Catherine Attard is a lecturer in the primary education program in the School of Education at the University of Western Sydney, Australia. This article is adapted from texts originally published on the University of Western Sydney's 21st Century Learning blog, 12 February 2012 and 6 February 2011.

To encourage the study of mathematics beyond the mandatory years we need to ensure that students are engaged and motivated to learn, both within and beyond the classroom. This raises the question of how well current practices in mathematics teaching serve to motivate and engage students.

At present, traditional practices continue to dominate most classrooms (McKinney, Cappell, Berry, & Hickman, 2009). Traditional mathematics lessons are characterised by a routine of teacher demonstration followed by student practice using multiple examples from a textbook. Traditional, teacher-centred approaches have been found to lower students' motivation and engagement when overused (Boaler, 2009).

Within the traditional approach, homework is likely to consist of textbook-generated questions that provide students with further practice of concepts introduced during lessons (Even & Tirosh, 2008; Goos, 2004; Ricks, 2009). While it is critical that students are provided with many opportunities to practice mathematical concepts learned at school, perhaps we need to consider more closely how homework can be structured so that it is motivating, engaging, challenging, and most importantly, relevant.

Making homework relevant

Today's students expect learning to be meaningful to them (AAMT 2009; NSW DET 2003). One of the most common complaints from students with regard to mathematics education is the lack of relevance to their lives outside the school, and it is true that the type of mathematics that students use outside school is often radically different in content and approach to the mathematics they encounter within the classroom (Lowrie, 2004). Homework provides the perfect opportunity for students to make connections between school mathematics and 'home' mathematics.

So what would motivating, engaging, challenging and relevant mathematics homework look like? An abundance of research supports the use of a constructivist, student-centred approach to learning, which includes rich problem solving and investigation-based lessons. When I was a year 6 classroom teacher, some of the homework activities most popular with students required them to make links to real life. One task – one of a number that drew on a commercial program for developing thinking skills (Ryan 2009) – called on students to find and describe examples of everyday situations that required them to use multiplication and division. Another idea for homework with younger students is to have them take photographs of their home environment that directly relate to the mathematics being learned at school. In a study of 3D objects, for instance, students might photograph and label such objects found in their homes. Students could also draw floor plans of their homes when learning about scale, position, area and perimeter.

A sample activity

In more senior years, students can solve real-life problems that require the application of a number of mathematical concepts such as selecting the best mobile phone plan, comparison of household bills, or budgeting. The following mathematics task illustrates the potential of a homework task to engage students in using 'school' mathematics applied to a 'real-world' context.

You have just been given permission from your parents to choose a new mobile phone and select a new phone plan. Because you now have a casual job and are earning $52.00 a week, you need to select a phone and a plan that you can afford (remember you need to have money left over for other expenses).

Prepare a proposal to your parents and include the following: the selected phone and plan; a list of your needs (calls, SMS, downloads, etc); the criteria you used to select the phone and plan; a comparison with at least three other phones and plans; any mathematics you used to help make your decision; and a monthly budget proving you can afford the phone and plan of your choice.

Selecting a plan calls on students to use a wide range of mathematics to critique the many options available in today's mobile phone market, and the value being offered by the various providers. In addition, tasks such as this one provide the opportunity for students to use technology to assist in their investigations and in the presentation of their findings. The phone task may be differentiated in various ways, allowing the diversity of learners the opportunities to achieve success and opportunities for the development of mathematical knowledge within a meaningful context.

A task such as this one aligns well with the Australian Curriculum: Mathematics. It has the potential to incorporate the content strands of Number and Algebra and Statistics and Probability, and provides students with opportunities to incorporate the Proficiency strands of the curriculum. First, students are required to show understanding through the need to interpret mathematical information and apply familiar concepts to new ideas. Second, the task provides practice at developing fluency at selecting appropriate procedures and calculating answers efficiently. Next, the problem solving aspect of the task provides a meaningful context for students to apply their existing strategies. Finally, the task requires students to apply their reasoning skills by justifying their choice of phone and phone plan.

Activities such as the phone task provide opportunities for students to make links across other key learning areas such as the social sciences and English. Making links such as these enhances the relevance of the tasks and highlights to students the fact that mathematics is not a pursuit that exists in isolation.

Planning and assessing homework

How much work would be involved in planning this type of homework? One approach to planning homework tasks is to work within stage/grade teams to design a bank of tasks that could be re-used from one year to another. Often ideas also come from the students. Consider tasks that vary in length from quick, one-day homework tasks to longer term tasks that may take two or three weeks for students to complete. Also consider your priority: quality or quantity?

If we expect students to engage with and complete their mathematics homework, then we must provide constructive feedback. In my previous research on student engagement with mathematics, some students were frustrated when their teacher did not mark homework. The way feedback is delivered depends on the nature of the task. Overall, however, marking and providing feedback on homework should be viewed as a critical part of the teaching and learning process.

When setting homework, we need to reflect on our purpose for doing so. Are we doing it to keep the parents happy and the students busy, or do we want to support students' learning in a seamless link between school and home, providing opportunities for students to apply concepts in real-world situations?

If we do need to set mathematics homework, it should provide students with opportunities to extend their learning in ways that highlight the relevance of mathematics in their lives outside school, while also practising and applying mathematical concepts learned within the classroom.

References

Australian Association of Mathematics Teachers (2009). School Mathematics for the 21st Century: Some Key Influences. Adelaide, S.A.: AAMT Inc.  

Boaler, J. (2009). The Elephant in the Classroom: Helping Children Learn and Love Maths. London: Souvenir Press Ltd.  

Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students' mathematical learning and thinking. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 202–222). New York: Routledge.  

Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258–291.  

Lowrie, T. (2004, 4–5 December). Making mathematics meaningful, realistic and personalised: Changing the direction of relevance and applicability. Paper presented at the Mathematical Association of Victoria Annual Conference 2004: Towards Excellence in Mathematics, Monash University, Clayton, Vic.

McKinney, S., Cappell, S., Berry, R. Q., & Hickman, B. T. (2009). An examination of the instructional practices of mathematics teachers in urban schools. Preventing School Failure, 53(4), 278–284.  

NSW Department of Education and Training (2003). Quality Teaching in NSW Public Schools. Sydney: Professional Support and Curriculum Directorate.  

Ricks, T. E. (2009). Mathematics is motivating. The Mathematics Educator, 19(2), 2–9.

Ryan, Tony (2009). Brainstorms. Headfirst Publishing.