Effective mathematics learning environments : primary teachers' beliefs and practices

A first priority for changing teaching practice is to make problematic for teachers aspects of their current practice. As part of a project on improving mathematics and science teaching in the middle years of schooling, teachers were asked to rate their practice against components of effective teaching and learning and to rate each of these according to their perceived importance. Findings suggest that primary teachers endorsed the components as representing effective practice, scoring most components higher than their actual practice. Gaps were particularly evident for items relating to challenging students conceptually and higher-order thinking, with these becoming the basis for some of the action planning for change.

To post or not to post : undergraduate student perceptions about participating in online discussions

Computer mediated conferencing (CMC) is now a common feature of blended learning environments where students learn in both face to face and online settings. While many teachers recognize the value of online discussions for learning, students appear to have different perspectives. Consequently, their participation in online discussions is often sporadic and not genuinely interactive. This paper examines these issues and provides student perspectives about participation in online discussions which arose from a case study in a conceptually difficult subject. Systems data indicated low numbers of posted messages. Student interviews provide some insights into this lack of participation, and identify the influence of the curriculum design, especially the nature of the learning activity, and its connection to other aspects of the course, for example, assessment and the regular class sessions. Other influential factors include the student’s ideas about learning, managing demands on their time and their acceptance of CMC. The paper also provides recommendations for improving participation in online discussions.

Innovative science education assessment : linking theory with practice

This paper presents an assessment approach which demonstrates the characteristics of excellent assessment. In a third year Science Education unit in an undergraduate degree in teacher education, assessment is seen as an integral part of the learning process. Learning outcomes are improved for the students and they appreciate the validity of the assessment. Assessment is an important aspect of any unit in higher education but should be seen, not as an end in itself, but rather as a means for educational improvement. Using the assessment task as an illustration, this paper will discuss the theoretical framework of assessment. It will describe how the unit, delivered in a school-based mode, provides opportunity for students to link their theoretical understandings with practical applications, drawing together the academic debates with the first-hand experiences. It will illustrate how the assessment task itself embeds the principles of constructivism and conceptual change models in science education. Finally, the paper will highlight the benefits of this assessment approach with particular reference to the student learning.

Is it worth the effort? How feedback influences students' subsequent submission of assessable work

This paper explores the extent to which students appear to their assessors to act on feedback they have received, and questions the assumption that providing feedback alone is sufficient to effect higher standards of work by students. Feedback provided to 51 undergraduate social work students, on two consecutive assignments involving a similar task, was examined to ascertain the number of problem areas noted from seven predefined categories. While the greatest increase in marks was associated with the greatest reductions in the number of problem areas identified in the comments, overall two-thirds of all students (66.7%) were awarded marks for both assignments within four percentage points. As such, this study found only limited support for the idea that students respond to feedback by making changes which are consistent with the intent of the feedback received. Hence the assumption that providing feedback alone is sufficient to effect higher standards of work by students was not supported. These findings invite educators to critically reflect on their own practices in providing feedback to students.

Teaching square roots: conceptual complexity in mathematics language

The article presents strategies for communicating the concept of square roots to limited English-proficient students. Instead of using mathematical terminology, mathematics teachers could communicate the concept of square roots by integrating the literal concept of square to the actual meaning of a square root. Such approach addresses the learning difficulty experienced by limited English proficient students who tend to associate square roots to geometric concepts. Several strategies for illustrating the concept of a square root using square figures are presented.

Staff exercising 'choice': students exercising 'choice': wholly online learning at an Australian university

The paper examines the implementation of institutional policy relating to mandating wholly online study at the undergraduate level in an Australian higher education institution. The realities of the ‘choice’ provided to teaching staff in designing such units, and students in studying in this mode, are considered. Staff members’ design experiences are reported, and data collected through the surveying of students’ experiences in learning wholly online are analysed. The value students attributed to various aspects of the wholly online learning experience is outlined. Observations are made more generally about the uniqueness of wholly online teaching and learning environments in mandated contexts, and where policy and practice developments may evolve in the future.

The answer is correct but can I explain it? Student explanations in mathematics

This paper explores an aspect of mathematics that has been overlooked often - student explanation, or communication. The data used is derived from a large-scale project in Victoria. Australia, the Improving Middle Years Mathematics and Science (IMYMS) project. Primary student explanations on two open-response items are examined to illustrate the bene tits of incorporating this type of item in mathematical assessments. Techniques for analysing the data and displaying the results of the analysis are presented. The analysis shows clearly how more sophisticated thinking and explanations develop - information of benefit to teachers of these students.

The stereotyping of mathematics: gender and cultural factors

The Who and mathematics instrument is used to measure the extent to which mathematics is considered a male, female or gender-neutral domain. Data from students in grades 7-10 in Australia and Greece were compared to explore the impact of the cultural environment. The data were also examined for within country gender differences and possible differences among males and among females across the two countries. An additional perspective on the influence of prevailing cultural norms - Greek ethnic home background and the broader Australian milieu - was provided by the findings from a small sample of Australian students who attended a school with a strong Greek affiliation and who completed a trial version of the Who and mathematics instrument.

Accounting graduates' perceptions of skills emphasis in undergraduate courses: an investigation from two Victorian Universities

This study investigated the emphasis placed on technical and generic skills developed during undergraduate accounting courses from the graduate perspective. It is motivated by two issues. First, calls by the accounting profession and international education committees regarding the professional adequacy of graduates. Second, the challenge facing educators and professional bodies to design accounting courses that address a diverse range of needs from students, the educational philosophy of the institution, and the changing dynamics of global business. Data obtained from 310 graduates from two Victorian universities provided insights into the types of skills development considered necessary for a successful accounting career.

Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.

Being explicit about aspects of mathematics pedagogy

It is conventional wisdom that contextualising mathematics tasks can make them more meaningful for students, and that open-ended questions create opportunities for student engagement. Yet concerns are emerging that strategies such as these may exacerbate the disadvantage of some. We report data from a project that seeks to address such concerns by encouraging teachers to be explicit about aspects of their pedagogy. Men teachers were explicit about aspects of the pedagogy, the students responded in the direction intended.

Describing elements of mathematics lessons that accommodate diversity in student background

We are researching actions that teachers can take to improve mathematics learning for all students. Structural elements of the lessons being trialled include making aspects of pedagogy explicit to seek to overcome differences in familiarity with schooling processes, and sequencing tasks with the potential to engage students. This article reports research on teachers building learning communities by preparing variations to set tasks in order to address differences in students’ backgrounds.

Using word problems in Malaysian mathematics education: looking beneath the surface

This paper reports on aspects of a project that investigated the influence of Chinese Malaysian students’ schooling in a tradition of abstract, technical mathematics and rote learning on ways that they responded to mathematical word problems. Data from an action research project are reported. Supposedly “shallow” and “ deep” learning are shown to be interlinked, and assumptions frequently made by Western educators about modelling and practice are questioned.

Planning and teaching mathematics lessons as a dynamic, interactive process

We are researching actions that teachers can take to improve mathematics learning for all students, with particular attention to specific groups of students who might experience difficulty. After identifying possible barriers to learning, we offered teachers mathematics lessons structured in a particular way. Teachers’ use of the model outlined in this paper seemed productive and their resulting planning and teaching proved to be dynamic and interactive. This paper uses excerpts from a conversation between two teachers to illustrate specific aspects of the model.

Sociocultural research on mathematics education : an international perspective

This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways:

* It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area.
* It is future oriented, presenting recommendations for practice and policy and identifying areas for further research.
* It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling.

As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.