Category Archives: Professional development

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

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!

These are a few of my favourite things: Essential materials for every maths classroom

What concrete materials do you have in your mathematics cupboard and why bother investing in concrete resources? Concrete materials provide opportunities for children to construct rich understandings of mathematical concepts. In addition, providing opportunities for children to physically engage with materials is much more meaningful than working with drawn or even digital representations. For example, if you are teaching students concepts relating to 3-dimensional space, it makes sense that it is better for children to be able to manipulate objects in order to explore their properties and relate their learning to real-life. Concrete materials also promote the use of mathematical language, reasoning, and problem solving.

I often get asked about the essential resources required for primary mathematics classrooms. There are quite a few, but if you have a limited budget or space, there are a few resources that are what I would consider to be essential, regardless of the year level that you are teaching. My advice would be to invest in materials that are flexible and able to be used in a variety of ways, perhaps in conjunction with other materials. Also consider collecting things that are not necessarily intended as educational resources but may have some mathematical value, such as collections of things (keys, lids, plastic containers, etc.) for activities that require sorting and classifying. Here is a list of basics that can be purchased from educational resources suppliers (some of the items can also be sources at normal retail and/or discount stores):

  • Counters
  • Dice (as well as the standard six sided dice, you could purchase many other variations including blank dice)
  • Calculators (yes, these are great, even in the early years. Think about using them to investigate numbers rather than simply computational devices)
  • Base 10 material (be careful how you ‘name’ these – using terms like ones, tens, hundreds and thousands limits their use. It is best to use the terms minis, longs, flats and blocks so they can be used flexibly to teach a range of whole number and measurement concepts)
  • Pattern blocks (great for more than just exploring 2D shape – these can be used to teach fractions, place value, area, perimeter etc.)
  • Dominoes (one of my truly favourite things!)
  • Playing cards
  • Unifix blocks

Of course, any resource is only as good as the teacher using it and the way it is integrated into teaching and learning. Prior to using any concrete material, think about the purpose of the lesson and the mathematical concepts being taught. Also consider how you can make the most out of the resources – how will you differentiate the task, and how will you capture evidence of learning? This is where technology can play a useful role and allow teachers and students to capture evidence when working with concrete materials. Technology can also be used alongside concrete materials. For example, work with pattern blocks can be recorded using the Pattern Block App on an iPad. Or students could integrate their use of concrete materials with a verbal reflection or explanation using the Explain Everything app.

The best way to get the most out of concrete materials is to research. There are many high quality resource books and there are also many great websites such as NCTM Illuminations that provide excellent teaching ideas. Once you see the potential of high quality, flexible concrete materials such as those in the list above, you and your students will become much more cognitively, affectively and operatively engaged with mathematics.