I wrote this post a couple of years ago and it was published on the UWS 21st Century Learning Blog and a slightly modified version was republished in the online journal, Curriculum Leadership. I am republishing it again here as I think the message is as important as ever!
The start of a new school year is a perfect time to reflect on and perhaps make adjustments to the pedagogical practices we use in our day-to-day teaching of mathematics. If our goal is to produce successful learners of mathematics and students who choose to continue the study of mathematics beyond the mandatory years, then we need to ensure our students are engaged and motivated to learn both within and beyond the classroom. The purpose of this post is to argue that if we need to set mathematics homework, it should reflect ‘best’ practice and should provide students with opportunities to extend their learning in ways that highlight the relevance of mathematics in their lives outside school while practising and applying mathematical concepts learned within the classroom.
The pedagogical practices employed within mathematics classrooms cover a broad spectrum that ranges from ‘traditional’, text book based lessons, to more contemporary constructivist approaches that include rich problem solving and investigation based lessons, or a combination of both. When asked to recall a typical mathematics lessons, many people cite a traditional, teacher-centred approach in which a routine of teacher demonstration, student practice using multiple examples from a text book and then further multiple, text book generated questions are provided for homework (Even & Tirosh, 2008; Goos, 2004; Ricks, 2009).
Traditional, teacher-centred approaches have been found to result in low levels of motivation and engagement among students (Boaler, 2009), and although there is an abundance of research that promotes a more constructivist, student-centred approach, one study found traditional practices continue to dominate, occurring more often than student-centred approaches in mathematics education (McKinney, Cappell, Berry, & Hickman, 2009). If many teachers are continuing to teach in such way, then it is likely that many set mathematics homework that continues to be repetitious and merely a provision of further practice of concepts learned during lessons.
While it is critical that students are provided with many opportunities to practice mathematical concepts learned at school, perhaps we need to consider how homework can be structured so that it is motivating, engaging, challenging, and most importantly, relevant. One of the most common complaints from students with regard to mathematics education is the lack of relevance to their lives outside the school. It is an expectation of today’s students that learning is meaningful and makes sense to them (Australian Association of Mathematics Teachers, 2009; NSW Department of Education and Training, 2003). There needs to be a directional shift in the way we establish relevance and applicability in mathematical engagement because the type of mathematics that students use outside school is often radically different in content and approach to the mathematics they encounter in school (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? That all depends on you and your imagination! When I was a Year 6 classroom teacher, one of the most popular homework activities amongst my students was based on Tony Ryan’s Thinker’s Keys. Students would be provided with a range of activities that included an element of choice. Each activity was much more creative than a typical mathematics task yet provided challenge for students and an opportunity for them to apply their understandings of mathematical concepts. For example, in a range of activities based on multiplication and division, one of the tasks, the Question Key, required students to respond to the following prompt: How is multiplication related to division? Write an explanation appropriate for a Year 4 child. Use an example to show how multiplication is related to division. The Brainstorming Key required students to make links to real-life: Brainstorm examples of everyday situations that require you to use multiplication and division. Record your responses in a mind map.
Another great 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. For example, in a study of 3D objects, students could photograph and label 3D objects found in their homes. Students could draw floor plans of their homes when learning about scale, position, area and perimeter. At a higher level, students could 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, budgeting, etc.
How much work would be involved in planning this type of homework? One approach to planning homework tasks would be to work within stage/grade teams to design a bank of tasks that could be re-used from one year to another. As with many things, once you begin to plan and design rich homework tasks, it gets easier. 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 from students to complete. Also consider your priority: quality or quantity?
How hard would it be to assess and provide feedback on homework tasks? 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: “If they don’t give you feedback then you don’t know if you’re doing it right or wrong, or if you need improving or anything.” Marking and providing feedback on homework should not be viewed as a burden but rather a critical part of the teaching and learning process. The way feedback is delivered depends on the nature of the task.
Finally, 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?
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.