Tom Lowrie

National Numeracy Tests: A Graphic Tells a Thousand Words

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (for example, maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australias inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items is more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

Relationship Between Visual and Nonvisual Solution Methods and Difficulty in Elementary Mathematics

Abstract The purposes of this study were (a) to identify differences in approaches used by students to solve mathematical word problems, (b) to determine the influence of visual and nonvisual methods on task success, and (c) to investigate whether methods employed to solve mathematical problems change as task complexity is reduced. One hundred and twelve Grade 6 students (11–13-year-olds) were required to solve 20 mathematical problems and to identify the method or approach undertaken to complete the task. Results indicated that students typically used visual methods to solve difficult or novel problems, whereas nonvisual strategies were used in less difficult situations.

Young children posing problems: The influence of teacher intervention on the type of problems children pose

This paper describes the type of problems young children (Grade 1 and Grade 3) generated in problem-posing situations as they worked, on a one-to-one basis, with a student teacher. In the initial stages of the investigation, the children posed one-and two-step problems that reflected the type of experiences the children encountered at school. With guidance, the children began to solve increasingly sophisticated problems that became more open ended and novel. The problem-solving situations provided opportunities for the children to pose problems they enjoyed solving and promoted both a more complex and motivating learning environment. The results indicate that the problem-posing actions of students can be nurtured by teachers’ actions.

Both ways strong: using digital games to engage Aboriginal learners

Engaging Aboriginal learners in the school curriculum can be quite a challenge given issues of cultural and linguistic differences. Even more so, these differences can be expanded when the students are in their adolescence. Creating learning environments that engage learners, while providing deep learning opportunities, is one of the biggest challenges for teachers in remote communities. This paper reports on a reform initiative that centred on the use of a digital game, Guitar Heroes, in a remote Aboriginal school. It was found that the digital media provided teachers with opportunities for new learning spaces and resulted in additional unintended learning outcomes.

An Instrument for Assessing Primary Students' Knowledge of Information Graphics in Mathematics.

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in‐depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics, and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross‐curriculum applications in learning about graphics, and the need to explicate the links among graphics.

“If this was real”: tensions between using genuine artefacts and collaborative learning in mathematics tasks

This investigation identified the interactions and discourse employed by students (11–12 years old) when challenged to solve a realistic mathematics problem in a collaborative group situation. The students were asked to use genuine artefacts (including brochures, menus, bus timetables and photographs) to complete an open-ended task in small groups. Although most students were able to establish their own sense of authenticity by aligning the problem to their personal experiences and understandings, it was also the case that the majority found it difficult to establish meaningful, realistic understandings in the group situation. The students were unable to regulate the collective ideas of the group because too much emphasis was placed on personalising the task.

An educational practices framework: the potential for empowerment of the teaching profession

This paper outlines new educational policy initiatives that have been recently introduced to Australian schooling contexts and describes the challenges of providing rich and empowering professional development opportunities for classroom teachers and educational leaders in an era of heightened accountability and change. A framework for large-scale professional learning is proposed; one that adopts a theoretical lens associated with practice architectures, situated within community- and individual-focused professional learning experiences. The theoretical component of the model has been utilised effectively in a number of countries, while the personalised learning component is drawn from an evidence-based project that established a national learning framework.

Measurement of Spatial Ability: Construction and Validation of the Spatial Reasoning Instrument for Middle School Students.

This article describes the development and validation of a newly designed instrument for measuring the spatial ability of middle school students (11-13 years old). The design of the Spatial Reasoning Instrument (SRI) is based on three constructs (mental rotation, spatial orientation, and spatial visualization) and is aligned to the type of spatial maneuvers and task representations that middle-school students may encounter in mathematics and Science, Technology, Engineering and Mathematics (STEM)-related subjects. The instrument was administered to 430 students. Initially, a set of 15 items were devised for each of the three spatial constructs and the 45 items were eventually reduced to 30 items on the basis of factor analysis. The three underpinning factors accounted for 43% of variance. An internal reliability value of .845 was obtained. Subsequent Rasch analysis revealed appropriate item difficulty fit across each of the constructs. The three constructs of the SRI correlated significantly with existing well-established psychological instruments: for mental rotation (.71), spatial orientation (.41), and spatial visualization (.66). The psychometric characteristics of SRI substantiate the use of this measurement tool for research and pedagogical purposes.

The tyranny of remoteness: Changing and adapting pedagogical practices in distance education

Abstract Distance education (DE) learning environments are considerably different to those of typical classrooms where students engage on a face-to-face basis with their teachers and peers. In remote settings these face-to-face opportunities are limited and sometimes non-existent. This investigation focuses on the infl uence of new technologies on the pedagogical practices of teachers and their students in remote DE settings. A place pedagogy framework was utilised to consider the changed practices of DE teachers using satellite communications for lesson delivery. Findings of the study detail the initial hopes and aspirations of these teachers, the realities of their new practice and the challenges and demands of teaching in DE settings.

Visual and Nonvisual Processes in Grade 6 Students' Mathematical Problem Solving.

Abstract This paper reports an investigation into the problem-solving methods employed by three Grade 6 students who, over the course of a school year, worked on a variety of mathematics problems. One of the students tended to solve problems in a visual manner; the second preferred a more verbal/nonvisual approach; and the third tended to use both visual and nonvisual strategies. Over the school year, the three students moved toward more nonvisual, verbal/analytic forms of reasoning as task familiarity increased.