Category Archives: technology

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.
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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

Setting up Your Students for Mathematical Success : Tips for Teachers

Many children begin the new school year with feelings of fear and anxiety. Will they like their new teacher or teachers? Will the work be difficult? What will the homework be like? As you prepare programming and planning for a new teaching year and new students, give some thought to the strategies and activities you and your students can do in the first few weeks of term to ensure everyone gets the most out of their mathematics lessons for the entire school year. Think about what you can do differently in 2017 to make your work more engaging for both you and your students. The following are some ideas to consider.

  1. Be a positive mathematical role model

I’m sure this won’t come as a surprise, but there are teachers in our schools who actually don’t like maths and don’t like teaching it. Why is this a problem? Student know! This knowledge perpetuates the common misconception that it’s okay to dislike mathematics, and worse still, it’s okay to be considered ‘bad’ at maths.  Unless the teacher is an award-winning actor or actress, it’s really difficult to hide how you feel about a subject – it’s obvious in body language, tone of voice and of course, the way you teach the subject and the resources you use. If you know someone like this, suggest they seek some support from a colleague or colleagues. Often the reason a person dislikes mathematics is related to a lack of confidence.

  1. Get to know your students as learners of mathematics

The foundation of student engagement requires an understanding of students as learners, in other words, the development of positive pedagogical relationships (Attard, 2014). Positive relationships require teachers to understand how their students learn, and where and when they need assistance. It’s also important to provide opportunities for ongoing interactions between you and your students as well as amongst your students.

Another way to get to know your students as learners is to use existing data. For example, if your school takes part in external testing such as PAT, you can use this data as a guide. However, keep in mind that things change quickly when children are young – what they knew or understood three months ago may be very different after a long summer holiday.

A great activity to do in the very first few maths classes of the year is to ask your students to write or create a ‘Maths Autobiography’. If required, provide the students with some sentence starters such as “I think maths is…” “The thing I like best about maths is…” “The thing or things that worry me about maths is…” They could do this in different formats:

  • In a maths journal
  • Making a video
  • Using drawings (great for young children – a drawing can provide lots of information)
  1. Start off on a positive note

Have some fun with your maths lessons. I would strongly recommend that you don’t start the year with a maths test! If you want to do some early assessment, consider using open-ended tasks or some rich mathematical investigations. Often these types of assessments will provide much deeper insights into the abilities of your students. You can even use some maths games (either concrete or digital) to assess the abilities of your students.

A great maths activity for the first lesson of the year is getting-to-know-you-mathematically, where students use a pattern block and then need to go on a hunt to find other students who have specific mathematical attributes. Encourage your students to find someone different for every attribute on the list, and change the list to suit the age and ability of your students. For example, in the younger years you could use illustrations and not words. In the older years, you could make the mathematics more abstract.

  1. Take a fresh look at the curriculum

Even if you’ve been teaching for many years, it’s always good to take a fresh new look at the curriculum at the start of each year. Consider how the Proficiencies or Working Mathematically processes can be the foundation of the content that you’re teaching. For example, how can you make problem solving a central part of your lessons?
Take a close look at the General Capabilities. They provide a perfect foundation for contextual, relevant tasks that allow you to teach mathematics and integrate with other content areas.

  1. Consider the resources you use: Get rid of the worksheets!

Think about using a range of resources in your mathematics teaching. Regardless of their age or ability, children benefit from using concrete manipulatives. Have materials available for students to use when and if they need them. This includes calculators in early primary classrooms, where students can explore patterns in numbers, place value and lots of other powerful concepts using calculators.

Children’s literature is also a great resource. A wonderful book to start off the year is Math Curse by Jon Scieska and Lane Smith. Read the book to your students either in one sitting or bit by bit. There are lots of lesson ideas within the pages. Ask your students to write their own maths curse. It’s a great way to illustrate that mathematics underpins everything we do! It’s also a great way to gain insight into how your students view mathematics and what they understand about mathematics.

  1. How will you use technology in the classroom?

If you don’t already integrate technology into your mathematics lessons, then it’s time to start. Not only is it a curriculum requirement, it is part of students’ everyday lives – we need to make efforts to link students’ lives to what happens in the classroom and one way to do that is by using technology. Whether it’s websites, apps, YouTube videos, screencasting, just make sure that you have a clear purpose for using the technology. What mathematics will your students be learning or practicing, and how will you assess their learning?

  1. Reach out to parents

As challenging as it may be, it’s vital that parents play an active role in your students’ mathematical education. They too may suffer from anxiety around mathematics so it’s helpful to invite them into the classroom or hold mathematics workshops where parents can experience contemporary teaching practices that their students are experiencing at school. Most importantly, you need to communicate to parents that they must try really hard to be positive about mathematics!

These are just a few tips to begin the year with…my next blog post will discuss lesson structure. In the meantime, enjoy the beginning of the school year and:

Be engaged in your teaching.

Engaged teachers = engaged students.

 

 

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.

Primary Mathematics: Making the Most of Technology to Assess Student Learning

As the school year rapidly draws to a close, many teachers are beginning the task of reporting student achievement. For some, there may be a scramble to collect assessment data, and often, due to a sense of panic, teachers revert to pen and paper testing to gain a snapshot of their students’ ability measured against syllabus outcomes…one of the main reasons students develop a dislike of mathematics in the first place. The purpose of this blog post is to ask you to consider using alternative assessment evidence, and in particular, consider taking advantage of some of the educational software tools you may already be using in your classroom.

Regardless of what technological devices you use, if you do use technology in your mathematics lessons, chances are you already have some good assessment data that you can use in your reporting. Take, for example, the use of apps on an iPad or other mobile device. If your students are engaging in different apps to either build on their mathematical fluency (typically game-type apps) or to express mathematical reasoning and communication (with apps such as Explain Everything, Educreations or ShowMe), then it’s rather easy to collect evidence of learning. Some apps offer the affordance of being able to save student progress, and others simply require students to take a screen shot of their results.

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Educreations allows you to save files that record audio and written mathematics, allowing assessment of content and process outcomes.

I recently conducted a research evaluation of the Matific suite of resources (access the research report here). One of Matific’s affordances is that it allows teachers to track student progress.

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The Matific website allows teachers to view assessment data in a number of ways

Interestingly, out of the 16 teachers involved in the study, only nine teachers used the ability to track student achievement and even fewer considered using it as assessment data. However, those who did use this affordance, considered it a valuable tool that allowed them to differentiate future tasks, tailoring the learning for individual student needs:

It was perfect in a sense that we made it a point that we started at the middle and we went down for those who needed extra support, which was fabulous because they were still doing it visually, they were doing the exact same thing, and then we also gave the option that they could go up if they felt confident enough but at the same time visually, it was exactly the same for those kids that don’t want to be different, that maybe do need that little bit of extra support (Year 6 teacher). 

Data from students’ interactions with educational apps such as Matific, game apps and productivity apps can provide valuable formative and summative assessment data that can remove the anxiety associated with formal pen and paper testing, particularly during the primary years when it’s critical that we foster high levels of student engagement. Consider the apps you currently use – how can you collect evidence and use it to your advantage and the students’ advantage…and also save you time? Isn’t it better to spend class time on learning rather than testing?

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.