embodied cognition

Embodied Cognition in Mathematics Acquisition

Justin M. Keel

Boise State University

November 11, 2012

EMBODIED COGNITION IN MATHEMATICS ACQUISITION 2

Abstract

The goal of this paper is to review the current research of embodied cognition and the

applications in the mathematics classroom. A summary of current research in this area will be

provided including how using imagination relates to embodiment. Finally, this paper will

discuss several current technologies that are being (or have potential for being) used in the

classroom to enhance mathematical learning which support embodied cognition.


At first glance, many educators may look at embodied cognition and compare it to the

theories that look at kinesthetic learning. Although embodied cognition is fairly new compared to

other learning and cognitive theories, researchers and scholars tend to agree on some basic ideas.

Most will agree “that mental processes are mediated by body-based systems, motor systems, and

the systems involved in sensation and perception” (Alibali & Nathan, 2012). This means that not

only is cognition, which includes learning, reasoning, and memory, influenced by physically

performing a task it is also influenced by imagination, perception , gesture, and simulation

(Nemirovsky & Ferrara, 2009; Gallese & Lakoff, 2005; Alibali & Nathan, 2012; Black, Segal,

Vitale, & Fadjo, 2012).

Additional research is showing that embodied cognition is a “two way street”. People do not

only create and enhance their mental processes; they also communicate their mental processes

through embodiment (Nemirovsky & Ferrara, 2009). Through this new research, embodied

cognition is giving mathematics educators at all levels a new perspective on how their students

are learning and communicating.

Understanding Thought Process

Often teachers of all disciplines ask the question about their students: “If I only knew

what they are thinking?” Current research is showing that it is possible to get a glimpse into the

students thought process by their embodiment, specifically their gestures, when contemplating,

describing, or demonstrating a mathematical problem.

Several of the studies that are referenced in this paper have conducted studies that

observe the gestures of the students or instructors. In most cases, you can determine the portion

of the problem a student is thinking about by a pointing gesture as they discuss the problem.

This can then be expanded to a specific example where as a student is describing his solution to

an equation, he used his left hand to gesture when discussing the left side of the equation and his

right hand to gesture when discussing the right side of the equation. The author of that article

concluded that even if the student did not arrive at the correct solution, he could tell from the

students’ gestures that he was aware that the equal sign in the equation divides the equation in

two separate parts (Alibali & Nathan, 2012).

In a different experiment, students were given a string, tape, and stick-on dots and asked

to graph equations in the complex plan using the tile floor as their graph paper. The groups of

students are given a multiplication problem in the complex plain and asked to graph where they

predicted the solution would be. The author of this article observed each of the students in the

group attempt to explain where the point would go and why. In each of their explanations, the

students used pointing gestures to signify where the point should go. They also used gestures

indicating they believed the point would rotate around the axis. The author asserts that these

gestures indicate a connection to previous knowledge about instances when things rotate around


an axis of symmetry. Imagination, which will be discussed later in this paper, is another key

aspect in embodiment. The students in this article had never graphed in the complex plain prior

to this, but they used prior knowledge to imagine how these graphs should look and how

multiplication should behave (Nemirovsky, Rasmussen, Sweeney, & Wawro, 2012).

Instructor Gesturing

Mathematics instructors have used gestures in their teaching for many years without

consciously thinking about it. In a study completed about gestures by an instructor, kindergarten

students whose lesson included gestures answered more than double the post-test items then the

students who received instruction without gestures (Alibali & Nathan, 2012). When a learner is

processing a lesson that is visual, a simple pointing gesture from the instructor can assist the

learner in knowing where his/her attention should be located. This will free up cognitive

resources to focus on the understanding of the concept.

In addition to pointing gestures, instructors of mathematics often use metaphorical

gestures. In a metaphorical gesture the instructor will use a motion that the learner understands

to represent a new concept. “In one example, a professor describes a sequence that ‘oscillates’

between two values, and he depicts this oscillation in gesture with his right arm moving back and

forth” (Alibali & Nathan, 2012).

Research has also shown that instructors use more gestures in the communication

following items that are difficult to understand. This leads Alibali and Nathan to conclude that

gesturing is a tool that instructors already use to assist in the communication of ideas (Alibali &

Nathan, 2012).

Imagination

Embodied cognition goes far beyond simple pointing and gesturing, even though this is

the start of our embodiment. As stated in the introduction to this paper, imagination is one of the

keys to embodied cognition. In neuroscientific research, scientists have shown many interesting

facts about the imagination.

When a learner uses visual imagery, many of the same parts of the brain are used as if

they are actually seeing. When a learner uses motor imagery, many of the same parts of the

brain are active during actual motor functions of the body (Gallese & Lakoff, 2005). The

following quote from Gallese and Lakoff explains how strong this connection is between actual

motor movement and motor imagery. “Motor imagery shows the same embodied nature as

visual imagery. Mentally rehearsing a physical exercise has been shown to induce an increase of

muscle strength comparable to that attained by a real exercise” (Gallese & Lakoff, 2005).


If this connection between motor imagery and actual motor functions is strong enough to

increase muscle strength, then surely it is strong enough to create cognitive responses similar to

those achieved through kinesthetic learning. Using the imagination aspect of embodied

cognition opens up new doors to those using embodied cognition in their classrooms. No longer

can this theory be applied only when the learners are physically able to perform an activity.

Embodied cognition can now be applied to classrooms in two additional ways.

Using visual imagery opens up discussions in mathematics classrooms. As Nemirovsky

and Ferrara state, using imagination “helps us to shift our attention from ‘what is’ to ‘what could

be’”. They continue on to state that “it is particularly essential to account for the experiences of

abstract realms” (Nemirovsky & Ferrara, 2009). In the article written by Nemirovsky and

Ferrara, one student sat behind two translucent screens in a “V” shape so the other students in the

class could not see her. The student behind the screen traced geometric figures with a “pointer

device” that consisted of two laser pointers aimed at the translucent screens. As the student

behind the screen traced the figure, the rest of the students could only see the movements of the

lasers on the translucent screens. By using visual imagery, the class discussions focused on the

possibilities of the shapes drawn behind the screen, not the actual shape. In this case using visual

imagery was the key to assisting the students to think abstractly (Nemirovsky & Ferrara,

Mathematical imagination and embodied cognition, 2009).

The second application of embodied cognition and imagination in the classroom is

simulation. Simulation has been used in the classroom previous to embodied cognition;

however, with the current advances in technology, it is becoming easier and more common for

instructors to have resources to perform meaningful simulations in their classrooms. In

classrooms of the past, a simulated activity could only be accomplished by great expense or time

by the instructor. With current technology, simulations can be achieved by using computer

programs or apps, virtual worlds, virtual experiments, and many others. With the increased use

of simulations, the learner has an increased ability to explore concepts without fearing the

consequences of breaking an expensive piece of equipment or “blowing up the lab”. Without the

hindrance of fear, the learner is free in his/her experimentation and can build connections that

were not even possible ten years ago.

Using Technology to Enhance Embodied Cognition

Over the last ten years, technology has rapidly progressed and has been included in

classrooms of all levels. Technologies range from computers, touch screen devises, and motion

sensors to gaming systems, virtual worlds, and robotics. With the availability of these

technologies, we can empower learners to connect with content and make stronger cognitive

connections than ever before.


Botzer and Yerushalmy had observed that their students consistently had problems with

2D motion graphs. These problems included understanding how position, time, and velocity

were related on a graph. Botzer and Yerushalmy then taught this topic by setting up motion

sensors and a computer program that records the motion as a graph. Groups of students then

walked, changed speeds, stopped, and resumed their path in front of the sensors to analyze what

the motion graphs would look like. This physical embodiment of the abstract concept supported

the learners’ conceptualization of motion (Boltzer & Yerushalmy, 2006). This scenario

demonstrates how technology can assist in the physical embodiment of a concept.

Gestures for both learners and instructors have been discussed earlier in this paper as a

method to convey meaning or interpret cognition. Gestures can also be used to construct

learning. There are now many multi-touch devises on the market and in classrooms today (i.e.

iPad, Surface, and Android devises). These multi-touch devises all have gesture based

interfaces. Another gestural interface that is starting to be researched for education is the free-

form gestural interface. In the free-form gestural interface, the user does not directly need to

touch the devise. The most common free-form gestural devise currently on the market is the

Microsoft Kinect. When using the Kinect a user only needs to stand in front of the sensor and

can gesture with arms, hands, head, feet, or legs. The Kinect has the possibility to change the

way a learner interacts with their environment to construct new learning. Although research into

these devices and their connection to embodied cognition is still in its infancy, some connections

have been made between a gesture based interfaces and thinking and learning (Black, Segal,


Several small studies have been conducted comparing touch based devises to the

traditional interface of a computer and mouse. The results of these studies indicate that if the

gestures are “congruent” with the concepts, touch based interfaces could benefit thinking and

learning (Black, Segal, Vitale, & Fadjo, 2012). As stated before, more research needs to be

completed to draw any conclusions about touched based devises, but the preliminary results look

promising.

Current technology also allows for an increase in the amount of simulations that learners

can experience. Simulations can include simulated laboratories to conduct experiments, virtual

worlds to interact with the environment or people, video games for interacting with the

environment, or using avatars or robots to embody the learner’s thought process for testing.

There are currently programs in secondary and post-secondary schools that are using World of

Warcraft, currently the most popular Massive Multiplayer Online Role Playing Game

(MMORPG), to connect with students and to place them in an atmosphere where they can learn

under the cover of an avatar without fear of failure or rejection.

Additionally simulations such as robot programming and video game design can assist

learners in constructing learning and understanding. By embodying a robot or avatar with a

learner’s current knowledge or understanding of a situation, the learner can test their knowledge


in a surrogate. This programing assists the learner in thinking through steps while programming

and then is able to watch if their programming had the desired effect. Even when this

programming is unsuccessful, learning and understanding are being constructed by the learner.

When a learner is given the opportunity to embody their thought process in a virtual environment

or robot surrogate, it “increases student learning, understanding, and motivation (Black, Segal,


Conclusions

Embodied cognition can have a profound impact on the mathematics classroom. By

closely looking at the gestures that instructors use and even planning these gestures, we have the

ability to enhance student learning. Instructors also have the ability to understand learner’s

thought process and can adjust learning activities based on close observation of the learner’s

gestures.

Embodied cognition will take on a significant role as technology continues to advance in

the education system. By expanding embodied cognition from purely physical acts to the realms

of simulation and imagination, we can enhance student understanding of particularly difficult

concepts including abstract concepts in the area of mathematics.

Finally, as technology continues to advance, more research needs to be completed in the

area of embodied cognition both from an educational standpoint and from a neuroscience

standpoint. If research can determine correlations between specific gestures and thought

processes, communication and instruction in the classroom could be greatly effected for the


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