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Mathematics Homework Tasks

Maths was headline news last month, and as is often the case it was for the wrong reasons. According to research done by the Institute of Education, top GCSE pupils in the UK lag two years behind their peers in Asia, and the sentiment of the news coverage was that the UK has a problem that has to be fixed.

Actually the findings weren't as disastrous as the headlines suggested. However one conclusion of the report stood out. It was that Asian teenagers do better at maths partly because they get more support at home – though in practice, it sounds like this is often in the form of private tutoring.

Many teachers would like to see more parental involvement in maths in the UK, and the IoE research will reinforce this. But what can teachers do to encourage parents of teenagers to get involved?

It's worth noting that the issues with parental engagement tend to change when a child moves from primary to secondary. In primary, I believe, there tends to be quite a lot of parent-teacher interaction. Parents are often very engaged with their children's maths, particularly their homework, and the main issue that they raise with teachers is their struggle with the different methods that their children use, particularly in arithmetic.

In secondary school, however, parental engagement can often drop away altogether. Sometimes it's because teenagers simply don't want to engage with their parents on anything. Just as often, though, it's because parents don't feel empowered to help. They don't recognise the maths their teenager is doing (or if they do, they can't remember how to do it) and in many cases they share their teenagers' doubts as to whether any of this stuff is relevant in any case.

So what can teachers do to help parents to support their teenagers in maths at home? You can pass on advice directly to parents, but since contact with parents is often very limited in secondary school, you may have to subtly enlist the help of your students in passing messages on.

Real-life problem solving: While school does what it can to make maths real, the artificial settings of maths questions don't always compare with the reality of everyday problems such planning a journey, choosing the best phone package or figuring out the layout of a new bedroom. So get your students working on maths problems that require them to gather data from home. A simple example might be estimating how much water a typical household uses in a day (as part of investigating how much water an individual uses a year). This sends parents a message about the link between maths and everyday life, and it also encourages the idea of estimation, an important skill that teenagers need to develop.
Engaging maths: Often there's not much time in the busy school schedule to fit in the more inspirational and enriching side of maths, even if a teacher wants to. Direct your students to online resources that have a mathematical content - three maths channels that have an avid teenage following are Numberphile (interesting short videos and clips about numbers), Vi Hart (blog of mathemusician Vi Hart) and Singingbanana (where maths meets comedy). Encourage them to share their favourite clips with other members of the family.

Connect maths to their interests: Many teenagers suddenly see the point of maths if it helps them with something they are interested in. Look for the hidden maths that is connected with something they care about, whether that's sport, cooking, horses, or choosing the best package for their next mobile phone. Set homework tasks that have some flexibility, so that the challenge (such as working out the the diagonal of a rectangle) can be set in a context that appeals to the individual student. A rectangle can be a football pitch, a map, a TV screen or a Justin Bieber poster. Games are also a fantastic way of making maths practice painless – set these for homework and encourage your students to teach their parents how to play. A good example is Manga High which has a high level of maths content and is popular too.

Parents are usually better at maths than they think they are, but they tend to call the maths that they can do "common sense". One particular area in which parents tend to be stronger than teenagers is in problem-solving, because they have the benefit of experience. That's why involving teenagers in problem-solving is so useful.

Rob's maths resources on the Guardian Teacher Network

Creativity in secondary maths
Three maths ideas for teaching circle theorem, probability distributions, algebra and the square root.

Creativity in primary maths
Four ways to inject creativity into your maths lessons, including number tricks, find the centre of a triangle and symmetry.

Rob Eastaway is a maths speaker and the co-author (with Mike Askew) of the book More Maths for Mums & Dads - The Teenage Years. For more information, see www.robeastaway.com. You can follow Rob on Twitter @robeastaway.

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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?

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.

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