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!

 

 

 

Making Groupwork Happen

I’ve been investigating complex instruction (CI) over the past few months as part of my M.Ed at the University of British Columbia. CI offers an approach for teachers to use in their classrooms to temper the status differences that inevitably arise in group work situations. I first came across the approach when doing some further research on a school called Railside, a name given by Stanford mathematics education professor Jo Boaler to an ethnically diverse, urban school in southern California. Boaler conducted a longitudinal study there and at two other local area schools to study learning gains and found something else.

At Railside, all of the teachers in the mathematics department were using CI, and their students not only demonstrated great learning gains, but showed an appreciation for the power and beauty of mathematics that teachers yearn to pass on to their students and a desire to improve they way they worked in groups so that they could sustain the learning community that had evolved in their classes. Intrigued, I decided to investigate further.

CI explores access issues that take place when group work is implemented. We teachers have all seen students who were too shy to contribute, or who were deemed unable to do the task, or who simply sat back and let others do the work while the rest of their classmates got frustrated. However, thinking of it in terms of an access issue, if we place students together for the purpose of learning and only some students do the work while others are forced out or choose not to participate, not all students have the same access to the learning that is meant to take place in groups.

For many teachers, group work is daunting to implement because of these and the plethora of other problems that can come up. How do I ensure that students truly work together to create a group product that they all contributed to? How do I ensure individual accountability for the contributions students make in their group? How do I ensure students are learning? Naturally, I was skeptical of this new approach. After all, if it is based on over 20 years of classroom research, and two books have been published, why isn’t it already widespread?

Components of Complex Instruction

The answer to that final question still escapes me. CI seems to have all the bases covered. CI starts with a multidimensional classroom – one where academic success is measured on many different abilities, such as coming up with different solutions, explaining solutions, justifying solutions, using different representations, making a model of your solution, asking good questions, and so on. Quite simply, more students have success because there are more ways to have success.

Tasks and group roles are structured to be “group worthy” – so that students have to work interdependently to complete the task successfully. The roles also enable the delegation of authority so that the class can achieve a state of decentralized control. This allows the teacher to move around to assist and prompt students as needed.

Two treatments are recommended as the teacher is circulating. First, the multiple abilities treatment involves the teacher continuing to reinforce – in words as well as through classroom structure – that no one will have all of the abilities to complete a task themselves, but everyone in the group has at least one of the abilities. Second, through the assigning competence treatment, teachers listen intently to group discussions and interject to purposefully raise the status of something a low-status student has shared in a group.

CI is incredibly ambitious in what it sets out to achieve. CI seeks to improve student achievement, collaborative skills, metacognition, equitable participation, student autonomy, and approaches to learning. That’s just about everything that any teacher could possibly hope for their class of students!

My Contribution

Founders of CI state very clearly that all of this hinges on the task that students gather around. So, for my final M.Ed project, I will be investigating what a CI task looks like and design my own task (perhaps a whole unit) and reflect on this design process. I have the fortune of being able to attend Designing Effective Groupwork in Mathematics, a workshop offered by CI practitioners at the University of Washington. As I move forward to teaching at Branksome Hall Asia next year, I am interested to move from theory to practice and examine the feasibility of the use of CI in my classroom, and will post my thoughts as I go here.

Resources

Free mathematics CI tasks are available on the NRICH and the Complex Instruction Consortium websites, and Dan Meyer intends that CI be used for his Three-Act Math Tasks. See a CI lesson presented by Dan Meyer from his talk given at Cambridge University in March of this year. This gives you a great look at some of the ideas I’ve discussed above.

Also, if anyone is interested, Boaler is offering a free online course for teachers and parents through Stanford University called How to Learn Math. It’s available July 15 to September 27, 2013. Pass this on to interested parents and teachers!