Tag Archives: iPads

Engaging children with mathematics: Are you an engaged teacher?

“The first job of a teacher is to make the student fall in love with the subject. That doesn’t have to be done by waving your arms and prancing around the classroom; there’s all sorts of ways to go at it, but no matter what, you are a symbol of the subject in the students’ minds” (Teller, 2016).

Teller (2016), makes a powerful point about teaching and engagement, and how important it is that we, as teachers, portray positive attitudes towards our subject and towards teaching it. Do you consider yourself an engaged teacher? Are your students deeply engaged with mathematics, and how do you know? In education we talk about student engagement every day, but what do we actually mean when we use the term ‘engagement’? When does real engagement occur, and how do we, as teachers, influence that engagement? In this post, I will define the construct of engagement and pose some questions that will prompt you to reflect on how your teaching practices and the way you interpret the curriculum, influences your own engagement with the teaching of mathematics and, as a result, the engagement of your students.

Student Engagement: On Task vs. In Task

In education, engagement is a term used to describe students’ levels of involvement with teaching and learning. Engagement can be defined as a multidimensional construct, consisting of operative, cognitive, and affective domains. Operative engagement encompasses the idea of active participation and involvement in academic and social activities, and is considered crucial for the achievement of positive academic outcomes. Affective engagement includes students’ reactions to school, teachers, peers and academics, influencing willingness to become involved in school work. Cognitive engagement involves the idea of investment, recognition of the value of learning and a willingness to go beyond the minimum requirements

It’s easy to fall into the trap of thinking that students are engaged when they appear to be busy working and are on task.  True engagement is much deeper – it is ‘in task’ behaviour, where all three dimensions of engagement; cognitive, operative, and affective, come together (see figure 1).  This leads to students valuing and enjoying school mathematics and seeing connections between the mathematics they do at school and the mathematics they use in their lives outside school. Put simply, engagement occurs when students are thinking hard, working hard, and feeling good about learning mathematics.

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There are a range of influences on student engagement. Family, peers, and societal stereotypes have some degree of influence. Curriculum and school culture also play a role. Arguably, it is teachers who have a powerful influence on students’ engagement with mathematics (Anthony & Walshaw, 2009; Hattie, 2003). Classroom pedagogy, the actions involved in teaching, is one aspect of a broader perspective of the knowledge a teacher requires in order to be effective. The knowledge of what to teach, how to teach it and how students learn is referred to as pedagogical content knowledge (PCK). The construct of PCK was originally introduced by Schulman (1986), and substantial research building on this work has seen a strong focus on PCK in terms of mathematics teaching and learning (Delaney, Ball, Hill, Schilling, & Zopf, 2008; Hill, Ball, & Schilling, 2008; Neubrand, Seago, Agudelo-Valderrama, DeBlois, & Leikin, 2009). Although this research provides insight into the complex knowledge required to effectively teach mathematics, little attention is paid to how teachers themselves are engaged with teachers.

Engaged Teachers = Engaged Students

It makes sense that teachers need to be engaged with the act of teaching in order to effectively engage their students. If we take the definition of student engagement and translate it to a teaching perspective, perhaps it would look something like Figure 2, where teachers are fully invested in teaching mathematics, work collaboratively with colleagues to design meaningful and relevant tasks, go beyond the minimum requirements of delivering curriculum, and genuinely enjoy teaching mathematics in a way that makes a difference to students. In other words, thinking hard, working hard, and feeling good about teaching mathematics.

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Are you an engaged teacher?

Teaching is a complex practice with many challenges. Teaching mathematics has the additional challenge of breaking down many stereotypical beliefs about mathematics as being difficult and only for ‘smart’ people, mathematics viewed as black and white/right or wrong, and mathematics as a simply focused on arithmetic, to name a few. However, there are elements of our day to day work that we can actively engage with to disrupt those stereotypes, make teaching more enjoyable, and promote deeper student engagement. The following section provides some thoughts and questions for reflection.

Curriculum

How do you interpret the curriculum? Do you view it has a series of isolated topics to be taught/learned in a particular order, or do you see it has a collection of big ideas with conceptual relationships within and amongst the strands? How do you incorporate the General Capabilities and Cross-curriculum priorities in your teaching? Do you make the Working Mathematically components a central part of your teaching?

Planning

How do you plan for the teaching of mathematics? Does your school have a scope and sequence document that allows you to cater to emerging student needs? Does the scope and sequence document acknowledge the big ideas of mathematics or does it unintentionally steer teachers into treating topics/concepts in isolation?

Assessment

How often do you assess? Are you students suffering from assessment fatigue and anxiety? Do you offer a range of assessment tasks beyond the traditional pen and paper test? Do your questions/tasks provide opportunities for students to apply the Working Mathematically components?

Tasks

What gets you excited about teaching mathematics? Do you implement the types of tasks that you would get you engaged as a mathematician? Do your tasks have relevance and purpose?  Do you include variety and choice within your task design? Do you take into account the interests of your students when you plan tasks? Do you incorporate student reflection into your tasks?

Grouping

How do you group your students? There are many arguments that support mixed ability grouping, yet there are also times when ability grouping is required. Is the way you group your students giving them unintended messages about ability and limiting their potential?

Technology

How do you use digital technology to enhance teaching and learning in your classroom? Do you take advantage of emerging technologies and applications? Do you use digital technology in ways that require students to create rather than simply consume?

Professional Learning

How do you incorporate professional learning into your role as an educator? Do you actively pursue professional learning opportunities, and do you apply what you have learned to your practice? Do you share what you have learned with your colleagues, promoting a community of practice within your teaching context?

There are many other aspects of teaching mathematics that influence our engagement as teachers, and of course, the engagement of our students. Many factors, such as other non-academic school-related responsibilities, are bound to have some influence over our engagement with teaching. However, every now and then it is useful to stop and reflect on how our levels of engagement, our enthusiasm and passion for the teaching of mathematics, can make a difference to the engagement, and ultimately the academic outcomes, of our students.

References:

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics (Vol. 19). Belley, France.

Attard, C. (2014). “I don’t like it, I don’t love it, but I do it and I don’t mind”: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.

Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal for Mathematics Teacher Education, 11(3), 171-197.

Hattie, J. (2003). Teachers make a difference: What is the research evidence? Paper presented at the Building Teacher Quality: The ACER Annual Conference, Melbourne, Australia.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualising and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Neubrand, M., Seago, N., Agudelo-Valderrama, C., DeBlois, L., & Leikin, R. (2009). The balance of teacher knowledge: Mathematics and pedagogy. In T. Wood (Ed.), The professional education and development of teachers of mathematics: The 15th ICMI study (pp. 211-225). New York: Springer.

Teller, R.  (2016) Teaching: Just like performing magic. Retrieved from http://www.theatlantic.com/education/archive/2016/01/what-classrooms-can-learn-from-magic/425100/?utm_source=SFTwitter

Tips for Parents: Helping Your Child Succeed with Mathematics

As another new school year approaches, parents are once again busy preparing their children to ensure they have the things they need to be successful. School uniforms, books, pens and pencils are important, but what’s even more important is the preparation and support parents can provide to help their children learn and be happy at school.

We often see and hear media reports that lament Australia ‘falling behind’ other countries when it comes to mathematics.  Unfortunately, some people think it’s okay to be bad at maths and sadly, many children develop anxiety around mathematics from a young age. Maths seems to be a problem.

Is there something you, as a parent, can do to help? Relying on teachers alone can’t fix the problem.  There are many things parents can do to help their children learn, understand, and appreciate mathematics  before they begin school and during the  school years. The following is a list of tips for parents that will help them to help their children succeed:

  1. Be positive about maths!

May people openly claim they don’t like maths or they’re not good at it, unintentionally conveying the message that this is okay. Unfortunately, this can have a detrimental effect on the children who hear these messages. In my research on student engagement, children whose parents made similar comments often used the same comments as mathematics became more challenging during the high school years. These behaviours can lead to children opting to stop trying and drop out of mathematics as soon as they can, ultimately limiting their life choices.

As a parent, be conscious of displaying positive attitudes towards mathematics, even when it’s challenging. Adopting what is referred to as a ‘growth mindset’ allows children (and parents) to acknowledge that mathematics is challenging, but not impossible. Rather than saying “I can’t do it” or “it’s too hard”, encourage statements such as “I can’t do it yet” or “let’s work on this together”. If you’re struggling with the mathematics yourself, and finding it difficult to support your child, there are options such as free online courses like Jo Boaler’s YouCubed website (www.youcubed.org), apps such as Khan Academy, or you can seek help from their child’s teacher.

If you choose to use a tutor to help your child, make sure it’s a tutor who knows how to teach for understanding, rather than memorisation. Too often tutoring colleges use the traditional teaching method of drill and practice, which won’t help a struggling student to understand important mathematical concepts. Find a tutor who understands the curriculum and can tailor a program to work alongside what your child is learning at school.

  1. Developing a positive working relationship with teachers

It’s important for parents to work with their child’s teacher to ensure they are able to support the learning of mathematics. This will help the teacher understand the child’s needs and be better able to support the child in the classroom, while at the same time helping the parents support the child at home. Often schools hold information evenings or maths workshops to help explain current teaching methods with few parents turning up. It’s important to attend these events as they are a good opportunity to learn ways to help children with mathematics at home.

  1. Know what maths your child is learning

Mathematics teaching and learning has changed significantly over the last few decades. Unfortunately, many of the older generations still expect children to be learning the same maths in the same way, regardless of how much the world has changed! Access to the mathematics curriculum is free to everyone. Parents have the opportunity to find out what their child should be learning simply by accessing the curriculum online, or talking to their child’s teacher. This can help parents who may have unrealistic expectations of what their child should know and be able to do, and will also help them understand that mathematics is not just about numbers or learning the multiplication tables.

One of the most common complaints when it comes to school mathematics is that children don’t ‘know’ their multiplication tables. Is this important? Yes, it’s still important that children gain fluency when dealing with numbers. However, it’s also important that we don’t just rely on rote learning, or repetition. Children need to understand how the numbers work. In other words, they need to be numerate, and have a flexibility with numbers. Once they understand, then fluency can be built. Using maths games is a good way of getting children to build up speed with number facts.

  1. Make maths part of everyday activities

Bring maths into daily conversations and activities with your child. After all, there’s maths in everything we do. For example, if you’re cooking you might ask your child to help you measure out ingredients. If you’re shopping, you could have a little competition to see who can make the best estimation of the total grocery bill or perhaps ask your child to work out the amount of change (this may be challenging given that we use credit cards most of the time).

If your child likes to play digital games, download some maths apps so they can use their screen time to learn while having fun at the same time. Alternatively, traditional games can provide opportunities to talk about maths and help your child. Games that use dominoes and playing cards are great for young children as are board games such as Snakes and Ladders or Monopoly. Even non-numerical games such as Guess Who have benefits for mathematics because the promote problem solving and strategic thinking, important mathematical skills.

Parents who can work with their child’s teacher, be proactive in their child’s education, and demonstrate positive attitudes towards mathematics can make a big difference to their child’s success at school. It’s an investment worth making.

 

 

Technology in the classroom can improve primary mathematics

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There’s much more to mathematics than computation, and that’s where more contemporary technologies can improve primary mathematics.
Shutterstock

Catherine Attard, Western Sydney University

Many parents are beginning to demand less technology use in the primary classroom due to the amount of screen time children have at home. This raises questions about whether technology in the classroom helps or hinders learning, and whether it should be used to teach maths.

Blaming the calculator for poor results

We often hear complaints that children have lost the ability to carry out simple computations because of the reliance on calculators in primary schools. This is not the case. In fact, there has been very little research conducted on the use of calculators in classrooms since the 80’s and 90’s because they are not a significant feature of primary school maths lessons. When calculators are used in primary classrooms, it’s usually to help children develop number sense, to investigate number patterns and relationships, or to check the accuracy of mental or written computation.

There is also evidence that children become more flexible in the way they compute through the use of calculators. It allows them to apply their knowledge of place value and other number related concepts rather than using a traditional algorithm.

The Australian Curriculum promotes a strong focus on the development of numeracy, including the development of estimation and mental computation. These are skills that children need in order to use calculators and other technologies efficiently.

The curriculum also promotes the thinking and doing of mathematics (referred to as “proficiencies”) rather than just the mechanics. There’s much more to mathematics than computation. That’s where more contemporary technologies can improve primary mathematics.

The importance of technology in learning maths

The use of digital technologies in the primary mathematics classroom is not an option. The Australian Curriculum and Reporting Authority (ACARA) has made it mandatory for teachers to incorporate technologies in all subject areas. Fortunately, schools have access to more powerful, affordable devices than ever before. Importantly, these are the same devices that many children already have access to at home, providing an opportunity to bridge the gap between the mathematics at school and their lives outside the classroom.

Literature around digital technologies and mathematics suggest new technologies have potentially changed teaching and learning, providing opportunities for a shift of focus from a traditional view to a more problem-solving approach. This notion is supported by research that claims the traditional view of mathematics that was focused on memorisation and rote learning is now replaced with one that has purpose and application.

When used well, technology can improve student engagement with mathematics and assists in improving their understanding of mathematical concepts.

In a recent research evaluation of the Matific digital resources, the findings were positive. The students found that they enjoyed using the digital resource on iPads and computers, and went from thinking about mathematics as something to be tolerated or endured to something that is fun to learn. An added bonus was that the children voluntarily started to use their screen time at home to do maths. Pre- and post-test data also indicated that the use of the technology contributed to improved mathematics results.

How technology is used in the classroom

Many would consider that the use of mobile devices in maths would consist of simple game playing. A search of the App Store reveals tens of thousands of supposedly educational maths games, creating a potential app trap for teachers who might spend hours searching through many low- quality apps. Although playing games can have benefits in terms of building fluency, they don’t usually help children learn new concepts. Luckily, there’s much that teachers can and are doing with technology.

The following are some of the different ways teachers are using technology:

Show and tell apps, such as Explain Everything, EduCreations or ShowMe, allow students to show and explain the solution to a mathematical problem using voice and images

– Flipped learning, where teachers use the technology to replace traditional classroom instruction. YouTube videos or apps that provide an explanation of mathematical concepts are accessed by students anywhere and anytime

– Subscription based resource packages such as Matific which provide interactive, game-based learning activities, allow the teacher to set activities for individual students and keep track of student achievement

– Generic apps (camera, Google Earth, Google Maps, Geocaching) that allow students to explore mathematics outside the classroom.

The ConversationJust as the world has changed, the mathematics classroom has also changed. Although technology is an integral part of our lives, it shouldn’t be the only resource used to teach maths. When it comes to technology in the classroom, it’s all about balance.

Catherine Attard, Associate Professor, Mathematics Education, Western Sydney University

This article was originally published on The Conversation. Read the original article.

For a list of maths apps, click here:

iPad apps and Mathematics 2015

Thanks for the iPads, but what are we supposed to do with them?

This blog was originally posted back in November 2012, on the UWS 21st Century Learning site. It was written when iPads began to appear in schools. We’ve come a long way since then in terms of the increasing popularity of iPads and other tablet devices. However, I wonder how much has changed in relation to the way they are being used to teach and learn primary mathematics? I thought it would be interesting to revisit this post, so I have adapted it slightly to contextualise it into 2015.

The fast pace of technology development has seen a rapid uptake in mobile technologies such as the iPad computer tablet. Although not originally intended for use within educational settings when introduced in 2010, the iPad has fast become the ‘must have’ item in today’s classrooms.

One result of this is that teachers are often expected to integrate iPads or similar technologies into teaching and learning without the support of appropriate professional development, particularly in relation to using the technology to enhance teaching, learning and student engagement. While some claim iPads and other similar mobile devices have the potential to revolutionise classrooms (Banister, 2010; Ireland & Woollerton, 2010; Kukulska-Hulme, 2009), there is still little research informing teachers exactly how the iPads can be integrated to enhance learning and teaching, and whether their use will have a long-term positive impact on student learning outcomes.

So what do we do when we are given a set of iPads and told to use them in our classrooms? Early during the iPad ‘revolution’ I conducted two research projects investigating how iPads were being used to teach and learn mathematics in primary classrooms. These projects gave me the opportunity to observe a variety of pedagogies and make some interesting observations regarding practical issues relating to the management of iPads.

In each of the projects, teachers had been provided with iPads for their classrooms with little or no professional development that related to integration into teaching and learning practices. The teachers involved experienced a ‘trial and error’ process of using different strategies to integrate the iPads into their mathematics lessons, a task they found harder to do than with other subject areas. The iPads were used in a wide variety of ways that appeared to have differing levels of success. The success of each lesson was determined by the observed reaction to and the engagement of the students with the set tasks and the teacher’s reflection following the lesson.

Several lessons that incorporated iPads utilised a small group approach where students worked either independently or in small groups of two to three students on an application that was based upon the drill and practice of a mathematical skill. The challenge with this approach was that it was difficult for the teacher to know whether the students were on task, if there were any difficulties, and whether the chosen application was appropriate in terms of the level of cognitive challenge. Often when this pedagogy was implemented it was done so without student reflection at the conclusion of the lesson. Without discussion of the mathematics involved in the task, students did not have the opportunity to acknowledge any learning that occurred.

The pedagogies that appeared most effective were those that were based on using the technologies to solve problems in real-world contexts. When used this way, the iPads were used as tools to assist in achieving a set goal, rather than as a game. An example of one of these lessons was in Year 5, when students were asked to plan a hypothetical outing to the city to watch a movie. The children were able to use several applications on their iPads ranging from public transport timetables to cinema session time applications to plan their day out. The lesson resulted in rich mathematical conversations and problem solving, and high levels of engagement due to the real-life context within which the mathematics was embedded.

The integration of interactive whiteboards with iPads was also a common element in the observed lessons, illustrating how such technologies can enhance teaching as well as learning. In several instances teachers projected the iPads onto interactive whiteboards to demonstrate the tasks set for the students. In other examples, it was the students’ work on the iPads that was projected for the purpose of class discussions and constructive feedback.

The variety of ways in which the technologies were used demonstrated their flexibility when compared to traditional laptop or desktop computers. All of the teachers involved in both projects found it challenging to integrate the technologies into mathematics in contrast with other subject areas such as literacy.

This challenge led to the teachers expressing a need for professional development in relation to integrating the iPads into existing pedagogical practices and a desire to have a platform from which ideas can be shared amongst peers. The incorporation of the iPads led to the teachers becoming more creative in their lesson planning and as a result, tasks became more student-centred and allowed time for students to investigate and explore mathematics promoting mathematical thinking and problem solving.

Overall, the use of iPads appeared to have a positive impact on the practices of the teachers and the engagement of the students participating in the projects. Benefits of the iPads included the flexibility in how and where they could be used, the instant feedback for students and the ability for students to make mistakes and correct them, alleviating the fear of failure and promoting student confidence.

The disadvantages of the iPads were mostly management issues relating to the sourcing and uploading of appropriate applications, the difficulties associated with record-keeping and supervision of students while using the iPads and the number of iPads available for use. The interactive nature of the technologies was engaging for the students at an operative level. However, when the tasks in which they were embedded did not include appropriate cognitive challenge, students were less engaged and became distracted by the technologies.

The incorporation of iPads in the two projects emphasised their potential to increase student engagement and the importance of providing professional learning experiences for teachers that go beyond learning how to operate the technologies. Rather, continued and sustained development of teachers’ technological pedagogical content knowledge (TPACK) (Mishra & Koehler, 2006) that builds on their understanding of mathematics content, ways in which students learn, the misconceptions that occur, and ways in which technology can enhance teaching and learning is required.

 References:     Banister, S. (2010). Integrating the iPod Touch in K-12 education: Visions and vices. Computers in Schools, 27(2), 121-131.    Ireland, G. V., & Woollerton, M. (2010). The impact of the iPad and iPhone on education. Journal of Bunkyo Gakuin University Department of Foreign Languages and Bunkyo Gakuin College(10), 31-48.     Kukulska-Hulme, A. (2009). Will mobile learning change language learning? ReCALL, 21(2), 157-165.     Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.

Technology and Mathematics: Have you fallen into the App Trap?

Over the course of the last few weeks I have presented several keynote presentations and workshops on the topic of technology and mathematics, and addressing the needs of contemporary learners in the mathematics classroom. When talking about meaningful ways of incorporating digital devices into teaching and learning, I always caution teachers of the danger of allowing the devices to become the focus of the learning, as opposed to the mathematics being the focus.

The increasing popularity of mobile devices has meant that teachers now have literally thousands of applications (apps) to choose from when considering the use of technology for their mathematics lessons. Unfortunately though, the quality of the majority of mathematics-specific apps is questionable. The reason for this is that many of the apps available promote a traditional, drill and practice approach to learning. In fact, many do not promote learning at all and require the student to have prior understanding of the topic or concept covered. However, the news isn’t all bad. If we consider that in Australia our curriculum incorporates the ‘proficiencies’ of problem solving, reasoning, understanding and fluency (in New South Wales we have the added component of communicating), then many of the apps available do promote the building of fluency, but little else.

Unfortunately, the temptation of having so many apps to choose from means that there are some ‘app traps’ that teachers can fall into. Firstly, if you use an app that is presented in a game format, it is easy to create a ‘set and forget’ task. Imagine the scenario where a teacher sets five different tasks, all based on the same mathematical concept. Students are grouped and each group participates in a different task each day. One of the tasks is based upon an app. The students are directed to engage with the app for the duration of the group activity time. They are left alone or with minimal supervision. No evidence of learning is gathered, in fact, there is no evidence that the students were able to interact with the mathematics embedded with the app successfully.

On the other hand, picture the same scenario where one of the students is asked to act as a ‘supervisor’ and record any errors made by the other students. The students are given a short burst of time to engage with the task and the teacher then calls the group together to address any errors identified by the ‘supervisor’. The group then returns to the task and a different child gets to play the role of ‘supervisor’. At the end of the lesson the students are given tailored, task specific reflection prompts that allow them the opportunity to think about the mathematics involved in the game and reflect on challenges and successes. They may even be asked to provide advice to the next group of students to use the app.

Another ‘app trap’ for teachers is the temptation to rely on mathematics specific apps rather than generic apps that provide the students to become authors or producers rather than simply consumers. Consider the following task from my most recent book, Engaging Maths: iPad Activities for Teaching and Learning:

Task_Page34 

The task takes advantage of a number of generic apps and the focus remains firmly fixed on the mathematics task and the mathematical thinking of the students.

One final app trap (for the moment) is that often we download apps that look as though they are going to satisfy our students’ learning needs, however, we don’t have enough time to thoroughly engage with the app to ensure there are no nasty surprises or disappointments. Once the students are using the app in a mathematics lesson, things start to go wrong and the learning time is lost. Technology once again becomes the focus of the lesson. The message here is to try and test each new app before letting students use it. Make sure it has appropriate challenge, aligns with the learning intentions and the curriculum, and is engaging.

The way to avoid the app trap is to keep your use of digital devices simple. Focus on task creativity and apps that promote the role of students as producers and authors, rather than consumers. Seek advice from others who have used the apps that you are considering – they may have insights they could share. Above all, use your apps in ways that will enhance how you teach and how your students learn – if they don’t, then why use them at all?

 

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.