculum design. How might we design learning environments that lead to constructive interaction of mind, body, and environment? Let’s look at the 4E cognition framework and consider how each element might apply to one critical area of education: elementary math.
4 Strategies To Use 4E Cognition In The Elementary Math Classroom
Embodied Learning: Mind In Body
20th-century scientists developed a model of the mind as an abstract information-processing system. This metaphor of a ‘mental computer’ was central to early cognitive science. (2)
But it turns out that we think and learn outside our heads, too.
Starting in the 1980s, researchers discovered that our language and our thoughts are shaped by the experience of being in a physical body. (3) Think about the words you use every day. You’re ‘in over your head’ on a difficult problem, you’re ‘almost there,’ it’s ‘so close you can almost taste it.’ These images and metaphors come from our lived, physical reality: our sense-memories of movement, touch, sight, and hearing. It turns out that many of our fundamental conceptual understandings and memories are grounded in these ’embodied’ interactions with the physical world.
More recently, researchers studying everyday learning interactions noticed that people use their bodies extensively as a resource for thinking, learning, and working with others. (4) People move around, point, count on their fingers, draw pictures in the air, raise their voices, exchange meaningful glances and use their bodies in countless other ways as they learn. These actions are part of a complex, coordinated learning system in which the body plays a central role.
Through these embodied actions, people make meaning and figure things out together. The body is also central to human cognition and learning in ways familiar to every teacher and parent: think of how hard it is to concentrate when you feel tired, stressed, hungry, anxious, or scared. The well-being of students is central to their experience in school. Although educators often talk about “social-emotional learning” as distinct from academic instruction, academics are in fact integrally tied into the emotions we feel in our bodies.
Strategy: If the body plays a central role in math learning, look for ways to bring it into the classroom. One easy way is to ask students to do math problems together … without talking. They will immediately find creative ways to use their bodies to communicate mathematical ideas. Afterward, they can share their strategies with the class – still silently. This activity will get students laughing and build community in the classroom.
Embedded Learning: Mind In Culture
Think about movies you’ve seen that use the ‘fish out of water’ trope: the rugged outdoorsman who finds himself in the big city, or the urban sophisticate who moves to the country. In these stories, we see that what counts as intelligence changes depending on where you are and who you’re with. In the outback, you’d better be able to use a knife and set up a campsite. In midtown Manhattan, you’d better know which fork to use at the nice restaurant and how to talk to the server.
School’s emphasis on individual achievement leads us to see thinking and learning as isolated processes. But cognition is embedded in culture. (5) From early childhood, other people are giving us objects to handle, tools to use, and situations to deal with. Being ‘smart’ means using objects and tools according to other people’s standards and acting in ways that other people approve of.
We all understand this on some level, and social scientists have studied it for decades, but school never quite figured it out. In the classroom, there’s only one way of knowing. School looks for this knowledge by placing students at desks and instructing them to make marks on a paper or type numbers and letters into a computer. When those scratches and symbols match the ones on an answer sheet handed down from the central office, school decides the student has learned.
That perspective serves us well in many ways, but it’s important to recognize that school’s traditional practices are just that: traditions. There’s room in a broader picture of learning and cognition for new, more culturally grounded ideas about what ‘counts’ as knowing and how we might look for it.
Strategy: Be on the lookout for practices in students’ everyday lives in which math is part of an activity that’s important to them or their families. Grandma has a special chicken soup recipe, the dog needs a certain amount of food twice a day, the local team came back to win in the 4th quarter. There are rich mathematical ideas and challenging skills embedded in each of these examples. Teachers can find ways to draw on cultural experiences that feel relevant to students in order to make math meaningful to them.
Enacted Learning: Mind In Action
There’s a famous expression: when all you have is a hammer, everything looks like a nail. Our knowledge and experiences shape our decisions and actions. And the corollary is also true: when you’re surrounded by nails, the first thing you do is look for a hammer. When the environment gives us problems to solve, we draw on—or develop—the skills we need to solve those specific problems. (6)
Progressive educators have always emphasized ‘learning by doing,’ but we now have a clearer picture of how and why this approach works. Our memories evolved to help us see and do things in a three-dimensional, action-oriented environment. (7) Neuroscientists have found that the motor neurons involved in controlling tools are the same ones that are activated when we merely see the tools, without actually using them. Similar findings show that memories encode patterns of interaction with the physical world.
If our minds are tuned toward our actions in the world, we can understand cognition as being organized around our practical goals. For example, imagine that you’re on vacation and walking through an unfamiliar city. If you’re hungry, you’ll notice and remember cafes, restaurants, and street vendors. If you’re seeing the sights, you’ll notice the buildings, parks, and other cultural attractions. Cognition, in this view, is for action in the real world.
The enacted perspective explains why students are always asking, “When will I ever use this?” It’s the right question to ask. Our minds evolved to use, not merely store, new information.
Strategy: School math is weakest in this area. With few exceptions, math activities exist only for doing math, rather than serving as a tool that enables students to do some non-math task. To break out of this bind, look for ways you can answer ‘right now’ when students ask “When will I ever use this?” Find pathways to practical, real-world-oriented applications of math concepts. One tried-and-true method: games. Many students enjoy playing games, and if there’s math to be done, students will be motivated to learn it in order to play and win. Find math games online that require students to develop math skills in order to play.
Extended Learning: Mind In Environment
You’re running low on groceries, so you make a shopping list and head to the store with your friend. On the way, your phone buzzes. It’s your roommate, who has a few things to add to the list. You’re driving so you can’t write them down, but you say them out loud and your friend remembers them. Right after the call, your friend recites them and you add the items to your list.
If we want to explain how you ‘knew’ how to get the right groceries, do we need to include the shopping list and your friend’s memory in our analysis? Many researchers now believe the answer is yes.
This view of an ‘extended’ mind isn’t just about finding answers on the internet or using a calculator to solve a math problem. It’s a different way of thinking about cognition and learning. To solve everyday problems, we organize not just the information inside our heads, but the objects and people around us. (8)
With the boundaries of thinking and learning redrawn in this way, we can start to see new possibilities for education. In life outside of school, people work in social and technical environments that enable them to solve problems and succeed. Classroom instruction can help students organize such environments for themselves.
Strategy: It’s not necessarily a sign of weakness when students look to one another for help. Nor is it a problem when students use notes and jottings to help them organize their ideas as they’re solving problems. Look for ways to actively encourage both. Design activities so that the coordinated efforts of multiple students are necessary for a group to succeed.
Give students diverse materials that they can use to help them work through a difficult problem. When students are sharing out their strategies, encourage them to point out how other people helped them and to describe the materials they used.
Many educators intuitively understand the principles of 4E cognition. Teaching practices that align with the 4E framework often travel under labels like ‘project-based,’ ‘hands-on’ and ‘student-centered.’ (See examples of student-centered teaching.)
Whatever the label, research on cognition shows that approaching mind, body, and environment as an integrated whole can open the door to authentic and powerful learning experiences.
1 Newen, A., De Bruin, L., & Gallagher, S. (2018). 4E cognition: Historical roots, key concepts, and central issues. The Oxford Handbook of 4E Cognition, 2-16.
2 Schank, R. C., & Abelson, R. P. (1977). Scripts, plans, goals, and understanding: An inquiry into human knowledge structures. Psychology Press.
3 Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.
4 Stevens, R. (2012). The missing bodies of mathematical thinking and learning have been found. Journal of the Learning Sciences, 21(2), 337-346; Vossoughi, S., Escudé, M., Kitundu, W., & Espinoza, M. L. (2021). Pedagogical “Hands and Eyes”: Embodied Learning and the Genesis of Ethical Perception. Anthropology & Education Quarterly.
5 Cole, M. (1998). Cultural psychology: A once and future discipline. Harvard university press.
6 Hall, R., & Stevens, R. (2015). Interaction analysis approaches to knowledge in use. In Knowledge and Interaction (pp. 88-124). Routledge.
7 Glenberg, A. M. (1997). What memory is for. Behavioral & Brain Sciences, 20, 1-55.
8 Hutchins, E. (1995). Cognition in the Wild. Cambridge, MA: MITPress. Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge, MA: MIT Press
Dr. Peter Meyerhoff is the CEO of 10storymath, a Chicago-based firm that develops project-based math supplements for elementary schools. A learning scientist and curriculum designer, he teaches courses in learning and organizational change in the School of Education & Social Policy at Northwestern University.
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