Cooperative Learning vs. Small Group Method

I am taking a course, Constructivism Strategies for E-Learning, through the Department of Educational Technology here at UBC, and we’ve been exploring different instructional strategies. It’s funny, but I thought I knew what “cooperative learning” was, but there are so many different definitions of it! I found the exercise in comparing strategies valuable, and decided to share my thoughts.

Cooperative learning and SGAM (small group activity method) are similar in that students discover content and teach it to one another and to the class, with the teacher is “guide on the side.”  The focus of the description of each focuses on the specific set up of the classroom activity, such as number of students in each group, how long each portion of an activity is, etc.

Cooperative learning differs from, and seems more effective than SGAM in that groups in cooperative learning are sustained over longer periods – perhaps working on a problem/project for a whole unit or a whole year, while in SGAM the description seemed only concerned with a 30 minute to 1 hour period. In addition, in SGAM, students are working with others, but the sources we were led to did not seem to be mention a focus on teaching students the skills necessary to work effectively in teams, such as listening effectively, interjecting politely and ensuring everyone has a voice.

Both cooperative learning and SGAM are problematic in that they seem to undermine some key aspects of constructivism. For instance, in cooperative learning, diversity of students is addressed but there is no provision for students to have individual thinking time – or at least this is not documented. I don’t think that a student should simply work alone and they need to learn how to work with others, but what if a student learns best by processing content alone first, then sharing their ideas? How do these students access learning?

Cooperative learning and SGAM each have students working in groups which addresses the social nature of learning and all the aspects of the works of Piaget and Vygotsky that speak to this. However, cooperative learning and SGAM are too prescriptive, which seems to contradict the “guide on the side” persona that the teacher is invited to take. Depending on the amount of control exercised by the teacher, the ownership over learning and the complex process of knowledge construction could be compromised. Hopefully, teachers wouldn’t be too invasive with their interventions and hopefully they wouldn’t just set up the class in groups and give an activity and assume the learning happens as long as the students talk it out. The question that teachers need to ask themselves constantly is where the balance lies between being too controlling and too “hands-off”?

Ethnomathematics

I’ve just recently been doing some readings on ethnomathematics. From what I’ve been able to figure out, ethnomathematics is the study of mathematics of different cultural groups. Its goal is to teach value for one’s own culture, respect for another’s culture, and curiosity to learn more about different cultures while teaching mathematics in a cultural context. That being said, it is a fairly new and ever growing and changing field of mathematics education, so the definition can vary significantly at this point, informed by the life experiences and culture of the person giving the definition!

Ethnomathematics is likely controversial because it does not conform to the needs of advocates who support traditional, computational, arithmetic and algebra driven curricula (see math wars). It requires a more exploratory and interdisciplinary approach to the subject. However, if one is to embrace ethnomathematics, one then opens themselves up to examining the way mathematics is done in all cultures, rather than only the canonically respected mathematics that was done in Europe that is still taught today. Often teachers balk at “multicultural mathematics” because it means an awkward application of mathematics to, say, number systems at the beginning of the year that quickly gets seen by the teacher as a waste of time because it doesn’t tick boxes on the list of curriculum objectives. This is an unfortunate misunderstanding.

Ethnomathematics also opens the door to issues of culture and representation in mathematics and in education in general, which many teachers may not be emotionally prepared and/or educationally trained for (or simply not be interested in dealing with). However, Ron Eglash (2009) exposes a way that we can use culture as a bridge to math – and nicely tick some of those curriculum objectives as well – while integrating art and mathematics in exploration of weaving or architecture or religion. While I can’t provide the article due to copyright, check out his TED Talk.

In addition, D’Ambrosio’s (2001) more philosophical piece seems to imply that ethnomathematics is a way to explore the diversity of cultures while simultaneously being something that students can gather themselves around. While cultures, such as Inuit and Navajo and Maya, may have different perspectives on the distribution of time, the heavens, and agriculture due to their proximity to the equator – in essence, they have different ethnomathematics – these cultures are united by the fact that they have come to ways of knowing through interaction with their environment – in essence, that they have ethnomathematics. Both D’Ambrosio and Eglash, it seems, agree on the rich, paradoxical “unity through diversity” that ethnomathematics can bring to the classroom.

This is an interesting area for teachers to explore if they’re looking for interdisciplinary learning to come alive in their classroom!

References

Eglash, R. (2009). Native-American analogues to the Cartesian coordinate system. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.). Culturally responsive mathematics education (pp. 281-294). New York: Routledge.

D’Ambrosio, U. (2001). Ethnomathematics: Link between traditions and modernity. The Netherlands: Sense. (Chapter 2).