Research in Our Classroom

Structure, Photo by p medved

Structure, Photo by p medved

I have been questioning lately what methods I can use to understand my students better – not just their work, but their experience of mathematics in my classroom and of the subject in general. I’m taking a uniquely structured (I mean this as a good thing!) research methodology class with Dr. Susan Gerofsky and Dr. Cynthia Nicol here at the Department of Curriculum and Pedagogy at UBC (In fact, it can only be characterized as “standard” insofar as it is a course requirement for my program). Our exploration of research methods has been helpful both in learning methods that one can use for academic research and in reflecting on ways I will be able to investigate my practice when I return to the classroom.

I’ve been used to some pretty standard ways of “getting to know” students. We give them assessments to perform – a variety of types of tasks from tests to open-ended, long-term projects – to give us a sense of their understanding of the concepts of the course they’re taking. Throughout the year we might give them written surveys telling us a bit about how they’re feeling about our teaching or about the course’s progress or our teaching subject in general. We likely give formative checks for understanding through observation, a quick chat, an “exit card“, or visible thinking routines. Regardless of how much information that can be gained from some of these standard and non-standard ways of collecting data, might there be something missing? Might there be something to be gained from collecting information through a different medium – and from involving them in the information gathering process?

Freedom, Photo by Josef Grunig

Freedom, Photo by Josef Grunig

In Donal O. Donoghue‘s (2007) article on boys’ masculinity in places outside the classroom, Donoghue uses photography and a/r/tography methodology to create meaning with boys aged 10 and 11 rather than to use them to discover and make truth claims (as most research does in treating research “subjects” as if they are being used to gain knowledge about something). According to Donoghue (2007), “doing research in and through art offers opportunities to capture and represent that which is not always linguistic – that which can be more profitably represented and understood through nonverbal forms of communication” (p. 63). My conflict with this type of research is that I see both sides. I see that it offers a different way to view a sensitive topic – using non-verbal “data” (i.e.: photographs) through the view of 10 and 11 year olds – a  view that has the potential to reveal something never before explored. However, I can see also the risk of  photographs to be open to a much wider scope of interpretation than written data might be. So, based on what this method offers us – and does not offer us – Donoghue’s (2007) words make me both optimistic and nervous: “how we do and represent research is inseparable from what gets communicated” (p. 64).

Comparing our work with interviewing methods for research purposes, and reflecting on similarities and differences with the use of photography as detailed by Donoghue (2007), I notice more similarities between them. As with interviewing, photography has the potential for inviting the participant into the research process, and offers non-verbal representation (interviewing does this through gesture and tone of voice). Both need to be examined within the social and cultural contexts in which the product (speech, photograph, art, etc.) is produced. However, which is liable to produce more accurate interpretation? For example, are we more likely to get an accurate view of what a child thinks of our subject if we ask them to tell us, or if we ask them to take a picture that represents how they feel and discuss the photo choice with us? The old cliché about pictures and words comes to mind, but beyond that, one could argue that reading and re-reading a script made from an interview can continue to create just as many new meanings as can having a look and a second/third/fourth look at a photo. The difference between interviewing and photography that I can see is that interviewing offers the potential for a much more fixed, rigourous process, whereas the use of photography, to a large extent, is itself a commitment to embrace a research method that involves the participant much more in the process.

Regardless of these structural aspects, there might be something to the use of photographs to find out more about students’ thinking. Consider school culture. When you ask a student to write down feedback, like in a survey, this structured written form is similar to what students experience in other parts of school and there may be strong psychological aspects at play governing their answers. However, exit cards are casual and quick, often on 3×5 cards which is not specifically how class tasks are done – which may cause them to open up a bit further. So, if you ask students to send you a digital photo with a description as a way of answering a question (of course, if this is logistically possible in your context), this could provide you with different information that you would have otherwise received using a different format.

References

Donoghue, D. O. (2007). “James always hangs out here”: making space for place in studying masculinities at school. Visual Studies, 22(1), 62–73. doi:10.1080/14725860601167218

Math and Place-Based Education

A scene from Central Vietnam, Photo by Rob DeAbreu

A scene from Central Vietnam, Photo by Rob DeAbreu

Place-based education (PBE) is based on the fundamental idea that places are pedagogical – they teach us about the world and how our lives fit into the spaces we occupy. It began with community education and community-as-classroom – the idea that students could learn by paying closer attention to their community and doing work within it. The idea has since expanded to investigate the learning that happens in field-trips or long-term projects outside of the classroom, to examine the pedagogy of places of all sizes and locations, and to explore the meanings that different people attach to place. One can argue, that – to an extent – there is an activism component against the current state of the education system, which – in most cases – assumes that the school (and the classroom) is the place where learning occurs.

For Dr. David Gruenewald (2003) – who now goes by the name David Greenwood – place-based education (PBE) is in large part a response to standards, testing, and accountability, the threefold education reform movement of the last two to three decades (though grounded in some much older ideologies). As mathematics is the gatekeeper discipline to many careers and university programs – whether with a mathematics component or not – it is a discipline that, it could be argued, is the target of PBE’s response. With this in mind, it is no surprise that Gruenewald/Greenwood (in Green, 2005) expressed his skepticism about the possibilities of developing place-conscious mathematics. However, is mathematics – the very tool incorrectly used to assess students, and thus misunderstood by so many – the ideal vehicle to drive PBE’s response to misguided education reform?

Classroom, by evmaiden

Classroom, by evmaiden

Much has been written about cultural border-crossing in science education – challenges that students come to when negotiating between their life-world and the culture of the discipline of science (Aikenhead & Jegede, 1999; Jegede & Aikenhead, 1999; Jegede, 1995). Similar arguments have been made by Boaler (1993, 1998) and Schoenfeld (1989) that a similar struggle, manifesting in difficulties in knowledge transference, goes on in mathematics education. PBE acknowledges the divide between students’ life world, and the culture of school and mathematics, and Gruenewald/Greenwood (in Green, 2005) cites it as a result of the disconnected place – the school and the classroom – that students are meant to learn in each day. So, PBE can contribute to mathematics education, and mathematics can contribute to the activist elements of PBE. I disagree with Gruenewald’s challenge that place-conscious math can’t exist.  Gruenewald/Greenwood (2003) himself says, “people make places and places make people” (p. 621). PBE embraces our agency to leverage the power of place in our lives and learning just as it acknowledges the influence that place has over our identity. While learning must take place in a physical classroom in most schools, with all the aspects of schools that this entails (timed periods, separate subjects, etc.), it does not mean that we should give up trying to transcend the barriers and isolation that schools can create. In the interview, Gruenewald/Greenwood (in Green, 2005) points out that in the process of “aligning” curriculum and standards, curriculum is treated as a means to an end (to meet the standards) and is forever altered. How do we mediate the two? If we can’t, what changes can we make to enable schools to connect students better with the outside world?

Technology is a given, by Scott McLeod

Technology is a given, by Scott McLeod

One could argue that the infusion of technology in our classrooms further removes us from our world – because technology forces us to perceive our world through a screen and interact with it through a machine. There are others who would argue that technology connects us – like I am connecting with you right now having made my ideas available for comment, or like many professionals and friends connect using Twitter and other social media.  In a different way, a framework like ethnomathematics is one way to enact PBE in mathematics – by inviting students to be aware of other places and cultures that surround us. Perhaps by being inspired by the mathematics embedded in others’ and our own cultural practices, students can transcend the classroom space and acquire the learning that we seek for them. Regardless of what solution is suggested, however, can we transcend place? Or does the fact that students are located in a classroom during the day completely undermine the ability to enact PBE? And, if we can transcend place – that is, if the place they are in (school and classroom) recedes from consciousness as teachers attempt to enact PBE – does this mean that we have enacted PBE successfully or failed to enact it?

I have more questions than answers about this at the moment. One of the purposes of PBE is to catalyze a dialogue about place and education, so perhaps finding “ways” to make it “work” isn’t really the point!

References

Gruenewald, D. (2003). Foundations of place: A multidisciplinary framework for place-­‐conscious education. American Educational Research Journal, 40, 3, 619-­‐654.

Green, C. (2005). Selecting the Clay: Theorizing place-­‐based mathematics education in the rural context (Interview with David Gruenewald). Rural Mathematics Educator. ACCLAIM.

Smith, G. (2002). Going local. Educational Leadership, September 30-­‐33.

Boaler, J. (1993) The role of contexts in the mathematics classroom: Do they make mathematics more ‘real’? For the learning of Mathematics, 13(2), 12-­‐17.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29, 41-­‐62.

Schoenfeld, A. H. (1989). Explorations of Students’ Mathematical Beliefs and Behavior. Journal for Research in Mathematics Education, 20(4), 338–355.

Aikenhead, G. S., & Jegede, O. J. (1999). Cross‐cultural science education: A cognitive explanation of a cultural phenomenon. Journal of Research in Science Teaching, 36(3), 269–287.

Jegede, O. J. (1995). Collateral Learning and the Eco-Cultural Paradigm in Science and Mathematics Education in Africa. Studies in Science Education, 25, 97–137.

Jegede, O. J., & Aikenhead, G. S. (1999). Transcending cultural borders: Implications for science teaching. Research in Science & Technological Education, 17(1), 45–66. doi:10.1080/0263514990170104

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”?

Power in Leadership

This semester, I am taking a survey course in educational leadership – Leadership in Educational Organizations – through the Department of Educational Studies here at UBC, which is taught by Dr. Mark Aquash. It has been good so far to explore issues in leadership and see how the research can aid decision making and actions taken in leadership positions. We read and responded to an article called The Seven Principles of Sustainable Leadership, by Andy Hargreaves and Dean Fink, and I wanted to share my thoughts.

In the article on Sustainable Leadership, by Hargreaves and Fink (2004), I most identified with the principle “Sustainable Leadership Spreads.” At my previous school, UNIS Hanoi, I was the grade level coordinator for sixth grade and had the opportunity to experience how difficult it really is to “spread” leadership around. While a school can offer a position where there is a need, this is just the first step. Some saw my position as one of simple busy work, while I saw it as an opportunity to make a difference in the lives of the students transitioning from elementary school to middle school. I never thought of it before, but a position could mean different things to different people, which could have any number of consequences! As the position evolved, more decision-making capacity was given to the “middle managers” like grade level coordinators, department heads, and the like at the school. This was an improvement as it “spread” leadership to more than just the administration team, allowing more teachers to have more input. In addition, the school “spread” leadership in different ways by providing opportunities throughout the year to present an element of one’s classroom practice, usually with educational technologies, in workshops set up in various forms, led by Clint Hamada and Michelle Matias. In this way, the school provided both long and short-term opportunities for its teachers to demonstrate leadership in their respective fields, which has positive effects for staff morale and collegiality.

I like the fact that C.M. Shields‘ article, “Hopscotch, Jump Rope, or Boxing” (2005), acknowledges the existence of power and the differences between men and women.  Often it’s so cumbersome to acknowledge these things due to peoples sensitivities, and some of the dangers inherent in stereotypes. I wonder, as a leader, how you can ensure that you are spreading power fairly among men and women – or among other categorizations of groups. I guess the first question is – is it your power to spread in the first place? Dr. Helen Timperley says that leadership is inevitably distributed, a point that I like. But that is a whole other discussion!

I felt the concept Shields mentions that the work at the university itself was gendered was the idea I most connected with in her article – but I think that’s due to a recent class I took with Dr. William Pinar. Shields’ article talks of a few of the women leaders in the university observing that the care for others and other elements of the jobs done in their universities were themselves gendered. I agree with Dr. Pinar that the teaching profession is gendered – whether there are a majority of women teaching at our schools or not, the caregiving role of teachers has for centuries been seen as feminine.  But Dr. Pinar goes further to state how he feels the teaching profession is treated with contempt and mistrust – and that the gendered state of the teaching profession is the reason why teachers are not given the same professional courtesy as, say, doctors, lawyers or engineers (have a look at one or two of his many books – they make an enlightening read).

Shields’ article only touched on this briefly, but I would be curious to know if the work of professors in higher education is gendered in a similar way – and how this affects the “spread” of leadership in this sector.  I’m also interested to see how the gendered status of the teaching profession affects the work of administrators.  Are administrators gendered feminine too since they work in this gendered profession, or do administrators transcend this gendered role since they are “in charge”, and is this status seen in public eyes as “male” and thus given the status it deserves?  And, whatever the answer is, how does this affect the “spread” of leadership.

There’s no simple answer to this question, but one worth considering. As you can see, these articles brought out a scatter of thoughts!

References

Hargreaves, A., & Fink, D. (2004). The seven principles of sustainable leadership. EDUCATIONAL LEADERSHIP, 61(7), 8–13.

Shields, C. M. (2005). Hopscotch, Jump-Rope, or Boxing: Understanding Power in Educational Leadership. International Studies in Educational Administration, 33(2), 76–85. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=19363506&site=ehost-live

Timperley, H. S. (2005). Distributed leadership: Developing theory from practice. Journal of Curriculum Studies, 37(4), 395-420. doi: 10.1080/00220270500038545