The Embodied Design Research Laboratory was established in the Fall of 2005, when I joined the faculty of the Graduate School of Education at UC Berkeley. The lab is the home of all our research and mentoring.
The phrase “embodied design” was first coined by van Rompay and Hekkert (2001), industrial designers who used Lakoff and Johnson's cognitive semantics theory of conceptual metaphor to predict the emotional affect that humans would attribute to architectural structures, such as bus stops. There was also a fleeting unarchived use by Thecla Schiphorst, circa 2007. I recycled the phrase into the learning sciences to describe an approach to the construction of pedagogical materials and activities that enables learners to objectify their tacit knowledge in cultural forms relevant to disciplinary content (Abrahamson, 2009). Later I elaborated thus: “Embodied design is a pedagogical framework that seeks to promote grounded learning by creating situations in which students can be guided to negotiate tacit and cultural perspectives on phenomena under inquiry; tacit and cultural ways of perceiving and acting” (Abrahamson, 2013, 2014). I demonstrated in those papers how I work both with sensory perception primitives, such as early sensitivity to color density in the visual field, and with human capacity to develop motor actions, such as learning new bimanual coordination.
At EDRL we have become increasingly interested in the idea that "learning is moving in new ways." This phrase has two meanings: It is both about students learning new concepts by physically moving in new ways and about the field's theoretical advances in conceptualizing the phenomenon of learning. Through our design-research studies, we are investigating for relations between moving and learning, particularly as these relations may be of relevance to mathematics education. Since Fall 2008 we have been building and evaluating a type of interactive technological system we call the Mathematical Imagery Trainer. The idea is for students to discover and practice a new way of moving, a purposeful mirco-choreography that is situated in the immediate context of achieving some task objective. For example, students sitting at a desk learn to move their hands up from the desk in such a way that the hands' respective heights over the desk maintain some goal proportion (e.g., 1:2). It is not easy to move this way. One has to figure something out, usually through trial and error. All the while, the students receive automatic feedback on whether or not they are moving correctly. We are curious about potential relations between learning to move this new way and learning the mathematics that these actions might be said to model, such as proportional equivalence. Moreover, we are curious how teachers guide this process of learning to move in new ways; how they frame this new way of moving as a conceptual performance. That is, we are engaged in research on the educational transition from action to concept.
We have published our findings in numerous peer-reviewed journal articles and conference proceedings, have received grants from federal agencies to fund this line of research, and have been increasingly collaborating on this line of research with other scholars, both in the US and worldwide.
This research on how goal-oriented action on objects gives rise to conceptual notions is theoretically fecund. It invites perspectives from diverse traditions of educational scholarship going back to the American John Dewey or the Belarusian Lev Vygotsky as well as the many international design luminaries who created materials and activities for children to play and learn, such as Italian Maria Montessori or the Hungarian Zoltan Diénès. The action/concept relation is treated by phenomenology philosophers, cognitive linguists, neuroscientists, kinesiologists, and many others. Theoretical models arising from this scholarship are often contested, and certainly their implications to educational practice are heatedly debated. And so, as scientists are wont to end their learned manuscripts, "More research is needed."
Our own research has brought us to the shores of Geneva, so to speak. That is, we realized that our findings resonate strongly with the work of Swiss cognitive-developmental psychologist Jean Piaget -- his theory of genetic epistemology. In particular, we have come to characterize learning to move in new ways as developing sensorimotor schemes (how you move) oriented on constructed realities in the field of interaction (what you move). That is, students working with the Mathematical Imagery Trainer apparently develop two interlinked things at the same time: a new form of bimanual coordination for engaging the field of action, and a new phenomenal category upon which this coordination operates. Perhaps most striking are the data visualizations of students' eye-gaze foci and paths as they figure our and master the interaction problem. We, the researchers, literally see new objects and gaze patterns emerge in the child's interaction that were not there before. As students look at new places and in new ways, they get better an manipulating the interactive device. Soon after, they report on the new objects and patterns they are seeing, and then we help them make mathematical sense of these new objects by way of introducing mathematical frames of reference.
Our work has become quite interdisciplinary. Some of our closest collaborators are dancers, martial artists, and somatic therapists. The biggest recent boost came from the quarters of sports science. Currently, we are corroborating our findings, refining our theoretical models, developing principles for pedagogical design, and looking to expand our work to other concepts and domains. These are exciting times, and we are constantly inspired. It seems that our learning, too, is moving in new ways.Now I wax eloquent: When chefs write recipes, they put those instructions on paper not by looking at the words they've written and wondering which other words would be a good fit. Rather, the chefs imagine and experience sensations of flavor. You know, "Aha! If I only added some lime to that salsa, it would be fantastic on the tilapia!" When composers write music, they don't ask themselves which are the most logical notations to put in the musical score. Rather, the composers imagine and experience sensations of sound. That's actually called to "audiate." You know, "Oh, if only a horn played the second theme now in a lower register, that would be mesmerizing!" So they make their decisions based on inspiration, creativity, and sense of structural constraints. Only then they put that down on paper in the musical score. And when mathematicians write proofs or solve problems, they don't expect the meanings to be in the symbols themselves. Rather, meanings are experienced as sensations. Now, these are not sensations of flavor or sound but of action in space, action on imagined objects that are experienced as real or realistic, even if they are not substantive in the sense of concrete things in the actual world, and even if they are not truly palpable -- so I am speaking about visual, kinesthetic, and somatic experiences. It's only after they think that way that mathematicians articulate their thoughts on paper or the blackboard. All this has been known for a century now, through ethnography and philosophy, and recently through empirical research. This is not at all to mitigate the challenge of articulating sensations in formal signs. Rather, it is to say that there is no point in education programs that ignore the formative role of embodied reasoning in mathematics learning. Embodied design is an approach to instruction that recognizes the formative role of sensations and motor-action in generating new meaning and then negotiating these new meanings with the formal mathematical structures that children are to adopt, understand, and apply as complementary to, and empowering of their sensations. We view this approach as vital, and we view technology as offering new opportunities for implementing these transformational experiences in classrooms. Our research base offers examples for the effectiveness of this approach. In all this, we recognize that the educational transformations we envisage are systemic: they demand of all stakeholders -- policy makers, teachers, students, and perhaps parents -- to think in new ways of what it even means to understand mathematical concepts.
About Me: I am an Associate Professor of Secondary Mathematics Education in the Area of Cognition and Development at UC Berkeley's Graduate School of Education. I was born in Haifa, a gorgeous, diverse, and harmonious city straddling the ever-green Mt. Carmel on the Mediterranean littoral. My background is in cognitive psychology, which I studied at Tel Aviv University. Then I achieved a Ph.D. in Learning Sciences at Northwestern University and continued as a postdoctoral fellow at the Center for Connected Learning and Computer-Based Modeling. I am a cellist.
Research Interests: I'm a mathematics-education researcher. Specifically, I am a design-based researcher of mathematics education, which means that I use the practice of pedagogical design as a context for my empirical research. That is, I investigate processes of learning and teaching through attempting to enhance their potential. These investigations are informed by, and lead to the development of theoretical models for understanding and critiquing these phenomena. In turn, these studies inform the development of frameworks for effective design. In March 2014 I gave a ISLS NAPLeS webinar in which I explain my work.
Ultimately, my research is about meaningful learning of mathematical concepts, and so I examine how students build and keep meaning for the cultural-historical forms that have evolved in the service of the mathematical discipline. In my attempts to promote and understand meaningful learning, I have been greatly inspired by Luis Radford's semiotic-cultural theory of objectification, because the theory has enabled me to conceptualize meaningful learning the way I had come to perceive it through my studies, that is, as the intentional, guided, mediated enmeshing of subjective sensations and received structures. Moreover, the theory has enabled me to hone my research on micro-events where the clash of subjective and received resources culminates. I am particularly interested in how students and instructors' work together to reconcile these oppositional resources. Specifically, if naive and mathematical visualizations of phenomena differ, how do learners adopt the mathematical view while keeping the naive meaning? For example, how do students adopt a rise-over-run analysis of a sloped line whose steepness they sense as a holistic, presymbolic, embodied sensation of intensity or effort?
Graduated Doctoral Students:
Message to the World
When you think of math, what do you see?
I bet you saw all kinds of equations and stuff, right? Ok, that makes sense, because that's what we see in textbooks, that's what the teachers write on the board, that's what we write on the test, and that's, well, what we see of math most of our lives. I mean, what else could you see?
Well, it turns out from research in mathematics education that being able to solve mathematical problems by following some sequence of rules -- an algorithm or solution procedure for writing and manipulating symbols -- is perhaps important for passing a test that assesses that kind of knowledge, but that the rules are soon forgotten and no sense of the content remains.
Kids study, yes, but they don't learn.
Actually, it turns out, thinking mathematically -- I mean really thinking, not just plug-and-chugging numbers -- is more about bringing to mind all kinds of ideas and manipulating these ideas creatively.
Hmm... the idea of an "idea" is a bit vague, isn't it? I'll get back to that in a moment. So bear with me.
But what this all means is that what many mathematics teachers are teaching and many tests are testing are actually just the tip of the iceberg in terms of what kids need in order to think mathematically; in order to really understand.
So, sure, I share with all educators the desire that children will learn and become fluent in mathematics. I mean, I'm a dad to kids in the educational system, and I want them to do well. Yet I'm concerned whether kids are actually making any sense of what they are learning rather than just following rote procedures, in the good case.
In fact, my life work is to create and evaluate new types of activities for kids to develop deep understandings of mathematical concepts. So I'm certainly not some kind of mad scientist up in the ivory tower inventing some weird ideas that are detached from the terrestrial need for core fluency with symbols. I've tutored thousands of hours, and I've been thinking about mathematics education for 20 years now.
Still, my worry is that basic sense-making is the most important yet most neglected aspect of mathematics education, to a great deal because of the accountability pressures that teachers experience. Because we teach for tests, we throw out the sense-making baby with the... wait, that metaphor didn't work, so let me try another one. Oh yes, the assessment tail is waging the sense-making dog. Hmm... not quite. Well, you know what I mean -- kids don't get math.
It starts from about fractions, right? The big crisis. Why there? I could tell you about the difficult transition from counting numbers to rational numbers. There's lots of research on that. But what is at the heart of this crisis? I mean, sure, so we can write papers about this until the cows come home. Or jump over the moooooon. But what can we do about it?
Let me tell you a story.
Just the other day, during my office hours -- I'm a professor you see -- I was chatting about this to an eager undergraduate student who is planning to become a teacher (yoohoo!). So I asked her what ‘addition’ is -- what is the meaning of the arithmetic operation of “addition”. She answered, “It’s just, you know” [gesture 1 + 1 = 2 using “magic” finger trick ]. And I said, yes, that’s certainly one way of thinking of addition. Now what is multiplication? And she said, “Well, you keep adding the same amount over an over, like in 5 times 3.” [gestures gyrating hand with 3 fingers splayed, 5 wrist rotations] Again I said, yes, that’s it. So I asked, “What is proportion?”, and she said, well… you have two numbers like in a ratio, and then you multiply them both by the same number and you get another ratio that is equivalent.” But this time she only gestured the numerical procedure - like, what you do to the digits themselves -- she didn’t seem to have any image underlying this rote procedure, she didn't handle the quantities themselves. That is, sure, a proportion is the set of two ratios that reduce to the same quotient. Ok, does that help you, uhhhhm, 'feel' what a proportion is? I mean, right, you told me how to make a proportion but what *is* a proportion -- what does it look like?
That's what I care for -- helping kids build useful mathematical pictures in the head. Well, not exactly pictures and not exactly in the head -- more like whole-body dynamic schematic images, sort of physically moving pictures... very simple pictures, like the "addition" picture we did with the fingers before [gestures 1+1 like before], so that we can all have a familiar gesture for proportion just like we have for addition. Let me show you what I mean. [enter demo]
Some Favorite Quotations:
Confession (well, you deserve one, gentle reader, having read all of this!): My nerdiest passtime is to find mean anagrams to the names of my numerous archenemies here.