Category Archives: teachers

Teaching with tablets: Pedagogy driving technology, or technology driving pedagogy?

If you are a teacher, then you have probably experienced the introduction of a new technology into your classroom at some point in time. Whether it was an interactive whiteboard, laptops or tablets, it is likely that you would have felt some pressure to use that technology as much as possible because of the expense involved. Often teachers are expected to incorporate new technologies without the support of appropriate professional development. That is, professional development that not only addresses the technical aspects of the devices, but the pedagogical considerations as well.

My research into the use of iPads in primary classrooms has revealed that many teachers find it a challenge to use technology creatively to teach mathematics when compared to other subject areas. I believe that the way technology is used in mathematics lessons often reflects how the teacher views and understands mathematics and the curriculum. The teachers who see mathematics as a collection of facts and rules to be memorised often rely on a drill and practice approach, and therefore limit the use of technology to applications that support this method. The plethora of drill and practice apps now available on tablets help perpetuate this teaching method. On the other hand, teachers who see mathematics as a collection of big ideas that need to be applied to rich, contextual activities are the ones who use tablets and other technologies in more creative ways, steering away from the mathematics specific applications. Often during the drill and practice approach, the technology becomes the focus of the lesson. However, when rich tasks are involved, the focus remains on the learning and the technology is used as a tool to promote the learning, access and present information.

So how can you make your use of technology more meaningful in mathematics lessons? Frameworks are often helpful in encouraging teachers to reflect on their practices, and one that is a good starting point is the SAMR model of technology integration by Puentedura (2006). The model represents a series of levels of technology integration, beginning at the substitution level, where technology simply acts as a direct substitute for traditional practices, with no improvement. The second level, augmentation, provides some functional improvement – imagine the use of a maths game app that gives instant feedback. The feedback component is the improvement. At the third level, modification, the technology has allowed for significant redesign of existing tasks. The final level, redefinition, allows us to create new tasks that were previously inconceivable.

I believe that we should be pushing ourselves to aim for the redefinition level of SAMR, however, this does not mean that technology should not be used at the lower levels. The most important thing to remember is that you must not let the technology determine the pedagogy – it should be the other way around, where the pedagogy is driving the technology. Another thing to think about is that no framework is perfect. Although the SAMR model is a good starting point, a major flaw is that it assumes that any use of technology is going to enhance teaching and learning. I disagree. I have seen lessons where the technology distracts students, and the focus is no longer on the mathematics: it’s on the technology. Technology driving pedagogy.

Apart from adding a ‘distraction’ level to SAMR, I would also like to suggest that consideration of student engagement sits as a backdrop behind the entire model. I would also want to consider how the proficiencies (Working Mathematically) align with the model. In the graphic below you will see that I have made some additions to SAMR, suggesting that the lower levels of the model align with the proficiency of fluency, and as you progress through the model, more proficiencies are added so that tasks that move beyond drill and practice promote understanding, problem solving and reasoning.

From: Engaging  Maths: iPad activities for teaching and learning, Attard, 2015.
From: Engaging Maths: iPad activities for teaching and learning, Attard, 2015.

This adapted model can be used as a tool to help plan and design tasks and activities that incorporate technology. On the other hand, it might help you make the decision to not use technology! Resist the temptation to use devices simply because you feel you have to – if it doesn’t enhance teaching and learning, don’t use it. If you are going to use those drill and practice type apps, then make sure they are embedded in good teaching – always include rich reflection prompts that provide children with the opportunity to talk about the mathematics involved in the task, the problems and challenges they encountered, and ways they can improve their learning. Remember, don’t let the technology drive the pedagogy – mathematics and learning should always be the focus!

Attard, C. (2015). Engaging maths: iPad activities for teaching and learning. Sydney: Modern Teaching Aids.
Puentedura, R. (2006). SAMR.   Retrieved July 16, 2013, from www.hippasus.com

Why saying “I’m not good at maths” is just not good enough!

How many times have you heard people say “I’m not good at maths”? Perhaps you’ve said it yourself. Often people make the statement with pride, almost implying it’s ‘cool’ to be bad at maths. Imagine if the same number of people claimed “I’m not good at reading”. I don’t think it would be deemed socially acceptable – in fact, most people would be embarrassed to make that claim. So why is it okay to by openly negative about mathematics? Why do so many in the media openly claim to dislike mathematics, and why is mathematics seen as a domain only accessible to an elite group of ‘smart’ people? Research has proven humans are born numerate, so what happens in those few years when children are in school to make them hate maths?

Firstly, we need to look at what happens in the home. Parents need to think carefully about how they talk to their children about mathematics. Regardless of how they experienced school mathematics and how they perceive mathematics, claims like “I was never good at maths when I was at school” are not helpful. Children notice. Molly, a  Year 6 participant in my PhD study, made this comment when asked about what her family think about mathematics: “My mum doesn’t really like me asking her because she thinks she doesn’t have a maths brain. She thinks that she’s got more of an English brain than anything else.” Not surprisingly, Molly was not the only child who made that kind of comment.

Parents’ negative attitudes or beliefs do have the potential to negatively influence children, particularly when not having a ‘maths brain’ can be used as an excuse for opting out of mathematics in the senior years of schooling. Evidence of this influence on children’s thinking can be seen in this quote, where Kristie, another participant, was describing her friends’ attitudes towards mathematics: “Maybe some just don’t enjoy it the way I do, they just think maybe it’s not their subject. They might enjoy English.”

So what can parents do to promote positive attitudes towards mathematics? Above all, they should never make negative comments about the subject. If you are a parent and you are having difficulty with helping your child, seek help. In the primary years, many schools are happy to provide parent workshops to help parents understand new teaching methods. Workshops could also be held to help parents ‘brush up’ on their own mathematics skills. If your child is in secondary school and the mathematics they are learning requires more than a quick revision, don’t panic. It’s okay to say “I don’t know” or “I don’t remember how to do that” – try and find a way to assist your child in finding an explanation, whether it is by seeking help online, encouraging them to seek help from their teacher, or, if required, finding an appropriate tutor who may be able to provide some remediation. It’s better to seek help early.

One of the challenges with mathematics is that the concepts are hierarchical. That is, if children don’t  don’t develop a deep understanding of foundational topics such as place value, gaps in learning begin to occur. When mathematics becomes more complex, children who struggle with the foundations of mathematics cannot keep up with their peers and fall behind, often leading to negative attitudes, poor self-efficacy, and disengagement.

And now we turn to the classroom. What can teachers do to stop the “I’m not good at maths” comments from perpetuating a fear of mathematics? Firstly, talking to parents about this issue needs to be a priority. Next, think about how you can promote positive attitudes – I’ve written much about engagement and mathematics and there are lots of great teaching and learning ideas on this website and elsewhere. Another comment that we often hear is “when an I ever going to use this?”. It’s a fact that there is mathematics that some of us will never use once we leave school. But that doesn’t mean we shouldn’t learn it – if we don’t we may be minimising future opportunities. Professor Edward Frenkel (one of my mathematical heroes) claims that school mathematics is often not presented in a way that highlights the connections to our daily lives (check out his video on YouTube). We don’t always have to understand the complex mathematics that lies beneath Facebook, online shopping, traffic systems, etc., but we do need to be aware that mathematics plays a critical role in many aspects of our daily lives, regardless of what we do or where we are from.

Finally, I strongly believe we need to stop allowing those around us, in our lives and in the media, to make such negative statements about mathematics – if we don’t take a stand things will never change, and it’s definitely time for a positive change. Start your school week with this statement: “I love maths!” Feels good, doesn’t it?

Beyond the Bells and Whistles: Using iPads and other devices in primary mathematics classrooms

This week my new book, Engaging Maths: iPad Activities for Teaching and Learning, was published so I thought I would write about some of the thinking behind the book, which provides a range of teaching and learning ideas based on my research on student engagement and the effective use of mobile technologies.

As a teacher educator, I was very excited by the introduction of iPads back in 2010 and the prospect of using these devices to teach primary mathematics. Having been a primary school teacher for some years before beginning my career as an academic, I sensed that many teachers would be dazzled and distracted by the number of applications (apps) available for use (particularly in mathematics). I was keen to investigate how the tablets were being used in classrooms, particularly as there appeared to be little or no professional development opportunities relating to the pedagogical considerations involved in using the devices, due to their newness. So I conducted two research studies, each six months long, in two different schools where iPads were being introduced (Attard, 2013; Attard & Curry, 2012). I investigated the ways teachers used the devices in their mathematics lessons and I spoke to teachers and students about their perception of iPads.

Not surprisingly, the introduction of the iPads did seem to result in higher levels of student engagement. Another benefit described by the participating teachers was that the students had begun to engage with mathematics more at home. They did this by downloading the same apps that were being used in their mathematics lessons.

The teachers involved in both studies recognised that iPads hold the potential to enhance mathematics teaching and learning due to their wide range of affordances that include a vast variety of applications, ease of use, and their ubiquitous nature. However, they found it challenging to incorporate creative iPad use into mathematics lessons when compared to their integration into other subject areas such as English and science. During the course of the two studies, the teachers tended to rely on apps that are specifically designed for mathematics, but focused on a drill and practice approach that simply replaced the repetition of a standard worksheet or textbook page with some added animation and colour. Sometimes the apps that were used in the observed mathematics lessons were based on games, with little or no opportunity for students to develop their problem solving skills or being able to reflect on their learning, and limited opportunities for the teachers to capture evidence of learning.

These challenges could have been addressed with the support of professional development and an opportunity to share ideas with other teachers. As one teacher stated: “it’s probably about having that conversation with other teachers.” It must also be acknowledged that at the time of the studies, iPads were a very new technology and professional development relating specifically to iPads and mathematics was not readily available and perhaps is still not sufficiently available five years after their introduction. Having said that, professional development opportunities should not simply focus on specific devices. Rather, due to the rapid pace of technology development, they should be focused on understanding the pedagogy related to the incorporation of any type of technology, and the development of teachers’ Technological Pedagogical Content Knowledge (Koehler & Mishra, 2009).

Although my new book has the word ‘iPads’ in its title, the theory underpinning the ideas and strategies apply to any technology, and in fact, any new resource you are considering using. The activities within the book can be adapted to suit different devices, different content, and a diversity of learners. More importantly, the book is intended as a form of professional learning for teachers struggling with finding meaningful, creative and powerful ways to use technology to enhance the teaching and learning of mathematics. Remember, don’t be distracted by bells and whistles: technology is only as good as the pedagogy driving it – careful consideration must be taken to ensure the focus remains on the learning, rather than on the technology.

Attard, C. (2013). Introducing iPads into Primary Mathematics Pedagogies: An Exploration of Two Teachers’ Experiences. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th Annual conference of the Mathematics Education Research Group of Australasia) (pp. 58-65), Melbourne: MERGA

Attard C., & Curry, C. (2012) Exploring the use of iPads to engage young students with mathematics, In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics Education: Expanding Horizons. (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia), pp 75-82. Singapore: MERGA.

Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technoogy and Teacher Education, 9(1), 60-70.

Free resources that every teacher, student and parent should know about!

There are two brilliant mathematics resources that I believe everyone should know about and use to improve mathematics in schools and in our community. One is designed for people of all ages, and the other is one of my favourite mathematics problem solving websites. Some of you would have seen and used these two websites. If you haven’t, I would encourage you to take a look – these resources are free and of high quality! Although quite different, these websites have educational resources that access a broad range of mathematics content, and more importantly, the processes of mathematics. That is, the Australian Curriculum: Mathematics proficiencies, or if you live in New South Wales, the Working Mathematically components of the current mathematics curriculum.

Last week I wrote about financial literacy and what it means in the context of mathematics and primary schools. Since then, I have spoken to several more teachers and children at schools in low socio-economic areas as part of my current research project on financial literacy and mathematics. A result of my conversations is that I am even more convinced of the importance of teaching consumer and financial literacy in the classroom and beyond, in the wider community.

Part of my research involves the participating teachers using the existing MoneySmart resources to introduce their students to consumer and financial literacy prior to developing their own context specific units of work. This requirement led to some professional development based on the MoneySmart resources (https://www.moneysmart.gov.au/), which have been funded by the Australian Securities and Investment Commission (ASIC). Prior to this professional development, almost all of the teachers I have spoken to did not fully understand that financial literacy is much more than being able to recognise currency and the adding and subtracting of dollars and cents. Some teachers also expressed a need to develop their own financial literacy to improve their own financial health.

After exploring the range of resources on the MoneySmart website I am convinced that this resource should be used in every school and community. The website provides educational resources for people of all ages and stages in life and could potentially change lives by promoting the development of healthy consumer and financial habits. It’s not enough that we are promoting financial literacy amongst children – the message needs to spread beyond the school gates, and I believe MoneySmart has the power to do this.

The second free resource that everyone needs to know about is the NRICH mathematics enrichment website (http://nrich.maths.org/teacher-primary), published by the University of Cambridge as part of the Millenium Mathematics Project. I have been using this site for many years now and it continues to improve and evolve. The standard of the mathematics problems on this site are excellent and an added benefit is that there are also many resources that provide professional development for teachers. Although the website is based on the British school curriculum, it aligns quite well with the Australian Curriculum.

The best thing about the NRICH website is that it is based on rich mathematical problem solving and investigation, which lies at the heart of our mathematics curriculum in Australia. The activities can be used in the classroom, for homework (if you have to set homework), and can be accessed by parents who are looking for some mathematics they can do with their children.

So what do these fabulous free resources have in common? Apart from the fact that they’re both free, they promote high quality mathematics education by using either contextual, real-life project based learning or rich tasks that can help children (and adults) learn mathematics in a much more engaging way than traditional text books and worksheets. They also promote the development of skills and understandings that can be applied beyond the mathematics classroom and have the potential to improve life opportunities – that’s got to be a good thing!

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!