Next Top Model: Quadratics in all their Glory


Watery Parabola by Martin Kenny

Watery Parabola by Martin Kenny

I’m currently refining a unit of study about quadratic functions that was co-developed last year with Kristina Sharma at Branksome Hall Asia. Our intention for the unit last year was to emphasize students seeing mathematics in the world around them and making connections between mathematics learned in class and real-life contexts in which that mathematics is used. We had some successes for sure, but were well aware that this unit – as any unit – was in need of some changes.

With the help of Will Percy, our Digital Technologies Coordinator, and Yumi Matsui, our EAL Coordinator, I’ve embarked on a journey of sorts to amp up the great work Kristina and I did last year. Students seemed to enjoy the final task last year that had them making video of themselves playing a sport in PE, then turning this into a still image much like videos of Will It Hit The Hoop? of Dan Meyer fame. Students then imported the image into GeoGebra, and used this program to help them model the path of the ball through the air with a quadratic function.

The unit is quite language heavy and, as our school population is mostly composed of English Language Learners (ELLs), I am keen this time around to provide them with more support. Yumi has provided excellent support for us to follow up from our EAL professional training with Dr. Virginia Rojas, and I’ve adapted her language supports and sentence frames for use in various activities. Here is one example of resources Yumi has shared with me that my students have found particularly useful for having constructive classroom conversations (and see Jeff Zwiers‘ work should you be interested in more of this great stuff!).

Sentence Starters for Building Ideas

My challenge right now is to retool the students’ final assessment for this task. I would certainly like to rewrite the questions, but my other goal is to put it in a format that would allow students a wider audience for their work. Last year’s task was rich, but the audience for their work was me, their teacher. Fine, but not terribly exciting. An idea that Will has suggested is to have students do podcasts as formative tasks and for students to complete a talking Pages document with a combination of video/audio and written text. This might be a manageable next step, setting me up for really making this unit solid in its next iteration. Attached is last year’s assessment for anyone’s perusal:

Sports Next Top Model Task NO RUBRIC

I am incredibly keen for anyone’s feedback about this as it is developed. Exciting things will be happening in the coming weeks!




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!

How to Learn Math – Jo Boaler Course Begins

Boaler – Session 01 – 1.1 – Math Perception Concept Map – DEABREU

I’ve just been able to start the Jo Boaler course – getting married this summer is exciting and means I’m not going to be able to give this course the attention I would like. On the other hand, I’m getting married this summer to a truly wonderful woman who I can’t be thankful enough for. 🙂

The course has started out great. Lots of data has been shared already about perceptions of mathematics and the journey people have taken with the subject. And it’s just beginning.

In session 1.1, Boaler asks students to make a concept map of the comments made by people interviewed about their experiences with mathematics. Here is that concept map.

Boaler - Session 01 - Math Perception - DEABREU


Groupwork on the Ground and in the Sky

Today was the first day of a five-day workshop with Karen O’Connell and Jess Griffin called Designing Effective Groupwork in Mathematics. As I’ve spent a year doing my M.Ed in cerebral mode, it was refreshing to talk with teachers about the nuts and bolts of how this might look in a classroom – the practical implementation of it all. I wanted to share here some of my initial take-aways and questions I still have.

I’m also planning to use this space to share my thoughts as my group and I move through the design of a groupworthy task. Watch this space! Your comments and feedback and questions are totally appreciated during this time as they always are!

Setting and Reactions

Karen and Jess have both been complex instruction (CI) practioners for a number of years and have a tremendous amount of experience to offer. In our opening activity, Jess led us through an origami box making task, with us in the role of students in groups of 4. The tables were cleared (KEY move), the task was introduced, roles (two of the many descriptions of roles: way one and way two) were introduced and explained (groupings were randomly assigned by the teachers), and a list of the abilities needed to complete the task successfully was presented. This was a key moment which I had been reading about – the first of two CI treatments called the multiple abilities treatment –  but seeing it in action stated with conviction while playing the role of student really hit home for me:

“Take a look at this list of abilities. There are quite a number of them that are needed to do this task. What are you bringing to your table? No one has all of these abilities, but each of you has at least one of them to offer.”

While doing the task, I immediately found myself with a role (resource monitor – and I love ticking lists and asking questions!), and ways to contribute to the task. I also found myself earnestly supporting others where I could, or being more verbal about my appreciation of other’s work.

As we were all doing the activity, Karen and Jess circulated, encouraging us to continue using “because” statements and asking good questions – like a coach, pointing out when a student is on the right track – while encouraging the group to recognize when a member was struggling with an idea or needed a voice. Yes, they were helping to move the math along, but they were also helping to move the talk along – talk which thereby facilitated the math moving along. This is the second of two CI treatments called assigning competence. Also incredibly key.

The task culminated in our making a “stand-alone” 1 page demonstration of our strategy and our prediction (for what the volume of a box made from a 20-inch sided square piece of paper might be given the four other boxes we had made, measured and analyzed). This was interesting – we couldn’t tell people about it. When showed to the class, no comments were allowed. Our paper explanations had to “stand alone” – and be understood just as they were. What a simple yet powerful idea as a way of presenting finished mathematics products to the class.


I already wrote about a number of “take-aways” throughout the “play-by-play” of the task, above. Here are some more.

There are some incredibly simple tweaks that Karen and Jess made to the task to encourage us to interact. First, there were four different sized pieces of paper (ergo, we needed to make 4 boxes), but only two task sheets and not enough cm cubes and beans to each have a sufficient supply for estimation. Thus we needed to share these latter two resources. The simple act of giving each student a task sheet or enough cubes for each student to work with might have kept us from talking until later in the task. In addition, the folding instructions (to move paper–>box) were naturally tough for some to follow, resulting in many group members needing help with others offering it.

One of our group members, Cameron, pointed out that the resource manager’s job had one crucial addition – to ask the teacher questions. Huge. Other group members were dependent on them as the way to communicate their questions to the teacher, thus the resource manager remained important throughout the duration of the task. Not including this has a student get resources, then (possibly) back right out of the task – “that’s it! Job done!” In addition, it implied that the teacher was just one of the many resources available in the room. Not the resource, but just one of them. A powerful implication. Instead of an “ask someone at your table then ask the teacher” rule, which could imply “don’t bother me” or “the teacher might be more useful (or more important) than the students,” we have a strong subtle implication of the equalized value of all in the room. Epic.

What strikes home most powerfully after today, however, is the self-similarity that is necessary for this kind of teaching to really be successful. We have all heard and likely agree that teachers must model for students what they want them to learn, yet we have all seen how teaching can sometimes be a bit lonely – whether self-imposed or not. The classroom door shuts, literally and figuratively. However, if we want our students to collaborate, must we not also collaborate? Must not our department meetings not be times for us to share things we are doing in our classrooms and get feedback? Must we not design tasks with our teaching partners to gain multiple perspectives on an activity in preparation for presenting it to students? Teaching is an incredibly creative profession, and creativity needs expression to be moulded, to evolve, to improve. (Many of you are likely already thinking the word “time!” over and over again in your heads. I recognize the practical and am indulging in a bit of optimism here 🙂 )

Questions Still Niggling

I have a TON of them, but my top 2 are:

1) How does CI look in a class with english language learners (ELLs)? CI is language (as in language of the classroom) heavy. Students are expected to talk in groups, to record findings understandably for others, to report their own learning in individual reports throughout units. How can we keep ELLs from losing status in the face of the great challenge they may appear to pose to their group members? How can they succeed and contribute?

2) CI works beautifully for exploratory tasks like the origami task. But CI practitioners readily admit we can’t do those all year long. How does CI look for more abstract and calculation based concepts like algebra, logic, functions, and the like? How could the teaching of this look different and be more engaging?

On From Here

Our task this week is to design a groupworthy task in a group of 3-5 people on a math topic – a task that we will then “micro-teach” during a 20 minute session. Fitting, especially considering my comments about self-similarity. As Lotan (2003) says: the creation of a groupworthy task is itself a groupworthy task. My group is pumped and ready for action! We have challenged ourselves to come up with a groupworthy way of involving students in learning algebra concepts connected with completing the square. Wish us luck!

Resources from Today

The book we are reading for this course is Smarter Together: Collaboration and Equity in the Elementary Math Classroom. Written by practitioners and researchers of CI, it’s already reaping great rewards in our explorations.

A colleague, Kate, suggested we look at Lab Gear, a manipulative designed for teaching algebra, during our lesson design. Have a look at Henri Piccioto’s site (he’s the creator) for a summary of what it can do and some free resources for how it can change teaching.

See the Lotan (2003) article that we read today – a short and sweet summary of “look-fors” when designing (or modifying old tasks/questions to make) groupworthy tasks.


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!

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!


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

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