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Curriculum & Leadership Journal
An electronic journal for leaders in education
ISSN: 1448-0743
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Abstracts

Pressing dilemmas: meaning-making and justification in mathematics teaching

February 2010; Pages 27–50
Karin Brodie

Reforms to the secondary mathematics curriculum put forward a range of goals for classroom teachers. In reform literature these goals are generally presented as complementary, but in practice they can come into conflict, creating dilemmas for the teacher. One dilemma is how to connect to and draw out learners’ existing knowledge and beliefs about maths, while also covering course content. Another dilemma is how to balance between individual and whole-class needs. For example, while a student's answers in class offer a chance to understand this individual's reasoning, the teacher must ultimately ensure that the whole class learns the correct answers. Over time, the teacher also needs to find ways to allow equal participation in class discussion to all students, by working with students' varying levels of knowledge and varying capacities to stimulate or disrupt class discussion. These dilemmas come into play when teachers apply the technique of 'pressing' students to extend their classroom contributions. Students can be pressed either to expand the meaning of what they say, or to justify it mathematically: these two dimensions of pressing may clash at times. The author investigated these dilemmas through research into two Year 10 maths classrooms in South Africa. The research involved videotapes of classroom discussions and interviews with the two teachers and with selected students. One class were low-SES black students with low academic performance, the other class was more mixed in ethnicity, SES and academic results. The two teachers were both accomplished educators familiar with reform-oriented maths. The results suggest that pressing students either for their meanings or for precise mathematical justifications needs to be combined with episodes of explanation by the teacher. It should also be recognised that teacher’s strategic choices about how to balance these different aspects of teaching are deeply embedded in particular classroom contexts. The classroom generates many fluid contexts for which even the best teachers cannot fully prepare, and they will inevitably let go of some opportunities as they pursue others.

Key Learning Areas

Mathematics

Subject Headings

Mathematics teaching
Secondary education
South Africa

How preservice teachers interpret and respond to student geometric errors

Volume 110 Number 1, January 2010; Pages 31–46
Ji-Won Son, Nathalie Sinclair

Understanding and addressing students’ thinking is an important component of current mathematics teaching, which aims to use students’ errors as a 'springboard for inquiry'. However, research has indicated that teachers in the USA tend to avoid addressing student errors or address them in ways that are more procedural than conceptual. Fifty-four preservice primary teachers in the USA were asked to interpret and respond to a student’s incorrect answer to a question involving reflectional symmetry. The respondents who approached the problem in a conceptual rather than procedural manner tended to be better at identifying the student’s error. However, most of the respondents resorted to procedurally-based suggestions rather than providing conceptual support. This may have been partly due to the fact that geometry, unlike a topic such as fractions, lends itself to procedural approaches, such as folding or flipping a page, that can be seen to support conceptual knowledge. However, the respondents also struggled to provide responses that were individualised or that were appropriately targeted. Many offered very generalised strategies that did not deal explicitly with the task in question, or offered approaches that were too basic and that may be time consuming in actual practice, or that assumed that the student understood but had forgotten how to complete the task. This suggests that preservice teachers may be inclined to impose formalised constructions and approaches in cases where they are unable to understand a student’s reasoning. Preservice teachers may benefit not only from increased content knowledge, but also from being given opportunities to reflect on their thinking and learn from their errors by being asked to explain and justify their ideas, and by helping others work through their own errors.

Key Learning Areas

Mathematics

Subject Headings

Middle schooling
Mathematics teaching
Thought and thinking
Teacher training

The short supply of saints: limits on replication of models that 'beat the odds'

Volume 26 Number 3, June 2010; Pages 237–263
Tamara Wilder, Rebecca Jacobsen

Struggling schools in the USA are frequently encouraged to replicate the strategies of individual schools that have achieved 'against the odds'. However, the rhetoric surrounding these exhortations often does not take into account the difficulties involved in large scale replication. Interviews with 12 teachers from KIPP schools, a collective of high-achieving charter schools serving disadvantaged students, were used to examine the typical practices of these schools. Several factors were identified as being key to their success. The teachers worked collaboratively to use student data to inform classroom approaches, and designed classes that were challenging and engaging, and that would support improvement. However, doing so required a substantial time commitment. Most of the teachers reported working between 60 and 70 hours a week, and often worked weekends and evenings, during which time students were encouraged to telephone them with questions about homework. While the teachers appreciated being part of a dedicated and professional staff, concerns were raised about work-life balance, as well as high levels of teacher burn-out and turnover. Many of the teachers were planning to leave their roles, or were uncertain about their future, while others expressed frustration over maintaining the school culture in the face of high staff mobility. The teachers suggested that their workload could be reduced with more flexible scheduling, job sharing, or by being more efficient with the school day. While many of the teachers enjoyed the challenging and positive environments of the KIPP schools, the time commitment required by the role posed a significant challenge to staff retention, with many KIPP teachers not seeing themselves as career teachers. While recreating the practices of KIPP schools across the wider school system may lead to gains, it would require teachers to significantly extend their working hours, which could have a substantial impact on teacher morale and retention. Rather than relying solely on teachers to help 'beat the odds', policymakers should seek to address other factors influencing student outcomes, such as economic and cultural issues.

KLA

Subject Headings

Socially disadvantaged
Teacher-student relationships
Teaching and learning
United States of America (USA)

Student-accessible science texts: elements of design

Volume 31 Number 3, May 2010; Pages 213–227
Erin M. McTigue, Scott W. Slough

Shifts in science textbook design that emphasise visual elements have led to the need to consider not only text readability but more general text accessibility. Traditional readability measures are insufficient to critically assess whether a textbook is accessible for students. Instead, teachers need to take into account a range of factors. Concreteness of language is one important factor in text accessibility. Young readers will be more interested and more likely to engage with a text that explains concepts in concrete language and that illustrates concepts with specific, supporting examples. Narrative voice is also important; those with a distinct and active voice are frequently more accessible to learners, although teachers should be aware of texts that are littered with 'seductive details' that interest readers but offer little purposeful information. Other considerations include a text’s cohesion and coherence, which involve the organisation of the text both overall and at the scale of the sentence or paragraph. Markers such as headings, summaries, preview statements and signalling words such as 'because' and 'therefore' also help improve overall accessibility by making links between pieces of information or by indicating causality. The degree of integration of visual elements into the text is also important. Visual elements should support textual elements and should be placed near relevant textual objects. Text supporting visual elements should help the reader to interpret these items: extended captions are one example of this. Graphical representations should also be relevant to the information being presented rather than being used simply for illustration. A variety of visual items such as tables, diagrams, flowcharts and graphs should be included.

Key Learning Areas

Science

Subject Headings

Science teaching
Science literacy
Science

Seeking a new deal on dyslexia

Elisabeth Tarica

Australia lags behind comparable countries in its policies to address dyslexia. The term dyslexia is applied to a range of conditions which hold back a child’s reading, writing and spelling, and it is sometimes also applied to maths. Dyslexia has a genetic, neurological foundation and persists over a lifetime. While as many as one in 10 people have the condition, few are diagnosed partly due to the variety of ways in which the condition appears. Research has found that dyslexic students are prone to behavioural problems, disengagement and early departure from school. The learning problems caused by dyslexia are unlikely to be overcome by usual instructional approaches, including synthetic phonics teaching, even from highly skilled teachers. Individual symptoms are commonly addressed in isolation, for example through reading recovery programs, which are also unlikely to be effective. In the USA, Canada and Britain it is compulsory for teacher education courses to cover dyslexia. In Australia however, it is recognised as a distinct learning disability only in New South Wales. Teachers 'are generally unaware of dyslexia's genetic and permanent nature', and the fact that dyslexia is independent of intelligence level. In Victorian schools it is grouped into the category of specific learning disabilities (SLD) and does not receive independent funding. In January an Australian parliamentary working party on dyslexia called for the introduction of a dyslexia-friendly school model, and mandatory teacher training to equip teachers to identify and assist students with dyslexia.

KLA

Subject Headings

Dyslexia
Reading difficulties
Education policy
Literacy
Australia

The growth of reflective practice among three beginning secondary mathematics teachers

Volume 38 Number 2, April 2010; Pages 147–159
Michael Cavanagh, Anne Prescott

Preservice teachers in Australian teacher education programs are encouraged to take a critical and reflective approach to their practice. However, true reflective practice takes time to develop. Over time teachers move from simply describing their practice, to searching for causes of particular outcomes, to analysing their experiences and considering different perspectives. The classroom experiences of three preservice secondary mathematics teachers undertaking a 50 day practicum over a one year period were examined. The three teachers initially tended only to offer descriptive assessments of their classroom practice and focused largely on technical aspects of teaching. They raised topics such as classroom management and the approaches of supervising teachers, and described students’ apparent learning preferences. However, over the course of the practicum the teachers came to reflect on their teaching in a more sophisticated way and identified a number of cause and effect situations. For example, one teacher realised that poor behaviour was caused by lack of understanding of material, and another that constructivist approaches tended not to be well received due to the prevailing school culture and the particular pedagogical preferences of a supervisor. However, while the extended duration of the practicum appeared to help the respondents develop their reflective skills enough to identify problems, they lacked the time and autonomy to seek solutions. The respondents' classroom efforts were significantly influenced by their supervising teachers, who tended to model particular approaches and to give advice rather than to help identify problems and their possible solutions. However, when the respondents were assigned their own classes, they began to demonstrate more sophisticated critical reflection. This may be because the teachers had greater opportunities to develop their own personal teaching identities and to work with self-selected mentors whose pedagogical outlooks mirrored their own.

KLA

Subject Headings

Pedagogy
Mathematics teaching
Teacher training
Teaching and learning

Classroom experiences with new curriculum materials during the implementation of performance standards in mathematics: a case study of teachers coping with change

Volume 8 Number 2, April 2010; Pages 349–372
Samuel Obara, Margaret Sloan

Appropriate support can help teachers change their classroom practices to meet the demands of new curricular innovations. Drawing on interviews, observations and classroom artefacts, the authors examined the experiences of three Grade 6 teachers in Georgia, USA as they attempted to implement a new standards-based state curriculum. The teachers participated in a five-day professional development program on the topics of collaborative and inquiry-based approaches to learning. They were also assigned a mathematics coach to help with implementation, and with the selection of resources such as textbooks. While the teachers valued this experience, they did not feel fully prepared to teach the new curriculum, and a number of challenges arose. The teachers struggled to varying degrees with the curriculum's emphasis on group work and the use of manipulatives, with some concerned that these approaches encouraged off-task behaviour. Rather than encouraging inquiry-based learning, the teachers largely continued to guide students through the learning process and to step in rather than allowing students to solve set tasks themselves. Another issue was the school's high number of ESL students, who struggled with the English demands of the new textbooks. To circumvent these language problems, and also to speed up the learning process to ensure that they were on track for high-stakes external tests, the teachers began supplementing the textbook with materials from the old curriculum. In addition, the professional development time intended for the teachers to address strategies and share student work frequently devolved into planning sessions focusing on meeting the requirements of high-stakes tests. While the teachers' classroom assessment practices changed somewhat, they remained influenced by the demands of external accountability measures. These challenges highlight the need to provide time and other resources to allow teachers an in-depth examination of new standards and content, and to try new approaches to teaching. Teachers may also need to be supported in adapting new materials to suit the needs of a particular group of students such as English-language learners.

Key Learning Areas

Mathematics

Subject Headings

Professional development
Primary education
Mathematics teaching
Standards
United States of America (USA)

Measuring teacher beliefs about curriculum orientations using the Modified-Curriculum Orientations Inventory

Volume 20 Number 2, June 2009; Pages 103–120
Sharon Billburg Jenkins

Teachers’ curriculum orientations influence the way that they select content for teaching, as well as their teaching methods. There are five dominant curriculum orientations. Academic rationalism reflects the approach taken by traditional academic studies, with learning seen as requiring mental discipline. In contrast, social reconstruction orientations emphasise social problems and participation in society and humanistic approaches emphasise students’ personal growth as individuals. The cognitive process orientation focuses on helping students develop cognitive skills for application across a range of situations, while the behavioural orientation emphasises individualised instruction rather than focusing on particular content or social issues. A survey was used to examine the curriculum orientations of 308 teachers in the USA, and to assess whether demographic factors influenced these orientations. Primary school teachers scored higher on the humanistic orientation, while secondary teachers scored higher on the social reconstruction orientation. This may be due to the impact of external stakeholders on secondary education, as well as state-mandated moves toward community-oriented programs such as community service. Science and mathematics teachers tended to score lower on the social reconstruction and humanist orientations than other groups. Female teachers were significantly more likely to have a humanistic orientation than male teachers, while highly experienced teachers tended to have behavioural or cognitive process orientations when compared with newer teachers. Teachers’ philosophical beliefs appear to run counter to recent educational policy decisions, which may have implications for teaching and learning, as well as teacher satisfaction.

KLA

Subject Headings

United States of America (USA)
Teaching profession
Education aims and objectives
Education philosophy

Developing challenging science activities for gifted pupils through action research

Volume 37 Number 3, August 2009; Pages 259–268
David Coates

Four senior primary science teachers in Britain undertook an action research project designed to improve their science teaching so that it was challenging and engaging for all students. Initial analysis by the teachers indicated a need for improved planning that incorporated differentiated learning, more questioning and links between other subjects; and a more flexible timetable that allowed science classes to be taught in longer blocks. This resulted in significantly changed classroom practices. The teachers made use of open questioning designed to challenge students and targeted particular questions to particular ability groups or individual students to assess and broaden understanding. They also outlined different expectations of student outcomes depending on students’ ability level and planned particular activities or investigations accordingly, with more capable students engaging in extension activities while the teacher ensured that other students understood the concepts being taught. These activities included challenging able students with problems involving complex variables, or by having them undertake research using more complex resources than those used by other children. Allocating larger blocks of time for science teaching allowed for more in-depth investigations, as well as time for consolidating work and ideas. Increased use of formative assessment allowed teachers to gauge students’ knowledge as well as to encourage higher-order thinking. Group work was also effective in giving students greater autonomy to examine and test their ideas, as well as undertake research. However, one issue that arose was that less able students often found the work being undertaken by their more able peers to be more interesting, particularly when it had a practical component. The teachers attempted to mitigate this by having stronger students undertake their work in areas away from the main class. The teachers found that the action research project improved their science content knowledge, their ability to plan and structure classes and their ability to draw on different types of resources. They found that reflecting on their teaching approaches encouraged them to examine their beliefs and practices, which had a positive influence on their pedagogy.

Key Learning Areas

Science

Subject Headings

Professional development
Gifted children
Great Britain
Middle schooling
Science teaching

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