Culturally Responsive Education in Mathematics

indigenous aboriginal education mousewoman

This artwork is of Mouse Woman, the Narnauk supernatural shape-shifter. This art was used as official artwork of the Aboriginal K-12 Math Symposium, held at the UBC Longhouse. Artist William (Billy) NC Yovanovich Jr.––whose Haida name is Kuuhlanuu––is a member of the Ts’aahl Eagle Clan of Skidegate, Haida Gwaii.

Last week, our Mathematics, Community, and Culture class discussed culturally responsive education – yet another controversial and evolving topic in mathematics education. It seems to me that culturally responsive education is a philosophy whereby a teacher (or a writer of curriculum) attempts integrate culture and curriculum in a way that emphasizes the ways of knowing of different cultures so as to provide a richer educational experience. In the context of indigenous issues consistently under consideration here in British Columbia, many of the members of the class wondered if there was bias in which culture education was meant to be “responsive” to. You can see how there can be a debate here about whether or not culturally responsive education aims to “respond” to a particular culture, or remove some of the emphasis from another.

Due to a prevailing dichotomous view of “dominant culture” and “less-dominant culture”, culturally responsive education can strongly imply a requirement of dominant cultures to recognize cultures that have long been less dominant. I agree that the role of culturally responsive education, according to Mukhopadhyay (2009), should be to treat all cultures fairly rather than equally. Education does need to recognize other less dominant cultures more than dominant ones simply because dominant cultures will prevail in other aspects of a student’s environment regardless of what we do as teachers. This does not mean total exclusion of dominant cultures, but it should mean an effort on the part of the teacher in all subjects (not just mathematics) to respond to many cultures positively and to expose students to many cultural paradigms.

How this is done is incredibly complex and likely looks different in each classroom, but, as was said by Christine Younghusband, speaker at the most recent Aboriginal Math K-12 Symposium (2012), if we want our students to be culturally responsive (or take on any other value), we as teachers need to be culturally responsive (or truly believe in that value). Storyknifing, for example, to introduce the idea of geometric visualization instead of, say, giving a worksheet and some plastic block manipulatives to students is a simple way that a teacher can introduce a mathematics topic (and tick those curriculum objectives!) while giving a strong message to students of the strong mathematical heritage inherent in many cultures. But this message will only be strong if a teacher uses a strategy like Storyknifing within a consistent effort in the classroom to invite students to think critically about culture and the perceptions that prevail. The message will only work if the cultural context of an activity, like Storyknifing, is preserved. One wouldn’t want students to see storyknifing while learning Cartesian Coordinates and get the impression that storyknifing was used in navigation.

If someone were to simply use the Math Catcher videos, for example, as one-off or as one of a few of intermittent cultural resources in their classroom, it would appear to the students as nothing more than a video version of an ordinary word problem stated in a Squamish context. Culturally responsive education is not about using storyknifing or Math Catcher videos in one’s classroom, but about a philosophy of classroom practice to expose students to different perspectives and cultures and to encourage them to investigate and question dominant paradigms.

References

Mukhopadhyay, S. Powell, A. & Frankenstein, M. (2009). An ethnomathematical perspective on culturally responsive mathematics education. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.). Culturally responsive mathematics education (pp. 65-84). New York: Routledge.

Lipka, J. Wildfeuer, S. Wahlberg, N. George, M. & Ezran, D. (2001). Elastic geometry and storyknifing: A Yup’ik Eskimo example. Teaching Children Mathematics. February, 337-343.

 

Cooperative Learning vs. Small Group Method

Cooperative Learning Tags - assigning students with roles for an activity.

Photo: Cooperative Learning by ielesvinyes

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”?

Categories of Research in Education

Photo: Balance, by BCth

Photo: Balance, by BCth

Humans characterize things as a way of gaining a better understanding. Research methodologies are no different. However, as Lawrence Sipe and Susan Constable (1996) point out in their article summarizing research paradigms, we need to beware the oversimplification that characterizations can bring – not so easy when what we naturally like to do as humans is categorize things, especially as we are coming to grips with them. We can’t stop characterizing altogether, but Sipe and Constable rightly point out that categorizations may imply a dichotomy (either THIS way or THAT way) or assume a univocality (neat word, eh?) – that there is only one way to look at a concept. The consequence in research, and anything else in life for that matter, is that unique characteristics get lost.

Sipe and Constable are specifically referring to the categorization of research as either “qualitative” or “quantitative” – but of course, one might use both these strategies to triangulate data, or a more reflective research method that doesn’t really fit into either of these categories. Then we run into the problem that these categorizations mean something slightly (or perhaps drastically!) different depending on the field you’re in. So here we see an example of where categorizations, especially long standing ones, fail us.

One aspect of the article that made me stop was Sipe and Constable’s (1996) point that characterization of a research methodology does NOT imply the use of a particular method. Surely some methods would lend themselves to be used by those utilizing certain research methodologies. For example, a clinical interview method might be used by someone prescribing to a qualitative methodology. However, one would not say uniformly that using one research methodology (i.e.: qualitative) means that the researcher is necessarily using a particular method (i.e.: interview). This makes perfect sense, but is not something I had thought of before reading this article. Quite a few of our guest presenters in my Research Methodology in Education course use multiple methods, each of which supports the use of the other!

Another place that made me stop was the characterization of the relationship between researcher and researched given by Sipe and Constable (1996). I have read enough educational research to know about clinical interviews and the various ways this is done to understand students and teachers and others in the educational research process. However, the characteristics given in the article highlight the importance for me in deciding whether or not the research subject should be informed about the research process or not, and to what extent the researcher her/himself lets themselves be analyzed as part of the research process. While some could argue that research data is confounded if the researcher becomes part of the research, there are other schools of thought – A/R/Tography and Currère as examples – where the subject matter is enhanced by the exploration and questioning of the researcher’s worldview (deconstructivist – see article). If we truly respect reflective practice in our teachers, then surely why not reflective practice in our educational research? I can see, of course, the difficulty this may cause for those in the context of copyright laws and BREB ethics approval applications that demonstrate the serious, disciplined side to research. However, I can see now the arguments that could be given for different forms of educational research and how heated the debate could become!

Ethnomathematics

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Image by Ron’s Iteractions (note: not Ron Eglash). Original photo by NASA/GSFC/METI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team

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).