How group composition can influence opportunities for spontaneous learning

Classroom video, and video-stimulated interviews of small group work, in a Grade 5/6 classroom are used to show ways group composition can influence learning opportunities. Vygotsky’s (1933/1966; 1978) learning theory on the spontaneous creation of knowledge as compared to the guidance of an expert other frames this group analysis. Illustrations from two groups show how opportunities to spontaneously create new knowledge can be limited or enhanced by psychological factors associated with the inclination to explore that have been linked to resilience in the form of optimism (Seligman, 1995, Williams, 2003). This study contributes to our knowledge on forming groups to promote deep learning. It raises questions about other ways in which learning may be influenced by optimistic orientation and about building this personal characteristic to enable deep learning.

Research into cyberbullying : student perspectives on cybersafe learning environments

This paper reports a qualitative study designed to investigate the issues of cybersafety and cyberbullying and report how students are coping with them. Through discussion with 74 students, aged from 10 to 17, in focus groups divided into three age levels, data were gathered in three schools in Victoria, Australia, where few such studies had been set. Social networking sites and synchronous chat sites were found to be the places where cyberbullying most commonly occurred, with email and texting on mobile phones also used for bullying. Grades 8 and 9 most often reported cyberbullying and also reported behaviours and internet contacts that were cybersafety risks. Most groups preferred to handle these issues themselves or with their friends rather then alert parents and teachers who may limit their technology access. They supported education about these issues for both adults and school students and favoured a structured mediation group of their peers to counsel and advise victims.

Mathematical power of special-needs pupils : an ICT-based dynamic assessment format to reveal weak pupils' learning potential

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require 'borrowing'. These problems, in which the value of the ones-digit of the subtrahend is larger than the ones-digit of the minuend, are known as a serious difficulty for weak pupils in mathematics. Seven of such problems from a standardised test were placed in the ICT environment. Data were collected from two test conditions: the standardised written test format and the ICT version of the test items including the tool that provided pupils with a set of virtual manipulatives. The 37 pupils involved in the study were 8–12 years old and from two special-education schools in the Netherlands. Comparison of the performance scores in the two formats showed that an ICT-based assessment format, including a dynamic visual tool, can reveal weak pupils' learning potential and strategy use. The study also pointed out that 'partial-tool use', ie, not carrying out the complete subtraction operation with the tool, can provide sufficient support to find the correct answer.

Calculators, mathematics and young children : a study of six children using calculators as part of the mathematics curriculum during their first two years of school

The thesis investigates the role a calculator can play in the developing number knowledge of three girls and three boys as part of their mathematics program, during their first two years at primary school. Random sampling was used initially to select six girls and six boys from the twenty-four children entering a 1993 prep class. These twelve children were interviewed on entrance to school and based on the performance of the twelve children on the initial interview, a girl and a boy were chosen from the higher, middle and lower achievers to take part in the full study. The class teachers involved were previously participants in the ‘Calculators in Primary Mathematics’ research program and were committed to the use of calculators in their mathematics program. A case study approach using qualitative methods within the activity theory framework is used to collect relevant data and information, an analysis of five interviews with each child and observations of the children in forty-one classroom lessons provides comprehensive data on the children's developing number knowledge during the two years. The analysis questionnaires establishes each teacher's perceptions of the children's number learning at the beginning and end of each year, compares teacher expectations with children's actual performance for the year and compares curriculum expectations with children's actual performance. A teacher interview established reasons for changes in teaching style; teacher expectations; children's number learning; and was used to confirm my research findings. An activity theory framework provides an appropriate means of co-coordinating perspectives within this research to enable a description of the child's number learning within a social environment. This framework allows for highlighting the mediation offered by the calculator supporting the children's number learning in the classroom. Levels of children's developing number knowledge reached when working with a calculator and as a result of calculator use are mapped against the levels recommended in ‘Mathematics in the National Curriculum’ (National Curriculum Council, December 1988), and the Curriculum and Standards Framework: Mathematics (Board of Studies 2000). Findings from this comparison illustrate that the six children's performance in number was enhanced when using a calculator and indicate that on-going development and understanding of number concepts occurred at levels of performance at least two years in advance of curriculum recommendations for the first two years of school.

Investigation into the skill levels achieved by mathematics students in the V.C.E. and the H.S.C. mathematics courses

This study examines whether recent changes to the mathematics courses offered in the final year of secondary school (Year 12) in the state of Victoria, Australia have affected the learning outcomes of students in terms of then: skill levels in algebra, calculus and problem solving; and in terms of their preparation for a tertiary mathematics unit. The impact of these changes on the transition from secondary to tertiary mathematics is also considered. A comparison is made between students who attempted a first year mathematics unit at the University of Melbourne (U. of M.) having completed the new V.C.E. (Victorian Certificate of Education) mathematics courses and mathematics courses from the previous H.S.C. (Higher School Certificate) system. The comparison involves the use of tests administered upon entrance to a tertiary mathematics unit at the U. of M., and questionnaires. In 1991, V.C.E, students and H.S.C. students attempted the same mathematics test at the U. of M. and their results were compared. In 1992, the tests were attempted by V.C.E. students only. To compare new V.C.E. students and H.S.C. students, questions on the 1991 test were matched with similar questions on the 1992 tests and a panel of experts determined what the H.S.C. students who attempted the 1991 test would have been expected to average on these matched questions on the 1992 tests had they attempted them. These expected average scores were then compared with the actual scores of the new V.C.E. students. The scores of the groups were scaled when necessary. Questionnaires were administered to 1991 U. of M, mathematics students who were part of the V.C.E. pilot group in 1990, secondary mathematics educators, tertiary mathematics educators, and 1991 V.C.E. (1992 U. of M.) students. The mathematical misconceptions exhibited by new V.C.E. students are discussed and their frequencies stated. The research indicates that the new V.C.E. mathematics courses have provided the V.C.E. mathematics students in this study with significantly lower skill levels and a significantly poorer preparation for a tertiary mathematics unit than those which were previously provided by the H.S.C. mathematics courses.

Teacher professional growth : a study of primary teachers involved in mathematics professional development

The overall purpose of this study was to examine whether professional development programs can act as appropriate vehicles for the professional growth of teachers of primary mathematics. A longitudinal study was conducted of primary teachers involved in a Victorian mathematics professional development program — Exploring Mathematics In Classrooms (EMIC). The professional growth of six teacher participants in one EMIC course was examined over a period of 18 months. The teachers selected were from four different schools located in the southern metropolitan region of Melbourne. The central interest of this study was in teacher professional growth and accordingly the perspective sought was predominantly that of the teacher. A case study research approach was adopted and data were gathered through observations, interviews, questionnaire, and the collection of teacher work documents. A theoretical model of teacher professional growth was used to represent the teachers' growth. The study generated data on the nature of teacher professional growth and the features of professional development programs likely to influence teacher professional growth. All of the teachers reported and demonstrated growth with respect to their mathematics teaching, in areas associated with their: Classroom Practice, Knowledge and Beliefs, and Professional Attributes. The teachers' growth was highly individualistic, with no two teachers demonstrating exactly the same professional growth outcomes, or the same growth processes. The data provided evidence to confirm that teacher growth is a complex and gradual learning process. For each of the teachers several different routes to change and growth were evident, drawing attention to the non-linear nature of growth. The teachers' responses to the professional development program were influenced by various contextual and personal factors. The data provided evidence of a strong link between the content and outcomes of professional development programs — the outcomes reported and demonstrated by the teachers reflected the content of the EMIC program. Key factors associated with mathematics professional development programs perceived as influencing growth were: program content; program structure; and program presentation. A significant finding was the strong influence on teacher growth of the presenters of professional development programs—some data suggested that the 'quality' of the program presenter is fundamental to the success of any professional development program. The study provided insight into the processes involved in teacher professional growth and factors associated with the way in which professional development programs influence growth. The theoretical model of teacher professional growth used in this study has been elaborated and recommendations which might inform the design and implementation of future professional development programs have been made.

Using everyday experiences in teaching secondary mathematics in Malawi : possibilities and constraints for change

Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Teaching mathematics using the internet

This paper examines teachers' use of the Internet in the teaching and learning of Mathematics. The study draws upon data collected via an online survey and interviews with six teachers. It reports on their beliefs, strategies for use and their perceptions on how it impacts on students and their learning of mathematics. Some comparisons are made between the ways teachers used the Internet.

Keeping all students on the learning path

A powerful notion to guide thinking about whole-class mathematics teaching is Vygotsky’s zone of proximal development (ZPD). Our research with primary and secondary teachers over the last six years has identified roles of teachers in relation to the ZPD, and ways of overcoming some typical barriers to students’ movement through their zones. Methods have included focus groups of experts, video analysis of classroom interactions, classroom observation, and analysis of lesson plans and teachers’ reflections teaching processes their outcomes. The research has involved the gradual development, trailing, evaluation, and adjustment of a six-component model for planning and teaching mathematics. The focus of this paper is on the use of one of its components, “differentiated learning trajectories”.

A problem-based learning project supported by the internet

This case study looks at how bank sites with interactive calculators can be used to enhance directed investigations of students in a Mathematics Studies course. In the course of these investigations, students access simulated contexts which enabled them to have a feel of how they would spend money in the real world. This case study reveals the confidence of students in carrying out searches and transferring data, learning about bank calculators and their role in real life, how hidden costs are incorporated into loans and being able to validate what is presented in these calculators with their own calculations. This case study also highlights the perceptions of the teacher regarding this strategy in teaching this topic and the areas that need improvement. This paper analyses what has happened in the teaching and learning process and endeavours to shed some light into how the Internet can be used to promote a quality mathematics education.

Continuous professional learning through school based strategic planning

There is ample evidence that in many countries school science is in difficulty, with declining student attitudes and uptake of science. This presentation argues that a key to addressing the problem lies in transforming teachers’ classroom practice, and that pedagogical innovation is best supported within a school context. Evidence for effective change will draw on the School Innovation in Science (SIS) initiative in Victoria, which has developed and evaluated a model to improve science teaching and learning across a school system. The model involves a framework for describing effective teaching and learning, and a strategy that allows schools flexibility to develop their practice to suit local conditions and to maintain ownership of the change process. SIS has proved successful in improving science teaching and learning in primary and secondary schools. Experience from SIS and related projects, from a national Australian science and literacy project, and from system wide science initiatives in Europe, will be used to explore the factors that affect the success and the path of innovation in schools.

Construction of social difference in mathematics education

This study investigated the social context in which the learning of mathematics occured. It examined the practices of schools and mathematics in order to identify the ways in which they contributed to the construction of social difference. Accordingly, this study was concerned with how schools and mathematics classrooms contribute to working-class students lack of success in mathematics. The differences that occurred in these practices could be seen to contribute to the different outcomes likely to occur in the later years of schooling. It was argued that these differences mean that students from middle-classes would be more likely to undertake and be successful in the study of mathematics than their working-class peers.

Australian teaching and learning centres through the eyes of their directors : characteristics, capacities and constraints

This paper is based on research to identify common factors that contribute to the effective strategic leadership of teaching and learning centres. The second of three phases of data collection involved a survey of Directors of Australian teaching and learning centres. The data collected were quantitatively analysed using a range of descriptive, parametric and non-parametric techniques. Based on a response rate of 81.6 percent, we present a contemporary, comprehensive and representative quantitative snapshot of Australian teaching and learning centres, as seen through the eyes of their Directors. The time since last restructure, incumbency of the current Director and total Directorship experience of the current Centre Director all have mean values of ‘sometime in the previous one to three years’. Most Centres would consider their work in the areas of ‘recognition and reward’ and ‘professional development of staff’ as high impact functions, and they would be pleased with their efforts in the former area, and wish to perform better on the latter. The principal constraint identified by Centres was ‘lack of staff time’, both in the Faculties and in the Centre, to engage in teaching and learning improvement activities. Overall, Centres feel well included in relevant university committees and other activities.

Using open-ended tasks for teaching, learning and assessment

This article explores the use and development of open- ended tasks in classrooms. Open-ended tasks can be used in teaching situations, for learning about student learning, and for assessment.