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Primary Mathematics: Engaged Teachers = Engaged Students June 29, 2016

Posted by Editor21C in Primary Education, Teacher, Adult and Higher Education.
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by Catherine Attard

“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).

A few months ago I published a post about the issue of teacher engagement and mathematics. The following is an updated version of that post. The issue of student engagement with mathematics is a constant topic of discussion and concern within and beyond the classroom and the school, yet how much attention is given to the engagement of teachers? I am a firm believer that one of the foundational requirements for engaging our students with mathematics is a teacher who is enthusiastic, knowledgeable, confident, and passionate about mathematics teaching and learning – that is, a teacher who is engaged with mathematics. Research has proven that the biggest influence on student engagement with mathematics is the teacher, and the pedagogical relationships and practices that are developed and implemented in day to day teaching (Attard, 2013).

A regular challenge for me as a pre-service and in-service teacher educator is to re-engage teachers who have ‘switched off’ mathematics, or worse still, never had a passion for teaching mathematics to begin with. Now, more than ever, we need teachers who are highly competent in teaching primary mathematics and numeracy. The release of the Teacher Education Ministerial Advisory Group (TMAG) (2014) report, Action Now: Classroom Ready Teachers, included a recommendation that pre-service primary teachers graduate with a subject specialisation prioritising science, mathematics, or a language (Recommendation 18). In the government’s response (Australian Government: Department of Education and Training, 2015), they agree “greater emphasis must be given to core subjects of literacy and numeracy” and will be instructing AITSL to “require universities to make sure that every new primary teacher graduates with a subject specialisation” (p.8). While this is very welcome news, we need to keep in mind that we have a substantial existing teaching workforce, many of whom should consider becoming subject specialists. It is now time for providers of professional development, including tertiary institutions, to provide more opportunities for all teachers, regardless of experience, to improve their knowledge and skills in mathematics teaching and learning, and re-engage with the subject.

So what professional learning can practicing teachers access in order to become ‘specialists’, and what models of professional learning/development are the most effective? Literature on professional learning (PL) describes two common models: the traditional type of activities that involve workshops, seminars and conferences, and reform type activities that incorporate study groups, networking, mentoring and meetings that occur in-situ during the process of classroom instruction or planning time (Lee, 2007). Although it is suggested that the reform types of PL are more likely to make connections to classroom teaching and may be easier to sustain over time, Lee (2007) argues there is a place for traditional PL or a combination of both, which may work well for teachers at various stages in their careers. An integrated approach to PD is supported by the NSW Institute of Teachers (2012).

Many teachers I meet are considering further study but lack the confidence to attempt a Masters degree or PhD. I am currently teaching a new, cutting edge on-line course at Western Sydney University, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators – a graduate certificate is definitely less intimidating than a Masters, and can be used as credit towards a higher degree. The fully online course is available to pre-service and in-service teachers. Graduates of the course develop deep mathematics pedagogical content knowledge, a strong understanding of the importance of research-based enquiry to inform teaching and skills in mentoring and coaching other teachers of mathematics.

In addition to continuing formal studies, I would encourage teachers to join a professional association. In New South Wales, the Mathematical Association of NSW (MANSW) (http://www.mansw.nsw.edu.au) provides many opportunities for the more traditional types of professional learning, casual TeachMeets, as well as networking through the many conferences offered. An additional source of PL provided by professional associations are their journals, which usually offer high quality, research-based teaching ideas. The national association, Australian Association of Mathematics Teachers (AAMT) has a free, high quality resource, Top Drawer Teachers (http://topdrawer.aamt.edu.au), that all teachers have access to, regardless of whether you are a member of the organisation or not. Many more informal avenues for professional learning are also available through social media such as Facebook, Twitter, and LinkedIn, as well as blogs such as this (engagingmaths.co).

Given that teachers have so much influence on the engagement of students, it makes sense to assume that when teachers themselves are disengaged and lack confidence or the appropriate pedagogical content knowledge for teaching mathematics, the likelihood of students becoming and remaining engaged is significantly decreased, in turn effecting academic achievement. The opportunities that are now emerging for pre-service and in-service teachers to increase their skills and become specialist mathematics teachers is an important and timely development in teacher education and will hopefully result in improved student engagement and academic achievement.

References:

Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569-587.

Australian Government: Department of Education and Training (2015). Teacher education ministerial advisory group. Action now: Classroom ready teachers. Australian Government Response.

Lee, H. (2007). Developing an effective professional development model to enhance teachers’ conceptual understanding and pedagogical strategies in mathematics. Journal of Educational Thought, 41(2), 125.

NSW Institute of Teachers. (2012). Continuing professional development policy – supporting the maintenance of accreditation at proficient teacher/professional competence. . Retrieved from file:///Users/Downloads/Continuing%20Professional%20Development%20Policy.pdf.

Teacher Education Ministerial Advisory Group (2014). Action now: Classroom ready Teachers.

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

 

Dr Catherine Attard is an Associate Professor in the School of Education and a senior researcher in the Centre for Educational Research at Western Sydney University, Australia. This article was first published in May 2016 by Catherine on her own blog site, Engaging Maths.

I don’t get it…..yet March 7, 2016

Posted by Editor21C in Engaging Learning Environments, Primary Education, Secondary Education, Teacher, Adult and Higher Education.
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by Karen McDaid

I love mathematics and not just a little! I really love mathematics, but when I recall my mathematical school experiences, I do so with a fairly dispassionate attitude. Don’t get me wrong, it wasn’t that I disliked school mathematics. On the contrary, I quite enjoyed learning and grasped most mathematical concepts fairly quickly, which meant I met with a small but consistent degree of success in mathematics. I did alright in standardised tests, was about middle in the class, but I was not ‘smart’ in an academic sense, or at least I didn’t think so. In saying that, I was always more than happy to persevere with a challenging problem and wouldn’t let anything get the better of me.

On the other hand, Paula White, who became my friend in Year 4, was my antithesis. I thought Paula was very ‘smart’. She was awarded first in class many times throughout primary school. I admired her greatly and aspired to be as ‘smart’ as her. However, my observations of her as a learner through the years, even to my young self, were puzzling. Although she was top of the class in most of the mathematics tests we undertook, when facing a challenging mathematical problem where the solution was not immediately obvious, often the first words she said were, “I don’t get this” or “This is stupid”. By Year 8 Paula had slipped into a cycle of avoidance and her achievements in primary school were not reflected in high school. It seems to me now that she was so caught up in proving her capabilities and successes that she forgot, or couldn’t embrace, the opportunity to learn. I frequently wondered what made us so different.

Many years later as a teacher I noticed the same traits in several of my Stages 2, 3 and 4 (Years 4 to 8) students in the first few weeks of the year. Some were keen to tackle challenging problems or at least persevere with problems; others used Paula’s mantra to indicate their displeasure. What I found interesting was that there was absolutely no correlation between my primary and high school students’ defeatist attitude and their actual ability in mathematics. I knew they could achieve if only they would try. In more recent years, while teaching Mathematics to primary pre-service teachers at university I often heard Paula’s “I don’t get this” from the adult students with whom I was working. Many also subscribed to society’s misconception that a person is either born with a mathematical ability or they are not. Unfortunately, this misconception has created a culture where it is socially acceptable for someone to openly proclaim that they are ‘no good’ at mathematics and where the belief is that intelligence is fixed and unchangeable (Boaler, 2013).

So began my quest to understand what influences attitudes towards, and self-efficacy in mathematics. My aim was to see if it was possible to develop resilience, motivation and foster positive self-efficacy in my students and in the primary pre-service teachers with whom I work. I became particularly interested in the research of Carol Dweck at Stanford University into fixed and growth mindsets. Dweck (2006) describes a fixed mindset as a significant impediment to learning as it affects the ability of the learner to ‘believe’ in themselves and thus impacts their cognitive development. She also defines mindsets as a set of powerful beliefs that are in the mind and as such are changeable. Dweck argues that those who have a tendency towards a fixed mindset are rarely willing to persevere with challenges for fear they will expose their perceived deficiencies. She believes that this attitude turns people into ‘non-learners’ and an examination of the brain-waves of people with a fixed mindset demonstrated a loss of motivation when faced with challenging problems (Dweck, 2006). On the other hand, people who have a growth mindset are more open to challenges, give up less easily and believe that intelligence is malleable.

I found Dweck’s work fascinating and when reflecting on Paula’s behaviour, I realised that she had exhibited many fixed mindset behaviours as did some of my students. A study into motivation conducted by Blackwell, Trzesniewski and Dweck (2007) followed hundreds of students transitioning to 7th grade. The study found that students who had been identified as having a growth mindset were more motivated and achieved at a higher level than those with a fixed mindset in mathematics and the gap between them continued to increase over the following two years. When a growth mindset intervention was implemented in further studies, Blackwell et al (2007) and Good et al (2003) found that the achievement gap reduced further and in particular that the gap between girls and boys was significantly reduced.

In recent times there has been a lot of talk about brain plasticity, and both Dweck and Boaler acknowledge that intelligence is malleable. My challenge has been to move the immovable from ‘I don’t get it’ to believe that they can ‘get it’. So, how did all this knowledge contribute to my teaching and learning objectives in the mathematics classroom? Well it didn’t, at least not in the beginning. While my teaching philosophy has evolved over a number of years, I have always strived to create a classroom culture where students were learners, not just in name, but really enthusiastic, motivated and driven learners. No doubt this is every teacher’s goal! As such, I set high expectations and wanted students to feel safe to be risk takers. My teaching philosophy mirrored a growth mindset classroom.

So I was working within a growth mindset, unfortunately, that was just it! ‘I’ was working using a growth mindset. While I had taken the time to set up a classroom culture with my school students, I didn’t communicate my philosophy to my university students. I didn’t expect the school children to know what was in my mind; I clearly communicated and worked with them to create a safe learning space. What made me think that my university students would know what was on my mind? They didn’t know about the classroom culture that I was striving to achieve, yet they were part of the classroom community too.

“Just the words “yet’ of “not yet,” we’re finding, give kids greater confidence, give them a path into the future that creates greater persistence”.

(Carol Dweck, 2014)

While teaching time is finite, instead of rushing headlong into content in the first tutorial, I have found that spending twenty minutes setting up our classroom culture has been valuable for student engagement and for students’ self-efficacy in mathematics. I communicate my teaching philosophy and acknowledge that ‘we’ create the culture of the learning space. We discuss how our attitudes can set us up for success and take five minutes in small groups to discuss a time when we learned something well through hard work. We explore the notion of fixed and growth mindset and malleable intelligence. We set high standards for our learning and revisit this notion throughout the semester. No question is ‘dumb’ and mistakes are actively encouraged. I have learned to change my thinking and my language and that praise should be connected to behaviour rather than achievement.

This is my story, which changes according to student dynamics and as I continue to learn and adapt my teaching. I don’t claim that it will work for everyone, but I have seen a marked improvement in the effort and determination with which all students engage with the mathematics activities in class. Students have eagerly embraced replacing the statement ‘I don’t get it’ with ‘I don’t get it yet’. But one of the greatest and most powerful transformations is when you see a student who might have given up in the past, collaborate to work really hard on a mathematical problem and then suddenly they see the value in their effort and shout ‘I get it now!’

References

Blackwell, L.S., Trzesniewski, K.H., & Dweck, C.S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development78. 246-263, Study 1.

Boaler, J. (2013). Ability and Mathematics: the mindset revolution that is reshaping education. FORUM, 55(1), Retrieved from http://www.youcubed.org/wp-content/uploads/14_Boaler_FORUM_55_1_web.pdf on 12th November 2015.

Dweck, C.S. (2006) Mindset: the new psychology of success. New York: Ballantine Books.

Dweck, C. S. (2014). The power of believing that you can improve. [Video/TED talk] Retrieved from https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve/transcript?language=en

Good, C., Aronson, J., & Inzlicht, M. (2003). Improving adolescents’ standardized test performance: An intervention to reduce the effects of stereotype threat. Applied Developmental Psychology, 24, 645-662.

Growth mindset Videos

https://www.youtube.com/watch?v=brpkjT9m2Oo

https://www.youtube.com/watch?v=ElVUqv0v1EE&list=PL4111402B45D10AFC

https://www.youtube.com/watch?v=-71zdXCMU6A

https://www.youtube.com/watch?v=hiiEeMN7vbQ

Growth mindset websites

https://www.mindsetworks.com/default.aspx

Growth mindset lesson kit

https://www.mindsetkit.org/static/files/YCLA_LessonPlan_v10.pdf

Karen McDaid is a lecturer in mathematics education in the School of Education at Western Sydney University, Australia.

Professional learning and Primary Mathematics: Engaging teachers to engage students February 24, 2015

Posted by christinefjohnston in Directions in Education, Engaging Learning Environments, Primary Education, Teacher, Adult and Higher Education.
Tags: ,
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Catherine Attard

The issue of student engagement with mathematics is a constant topic of discussion and concern within and beyond the classroom and the school, yet how much attention is given to the engagement of teachers? I am a firm believer that one of the foundational requirements for engaging our students with mathematics is a teacher who is enthusiastic, knowledgeable, confident, and passionate about mathematics teaching and learning – that is, a teacher who is engaged with mathematics. Research has proven that the biggest influence on student engagement with mathematics is the teacher, and the pedagogical relationships and practices that are developed and implemented in day to day teaching (Attard, 2013).

 

A regular challenge for me as a pre-service and in-service teacher educator is to re-engage teachers who have ‘switched off’ mathematics, or worse still, never had a passion for teaching mathematics to begin with. Now, more than ever, we need teachers who are highly competent in teaching primary mathematics and numeracy. The recent release of the Teacher Education Ministerial Advisory Group (TEMAG) (2014) report, Action Now: Classroom Ready Teachers, included a recommendation that pre-service primary teachers graduate with a subject specialisation prioritising science, mathematics, or a language (Recommendation 18). In the government’s response (Australian Government: Department of Education and Training, 2015), they agree  “greater emphasis must be given to core subjects of literacy and numeracy” and will be instructing AITSL to “require universities to make sure that every new primary teacher graduates with a subject specialisation” (p.8). While this is very welcome news, we need to keep in mind that we have a substantial existing teaching workforce, many of whom should consider becoming subject specialists. It is now time for providers of professional development, including tertiary institutions, to provide more opportunities for all teachers, regardless of experience, to improve their knowledge and skills in mathematics teaching and learning, and re-engage with the subject.

 

So what professional learning can practicing teachers access in order to become ‘specialists’, and what models of professional learning/development are the most effective? Literature on professional learning (PL) describes two common models: the traditional type of activities that involve workshops, seminars and conferences, and reform type activities that incorporate study groups, networking, mentoring and meetings that occur in-situ during the process of classroom instruction or planning time (Lee, 2007). Although it is suggested that the reform types of PL are more likely to make connections to classroom teaching and may be easier to sustain over time, Lee (2007) argues there is a place for traditional PL or a combination of both, which may work well for teachers at various stages in their careers. An integrated approach to PD is supported by the NSW Institute of Teachers (2012).

 

In anticipation of the TEMAG recommendations for subject specialisation, I have been involved in the design and implementation of a new, cutting edge course to be offered by the University of Western Sydney, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators. The fully online course will be available from mid 2015 to pre-service and in-service teachers. Graduates of the course will develop deep mathematics pedagogical content knowledge, a strong understanding of the importance of research-based enquiry to inform teaching and skills in mentoring and coaching other teachers of mathematics. For those teachers who are hesitant to commit to completing a full course of study, the four units of the Graduate Certificate will be broken up into smaller modules that can be completed through the Education Knowledge Network (www.uws.edu.au/ekn) from 2016 as accredited PL through the Board of Studies Teaching and Educational Standards (BOSTES).

 

In addition to continuing formal studies, I would encourage teachers to join a professional association. In New South Wales, the Mathematical Association of NSW (MANSW) (http://www.mansw.nsw.edu.au) provides many opportunities for the more traditional types of professional learning, casual TeachMeets, as well as networking through the many conferences offered. An additional source of PL provided by professional associations are their journals, which usually offer high quality, research-based teaching ideas. The national association, Australian Association of Mathematics Teachers (AAMT) has a free, high quality resource, Top Drawer Teachers (http://topdrawer.aamt.edu.au), that all teachers have access to, regardless of whether you are a member of the organisation or not. Many more informal avenues for professional learning are also available through social media such as Facebook, Twitter, and Linkedin, as well as blogs such as this.

 

Given that teachers have so much influence on the engagement of students, it makes sense to assume that when teachers themselves are disengaged and lack confidence or the appropriate pedagogical content knowledge for teaching mathematics, the likelihood of students becoming and remaining engaged is significantly decreased, in turn effecting academic achievement. The opportunities that are now emerging for pre-service and in-service teachers to increase their skills and become specialist mathematics teachers is an important and timely development in teacher education and will hopefully result in improved student engagement and academic achievement.

 

References:

 

Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for

engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569-587.

 

Australian Government: Department of Education and Training (2015). Teacher

education ministerial advisory group. Action now: Classroom ready teachers. Australian Government Response.

 

Lee, H. (2007). Developing an effective professional development model to enhance teachers’ conceptual understanding and pedagogical strategies in mathematics. Journal of Educational Thought, 41(2), 125.

NSW Institute of Teachers. (2012). Continuing professional development policy – supporting the maintenance of accreditation at proficient teacher/professional competence. .  Retrieved from file:///Users /Downloads/Continuing%20Professional%20Development%20Policy.pdf.

 

Teacher Education Ministerial Advisory Group (2014). Action now: Classroom ready

Teachers.

Mathematics, technology, and 21st Century learners: How much technology is too much? February 10, 2015

Posted by Editor21C in Directions in Education, Early Childhood Education, Primary Education, Role of the family.
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3 comments

from Catherine Attard

On a recent visit to a shopping centre in Sydney, I noticed a new children’s playground had been installed. On closer inspection (see the photos below) I was amazed to find a cubby house structure that had a number of iPads built into it. There was also a phone charging station built less than a metre off the ground, for users of the playground to access.

The playground had obviously been designed for very young children. So what’s the problem? Shouldn’t playgrounds be meant for physical activity? What messages are the designers of this playground sending to children and their parents? Does technology have to pervade every aspect of our lives? What damage is this doing to children’s social and physical skills?

attard 2

While considering the implications of this technology-enhanced playground, I began to reflect on the ways we use technology in the classroom.

Is there such as thing as having too much technology? I am a strong supporter of using technology to enhance teaching and learning, and I know there are a multitude of benefits for students and teachers, particularly in relation to the use of mobile technologies (Attard 2014, 2013).

However, there are issues and tensions. How do we, as educators, balance the use of technology with what we already know works well? For example, in any good mathematics classroom, students would be manipulating concrete materials to assist in building understandings of important mathematical concepts. Children are engaged in hands-on mathematical investigations and problem solving, arguing, reasoning and communicating through the language of mathematics.

Can technology replace the kinesthetic and social aspects of good mathematics lessons? How do we find the right balance? Do students actually want more technology in the classroom, or do they prefer a more hands-on and social approach?

attard

Often we use technology in the classroom to bridge the ‘digital divide’ between students’ home lives and school. We know this generation has access to technology outside the school, and we often assume that students are more engaged when we incorporate digital technologies into teaching and learning.

In the The App Generation, Gardner and Davis (2013) discuss how our current generation relies on technology in almost every aspect of their lives. They make some important points that can translate to how we view the use of the technology in the classroom:

 Apps can make you lazy, discourage the development of new skills, limit you to mimicry or tiny trivial tweaks or tweets – or they can open up whole new worlds for imagining, creating, producing, remixing, even forging new identities and enabling rich forms of intimacy (p. 33).

Gardner and Davis argue that young people are so immersed in apps, they often view their world as a string of apps. If the use of apps allows us to pursue new possibilities, we are ‘app-enabled’. Conversely, if the use and reliance on apps restricts and determines procedures, choices and goals, the users become ‘app-dependent’ (2013). If we view this argument through the lens of mathematics classrooms, the use of apps could potentially restrict the learning of mathematics and limit teaching practices, or they could provide opportunities for creative pedagogy and for students to engage in higher order skills and problem solving.

So how do educators strike the right balance when it comes to technology? I often promote the use of the SAMR model (Puentedura, 2006) as a good place to start when planning to use technology. The SAMR model (Puentedura, 2006) represents a series of levels of “incremental technology integration within learning environments” (van Oostveen, Muirhead, & Goodman, 2011, p. 82).

However, the model is not without limitations. Although it describes four clear levels of technology integration, I believe there should be another level, ‘distraction’, to describe the use of technology that detracts from learning. I also think the model is limited in that it assumes that integration at the lower levels, substitution and augmentation, cannot enhance students’ engagement. What is important is the way the technology is embedded in teaching and learning. Any tool is only as good as the person using it, and if we use the wrong tool, we minimise learning opportunities.

Is there such a thing as having too much technology? Although our students’ futures will be filled with technologies we haven’t yet imagined, I believe we still need to give careful consideration to how, what, when and why we use technology, particularly in the mathematics classroom. If students develop misconceptions around important mathematical concepts, we risk disengagement, the development of negative attitudes and students turning away from further study of mathematics in the later years of schooling and beyond.

As for the technology-enhanced playground, there is a time and a place for learning with technology. I would rather see young children running around, playing and laughing with each other rather than sitting down and interacting with an iPad!

 

References:

Attard C, 2014, iPads in the primary mathematics classroom: exploring the experiences of four teachers in Empowering the Future Generation Through Mathematics Education, White, Allan L., Tahir, Suhaidah binti, Cheah, Ui Hock, Malaysia, pp 369-384. Penang: SEMEO RECSAM.

Attard, C. (2013). Introducing iPads into Primary Mathematics Pedagogies: An Exploration of Two Teachers’ Experiences. Paper presented at the Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th Annual conference of the Mathematics Education Research Group of Australasia), Melbourne.

Gardner, H, & Davis, K. (2013). The app generation. New Haven: Yale University Press.

Puentedura, R. (2006). SAMR.   Retrieved July 16, 2013, from www.hippasus.com

van Oostveen, R, Muirhead, William, & Goodman, William M. (2011). Tablet PCs and reconceptualizing learning with technology: a case study in higher education. Interactive Technology and Smart Education, 8(2), 78-93. doi: http://dx.doi.org/10.1108/17415651111141803

 

Dr Catherine Attard is a senior lecturer in mathematics education at the School of Education at the University of Western Sydney, Australia. She is is currently the president of the Mathematical Association of New South Wales and secretary of the Mathematics Education Research Group of Australasia, and has contributed a number of posts on mathematics education to this blog.

Thanks for the iPads, but what are we supposed to do with them? Integrating iPads into the teaching and learning of primary mathematics November 18, 2012

Posted by Editor21C in Directions in Education, Engaging Learning Environments, Primary Education.
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4 comments

from Dr Catherine Attard

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 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? Since my last blog post on the use of technology in July 2011, I have been involved in two research projects investigating the use of iPads to teach and learn mathematics in the primary classroom. These projects have given 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.

Catherine Attard is a Lecturer in mathematics education in the School of Education at the University of Western Sydney, Australia. She has a strong interest in the application of learning technologies to effective learning and teaching in mathematics, and teaches in our Master of Teaching (Primary) program. You can search for her other blog contributions by typing her name into the search the facility at the top of the page.

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