Our Year 7-9 students complete rich tasks for each topic (new topic every two weeks or so). The tasks are designed to be RICH:
- Real: often real-world application or real for the student because they developed the question themselves;
- Interesting: some tasks are based on puzzles or games and make connections for conceptual understanding;
- Creative: there is more than one way to complete a task, usually involving making something; and
- Hard: students should be challenged at the level they are working.
Students have choice in which level of task they choose (based on a diagnostic task – they don’t tend to pick too hard or easy more than once to avoid feeling frustrated or bored!) and also choice in how they demonstrate their understanding (e.g. written, poster, video, multimedia etc). We have a BYO device policy/programme at the school and most tasks will involve student devices in some way (taking photos, recording video, using tools like spreadsheets, desmos.com etc). Students submit their work online (taking photos or video of paper work or models) for assessment (with plans for more peer and other feedback in future).
We have tasks for each topic at levels ranging years 5 to 10 and so there is multiple levels operating in a class at once. We support this with team-teaching, videos of the explicit teaching and because the topics are aligned, all students can contribute to class discussions.
Task descriptions, videos and a teacher guide here: http://maths.crusoecollege.vic.edu.au
For example, Year 7 students designing blocks of land for an estate out of geometric shapes. They need to calculate the area to work out the price for the blocks and the perimeter for fencing. Some students are only working with rectangles, while others also include triangles, parallelograms and other quadrilaterals. Some students are making a scale diagram on cardboard, others in CAD and still others in Minecraft. Much of the explicit teaching is just-in-time with small groups. Some students have already showcased their work-in-progress.
The other half of their maths time each week is spent on skills practice (completing booklets on that topic at the same level) and working mathematically (problem solving).
We use Mathletics online for regular skills practice. Because the online activities give instant feedback, they make for good homework tasks.
Case Study : Personalised Mathematics at Crusoe College
The Crusoe College Rich Mathematics Course has been designed to increase student achievement and engagement in Mathematics. In addition, the Course aims to improve student attitudes to school; create independent learners; and promote authentic, student centred use of technology at the school.
There are common themes around how educators would envisage an ideal Mathematics class. These themes include:
- learners involved in rich tasks that create understanding;
- learners choosing how they show understanding;
- students identifying what they already know and what they need to learn;
- teaching at the “point of need” through workshops;
- authentic use of technology; flexible use of physical space; and
- teachers working together, in and out of the classroom.
The Rich Mathematics Course attempts to bring all of these elements together. It has been trialled in 2013 with great success and will be implemented in all Mathematics classes from Year 7 to Year 9 at Crusoe College from 2014.
The Rich Mathematics Course represents around 60% of the time students spend engaged in Mathematics at Crusoe College; the remainder of the time is spent developing fluency through more traditional Mathematical exercises, improving the capacity of students to interpret written problems, and the Scaffolding Numeracy in the Middle Years (SNMY) program. Two key elements of the Rich Mathematics Course are the presence of rich tasks that enable students to explore and build understanding in the concepts encountered in class. The rich tasks involve students playing and creating games; explaining concepts through stories; solving and creating puzzles; and real-life applications of Mathematics. These tasks share common features, namely that they lack a single “right answer”, require some aspect of student choice and often creativity, and require students to engage in multiple representations of the concept and show how they link together. Students have the option to show evidence of having completed the task in any way they prefer.
The tasks are created from the Victorian Curriculum curriculum outcomes, and are assigned a letter code, ranging from “E” (equivalent to a Grade 4 level) up to “K” (year 10 level). To support students choosing the right task, when first encountering a topic, students engage in a “Diagnostic Task”. This diagnostic task would often be introduced to several classes at once, ranging in number from two to four. This task, pitched around the expected level for that year level, enables both students and teachers to judge what students already know and need to know. After a period of time engaged in the diagnostic task, students will be asked to make a decision as to which task they will attempt to complete, based on their understanding of the diagnostic task.
Students are able to choose the level of task which “feels right”. The language used with the students is consistent – students understand that if a task is too easy, that is, if it can be done without any assistance, it is the “wrong task”. Similarly, if the task requires students to obtain assistance every few minutes, it is also the “wrong task”. Students are encouraged to identify the “right task” based on the need to “stretch” their thinking and require occasional assistance. The vast majority of students choose the right task –those that don’t can still be directed by the teacher to the right task.
Once students have chosen their task, each teacher takes responsibility for a task or set of tasks. Students are free to work wherever they like within the open learning space, so that students working at academic levels years apart may be working and collaborating side by side. Teachers responsible for a particular task may call their students together to give instruction or address a misconception, or clarify what evidence is needed to complete the task. At other times, teachers roam the open space, identifying students working on the task for which they are responsible and supporting their learning.
Technology has two critical roles in the process. The first is to support students’ independent learning skills by providing an instructional video for each task. Each video contains both the instruction for completion of the task and the explicit teaching of the Mathematical concepts involved. These videos are not designed to replace teacher instruction, but augment it – students can access the videos if they wish to skip ahead; need assistance at home; need to catch up after absence; or need to revisit the material in class. The videos can be accessed in two ways: firstly, through a website which houses the course (maths.crusoecollege.vic.edu.au) and through cards placed around the learning space which contain QR codes that students can scan.
The second role is the collection of evidence that a student has completed a particular task. With students able to choose how they show their understanding, and with the use of concrete materials far more prominent in the tasks than in traditional secondary school Mathematics, a more sophisticated version of the exercise book is needed. Each student has their own blog, to which they upload evidence of their completion of the task. The blogs facilitate greater choice in how students show their understanding; enable greater sharing of work with peers, teachers and parents; and enable teachers to keep track of their students who may be completing different tasks and working with different teachers. The blogs have the additional benefit of being easily added to through mobile technology including mobile phones and tablets. This widens the choice for students in terms of the technology they are able to use in a classroom context.
During the trial of the course, we have observed increased engagement in Mathematics across all learning styles and abilities of students; increased teacher collaboration and discussion of the teaching and learning of Mathematics; and increased capacity of students to work independently, take responsibility for their learning, use technology appropriately, and think creatively. Early On Demand test results are encouraging, and La Trobe University in Bendigo will support a more rigorous assessment of the impact on student learning in 2014. In addition Mathletics have shown an interest in the course due to a shared focus in the development of rich tasks, and have already contributed a number of electronic resources to support the process.
Future directions for the course involve a Bring Your Own Device program at Crusoe College to improve student access to technology; improving the quality of the tasks already created; encouraging students to create richer forms of assessment, in particular, the creation of video; and exploring the possibility of collaborating with other schools, both from the teaching point of view with the sharing of rich tasks, and from a student point of view with the possibility of students in different schools working on the same task collaborating virtually. Of particular interest would be collaboration with other Bendigo Education Plan schools, which have strong similarities in the physical space at Crusoe College.