Tag Archives: tablets

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?

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:

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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