Recent years have seen a number of policy and curriculum initiatives which continue to emphasise the role of technology in effective mathematics teaching and learning. For instance, the Standards for Excellence in Teaching Mathematics in Australian Schools (Australian Association of Mathematics Teachers 2006) describes excellent teachers of mathematics as those who purposefully and responsively adopt a wide range of strategies and techniques for using ICT in the classroom. More recently, the Shape of the Australian Mathematics Curriculum document (Commonwealth of Australia 2009) noted the important role of digital technologies as a tool for learning mathematics:

Modern mathematical technologies (hand-held devices or computer software) support numerical, statistical, graphical, symbolic, geometric and text functionalities. These may be used separately or in combination … [and] allow greater attention to meaning, transfer, connections and applications. (p.13)

Teachers exert a powerful influence over how and how often technology is used in the classroom (Norton et al. 2000). So, whilst the range and availability of technological tools and software applications have increased dramatically, research continues to highlight the crucial role of teachers in ultimately determining the impact of technology in the classroom (Zbiek and Hollebrands 2008). Many mathematics teachers have limited personal experience using technology (Wozney et al. 2006) and there are few opportunities to learn new skills (Goos 2005). Teachers often report inadequate access to hardware, software, and teaching materials (Forgasz 2006), so they remain largely unaware of the new possibilities that technology offers in teaching and learning mathematics (Berry et al. 2007). As a result, many teachers lack confidence in their ability to integrate technology effectively in the classroom (Thomas and Hong 2005; Levin and Wadmany 2008). In spite of significant investment in school technology infrastructure and resources, the use of technology in schools is compromised in that it is often peripheral and confined largely to traditional learning experiences (Pegg et al. 2007).

The roles adopted by teachers as they use technology in the classroom are critical in determining how the technology is used. Goos et al. (2000) conducted a three-year longitudinal study of the role of graphics calculators in facilitating students’ mathematical investigations and in mediating exchanges between teachers and students in five secondary classrooms. The authors proposed four roles to describe the interactions they observed between the teacher and the technology: technology as master, where the teacher is subordinate to the technology due to limited knowledge of its functioning or the influence of the classroom context; technology as servant, where technology is used to support preferred teaching approaches; technology as partner, where the teacher’s familiarity with the class and the technology allow for more creative uses that afford collaborative approaches to learning and teaching; and technology as extension of self, the highest level of implementation characterised by powerful and creative uses of technology aligned to sophisticated pedagogical skills.

Another aspect consistently associated with the uptake of technology in schools is the provision of teacher professional development and training (Bennett and Lockyer 1999; Bennison and Goos 2010; Fitzallen 2005; Lawless and Pellegrino 2007). Previous studies have highlighted how effective professional development activities are intensive (Darling-Hammond 1998) and sustained over time (Guskey 2003). For professional development in the use of technology, researchers suggest that programs move beyond simply enhancing teachers’ technical skills (Watson 2001; Fitzallen 2005) to influence teachers’ beliefs about what constitutes effective teaching (Goos and Bennison 2007) and to demonstrate how technology can transform traditional classroom roles (Windschitl and Sahl 2002; Thomas and Chinnappan 2008). However, the process of scaling up professional development programs to sustainable, on-going experiences which operate effectively across a number of schools can be a challenging task for education systems (Goos et al. 2007). The reality for most teachers is that professional development activities are short-term and sporadic, so the focus tends to be on learning to operate the basic functions of the technology rather than considering how it might be used to improve teaching and leaning (Fitzallen 2005).

One possible solution to some of these professional learning issues might lie in the design of the technological tools themselves. The authors have been studying how teachers use online mathematics learning systems which, we believe, may have the potential to support teachers who wish to make greater use of technology in mathematics lessons without the need for intensive (and often expensive) professional development. Such systems typically incorporate several of the following student learning activities:

  • Lesson notes (textual material) linked to an explicit curriculum

  • Worksheets (investigations and activities that include puzzles and games linked to each lesson)

  • Lesson Questions (multiple choice and short answer questions graded at four levels of difficulty)

  • Timed drill and practice questions on basic skills (sometimes called a Basic Scorcher)

  • Lesson Scorchers (like the Basic Scorcher, but with questions focussed on particular lesson topics)

  • Walkthroughs (problems similar to those typically found in school textbooks that students solve online with step-by-step explanations and feedback)

  • Widgets (interactive animations linked to a particular topic).

All of these features can be used by students working at the computer for individual practice and investigations, or with a data projector for whole-class demonstrations and investigations on a whiteboard.

This paper reports on an investigation into whether the inbuilt structure of an online mathematics learning system might assist teachers who are inexperienced users of ICT to develop their ability to teach mathematics with technology in new and different ways that constructively engage students in their learning. The specific online learning system used in the study was Cambridge HOTmaths (http://www.hotmaths.com.au), a system that incorporates all the student activities listed above as well as a student messaging and reporting facility.

In designing the study, we were mindful of the call by Arnold (2004) that researchers seek to carefully examine the possibilities and potential of new technologies in realistic classroom settings, and of the suggestion of Thomas and Chinnappan (2008) that in-depth studies of classroom practice are likely to be more fruitful in helping to understand the issues concerning how and why teachers adopt technological tools. The aim of our research was to seek answers to the following questions:

  • What happens in a classroom situation where the online mathematics learning system is implemented with minimal professional development by teachers who have limited experience with technology?

  • Do teachers become more confident users of the technology?

  • Do teachers shift towards more student-centred teaching approaches?

The significance of the research is that it provides insights into how teachers who lack technology experience and training begin to use technology in the classroom.

Theoretical framework

The ways in which teachers use technology to teach mathematics are based on a complex web of relationships between their knowledge and skills relating to mathematical content, pedagogical practices and an understanding of how the technology operates (Koehler and Mishra 2005). While it is important for teachers to possess a basic grasp of how to control the functioning of the technological tool, they also need to know how to use technology effectively to enhance students’ learning (Lee and Hollebrands 2008).

Thomas and Hong (2005) extended Schulman’s (1986) idea of pedagogical content knowledge (PCK) to relate it to the particular requirements of teaching with technology. They investigated how seven mathematics teachers from two secondary schools began to integrate graphics calculators into their lessons. Thomas and Hong examined how the teachers developed their classroom roles when using graphics calculators and found that the teachers achieved different levels of progress in teaching with graphics calculators. As part of their research, Thomas and Hong developed the notion of pedagogical technology knowledge (PTK) or “knowing how to teach mathematics with the technology” (p. 258). PTK involves a teacher’s appreciation of the role that technology can play in teaching and learning mathematics, and includes decisions teachers make about how to adapt technology to assist students learn particular mathematical concepts and processes. PTK therefore encompasses the techniques and approaches teachers use to teach mathematics in qualitatively different ways through technology. Hence, teachers who have well-developed PTK will be in the best position to take advantage of the unique features of technology to transform teaching and learning in ways that are not possible without technology (Garofalo et al. 2000).

The research in this paper focuses on three teachers from one school and documents how their PTK developed as they began using an online learning system in their mathematics lessons.

Method

The data described in this paper are drawn from a larger study in which we investigated how 14 mathematics teachers at three schools used the selected online learning system in their Year 7 and 8 classes. The schools were deliberately chosen because of their low levels of technology in mathematics instruction and disadvantage prior to the commencement of the study.

Hope Springs High School

Hope Springs High School (not its real name) is a Year 7–10 campus of approximately 700 students in a low-socioeconomic area of western Sydney. The school had recently received government funding to purchase technology resources and there were three interactive whiteboards in the school, one of which was for the exclusive use of mathematics teachers. There were three designated computer laboratories and about 30 computers in the library. In addition, the school had recently purchased 12 data projectors and laptop computers for teachers to use and installed wireless internet access in all classrooms. However, most of the teachers in our study reported a lack of confidence and limited experience with technology, both in their personal use and especially for teaching.

Significantly, the level of technical support at the school was intermittent at best and the computer system was prone to breakdown or vandalism by students. The mathematics teachers also commented that many classes from other subjects had permanent bookings in the computer laboratories, so the rooms were often reserved well in advance. Only one participating teacher had accessed the computers during two lessons before we began our research, and none of the teachers had previously used an interactive whiteboard or data projector in their lessons.

The students at Hope Springs tended to be disinterested in school work and there were significant problems with absenteeism and misbehaviour. Students typically did not achieve a high standard in national numeracy tests and our observations indicated that their basic computing skills were poor (e.g., many students encountered major difficulties entering their school usernames and logging on to the internet so they could access the learning system). A random sample of 35 participating Year 7 and 8 students revealed that, while about three-quarters had a computer at home, only about half of those computers had internet access.

Procedures

At the start of the project in Term 1, an experienced teacher from the company which developed the selected learning system presented a half-day professional development session for the teachers. The aim was to show the teachers the main features of the system and how to navigate around them. The presenter also demonstrated three Widgets, but there was little discussion concerning their use or educational value. The teachers’ greatest concern was how to ensure they and their students were correctly logged on to the system.

Classroom use of the system was intensively studied in 5 Year 7 classes at the school during three periods: 4 weeks at the end of Term 2, 2 weeks in the middle of Term 3, and 4 weeks at the start of Term 4. In the following year, we studied three of the Year 7 classes into Year 8 and observed the classes for 4 weeks at the start of Term 2. A research assistant visited each classroom to observe between one and three mathematics lessons per week. An observation schedule was developed for recording teacher and student actions during the lessons, and the research assistant made detailed field notes in an observation log. Following most of the observed lessons, the research assistant interviewed the teacher to discuss the ways that the system had been used. The teacher interviews were not designed to mentor teachers or influence their practice but rather to elicit their reflections on how they had used the system in their lessons. On 11 occasions, the research assistant also interviewed a sample of students from the class on their use of the system during the lesson. All of the interviews were audio-recorded and transcribed for analysis.

Data analysis proceeded as follows: The research assistant sent all her notes and recordings on the classroom observations on all 14 teachers, along with the teacher and student interviews, to the authors. We first compiled a profile for each teacher outlining how they changed over the period of observation and made an initial comparison between them. After finding that teacher behaviour could be classified using Thomas and Hong’s (2005) notion of pedagogical technology knowledge, we selected three teachers at Hope Springs who best illustrated the range of variation. We then examined the profiles of these three teachers in more detail, consulting the original notes and recordings to ensure that our descriptions were accurate and selecting excerpts that would best illustrate their behaviour at different times. We then jointly identified up to three broad stages in the development of each teacher’s PTK and noted some similarities to the technology roles theorised by Goos et al. (2000). Finally, we sought possible explanations for the changes we had documented and formulated implications for professional development.

Results

Teacher HA

Teacher HA had taught mathematics for over 25 years, including the last 7 years at Hope Springs. HA’s teaching had a strong emphasis on students copying notes from the board or the textbook and he was insistent that students kept a neat exercise book, but he also included group work and discovery learning activities into his lessons from time to time. Prior to the study, HA had completed some in-service days learning about computers and was familiar with email, word processing, and spreadsheets. He also briefly used the selected learning system at home with his own children, but he had not used computers in teaching before and was even unsure about how to book a computer laboratory.

HA’s initial use of the online learning system involved taking his classes to a computer laboratory and allowing students to work on any part of it, as long as it was related to the mathematics topic they were learning. This pattern continued well into the fourth term.

HA showed a lack of awareness about how to support student learning with technology. In his initial lessons he made no attempt to show students the different levels available in the Lesson Questions or demonstrate how to navigate the system. Over the following months, he continued to use the system exclusively in the computer laboratory, with students working on their own at activities of their own choosing, even when this approach was unproductive.

Students would usually start with a Widget because it was often the first thing they saw when they started up the system, but the Widgets were of little educational value without first understanding the purpose behind them; so although the students enjoyed playing with Widgets, they did not learn a great deal from them. For example, in a Year 7 lesson in Term 4, students were observed using a hundreds chart Widget which could have helped them understand more about factors and multiples, but they simply created colourful patterns in the boxes of the hundreds chart without paying any attention to the numbers. On another occasion, students were observed attempting a Walkthrough without first reading the accompanying notes and then abandoning the activity as soon as they struck something they could not understand.

In most computer lessons, students who were unsuccessful at one task quickly became bored and began the regular Scorcher questions to practise basic arithmetic, even though this was not related to the topic they were studying. However, HA appeared largely unaware of how the students were using the system. In discussing the lesson with the Walkthrough, HA commented that “a fair amount of learning had taken place” because “the activities are more interesting than what you can do in the classroom.”

Near the end of Term 4, HA mentioned the possibility of using the system in the normal classroom by projecting the activity onto the whiteboard so all students could work together on a task which he had chosen for them. HA had heard some of the other teachers talking about their lessons with the system in the classroom and thought that approach might work well, but he did not yet feel ready to try it for himself. At the start of Year 8, HA began to teach with the system in this manner and he reported that his initial attempts to employ the system in the classroom were based solely on having students answer Scorcher questions. He was observed using this approach with a Year 8 class in Term 2. HA displayed the Scorcher questions one at a time on the whiteboard but sat with his back to the class while operating his laptop and allowed students to shout out their answers. Students were not required to provide reasons for their answers and he awarded a point to the first person to get the question correct. The increased noise levels as students competed for scores made it difficult to hear all of their responses.

As he became more familiar using the system in the classroom, HA was observed to use the Scorcher on fewer occasions and the Lesson Questions more often, and he did so without recording the names of students who had provided the correct answers. This approach meant that there was less competition among students to be the first to call out the answers, so the rowdy behaviour seen in earlier lessons was reduced.

In an interview near the end of the study, HA reflected on the lessons he had taught using the online learning system and commented that he liked the discussion which selecting answers to the Lesson Questions could produce in the classroom since “when students challenge each other’s answers they really get involved”; however, we observed little student involvement in class discussions. HA also remarked that the wide range of ability levels in his classes made it difficult for him to keep all of the students working together when he used the system as a tool for whole-class discussion, and students who could not keep pace with the lesson were prone to become disruptive. He concluded that in future he would revert to taking his classes to the computer laboratory “where they can work on their own at their own pace and those who are off task do not disrupt others or interfere with their learning.” He added that he would require students to attempt more of the Lesson Questions in place of the Scorcher, because that way he could monitor their progress using the data from the reporting system.

Teacher HB

Teacher HB had completed a postgraduate research degree and was the most competent and confident user of technology in the mathematics department. She was often called on by colleagues to help them when they encountered difficulties operating the system. She had been teaching for 12 years, including 7 years at Hope Springs. She had explored the selected system with her own children at home and had prepared a lesson with it, although technical problems with the school computers prevented her from giving the lesson as planned.

Her initial use of the online system was observed to be more varied than the use by other teachers in the study. She was the first teacher to monitor students’ progress using the reporting system and the only teacher who used the messaging system to alert students to upcoming lesson topics. Early in the project, HB was observed using a variety of the system features in her lessons, although she continued to adopt a very teacher-centred approach as she taught with the system throughout the study. For example, at the end of Term 3 HB gave a demonstration lesson to her Year 7 class which was observed by the school principal. HB commented that she was very pleased with the lesson, but the principal described it as “not at all impressive, just the usual ‘chalk and talk’ lesson with nothing interactive about it.”

As HB used the system for Year 7 lessons in the computer laboratory, she began to recognise that students needed her support to maximise their learning with the system. She spoke in an interview at the end of Term 2 about how students, when working alone at the computer, would often go straight to the lesson questions without first reading through the accompanying Lesson Notes and this meant that they could not answer the questions. HB therefore ensured that she spent time teaching the concepts in the laboratory before the students were allowed to attempt the related system topic on the computers. HB also insisted that students read through the Lesson Notes when they first accessed the system on the computer, though many still did not do so and they needed to call on HB for assistance many times.

HB also spoke about how students would often arrive for a computer laboratory lesson without all of the equipment they needed to complete the activities. So she created her own “resources bag” containing everything she needed to take with her to the computer laboratory—written instruction sheets about how to use the system, a list of passwords for students who had forgotten theirs, spare calculators and writing materials for students, and extra whiteboard markers in case none were available in the room.

When discussing her use of the system in an interview at the end of Term 2, HB commented that some of the terminology was slightly different to that which she typically used in the classroom and this was causing students to become confused when they were using the system in the computer laboratory. HB reported that she had started to modify her classroom teaching and align it more closely to the system activities. For instance, she noticed that the system only accepted fraction answers given in simplest form and required a zero before the decimal point for values between zero and one, so she emphasised those conventions in her lessons.

HB was the first teacher at the school confident enough to teach with the system away from the computer laboratory. In a lesson given in Term 3, she taught Year 7 about surface area using the interactive whiteboard in the normal classroom. HB had a free period immediately beforehand which gave her time to set up the data projector. She taught the class in her usual transmissive style by explaining everything to students as she went. Her lesson was based on a Widget called “Observing surface areas,” which she used in quite a sophisticated manner by combining it with her own explanations to highlight various aspects of the solids displayed on the interactive whiteboard and their surface areas. However, her explanations were given too quickly and it was clear that students found them difficult to follow. The research assistant noted that most students were not paying attention, with the result that the activity was largely unsuccessful in helping students to learn about surface areas.

HB had ongoing difficulties in managing the behaviour of some students and this began to affect her use of the system. Her approach became even more teacher-centred as she sought to maintain control of her classes. One of HB’s Year 7 lessons observed early in Term 4 was on highest common factor (HCF), lowest common multiple (LCM), and the rules for divisibility. She started the lesson by teaching the students about HCF and LCM on the whiteboard. Then she used the data projector to display three Widgets – “Finding HCFs”, “Finding LCMs”, and “Divisibility tests” – but raced through them answering all the questions herself without allowing for any involvement from the students. Next, she did a few rounds of Lesson Scorcher questions on LCM; however, HB simply typed in the first answer shouted to her by a member of the class and many of the values which she entered were incorrect; but no time was spent explaining why. The remaining time was spent trying to get students to copy down all the rules for divisibility with examples, as given in the system Lesson Notes. There were complaints about this from students, and although most eventually did it there were significant behavioural problems with three of the boys.

HB took up a teaching position at another school at the end of the first year of the study and so did not take part in the second phase of the project.

Teacher HC

Teacher HC had first trained as a primary school teacher and had a qualification in special education. She had taught English, history, and geography for nearly 30 years before moving to Hope Springs 8 years prior to the commencement of the study to teach mathematics. HC had a good rapport with students and was an excellent classroom manager. She had attended an in-service course on interactive whiteboards and previously used computers to prepare worksheets and tests for her classes, but had not used technology in the classroom. Based on initial observations of her lessons, the research assistant characterised HC’s teaching style as teacher-centred and traditional.

HC’s early use of the system was similar to the approach adopted by the other teachers and involved taking her classes to the computer laboratory. But, unlike HA and HB, she always prescribed activities for students to complete in a specified order: Widgets first, then the Walkthrough, the Lesson Questions, and finally the Scorcher. HC said that she liked to start with the Widgets because students found them engaging, but it was observed that students often had difficulty working out what the Widgets were about when they had not been given any prior explanation. For example, many students failed to understand the significance of a Widget showing the tallying of results from a spinner and their expression as percentages. HC commented that she required students to complete the Walkthrough prior to the Lesson Questions because that consolidated their understanding of the topic before they attempted the questions. Also, she used the Scorcher last as a reward for students who finished all of their other work, since she knew that many students liked competing against their classmates by trying to improve their Scorcher scores and times. Significantly, HC quickly realised the potential difficulties for students who attempted the activities on their own at the computer without a good understanding of the topic, so after just 2 weeks she started to split the lesson time between the classroom (where she introduced a mathematical concept) and the computer laboratory (where the students used the system to consolidate it). HC also made the trip to the computer laboratory conditional on students’ good behaviour in the classroom, providing an incentive for them to complete their work.

However, in the computer laboratory, HC’s students sometimes became confused when the activity included explanations or questions that were different to those they had seen in the first half of the lesson. HC noticed this and began to adjust her classroom activities so that they followed the same teaching sequence as the Walkthroughs she had chosen for the second half of the lesson. In this way, the computer time more closely mirrored what they had just learnt in class with no surprise questions on things they had not covered. The research assistant observed that this approach was much more effective.

HC’s split-lesson method was proving successful and HC saw “some definite advantages in integrating the system with the normal classroom lessons.” But she commented in Term 4 that it was difficult to monitor student behaviour in the computer laboratory and some students would visit other websites unless closely supervised. She also noted that the system activities contained too few basic questions pitched at the level of her students, many of whom were not yet working at a level commensurate with the Year 7 outcomes in the New South Wales mathematics syllabus. HC commented that she would like to start using the system in the classroom, although she would also “like to have some professional development on the use of the system with a data projector.”

By the following year, HC reported that she no longer took her classes to the computer laboratory and instead used the system exclusively in the classroom. A revision lesson on fractions observed early in Term 2 of Year 8 demonstrated her more sophisticated use of the system. She began with an assortment of her own revision questions written on the board; while students attempted these questions, she set up the data projector. The online system was then used to teach fractions, beginning with a Widget on “Representing fractions.” The Lesson Notes were read aloud by a volunteer student but HC interrupted three times to give a further example or explanation which she wrote on the whiteboard. She also circled or underlined parts of the text to emphasise key ideas. Students were then asked to copy in their exercise books HC’s own definitions of the different types of fractions.

The rest of the lesson started with a competition in which the class was divided into three competing groups. Students worked individually and wrote their answers; then they marked their own work. The first two rounds of the competition were Lesson Scorcher questions based on what the class had just learnt about fractions. There was a considerable improvement in scores from Round 1 to Round 2 as students learned from their errors after the marking of Round 1. HC then started a different Lesson Scorcher on the same topic (changing improper fractions to mixed fractions) but soon realised that this was too difficult for the students as they had not remembered the content from the previous year. Instead, she organised three rounds of Basic Scorcher for the class. This time, students wrote their answers in their books and HC corrected them all at the end of the third round.

When interviewed following the lesson, HC reflected on her use of the system over the course of the study. She remarked that she liked using the system to teach because she believed that her students were largely visual learners who concentrated more closely when the work was presented on the whiteboard. She liked being able to quickly display the Lesson Notes on the board rather than have students read them from a textbook, because students paid more attention that way. HC also commented that many of the system demonstrations and notes were often better than anything she could devise on her own. She also felt that levels of student engagement were normally higher when she combined the system with her usual approach of standing and talking at the front of the room. She was particularly impressed with the interactive nature of the Widgets, which allowed her to engage students in whole-class discussions in a way that she had not done before; students seemed captivated by the images and more willing to share their ideas about them. She described the Scorcher game as “highly motivating.” However, HC noted that it was important to supplement the system Lesson Notes and Lesson Questions with her own ideas and examples, because this reinforced the concepts for students and also helped to “bridge the gap” when the system explanations or exercises lacked sufficient basic material for her students.

Discussion

The results of our study allow us closer insight into how teachers’ PTK develops. We identified three sequential stages to describe the changing roles we observed. We call these roles technology bystander, technology adopter, and technology adaptor. We also conjecture a fourth role which we call technology innovator. As the teachers move from one stage to the next, the ways that they use technology become increasingly more varied and sophisticated.

Our four stages resemble the metaphors of technology as master, servant, partner, and extension of self, as proposed by Goos et al. (2000). But whereas Goos’s terms refer to the roles of technology, we have chosen to focus on the roles of teachers as they use technology to support student learning.

Technology bystanders

All three teachers began teaching with the system in the computer laboratory where students worked individually at their own pace; teachers HA and HB allowed students to work on any aspect of the system they wished, while teacher HC mandated specific tasks for students to complete. Observations of all three teachers in the first weeks of the project showed that teacher-student interactions were minimal while students used the system on their computers, focussing mainly on managing student behaviour or sorting out students’ difficulties in operating the system, so there was little actual teaching taking place. At this stage, the teachers’ PTK did not advance beyond developing an initial familiarisation with the features of the system.

We describe the teachers’ role in these early lessons as technology bystanders, because they essentially allowed students to work on their own. For instance, teachers HA and HB provided little guidance for students and virtually left them to work unsupervised, and although teacher HC identified the order in which students should attempt the system activities she did not offer any instruction on how to do so. Even though HB modified her computer lessons by teaching the knowledge and skills students would need to attempt the system tasks before letting them use the computers, there was no teaching during the second phase of her lessons.

With the benefit of hindsight, it is possible to view the initial computer laboratory lessons as an essential first step in developing the teachers’ confidence in their ability to use the system. These lessons allowed teachers to become familiar with the system’s features and to learn how to navigate around them. They also provided opportunities for learning how to deal with relatively prosaic issues such as how to assist students who had forgotten their passwords or could not login to the system.

Although the computer lessons could serve as a catalyst for the development of a teacher’s PTK, the lesson observations of the three teachers suggest that the crucial factor was how the teacher responded to the ways that students were using the system. Teacher HA persisted in allowing students to select the system activities for themselves and expressed satisfaction with the amount of student learning which occurred despite the poor behaviour of students and their lack of progress observed by the research assistant. HA seemed content that students were occupied at the computer without attempting to control or evaluate what they were learning. For example, it did not take the research assistant long to notice that HA’s students were using the Scorcher primarily because they did not understand the Walkthroughs and could not answer the Lesson Questions; but HA allowed that situation to continue well in to Term 4. On the other hand, both HB and HC soon became aware of the difficulties students were experiencing under their initial teaching procedure and modified their behaviour accordingly.

Technology adopters

The three teachers gradually became more aware of some of the difficulties students experienced when using the system and they searched for possible causes to explain the problems that arose. The teachers also started to use the system differently in the computer laboratories. For example, HA eventually started to insist that students complete the system activities in a sequence which he specified. HB provided even more direct guidance about which parts of the system students worked on, because she realised that they were unable to complete the activities successfully unless they did them in a specified order. HC divided her lesson time between the classroom and the computer room, because she recognised that students could maximise their learning at the computer by reviewing concepts they had already studied rather than by exploring new concepts on their own. Both HB and HC also modified their classroom teaching to align it more closely with the system sequences and terminology, as this helped students make better use of the system at the computer.

At different times in the project all three of the teachers also began to deploy the system in the classroom in conjunction with their usual teaching practices, so that the technology was essentially used to support already established pedagogies. However, the success of the teachers’ classroom use of the system was heavily dependent on their general pedagogical skills.

Teacher HA was the last to begin employing the system away from the computer laboratory and the least successful in doing so. As in the computer laboratory, HA had difficulties managing student behaviour and his primary focus continued to be on keeping students occupied. For example, although HA started to use the Lesson Questions more often in an attempt to encourage discussion, he was unable to keep the class working together for any prolonged period of time. His intention to revert to teaching with the system solely in the computer laboratory where students could work at their own pace suggests he was likely to adopt his previous hands-off teaching approach, though he did say that he would require students to attempt more Lesson Questions. His PTK showed negligible development over the course of the project and was characterised by an emphasis on trying to keep students busy regardless of how much they were learning, but his limited ability to engage students and manage their behaviour made even this goal difficult to achieve.

Teacher HB was the most experienced user of technology; her personal confidence with computers and her understanding of how to operate a data projector and interactive whiteboard allowed her to transfer to the classroom earlier than the others. She also expressed concern that students were not making optimal use of the system when working on their own in the computer room and stated that she wanted to try a different approach where she could exercise greater command over the lesson. Her PTK began to shift from an exclusive focus on helping students operate the system efficiently to a point where she was starting to think about how the system could be used to help students learn new concepts. HB’s ability to display a Widget on the interactive whiteboard and augment it with her own explanations to highlight various aspects of the animation is an example of the tentative integration of the technology into her teaching. However, her strongly teacher-centred approach, combined with a hurried delivery and an insistence on maintaining tight control over the class, meant that students were unable to participate fully in the activities.

Teacher HC commenced using the system in the classroom after she noticed that there were insufficient system activities pitched at the students’ ability level and because she was finding it increasingly difficult to monitor their work at the computer. She decided to supplement the system activities with her own examples and explanations and reasoned that this would be easier to achieve in the classroom where she could establish a stronger presence at the front of the room.

Teachers HB and HC changed their use of the online learning system much more than Teacher HA. Not only did they both modify their use of the system in the computer lab, but they also grafted the system onto their preferred classroom teaching method with the intention of making it more effective. Because these two teachers took the system fully into their repertoire of teaching actions, without making significant changes to those actions, we describe them at this stage of their PTK development as technology adopters. By contrast, Teacher HA essentially remained a technology bystander.

Technology adaptors

Teacher HC was the only one of the three teachers who progressed beyond the technology adopter stage. HC’s lessons increased in variety and creativity as she became more practised in setting up and using the data projector. Her more sophisticated practice in the second year of the study reflects the early stages of what we call a technology adaptor role characterised by a more student-centred approach that teaches through rather than with technology to promote students’ mathematical sense making and reasoning.

HC gradually learned how to integrate the system more successfully into her teaching, as evidenced by the increased number of transitions between the online system and other activities during her lessons. Observations of her Year 8 lessons demonstrated that she was aware of keeping students on task by, for example, giving them some revision questions to complete at the start of the lesson while she set up the data projector. Similarly, HC’s comments about the advantages of the system as a tool to quickly display diagrams and notes show that she was conscious of the need to make smooth transitions between the different phases of her lesson. The Scorcher evolved from being an activity HC used to reward students’ good behaviour to one which helped them consolidate their understanding of mathematical concepts. For example, HC prioritised the Lesson Scorcher (related to the lesson topic) over the Basic Scorcher (arithmetical drill and practice). Also, she required students to write down their Lesson Scorcher answers, discussing them while going on so that students had an opportunity to learn from their mistakes.

HC’s interview comments about how well her students responded to visual images such as Widgets show that she had changed her focus from teaching with the system to consider how the system could assist student learning. Her PTK advanced from an emphasis on the technology to one where using the system to help students learn new mathematical concepts was more prominent in her thinking. The system was becoming an integral part of her teaching rather than an add-on to the lesson.

Technology innovators

An online mathematics learning system can be used in much more creative ways than any we observed in the present study. For example, there are many opportunities for setting individual or group work. Students can follow ideas discussed in class to varying levels of complexity, depending on their interests and ability. They can even be set to explore concepts informally before they are discussed in class.

We conjecture that some technology adaptors will eventually recognise the affordances of the system and promote a greater focus on problem solving and student-centered learning. We describe this role, in which teachers use technology to encourage and support students’ mathematical development in novel ways to promote student-generated knowledge, inquiry and reflection, as a technology innovator.

Changes in classroom practice

We observed many changes in the technology roles adopted by the three teachers (and among the other participants in our larger study), but the nature of the improvements made in their classroom practice and the rate of change varied considerably. Somewhat surprisingly, the teacher who was the most expert user of technology at the start of the project and whose early uses of the system were the most promising was not the one who made the most progress. Rather, the most significant factors which differentiated the teacher whose PTK progressed least and remained a technology bystander from those who advanced towards taking on a technology adaptor role was how astute they were at noticing what students were doing when they used the system and how well they responded. Teachers who were skilled at identifying the problems students experienced when using the system and could ascertain the source of students’ difficulties were more likely to change their practice and develop more sophisticated technology roles for themselves and their students. These teachers were better at integrating the system into their lessons and using the technology to support student learning in partnership with their usual teaching approach. The general pedagogical skill of the teacher was therefore crucially important in developing their PTK.

The structure of the system itself also seemed important in helping teachers advance their PTK and assume new technology roles in the classroom. System features such as the Scorcher and Walkthroughs allowed teachers to immediately incorporate the system into their computer laboratory lessons, helping teachers and students develop a growing familiarity with the system. The time teachers spent as technology bystanders may have provided a solid foundation for future professional growth as they learned about the features of the system and how to navigate between them. Our results suggest that teachers would not make the transition from the computer laboratory to the classroom until they had acquired sufficient confidence in using the system. Once in the classroom, the Scorcher and the Walkthroughs provided a familiar context for teachers to learn how to operate the data projector effectively. Also, the Widgets encouraged teachers to shift from technology bystanders, who essentially observed students work on their own at the computer, to technology adopters who were more active decision makers in using technology to support their teaching.

All the teachers were able to use the system in conjunction with their usual pedagogical style, so their initial uses of the system did not require a great leap into a radically different way of teaching. As a result, there was a gradual transition in teachers’ roles, which further increased the confidence of those teachers who possessed good classroom management skills and led to significant improvements in their classroom practice.

Another significant development over the course of the study was the more flexible use of the system within lessons by teachers HB and HC – from merely as an “add-on” to greater degrees of integration with other lesson activities. These two teachers began to incorporate a mix of the system activities and activities from other sources within a single lesson. Such a mixed approach became more noticeable in HC’s classroom as she developed greater confidence in using the data projector. Teachers were also starting to make judgements about how the system could support or complement their lessons rather than simply using it to fill in time. Transitions between the system and other activities became smoother and this also encouraged a more integrated approach.

The improved use of the system in the classroom was commensurate with teachers’ growing proficiency with computers and their increased knowledge of the system, but was often constrained by their rather traditional methods of instruction. In other words, although the teacher required a range of knowledge and abilities to use the system effectively with students, by far the most important ingredient was the pedagogical skill of the teacher. This is evident in the fact that although HB was the most expert user of technology it was HC, the better classroom practitioner, whose PTK advanced most during the study.

Teachers such as HC who had a good rapport with students and could manage their behaviour effectively were also better able to maintain student engagement and ensure that students were quickly brought back to attention when they started to become disinterested in their work. Similarly, teachers HB and HC were mindful of students’ relatively short attention spans (particularly of the lower-achieving students), varied the lesson activities, and were more successful in maintaining student engagement. On the other hand, teachers like HA, who needed to spend regular and prolonged periods of time in lessons trying to manage student behaviour, quickly lost momentum in their lessons. Interruptions to the continuity and flow of the lesson reduced student engagement and the effectiveness of the system activities.

The nature of the activity was also important. Activities pitched at a level of difficulty that was equal to or just beyond the capabilities of the majority of students could be extended for longer periods of time while still maintaining relatively high levels of student engagement. Students who achieved early success in an activity were more likely to persevere, even when the tasks became more challenging. This factor led to teacher HC’s success when supplementing the system activities with tasks and resources of her own.

It is also likely that the teachers’ participation in our study influenced their classroom practice. The research assistant’s presence at the school over five school terms probably served as a constant reminder for the teachers to think about the system and how they were using it. Having the research assistant observe their lessons so consistently may also have encouraged the teachers to change their practice and use the system in ways that they might not otherwise have done. Even the neutral prompts of the post-lesson interviews probably encouraged the teachers to reflect on their uses of the system and assisted them in starting to think about alternative ways of using the system with their classes.

Implications and conclusions

The results of our research show that teachers can learn to use an online mathematics learning system to advantage, even after minimal professional development. We conjecture that this may be due to the structure of the system, which appeared to scaffold teachers’ technology learning and support the development of their PTK.

The teachers’ initial use of the system in essentially the same way as they had previously taught mathematics is probably not as detrimental as we initially thought. The changes we observed in teachers’ roles – from being bystanders who were subservient to the technology to taking ever greater control over how students used it – were more evolutionary than revolutionary. In this process, the teachers gradually built their confidence in using technology in their lessons.

Our research demonstrates that teachers who wish to use online learning systems (and other digital technologies) as tools for learning and teaching do require a basic familiarity with computers and some understanding of how technology can be used effectively in the classroom. It is clear from the study that not all teachers possess even rudimentary computing skills; but these can be learned relatively quickly and consolidated over time as long as teachers are provided with appropriate initial training.

Next, teachers require some knowledge of the structure of the selected learning system and its various features so they can find activities suitable for different stages in a lesson. Teachers would then know where to look for tasks designed to introduce new concepts, review material already taught, and allow for student practice of basic skills and techniques. Training in these aspects need only be minimal because once teachers become acquainted with the basic operation of the chosen learning system, the most effective way for teachers to learn about it is to begin using it themselves.

A far more important role for professional development activities is to assist teachers develop their pedagogical skills in using the system – their pedagogical technology knowledge. The results of the present study show that online learning systems have the potential to change the dynamics of the teacher-student relationship in the classroom and make learning more student-centred – but only if teachers learn how to use the system in ways that involve students more actively in lessons. For example, even basic skills (such as ensuring that the laptop is turned around so the teacher can face the class to monitor students more easily) need to be learned and practised. Teachers also require more opportunities for learning how to use Widgets and other parts of the system when using a data projector, so that the technology is not used simply as an adjunct to traditional “chalk and talk.”

But not even a discussion of the potential uses of an online learning system in the mathematics classroom is likely to cause teachers to use it in the most effective way possible. Professional development activities that attempt to demonstrate how technology can transform traditional classroom roles may not be successful unless teachers are already familiar with the particular tool and confident that they can operate it efficiently in the classroom. Instead, training is likely to be most effective after teachers have had time to progress from technology bystanders to technology adopters, since only then will they be in a position to become technology adaptors.

We conjecture that a more hands-on professional development program, such as working with an expert who could provide demonstration lessons with the system in the classroom, may be required to reveal to teachers how all the features of the system can be used more effectively and encourage progress towards a technology innovator role. The expense need not be exorbitant: Given the changes we observed in two of the teachers after a brief professional development session and occasional visits from the research assistant, it may be that a minimal intervention could lead to significant change. We surmise that two or three demonstration or team-teaching lessons may be sufficient to effect a substantial change in classroom culture. We are already investigating such an approach in another school and intend to report the results soon.