Tag Archives: engagement

Financial Literacy: What does it mean, and how can we teach it in schools and at home?

I am currently working on a research project funded by Financial Literacy Australia that is investigating the use of financial literacy education as a tool to promote primary students’ engagement with mathematics in low socio-economic areas. While working on the project, it has struck me that often we have a simplistic view of what financial literacy for young children means, and how influential it can be in their future lives.

There are many definitions of financial literacy, ranging from “basic money management: budgeting, saving, investing and insuring” (Hogarth, 2002) to definitions that incorporate a more critical perspective, such as that proposed by the Australian Association of Mathematics Teachers (AAMT): “enabling people to make informed decisions at the personal level…allowing citizens to properly analyse and make judgements about broader issues such as government policy, the influence of the media and activities of the finance industry” (AAMT, 2010, p.2). In the context of primary schools, financial literacy is much more complex than just teaching children to recognise currency, to add and subtract money amounts, or to be able to estimate the costs of items. It is about learning how to apply a range of mathematical skills and knowledge to consumer related situations in an informed, analytical and critical manner. These skills should be learned in the classroom, and just as importantly, at home.

So why teach mathematics through financial literacy? We know there is an ongoing problem around children disengaging from mathematics, and this often occurs from an early age. One of the biggest causes of students’ disengagement with mathematics is the fact that they fail to see the relevance of mathematics or its applications to real life situations. Added to this, there is concern relating to young people from low socio-economic areas in particular, as presented in a recent report by Thomson (2014):

  • In Australia, 75 per cent of socioeconomically disadvantaged students hold a bank account compared with 89 per cent of advantaged students.
  • “More students from disadvantaged backgrounds than students from an advantaged background responded that they were influenced by advertising in magazines, flyers and newspapers, and by the need to ‘fit in’ when making decisions about spending money” (p. viii).

Teaching mathematics via financial literacy makes sense. By using real-life contexts that involve financial literacy that is age appropriate and interesting to students, we can teach a range of mathematics and numeracy skills. Students are more likely to remember and understand because they have applied them to something they are interested in and something that is relevant to their present lives.

The following is some advice for teachers and parents in relation to promoting mathematics in the context of financial literacy education.

For teachers

In their Position Paper on Consumer and Financial Literacy in Schools (2012) the AAMT note that mathematics teachers need to address the cross-curricular learning in financial literacy though the mathematics curriculum and through “broader concepts and understandings” (p.3) of other key learning areas and in real life situations, with relevant contemporary resources. Such contemporary resources are available from the MoneySmart website (https://www.moneysmart.gov.au/teaching/teaching-resources/teaching-resources-for-primary-schools) at no cost. These resources are an excellent way to begin teaching financial literacy concepts with some units of work specifically designed around mathematics, however, if we want to ensure teaching and learning is truly contextual with the aim of engaging students with mathematics, these units can and should be adjusted to suit the specific needs of the students in your classroom.

Alongside the MoneySmart resources, consider using resources that are familiar to students’ everyday lives. These could include items that are in the news media, shopping catalogues, television commercials etc. Keep watch for interesting photographs or misleading advertisements such as the one above. They are great for instigating mathematical discussions. There is also a range of iPad apps that could be used alongside mathematics and financial literacy explorations, including budgeting apps and supermarket apps. If you like using picture books to introduce and teach concepts, the following website has an extensive list of books relating to financial literacy: http://www.moneyandstuff.info/books.htm

For Parents

Many young children don’t understand where money comes from and it’s important that they begin to develop some understanding of how our economy works, even from a young age (many children believe that money comes out of a hole in a wall). In my research there appears to be a pattern emerging where children whose parents talk to them about money develop an earlier understanding of its importance and are provided with more opportunities to deal with money and make decisions about money. If you have young children, it’s a great time to start their financial literacy and mathematics education. Take opportunities when you are out shopping to either include your child in discussions and decisions where appropriate, or explain financial decisions that are made on their behalf. Talk about the mathematics involved in financial decision-making and where possible, encourage children to make their own financial decisions with pocket money, banking, etc. If you feel you need to improve your own financial literacy first, MoneySmart have fantastic resources for adults too (https://www.moneysmart.gov.au/).

The benefits of engaging children with mathematics through financial literacy are clear. By highlighting the relevance of mathematics to children’s current and future lives through real-life learning contexts relating to money we can better position young children for academic success and success in relation to their future economic lives.

View an interview about financial literacy on Weekend Sunrise on Sunday 26th April 

References

Australian Association of Mathematics Teachers (2012) Position paper on Consumer and Financial Literacy in Schools. retrieved January 2015 from www.aamt.edu.au

Hogarth, J.M. (2002). Financial literacy and family and consumer sciences. Journal of Family and Consumer Sciences, 94, 15-28.

Thomson, Sue. (2014). Financing the future: Australian students’ results in the PISA 2012 Financial Literacy assessment. Victoria: Australian Council for Educational Research.

Woolworths and Dominoes (Part 2): Even more mathematical opportunities for parents and teachers!

My last blog about the marketing promotion being run by Woolworths and Disney Pixar attracted so much interest that I thought I would look deeper into the mathematical potential of the whole campaign. Somehow, the incentive of receiving a domino for every $20 spent seems to be very appealing to consumers, young and old. What is it about these little plastic objects that is so attractive? Perhaps the appealing aspect of the dominoes is the fact that children can actually play with these, as opposed to collections of character cards that are usually given away in such promotions.

So why are the dominoes appealing to teachers like me? My research on student engagement with mathematics has shown that when children have an interest in something, they are more likely to want to learn. They also like to use concrete materials to help them learn – things they can see, touch and manipulate (as opposed to the traditional maths worksheets and textbooks). In the case of Woolworths and dominoes, this is a perfect opportunity for parents and teachers alike to seize this amazing opportunity, take advantage of the hype and do some really good, interesting mathematics!

During the week, as I watched the statistics on my blog increase, I thought I would explore the Woolworths web site and dig around a little. I didn’t find too much of interest, although they have made an effort to publish some very basic educational ideas relating to the dominoes. What I did find, however, was that people are actually selling dominoes on eBay! You can buy whole sets (of characters), individual dominoes of specific characters (some up to $3 each), or unopened dominoes. At this point my head started to hurt…..so many mathematical possibilities! Imagine children investigating the cost of dominoes (in shopping dollars), compared to the apparent worth of dominoes as advertised on eBay. All week I have had fantastic (well, I think they’re fantastic) ideas popping into my head, and these are a few that you might want to try out at home (if you are a parent), or at school, if you are a teacher. I will begin my list with simple tasks for younger children, and finish it with more complex tasks for older children:

  • How many dominoes do you think you could hold in one hand? Try it and see if you were right or wrong. How close were you? What if you could use two hands? How many dominoes can you hold? Is this the same as an adult?
  • How many dominoes have a one dot? Two dot? Three dot pattern?
  • If I lay my dominoes flat, end to end (the short end), how long will my line be? How many dominoes will I need if I wanted to make a flat line that is as long as my foot? My leg? My arm? My body?
  • Keep your character doubles, and use pairs of doubles to play a game of memory.
  • Using the picture side of the dominoes (the characters are numbered), order the dominoes from 1 to 44.
  • Are you missing any dominoes? What numbers are missing and how do you know?
  • Using the picture side of the dominoes, imagine that the number of the character is equivalent to its worth. That is, character number 1 is worth $1, character number 2 is worth $2, etc. What would be the value of your collection? If you had every domino from number 1 to number 44, what is it worth?
  • If I lined up my dominoes so they were standing (like in the photo), what would be the best distance apart (if they’re too close together, you might knock them down accidently).
  • How many (standing) dominoes would you need to make a line of 1 metre? Imagine you needed to make a domino line for one kilometre – can you use the number of dominoes you have to work out how many dominoes you would need? How much would you have to spend at Woolworths to have enough dominoes?
  • How long would it take to knock down a one metre line of standing up dominoes? Who can make the longest line?
  • I received 18 dominoes with my shopping this week. How much did I spend?
  • Do you think the Woolworths marketing campaign has been successful? Design a set of survey questions and conduct some research at your school. Analyse your data and prepare a report that you could send to the Chief Executive Officer of Woolworths.

Of course, there are many more ideas – perhaps there will be a Part 3 blog post over the Easter weekend. Oh, and by the way, Woolworths are giving away ‘double’ dominoes at the moment – this opens up another world of mathematical opportunity!

“I wonder…..”: Promoting curiosity in the mathematics classroom

I recently came across an article published in the neuroscience journal, Neuron that caught my attention. The article, by Gruber, Gelman and Ranganath (2014), describes a scientific investigation that explored how curiosity influences memory. The authors found a “link between the mechanisms supporting extrinsic reward motivation and intrinsic curiosity and highlight the importance of stimulating curiosity to create more effective learning experiences” (p. 486). In other words, students will learn more about topics they are interested in – something we’ve known along in the education world, but now we have scientific evidence!

Gruber et al. (2014) claim high curiosity results not only in the learning of interesting information but also incidental material. They also discuss how most of the events a person experiences in a day will be forgotten. If we translate this to children and their classroom experiences, can we expect that they won’t remember much of what happens during the average school day? This certainly presents a strong argument against the use of traditional approaches to teaching and learning, particularly the use of textbooks. How can we expect children to get excited and curious about mathematics from a worksheet? We need to ensure we find ways to ‘hook’ students into mathematics and provide opportunities for them to experience the joy of mathematical exploration and discovery.

So what kind of mathematics tasks and activities could be used in the primary classroom to promote curiosity? We know that the teacher is the biggest influence on student engagement with mathematics, and I firmly believe that curiosity is something that must be modeled by the teacher. There are many types of activities that would assist in promoting curiosity amongst students. For example, mathematical magic tricks, or ‘mathemagic’ is a great place to start.

Here’s one (it’s a favourite of mine) that uses three dice:

This trick is based on a simple mathematical fact: Each pair of opposite faces on a six-sided die always adds up to seven. All you need for this trick is three six-sided dice and basic multiplication, addition and subtraction skills! If you’ve got that, you’re ready for the trick.

Instructions:

  • Hand a student the three dice and ask he or she to stack them together so that they form a column
  • Turn your back to the student while he/she silently adds up the numbers on the five hidden dice faces. Tell your student to memorise the sum and keep it a secret.
  • When three dice are stacked together there are five faces that you can’t see: the bottom and top faces of the lowest die, the top and bottom faces of the middle die and the bottom face of the top die. Altogether you get five hidden faces.
  • When your student is ready and has figured out the sum of the numbers on the five hidden faces, you can turn around. Tell him/her that you will use your magical powers to name the sum of the five hidden faces, without looking.
  • Look at the top face of the stacked column, and subtract the number from 21 (For example, if the top number is 3, subtract three from 21) “Abracadabra, the sum is 18!”

When students (and most adults) first see this trick performed, they are amazed. Perform it a couple of times to prove that you are, indeed, magical, before asking them to explore how the trick works. Non-threatening, engaging activities such as this not only spark curiosity, they provide opportunities for mathematical discussion, reasoning, and generalising. An added bonus is that when students ‘get’ the trick, they feel empowered because they can go home and trick their families and friends!

Other activities that promote curiosity include explorations of magic squares, investigating number patterns, which can be as simple as using ten-point circles to explore the patterns with the multiplication tables or simply asking questions that begin with “I wonder …” about some of the day to day contexts that students find themselves in.

There are endless ways that teachers can arouse mathematical curiosity in their students and many resources, educational and otherwise, that could be used. Consider using picture books, non-fiction books such as the Guinness Book of Records, puzzles, video clips, and the list goes on. Anything that gets children interested in mathematics and encourages them to continue with and be successful in the study of mathematics has to be a good thing!

Gruber, M. J., Gelman, B. d., & Ranganath, C. (2014) States of curiosity modulate hippocampus-dependent learning via the dopaminergic circuit. Neuron, 84(2), 486-496.

Professional Learning and Primary Mathematics: Engaging teachers to engage students

The issue of student engagement with mathematics is a constant topic of discussion and concern within and beyond the classroom and the school, yet how much attention is given to the engagement of teachers? I am a firm believer that one of the foundational requirements for engaging our students with mathematics is a teacher who is enthusiastic, knowledgeable, confident, and passionate about mathematics teaching and learning – that is, a teacher who is engaged with mathematics. Research has proven that the biggest influence on student engagement with mathematics is the teacher, and the pedagogical relationships and practices that are developed and implemented in day to day teaching (Attard, 2013).

A regular challenge for me as a pre-service and in-service teacher educator is to re-engage teachers who have ‘switched off’ mathematics, or worse still, never had a passion for teaching mathematics to begin with. Now, more than ever, we need teachers who are highly competent in teaching primary mathematics and numeracy. The recent release of the Teacher Education Ministerial Advisory Group (TMAG) (2014) report, Action Now: Classroom Ready Teachers, included a recommendation that pre-service primary teachers graduate with a subject specialisation prioritising science, mathematics, or a language (Recommendation 18). In the government’s response (Australian Government: Department of Education and Training, 2015), they agree “greater emphasis must be given to core subjects of literacy and numeracy” and will be instructing AITSL to “require universities to make sure that every new primary teacher graduates with a subject specialisation” (p.8). While this is very welcome news, we need to keep in mind that we have a substantial existing teaching workforce, many of whom should consider becoming subject specialists. It is now time for providers of professional development, including tertiary institutions, to provide more opportunities for all teachers, regardless of experience, to improve their knowledge and skills in mathematics teaching and learning, and re-engage with the subject.

So what professional learning can practicing teachers access in order to become ‘specialists’, and what models of professional learning/development are the most effective? Literature on professional learning (PL) describes two common models: the traditional type of activities that involve workshops, seminars and conferences, and reform type activities that incorporate study groups, networking, mentoring and meetings that occur in-situ during the process of classroom instruction or planning time (Lee, 2007). Although it is suggested that the reform types of PL are more likely to make connections to classroom teaching and may be easier to sustain over time, Lee (2007) argues there is a place for traditional PL or a combination of both, which may work well for teachers at various stages in their careers. An integrated approach to PD is supported by the NSW Institute of Teachers (2012).

In anticipation of the TMAG recommendations for subject specialisation, I have been involved in the design and implementation of a new, cutting edge course to be offered by the University of Western Sydney, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators. The fully online course will be available from mid 2015 to pre-service and in-service teachers. Graduates of the course will develop deep mathematics pedagogical content knowledge, a strong understanding of the importance of research-based enquiry to inform teaching and skills in mentoring and coaching other teachers of mathematics. For those teachers who are hesitant to commit to completing a full course of study, the four units of the Graduate Certificate will be broken up into smaller modules that can be completed through the Education Knowledge Network (www.uws.edu.au/ekn) from 2016 as accredited PL through the Board of Studies Teaching and Educational Standards (BOSTES).

In addition to continuing formal studies, I would encourage teachers to join a professional association. In New South Wales, the Mathematical Association of NSW (MANSW) (http://www.mansw.nsw.edu.au) provides many opportunities for the more traditional types of professional learning, casual TeachMeets, as well as networking through the many conferences offered. An additional source of PL provided by professional associations are their journals, which usually offer high quality, research-based teaching ideas. The national association, Australian Association of Mathematics Teachers (AAMT) has a free, high quality resource, Top Drawer Teachers (http://topdrawer.aamt.edu.au), that all teachers have access to, regardless of whether you are a member of the organisation or not. Many more informal avenues for professional learning are also available through social media such as Facebook, Twitter, and Linkedin, as well as blogs such as this (engagingmaths.co).

Given that teachers have so much influence on the engagement of students, it makes sense to assume that when teachers themselves are disengaged and lack confidence or the appropriate pedagogical content knowledge for teaching mathematics, the likelihood of students becoming and remaining engaged is significantly decreased, in turn effecting academic achievement. The opportunities that are now emerging for pre-service and in-service teachers to increase their skills and become specialist mathematics teachers is an important and timely development in teacher education and will hopefully result in improved student engagement and academic achievement.

M

References:

Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569-587.

Australian Government: Department of Education and Training (2015). Teacher education ministerial advisory group. Action now: Classroom ready teachers. Australian Government Response.

Lee, H. (2007). Developing an effective professional development model to enhance teachers’ conceptual understanding and pedagogical strategies in mathematics. Journal of Educational Thought, 41(2), 125.

NSW Institute of Teachers. (2012). Continuing professional development policy – supporting the maintenance of accreditation at proficient teacher/professional competence. . Retrieved from file:///Users/Downloads/Continuing%20Professional%20Development%20Policy.pdf.

Teacher Education Ministerial Advisory Group (2014). Action now: Classroom ready

Teachers.

“If you like the teacher, you’ll ‘get’ maths more”: Students talk about good mathematics teachers

This post was originally published in 2010 on the UWS 21st Century Learning Blog. The discussion relates to my PhD research on the influences on student engagement in maths during the middle years of school and findings have subsequently been published in academic journals (see, for example, Attard 2011, 2012). I thought it would be interesting to revisit since things don’t seem to have changed much in relation to the issue of students ‘turning off’ maths.

Many students during the middle years of schooling (Year 5 to Year 8 in New South Wales) are experiencing emotional, social, physical, and cognitive changes that must be dealt with in the mathematics classroom. Mathematics curriculum and instruction must address the particular needs of these students because so many jobs and indeed the demands of everyday living now and in the future, require complex mathematical thinking. Over the last 20 years research has overwhelming documented an increasingly smaller percentage of students pursuing the study of mathematics at upper secondary level and beyond. The choice not to pursue mathematics has been seriously influenced by students’ attitudes towards and performance in mathematics, in turn deeply shaped by school mathematical experiences and the teaching they experienced in school (Nardi & Steward, 2003).

So, what makes a good mathematics teacher? There are several frameworks that address ‘good’ teaching including the Quality Teaching Framework (NSW Department of Education and Training, 2003) and the Standards for Excellence in Teaching Mathematics in Australian schools (Australian Association of Mathematics Teachers [AAMT], 2006). But how do the frameworks compare to what students think about the qualities of a good mathematics teacher? My PhD thesis was a longitudinal study on engagement in middle years mathematics and early in the study I asked a group of 20 Year 6 students at a Western Sydney school to name the qualities that make a ‘good’ mathematics teacher. The students perceived a good maths teacher to be someone who:

  • is passionate about teaching mathematics;
  • responds to students’ individual needs;
  • gives clear explanations;
  • uses scaffolding rather than providing answers;
  • encourages positive attitudes towards mathematics; and
  • shows an awareness of each students’ prior knowledge.

The study followed the same group of students through their transition to high school, and into Year 8. During their time in secondary school, the students’ experiences included a wide range of practices and teachers, and significant exposure to technology within the mathematics classroom (a one-to-one laptop program). Despite being exposed to an integrated curriculum and a school that was purpose built to cater for ‘next-practice’ learning and teaching, it was the teachers and the relationships that were developed within the classroom that had the most significant impact on student engagement in mathematics. It appeared that the introduction of technology during Year 7 had removed many of the opportunities for student/teacher and student/student interaction that are such an integral aspect of learning mathematics. During their time in Year 7 the students experienced lowered engagement as a result.

Two years after the study began, when the students were in Year 8, their secondary school underwent some significant changes in terms of its curriculum delivery (no longer integrated) and the use of technology in the mathematics classrooms. There was significantly less reliance technology and a much heavier emphasis on direct instruction. The students began to build relationships with their teachers and in turn, this saw their engagement in mathematics begin to build. The students spoke about how they now felt their teachers ‘cared’ about them and ‘knew’ them. This comment from one of the students indicates the importance of positive student/teacher relationships: “if you like the teacher, you’ll get maths more. You’ll know what’s going on more.”

Although some of the pedagogies these students experienced during the study were not necessarily considered ‘best practice’, it appears the students were able to overcome this where it was difficult for them to overcome the lack of positive interactions with some of their mathematics teachers. It is proposed that regardless of the school context, students in the middle years have a need for positive teacher-student and student-student relationships as a foundation for engagement in mathematics. This relationship is built on an understanding of students and their learning needs. Unless such a relationship exists, other pedagogical practices including the use of technology may not sustain engagement in mathematics during the middle years.

Attard, C. (2011). “My favourite subject is maths. For some reason no-one really agrees with me”: Student perspectives of mathematics teaching and learning in the upper primary classroom. Mathematics Education Research Journal, 23(3), 363-377.

Attard, C. (2012). The influence of pedagogy on student engagement with mathematics during the middle years of schooling. In A. L. White & U. H. Cheah (Eds.), Transforming School Mathematics Education in the 21st Century (pp. 140-157). Penang: SEAMEO RECSAM.

Association of Mathematics Teachers [AAMT]. (2006). Standards of Excellence in Teaching Mathematics in Australian Schools. Adelaide: Australian Association of Mathematics Teachers.

Nardi, E., & Steward, S. (2003). Is mathematics T.I.R.E.D? A profile of quiet disaffection in the secondary mathematics classroom. British Educational Research Journal, 29(3), 345-367

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

Making mathematics relevant: Putting the ‘home’ back into homework

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.

New Years Resolutions, primary mathematics, and technology

Welcome to the first blog post on my Engaging Maths site! I thought I’d try setting up a website that will host some of my resources, thoughts, videos, ideas and anything else I think of! I hope you enjoy 🙂

This year, for the first time, I volunteered to teach one of my primary mathematics units during the summer school session. That meant that I had to begin teaching in the first week of January….a shock to the system. As challenging as it was to summon my enthusiasm, the first week has been excellent and working with keen pre-service primary teachers has got me thinking about all the teachers still on holidays. Most of you would have already started thinking about and perhaps planning for your new class in 2015. I wonder if anyone made a new year’s resolution relating to teaching? I always enjoyed that period of planning new things to do with a fresh group of students, in fact, I still do, but it’s at the tertiary level. This year I am committed to integrating even more technology into teaching and learning, and making more use of the mobile technologies that students bring with them. Having said that, I need to make sure my use of technology is going to enhance what I do, and not distract students.

Can I use technology to make mathematics more relevant, and can this be replicated in primary mathematics classrooms? I think the answer is yes! An example of how I have done this occurred two days ago with my university students through the use of a maths trail. If you don’t know what a maths trail is, it’s really like an outdoor adventure/treasure hunt where students are taken out of the school environment and using maps, photographs, and all sorts of equipment, get to follow a trail and do some really engaging, relevant and real life mathematics activities. Here is an example from the maths trail I have designed at the UWS Bankstown campus based on the giant rabbit sculpture that sits outside the pre-school on campus (the students are provided with a photograph to help them find the site):

Somewhere on campus is a giant rabbit…..can you locate it?

  1. How many times bigger than a normal rabbit do you think it is? Explain the mathematics you used to work this out?
  2. If the university wanted to build a sculpture of a human adult to stand beside the rabbit, how tall would the sculpture have to be? Use your iPad to record the group’s working out and your findings.

Once the students have finished the maths trail and are back in the classroom, a follow-up activity based on the giant rabbit tasks is provided along with a QR Code:

If two newborn rabbits (one male and one female) are put in a pen, how many rabbits would be in the pen after one year? How many would be in the pen after 18 months?

Use the QR Code for extra help: Rabbit problem

That is just one example of a number of different maths trail ‘stations’. The task above could be replicated in any number of ways, with many benefits for students and teachers. First, the original maths trail tasks require students to apply their knowledge, understanding, and higher order thinking skills rather than complete a simple computation or regurgitate a set of rules or facts. Secondly, the tasks are open-ended, allowing for creativity. The use of the iPad on site to record students’ responses promotes discussion and the use of mathematical language, and takes away the burden of having to use pen and paper to record absolutely everything – it can all be done on one device. Extending the task through the use of an interesting problem and some help (you need to access the QR code), allows you to promote sustained engagement.

So that’s one way I have kept my new year’s resolution to incorporate more technology into the teaching and learning of mathematics….more ideas coming soon!