In Embodiment in Mathematics Teaching and Learning: Evidence From Learners’ and Teachers’ Gestures, Martha W. Alibali and Mitchell J. Nathan present research that shows how the gestures teachers and learners use show mathematical knowledge. Specifically, they discuss 3 types of gestures, which occur in instruction and explanations:
- Pointing gestures, which link speech to the physical environment.
- Representational gestures, which include a person, teacher or learner, using body movements to communicate a specific meaning.
- Metaphoric gestures, which are visual representations of abstract ideas.
The researchers mention that pointing gestures were by far the most commonly seen types in elementary classroom, likely because of the prevalence of manipulative in those classrooms. All of the types of gestures were used by speakers when thinking and explaining mathematical ideas were thought to be intentionally produced to facilitate communication.
Alibali and Nathan conclude “embodied knowledge is an integral component of mathematical thinking and learning. Gestures thus provide a unique and informative source of evidence regarding the nature of mathematical thinking” (p. 274) They believe that gestures should be implicitly taught in teacher education programs, as they are as important as managing and assessing a classroom.
I had several stops in this article. One of the parts of their research that I wondered about was how the data was collected. Were they recording classes? They must have been, but there is not much discussion on this point. I was also wondering how many teachers and learners they studied and at what ages. They do discuss how elementary teachers use pointing gestures more frequently than the other two types, but what is the difference? Is it significant? I would assume so, as it is mentioned as an important fact.
I found it interesting that elementary teachers used pointing the most often. Certainly I can appreciate that it makes sense that they wouldn’t use the metaphoric gestures as frequently, as they are connected to abstract ideas and mathematics-based abstraction is only introduced at the end of elementary. But I was a little surprised that elementary teachers didn’t use representational movements more. I think of these movements as a way to connect the concept to the students. When you get students moving and doing, I have found they are much more likely to learn and remember the concept in the following year.
As the article mentions, it provides compelling proof that gestures are very important to cognition in the mathematics classroom. It made me wonder whether most teachers are aware both of the importance of gesturing, but also if they are doing the gesturing consciously or unconsciously. Are learners gesturing only if they have had a teacher who consciously uses gestures in the classroom?
Do you see gestures as being an integral part of your teaching? Upon reflection, do you think you use one type of gesture more frequently than others? Or are you not aware of the gestures you use?
Movement, exercise, and body/kinaesthetic expression (including physical drama games) have always been a big part of my teaching generally. Measuring the school grounds, finding patterns in architecture, writing on windows with markers and blacktop with chalk are all examples of how I have had students physically interact with the environment in mathematics. However, I don't think that I have done much metaphoric gesturing with student. I like the idea of students embodying more complex mathematical concepts.
ReplyDelete(Continued..) The use of memory and movement connected to mathematics intrigues me. In the way our bodies learn dance or we can be reminded of an experience through a song or a smell seems similar to this process. But what is the role of repetition in this memory process? I think of military drills or piano scales. Could there be a times table dance?
ReplyDeleteIt is fascinating for me to categorize the gestures in several groups and individually define each group. I assumed all of these moves are simply gestures and never thought of arranging them. I think all teachers intentionally or not intentionally have used the gestures as a part of their teaching strategy. I believe most topics in mathematics are abstract and without having gestures, it might be a little difficult to teach them.
ReplyDeleteI am teaching high school math, and although I never thought of having gestures, I am using all of these three kinds of gestures (right now I have in mind my gestures). I have used Pointing gestures at the most to put emphasis on what I have written or to get the attention of the students on the particular matter. Sometimes I ask a question by pointing gestures on the mathematical subject on the board. However, I have used the representational gestures more often too. Most of the time it is much easier to draw a picture to describe a subject compare to verbal explanation. Also, a picture makes a common language between my student that makes me sure students gets the point. For example, when I am teaching the vertex of a parabola it is much easier to draw a parabola and Point to its vertex compare to describe it. It is fascinating that, as a teacher, sometimes I have used all three types of gestures at the same time to describe a topic. For instance, as a metaphoric gesture, I usually draw a wave by my figure in the air to show a Sin graph, then to show its characteristics I draw it on the board and then point to its parts.
To be honest, I think that I am mainly unaware of the gestures that I use. I think that I use gestures when I am talking about attitude or feelings but not as much when I talk about abstract ideas.
ReplyDeleteI do a lot of skits in all of my classes, including math. For instance, we have acted different episodes in archimedes life or we will act out word problems. I have also used gestures in big picture drawings. I think I have a long way to go in terms of using gestures for representing concepts.