A Reflection: Roles and Complex Instruction

Think First. Photo by Jason Devaun

Think First. Photo by Jason Devaun

A few months ago, I wrote a post entitled Roles and Complex Instruction: Getting the School Year Started. It was written during a period of particular optimism and excitement as all we teachers feel at the start of a new school year. After returning to this post and having a re-read, I had some thoughts that I wanted to get down about how it has all turned out so far. As always, I am very much open to comments from anyone who might have some suggestions for how I might improve learning experiences for my students!

I came into the year with a goal to start my grade 9 students off with the language of functions that they would need to be successful during the school year. Our school offers all three IB programs and so their MYP program requires them to investigate patterns, apply mathematics to real world situations, and communicate themselves effectively. It seemed logical to apply complex instruction in this case to get them verbalizing their thought process while gathered in dialogue around mathematical concepts.

Unfortunately, I haven’t gotten roles to work as well as I’ve wanted as students tackle a task together in groups. It often seems that students have so much language to deal with as English Language Learners (ELLs) that focusing on the roles has gotten in their way of getting the task done. The purpose of the roles is to help them work better together on a task as the roles themselves are interdependent rather than acting as a division of labour. Getting them to follow the roles has been more challenging than I expected, and it has a lot to do with how much attention I give this during a lesson. In the end, I just want them to gain understanding and whether they follow the roles or not becomes secondary as valuable seconds of a lesson tick away. Naturally, they have been very quick to figure this out!

Another challenge I face is that a lot of my students’ conceptual work together takes place in their Mother Tongue (often Korean, though some Chinese students attend our school) as it needs to for maximum learning gains (much research has shown this, but here is one example). So the bigger challenge that I face is how to get the students speaking in English and learning academic language that I require of them in English. And when in their conceptual process do I do this?

Looking back, I should have had students learning math language and group work language in smaller chunks. I wonder if I introduced the roles too soon as well. Having a unit where I simply focused on the mathematical language was a good idea, but it also came at a time when a whole host of other words needed to be in their vocabulary too. That was just too much.

My plan now is to take a step back and deal with math language. I will not disregard the roles, and when a task really calls for them, I will use them. So far, however, a strength in my classroom is that the tasks I have been able to present are group-worthy, and so I am getting the students together in productive discussion about mathematics, which is an achievement. I will continue to work to make tasks that are group-worthy, and I will use more visible thinking routines to make the key concepts from lessons more explicit. I have provided sentence frames for students at their tables, but these need to be a more central part of each lesson as they have been often overlooked. I think these things and my expectation that they speak in English at appropriate times in the lesson will go a long way to bringing up their use of academic mathematical language.

By the way, if you’re looking for some examples of math group-worthy tasks, check out NRICH.org. They have a great selection of resources for mathematics teachers, making learning tangible and encouraging students to gather together around a great problem.

I want my classroom to be a place where students are building confidence in their problem solving skills and their intuition for innovation. Math is, after all, where you can learn how to work within parameters to make your own possibilities, not follow a set of rules that someone else gives you. It sometimes feels like the steps I’m taking to get my classroom there are SO small! But I have to remember that it’s the taking of the steps that matters.

Roles and Complex Instruction: Getting the School Year Started

small group work by susan sermoneta

small group work by susan sermoneta

This past week, I have started preparing for a new school year and reflecting on some of the classroom structures I want to refine. While I’ve studied complex instruction during my M.Ed, I am still very new to implementing it in the classroom so I thought I would throw out some ideas here about group work structures that I’m thinking about implementing. Particularly, I’m wondering about some of the specific aspects of these structures and whether they may have impact on positive outcomes I’m trying to achieve. In this post, I will particularly discuss the administration of roles in group work and complex instruction. Please post suggestions or thoughts below in the comments.

First, I’ve been reading Smarter Together with interest, and have decided to implement their suggested roles for group work: Facilitator, Inclusion Manager, Recorder/Reporter, and the Resource Manager.

  • The facilitator’s role will be to encourage the completion of the task by getting the group off to a quick start, and checking if all of the group members understand what is going on along the way.
  • The inclusion manager will oversee the behavior in groups, keeping people on task, keeping discussion focused on the task at hand, and ensuring students play their roles.
  • The recorder/reporter will make sure data is being recorded and will present group findings at the end of the class.
  • The resource manager will obtain and put back resources that are needed for each task, supervise clean-up of the group’s table, and will bring group questions to the teacher.

I’m keen to use this structure as these roles and the responsibilities are not completely separated. There is enough overlap to avoid confusion among students regarding what each is supposed to do, yet the responsibilities are structured so that students remain interdependent throughout the task ahead of them. I’m planning to rotate these roles to give each student a chance to fulfill different group work responsibilities and build different skills needed in group work – and so students each have access to all the roles. I won’t rotate mechanically but rather plan to use a developmental framework developed during the Assessment and Teaching of 21st Century Skills project coordinated by Patrick Griffin, Esther Care, and others at the University of Melbourne. I hope to use this developmental framework to help me decide when to place students in particular roles, and what kinds of interventions are needed to help them build collaborative problem solving skills. It’s my first time through trying this out after their MOOC this summer, and so wish me luck!

Which way for happiness? by Andrea Marutti

Which way for happiness? by Andrea Marutti

Last year, I struggled with deciding when to rotate groups and their members. Some of the literature I read suggested randomly choosing members for groups and reshuffling (again, randomly) groups and members after every two weeks, enforcing the fact that students couldn’t just change groups and had to learn to work with those they were paired with. However, I found that the group folders – where students put their collaborative work for reference at a later time – broke down as a system since students might have been part of two or three groups during an entire unit of study. My feeling this year is that I will only randomly choose group members after a unit of study has been completed and each of the groups has gone through that complete journey together. I wonder, though, whether this will cause conflict for students if they end up in groups with someone they don’t work well with. It remains to be seen what issues come up and I welcome any ideas about this.

A second wondering I have is how to teach my students about these roles and structures when all of them have the added challenge of being EAL/ELL learners to varying degrees? Specifically, I am thinking about the plethora of information that I will need them to take in and act on: roles and their responsibilities, norms for behavior when working in groups, language they should use to perform each role effectively, language they should use in general when working through a math problem (making observations, analysis, etc.), and the language of the developmental framework so they can understand how to develop their collaborative skills. When I consider as well the other classroom administrative vocabulary that come along with teaching in the MYP and communicating changes for Next Chapter, the challenge becomes so much more daunting. Of course, I don’t expect them to “get it” right away, but I don’t want to throw so much at them that they just turn away from it completely. I plan to put posters up, and refer to them often as I roll through activities at the start of the year particularly directed at helping to make these roles and group work behaviours explicit.

For all learners, skills to promote successful collaboration are essential to learn for many aspects of living in the world. For EAL/ELL learners, collaborative activities can create the need for them to practice vocabulary and promote language acquisition at the same time. However, I am keenly aware that piling too many challenges on students creates the danger of doing many things a satisfactory level instead of doing a few things well. Still, one can’t develop a system that works in their classroom without some thoughtful experimentation!

Change in Schools and Complexity

In a 2003 paper*, Brent Davis and Elaine Simmt write about the application of principles of complexity to the teaching of mathematics. Complexity science is essentially the study of living systems that are adaptive and emergent – and so it is a wide-ranging branch of scientific study. I enjoyed their article as their consideration of a school, of a classroom, of a department – of learning in general – as a living system really highlighted some important aspects of teaching and learning for me. Again, I know that this article is over 10 years old, and this may be considered “old” information, but I think the article falls into the “oldie but a goodie” category and I wanted to reflect on it here because it is such a good read.

Davis and Simmt outline several conditions that must be present for a complex system to emerge. While reading these, think of the different layers of a school – a concept to be learned, a group of four students working on an activity, a classroom as a whole, a mathematics department, a grade level team, a middle-high school faculty, an entire school staff (K-12), a school community as a whole, the administrative team, etc.:

1)   Internal Diversity: members of the system must be diverse enough to be able to contribute different things to their purpose.

2)   Redundancy: members must have enough in common in order to interact more favourably.

3)   Decentralized Control: members’ results are collective, not the result of one member or a central “leader”.

4)   Organized Randomness: Proscriptive rather than prescriptive. Members come to a result by “living in the boundary defined by the constraints, but also using the space to create something greater than the sum of its parts” (Johnson, 2001, 181 – quoted in Davis and Simmt).

5)   Neighbour Interactions: Members must be allowed to interact with one another for new results to emerge.

Concerning change, there are so many things that come out of this article for me. One of the main thrusts of the article is that complex systems need to be self-similar – such a sweet idea that is incredibly mathematical. In the context of a school and educational change, for me this means that all layers of a school, from administration to faculty and staff to students to parents, need to be operating in self-similar ways. If teachers are meant to be distributing leadership to students to develop their confidence and independence, then so should department heads and grade level leaders distributed leadership for this purpose, and so should administrators do the same for grade level leaders and department heads – and so should school structures be set up to develop the confidence of community members such as parents to contribute their expertise to the learning process. If we wish for students to respect the value of working together with one another in groups, so should teachers and administrators and staff and the school community also demonstrate their respect for this through meaningful action. In short, my feeling is that meaningful change does not happen unless the school as a complex system is self-similar.

My feeling also is that change is most ideally achieved if a school becomes a complex system as Davis and Simmt outline. A school working towards positive change is able to maintain a balance of redundancy and diversity so that people will be motivated to come together yet there will also be enough diversity among people to allow them to develop new ideas. Members of the complex system will be allowed to freely interact so that new ideas can be developed and they should be free from outside control to do this. We can see this latter characteristics of a complex system in the common complaint from teachers about the lack of planning time with other teachers to properly put together a unit of inquiry, or to work in grade level teams on interdisciplinary work.

The most challenging of these aspects – and where the article hits home regarding educational change – is the idea of control. Too often, change makes people nervous and can rattle their confidence. Using a teaching example, often when changes take place or a teacher is not feeling confident or comfortable, they will seek to gain control in other ways, and this is usually when one might see in their classroom more teacher-centered lessons and other such decisions that take independence away from students. Interestingly, this in turn takes confidence away from students. If a teacher doesn’t let students answer a question, or doesn’t let them freely explore a problem, maybe this means the teacher feels they can’t do it. And so we see here that the desire for control in education can powerfully usurp positive change.

Sorry this isn’t a completely thought out post – your thoughts on how to grow this idea are appreciated!

 

*Davis and Simmt. Understanding Learning Systems: Mathematics Education and Complexity Science. Journal of Research in Mathematics Education. 2003. Vol. 34, No. 2, 137-167.

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

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.

 

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