Mathematics teachers' development, exploration, and advancement of technological pedagogical content knowledge in the teaching and learning of algebra
Volume 9 Number 2, 2009; Pages 117–130
A professional learning project in the USA has sought to develop Year 8 mathematics teachers' pedagogical content knowledge of algebra, and their knowledge of how technology can inform their teaching of the subject, that is, develop their 'technological pedagogical content knowledge' (TPCK). The project involved 20 female teachers, with widely varied years of professional experience, from three rural and three urban schools in the same area. They undertook 60 hours of summer sessions and 60 hours of academic year sessions, organised and conducted by the author. The participants experimented with the use of mathematical software, designed technology-based curricular materials, and maintained electronic journals. Participants' journal entries, and their interactions and discussions with each other, were recorded and classified using a TPCK content analysis framework. The article describes three of the topics covered in the sessions. The first involved the participants' use of graphing software to solve problems that required transfers between algebraic, numeric and graphic representations, often difficult for school students. Through this experimentation, and reflection about it through discussion and journal entries, participants were stimulated to explore 'how to teach' issues that challenged their usual teaching practices and helped integrate their TPCK. The second activity involved the use of virtual manipulatives, on-screen representations of three-dimensional objects that could be repositioned, of the kind available through the National Library of Virtual Manipulatives. The participants integrated the use of the manipulatives into five lesson plans, learning to select the type most suited to each lesson, and were 'challenged to explain how the manipulative worked through extracting the mathematics from the activity'. The third activity involved use of the free, interactive GeoGebra program that simultaneously represents mathematical objects in algebraic and graphical forms. Analysis of project results highlighted the need for further professional learning to help teachers apply their knowledge of content and technology to their pedagogy, and to move from the use of technology simply to illustrate mathematical concepts to the use of the technology for exploration and discovery by students. There is also a need to examine the possible limitations in the application of technology to the teaching of algebra.
Key Learning AreasMathematics
Subject HeadingsInformation and Communications Technology (ICT)
United States of America (USA)
26 August 2009
Policy-makers in Australia need to reverse the current decline in Asian literacy: the need for more widespread knowledge of Asian languages is 'not really a matter of choice but an imperative'. Trade with Asia generates the 'most overwhelming case' for developing this knowledge through its demands for interpersonal communications and intercultural awareness. China is well-known to be Australia's largest trading partner, but the ASEAN bloc of countries, taken together, is bigger still, and together ASEAN and China dwarf Australia's trade with the West. The depth of trade and the robustness of Asian economies have allowed Australia to resist the worst impact of the global recession. It is naïve to imagine that Asians will solve language problems for Australia by learning English: in some Asian countries, such as Malaysia, there is in fact a trend to reduce the stress on English language learning, and even where English has spread further, as in Hong Kong and Singapore, it remains restricted to elite circles. Asian language learning is also essential for strategic reasons, including Australia's current involvement in two wars in Asia, the strategic importance assigned to China, and the need for sophisticated local knowledge of Asian countries in order to combat terrorism. Individual Australians 'keep getting embroiled in commercial, legal and political systems' of Asia, requiring diplomatic interventions. The current state of Asian language learning in Australia does little to address these needs. Australia continues to have the lowest level of second-language knowledge in the OECD. Language knowledge in the private sector is inadequate and shrinking. Australia 'now looks worse than it did before NALSAS', the previous Australian government’s Asian language program. The current government's replacement program, NALSSP, provides for only half the levels of annual NALSAS funding. The drive for Asian literacy needs far higher levels of support.
Key Learning AreasLanguages
Subject HeadingsLanguages other than English (LOTE)
Language and languages
Volume 19 Number 1, May 2009; Pages 34–47
There is strong interest in researching classroom life as a means to understand and improve student learning. Traditionally, video-based research was quantitative in approach: it was planned in advance and targeted selected, narrow activities removed from the context of wider classroom events; it also tended to be costly and intrusive. The 1980s brought greater interest in qualitative research that investigated the beliefs and general characteristics of students and teachers through the collection of detailed descriptive information. The authors describe an effort to apply current ICT to qualitative classroom research. They relate these efforts to six characteristics of qualitative research identified by Michael Patton. First, such research aims to capture naturally occurring situations as they unfold using unobtrusive and subtle mechanisms, and collects rich, contextualised information. Small digital recorders with wide-angle lenses, and inconspicuous wireless microphones for teachers were used to facilitate this. Second, the research must be flexible in its design. In this case, the teachers were able to choose which activities were recorded at which time; discreet hand-held devices were used for recording. Third, purposive sampling should be used. In this study the six teacher participants were all first-year teachers in South Australian Catholic primary schools. Fourth, qualitative data is obtained. Qualitative data is complex, contextualised, and 'not easily reduced to numbers'. The fifth and sixth characteristics are recognition of the researcher's personal experiences and insights, and a non-judgmental, empathic neutrality toward the participants. Significant technical challenges arose in the current study. One was to find mountings for the video cameras that allowed them to capture routine classroom life and which were also safe, stable, unobtrusive, sheltered from sunlight, near a powerpoint, and easy to access and retrieve. Mechanisms were also needed to remind teachers to activate all necessary devices and to ensure they were reconnected after any interruption, such as by school cleaners. Non-participating students, including visitors from other classrooms, had to be excluded from the footage. Most significantly, the researchers were unprepared for the sheer volume of potentially valuable material captured by the technology, which generated technical problems related to storage and transfer that required the purchase of further software.
Subject HeadingsTeacher-student relationships
Information and Communications Technology (ICT)
School principal expertise: putting expert-aspiring principal differences in problem solving processes to the test
Volume 8 Number 2, April 2009; Pages 128–151
A study has compared the problem-solving strategies used by expert principals with those of educators aspiring to principal positions. It builds on earlier research suggesting that experts in diverse fields show similarities in their approach to problems: they generally put effort into interpreting and clarifying the problem, reflect more deeply on how it may be addressed, and articulate proposed solutions in more complex and abstract terms. Earlier studies distinguish expert principals as those who are more aware than their peers of the specific nature of a problem and the influence of local contexts upon them. They are more likely to situate the problem in terms of its impact on student learning, collect evidence, keep parents informed, have a planned and long-term approach, follow it up later, face up to conflicts and delegate authority. They are also more likely to relate relevant anecdotes about the problem when explaining it. The current study compared 20 expert and 24 aspiring principals in a disadvantaged area of Iowa. The experts were identified using longitudinal teacher survey data, and statewide student test results. During individual interviews participants in both groups were asked to respond to six written scenarios, all of which presented ill-structured problems, and four of which related to classroom teaching of maths or language arts. The responses of the expert principals aligned with findings of previous studies in several respects: the principals were substantially more likely than aspiring leaders to identify contextualised solutions; to critique, dissect and rework the initial scenario they were given; and to explain the problem in terms of a relevant anecdote. However, results contrasted to earlier studies in two respects. First, the experts were more likely than the aspirants to make assumptions about the problem: the length of their time in leadership roles may have encouraged them to position problems in terms of their prior experiences. Second, experts were less likely than the aspirants to situate a proposed solution in relation to long-term goals: this may reflect the more idealised quality of aspirants' proposed solutions.
Subject HeadingsSchool principals
Volume 29 Number 2, April 2009; Pages 109–127
Trends toward autonomy and decentralisation, as well as the ongoing changes associated with the rise of the knowledge society, have demanded new forms of leadership. However, examination of effective leadership traits and behaviours has led to the development of long 'shopping lists' of competences that are unwieldy for self-evaluation purposes. The author draws on the extensive literature around leadership to formulate a series of five core competences, based on Bossert et al's model, designed to support school leaders in their own and their teams' development. Vision orientation involves the leader developing and communicating a vision to realise learning outcomes. Context awareness involves taking into account the school’s situation in optimising learning and achievement. Deployment of strategies that match new forms of leadership comprises using transformational, inspiring, ethical and inquiry-based leadership approaches to promote school development and improvement. Organisation awareness is the capacity to mould the domains of school and instructional culture, school personnel and school facilities. Higher-order thinking is the leader's ability to insightfully cohere the various factors that affect student learning. Abilities such as entrepreneurship and communicative skills, commonly considered to be competences, should be conceived of instead as sub-competences falling within one of the five core competences. The general basic competences can be shaped to the specific situation of the individual school leader to develop an action plan. School leaders can work alone, or with a colleague, to describe their own situation with regard to each competence, identify the context-specific competences, determine in which situations the competence must be displayed, and decide upon development targets. The competences can be used in developing personal and team development tracks, as well as in performance reviews and in recruitment and selection procedures. They can also identify areas where professional development might be required.
Subject HeadingsSchool culture
Cinderellas and ugly ducklings: positive turning points in students' educational careers – exploratory evidence and a future agenda
Volume 35 Number 3, June 2009; Pages 351–370
Educational 'turning points' are key experiences that result in a change of trajectory for a student. The author examined accounts of 'positive turning points' drawn from 1100 respondents' reports of key educational experiences. Turning points can be categorised into three types: transformations in attitudes toward a specific subject or more generally; more extreme 'dropout to student' transformations; and transformations in attitudes, self-worth and efficacy. Students' accounts typically involved experiences of continued failure and feelings of despondency that were 'magically transformed' by a teacher. Such teachers were usually new to the student, and were encountered at the beginning of the new year or when the student moved schools or changed academic paths or classes. The new teacher represented an opportunity for students to begin anew with a 'clean slate'; many students reported being singled out for support, which gave them a sense of empowerment, self-efficacy and agency. Reports of transformative teacher–student relationships were characterised by the teacher's high expectations and enthusiasm, as well as by trust and acceptance, which were considered the critical components in precipitating the turning point experience. These relationships contrasted sharply with students' earlier perceptions of being neglected and stigmatised, and students felt challenged to reciprocate by reorienting themselves towards a positive educational trajectory. However, the 'new teacher' theme had a strong organisational aspect, with students likely to meet such teachers when schedules or contexts changed. Students from higher socioeconomic backgrounds, who have greater opportunities to attend after-school programs and have greater educational choice may therefore be more likely to experience 'turning point' transformations than students who may not have access to these opportunities due to financial or linguistic barriers. The author notes that the article's focus on positive turning points necessarily excludes accounts of negative turning points. These accounts were substantially more prevalent, and indicated that many students lacked opportunities to correct prior mistakes, resulting in students becoming 'locked into' negative learning trajectories that became difficult to turn around.
Subject HeadingsTeacher-student relationships
Volume 31 Number 10, July 2009; Pages 1307–1332
Concept cartoons, when used in addition to scaffolding devices, can be used in science classrooms to elicit students' ideas, and promote discussion and debate, as well as in formative assessment. Concept cartoons depicting contradictory points of view were used in a Grade 5 and a Grade 6 science class in Singapore as the main stimulus for eliciting students' ideas around topics such as photosynthesis and heat transfer; students then used scaffolding tools designed to support their discussion. After an introduction to the topic by the teacher, all students were required to agree or disagree with the statements posed by the concept cartoons, and to justify their response. The concept cards provided an effective means to encourage students to voice and discuss their ideas, and promoted questioning and reflective thinking. This approach facilitated formative assessment, allowing the teacher to address misconceptions and guide students' thinking in a non-explicit way using a question-and-answer approach. Students' subsequent small-group discussion was then guided by two types of scaffolding devices: Grade 5 students wrote down their positions and reasoning on discussion templates, while Grade 6 students undertook 'paper dialogues', conducting question and answer sessions on a single sheet of paper. Students were encouraged to challenge each others' ideas. The questions and ideas posed on the discussion template served to focus students' thoughts and to direct their questions, leading to involved discussion of hypothetical scenarios and consideration of evidence and opposing viewpoints. Similarly, the paper dialogues were used in tandem with the concept cartoons to make assertions, question and rebut peers, and generate discussion and explanations. The tools allowed the documentation of each group's discussion, providing the teacher with information about students' ideas, questions, reasoning and misconceptions, which could then be addressed. In addition, the teacher played a valuable role in designing appropriate scaffolding structures to allow discussion of key topics and in establishing rules for collaborative discussion. When guiding whole-class discussions around concept cartoons, teachers should use questioning techniques that probe, prompt and challenge or build on students' prior responses.
Key Learning AreasScience
Subject HeadingsClassroom activities
Volume 7 Number 28, April 2009; Pages 813–831
Advanced Placement (AP) is a program where secondary students in the USA take and earn credit for tertiary-level courses. It is used increasingly in mainstream schools but is being abandoned by the elite schools who were the first to adopt it. The authors trace the history of the program, exploring the equity-based motivations behind its growth, as well as the related issues of educational inequality and access. The AP program, developed within the context of the Cold War, aimed to track and challenge college-bound students in select high-status schools, and to quickly promote these students through their education and into the workplace. However, as competition for university enrolments grew in the 1950s, AP became a mark of academic prestige, and its adoption became more widespread as schools sought to maintain a competitive edge in the admissions process. Trends toward equal access and educational democratisation saw a greater push for uptake of AP, which was increasingly seen as essential to university admission, and state- and local-level policies saw the program's reach expand to less advantaged communities, although issues of inequity and access persisted. However, a consequence of the expansion of the program was the decline in the prestige and achievement associated with AP, as well as concerns over differences in the quality of provision between schools. Prestigious tertiary institutes responded by raising their admissions requirements. To maintain their competitive edge, high-status schools began to pursue alternatives to AP, adopting newly challenging curricula and pedagogical approaches, using their 'enviable reputation' to garner the support of tertiary institutions. However, while AP was no longer a mark of distinction for these schools, whose elite status gave them freedom to explore alternative approaches, low-status schools had little recourse but to continue with AP as a means of gaining an advantage in the admissions process, particularly with lower status institutions. With the status of AP being gradually undermined by its abandonment by elite institutions, issues of equity for low-status and under-served schools, who lack the same educational freedom to distinguish themselves, will likely persist and widen.
Subject HeadingsCurriculum planning
Gifted and talented (GAT) children
Transitions in schooling
United States of America (USA)
Veiled and overt school choice: a consideration of the ways in which different forms of school choice affect student experiences
Volume 35 Number 4, August 2009; Pages 539–555
Parental choice and the diversity of school provision are central to current education policy in Britain, together with an emphasis on standards and accountability. School performance data is made available: designed to inform decision-making around school choice. Drawing on interviews conducted with 46 groups of Year 8 and Year 10 students, a study examined perspectives and experiences of school choice in two cities in England. 'East Town' had a history of school selection, with certain prestigious schools oversubscribed, and other less parentally desirable schools struggling to retain staff and students. In contrast, students in 'North Town' typically attended their nearest school; as a result, there was very little competition between schools. North Town students tended to be unaware of school choice-making processes, or felt they were unimportant: school choice occurred in a covert manner through parents' choosing to live in a particular area. In contrast, all students and teachers interviewed in East Town were very aware of school choice, with choice-making processes including assessing, comparing and discussing schools, and appealing selection processes if necessary. All students selected the prestigious Poplar School as their first preference: those who were accepted had a positive perception of themselves as potentially high-achieving learners. Conversely, students who were accepted into less prestigious schools displayed negative perceptions of their education, their identities as learners, and their future prospects. Similarly, East Town teachers internalised notions of success or failure depending on where they taught. No such issues around school choice were evident in North Town, where all students considered their school to be good. North Town teachers, who were not engaged in competition with other schools and who did not place such emphasis on outcomes, viewed their students more positively. The study highlights issues of equity around current school choice policies, as well as raising issues of self-concept and social exclusion. The potentially negative consequences for students unable to attend their chosen school should be addressed, as should issues of whether families and their children have similar access to choice, and to schools of equal quality.
Subject HeadingsGreat Britain
School and community
There are no Conferences available in this issue.