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We assessed the efficacy of two spatial learning programs grounded in early years learning pedagogical theory to improve numeracy performance in preschool. Engagement with a play-based spatial program led to better overall spatial reasoning and transferred to better numeracy compared with a business-as-usual control, underscoring the importance of embedding spatial learning within strong pedagogy and authentic preschool contexts. Engagement with the same spatial program using a spatialized curriculum (e.g., gesture, sketching) showed large additive effects, highlighting the role of spatial reasoning tools to support transfer of spatial reasoning to numeracy. The effects of the two interventions were moderated by spatial reasoning, with children with lower spatial reasoning making the most gains in numeracy. [ABSTRACT FROM AUTHOR]

The present study conducted a randomized control trial to assess the efficacy of two spatial intervention programs aimed to improve Grade 4 (N = 287) students' spatial visualization skills and math performance. The first treatment (N = 98) focused on isolated spatial training that included 40 min of digital spatial training across fourteen weeks. The second treatment (N = 92) embedded spatial visualization skill development into math lessons, along with the digital spatial training that provided practice of the newly acquired skills. A business-as-usual group acted as a control (N = 97). Engagement with the embedded intervention program (i.e., both lessons and digital training) showed large additive effects, highlighting the role of spatial reasoning tools to support the transfer of spatial reasoning to math. The isolated intervention program with the digital spatial training had a transfer effect on math, compared to a business-as-usual control, while spatial reasoning improvements for this group were mixed. The spatial skills targeted in the digital training had a mediation effect on math performance, despite not increasing in the pre–post-test design. The effects of the digital training cohort were moderated by initial spatial skill, with students with lower spatial reasoning making the least gains in math. [ABSTRACT FROM AUTHOR]

Large-scale spatial representations are rarely a perfect replication of the corresponding environment. Factors such as age, experience and environmental association play a significant role in each person's cognitive map. Yet, traditional spatial tasks remove these contextual elements in determining a person's spatial orientation skill, which has contributed to the apparent widening gap in spatial skills for children in non-urban areas. In this study we examined children's sketch maps of their route between home and school from four geographically diverse sites (urban, regional, rural, and remote Indigenous communities). Our findings suggest children from rural and remote communities possess highly detailed and sophisticated mental representations of their local environment, outside of traditional developmental frameworks. This work provides insights into these representations through student work samples. We suggest future work consider the contextual nature of spatial skills when comparing students. [ABSTRACT FROM AUTHOR]

There is increasing evidence for the impact of spatial training on mathematics performance in early years of education, however little research has focused on secondary school environments, which are traditionally more discipline driven. In the present study, a large-scale classroom-based intervention saw the introduction of twelve hours of spatial training instead of standard mathematics instruction across a ten-week term with grade eight students. The intervention program was delivered by classroom teachers within the Experience-Language-Pictorial-Symbolic-Application (ELPSA) pedagogical framework (Lowrie & Patahuddin, 2015). Differences in spatial and mathematics performance after the intervention, assessed by Hierarchical Linear Modeling, indicated that the intervention group (thirty-two classes) improved on spatial reasoning and mathematics achievement significantly more than a business-as-usual control group (eight classes). Improvement was found across geometry and measurement and number and algebra content for the intervention group, relative to the control group. This study provides evidence for an effective implementation of spatial learning with impact on mathematics performance, led by classroom teachers in a secondary school context. [ABSTRACT FROM AUTHOR]

Background: The role of gender in both spatial and mathematics performance has been extensively studied separately, with a male advantage often found in spatial tasks and mathematics from adolescence. Spatial reasoning is consistently linked to mathematics proficiency, yet despite this, little research has investigated the role of spatial orientation and gender in the relationship between spatial reasoning and mathematics. Aims: In the present study, three spatial reasoning constructs (mental rotation, spatial visualization, and spatial orientation) were examined for their unique contributions to mathematics performance in two samples (Study 1: grade 5; Study 2: grade 8). In light of the emerging gender gap in mathematics as children develop, these relationships were explored as a function of gender. Sample: Eighty‐four fifth‐grade students participated in Study 1 (43 females, 41 males; mean age = 11.19 years). Nine hundred and three eighth‐grade students participated in Study 2 (498 females, 405 males; mean age = 13.83 years). Methods: The three spatial reasoning constructs (mental rotation, spatial visualization, and spatial orientation) were examined for their unique contributions to mathematics performance for females and males in general and across different mathematical content (geometry–measurement and number sense). Results: Spatial factors accounted for 51% of the variance in math scores in Study 1 (grade 5) and 32% of the variance in math scores in Study 2 (grade 8). In both studies, spatial factors predicted a larger proportion of variance in geometry–measurement than for number sense. Spatial orientation was found to be a unique contributor in all mathematics models, object‐based spatial skills (mental rotation and spatial visualization) varied in their contribution to math performance depending on mathematics content and gender. Conclusions: The present work highlights the unique contribution of spatial orientation in the spatial–mathematics relationship and provides insights into the nature of gender differences in mathematical problem‐solving as a function of spatial reasoning and mathematics content. [ABSTRACT FROM AUTHOR]

This paper presents an heuristic that underpinned the development of a range of early years applications (apps) as part of the Early Learning Science, Technology, Engineering and Mathematics (STEM) Australia (ELSA) project (2016–19). The heuristic was developed to address a range of challenges that accompany the use of digital technologies in the year before formal schooling. These include the role of digital technologies in play‐based learning environments, screen time and the importance of agency when young children are using digital technologies. In an increasingly digital world, the issue of screen time looms large as a particularly contested aspect of technology use by young children. The ELSA project responded to this challenge by developing a pedagogical framework that embedded digital technologies into context‐rich, play‐based STEM learning. The Experience, Represent, Apply (ERA) heuristic discussed in this paper is a component of the project's overall pedagogical framework and provides early years educators with the opportunity, and the know‐how, to integrate digital technologies into STEM activities through intentional teaching and play‐based engagement. It was evident from educator feedback at the four days of workshops we delivered, and in other comments throughout the year long trial, that the educators were able to embrace the cyclic nature of the ERA heuristic and ensure that the time spent on the tablet (Represent) was connected to contextualised learning opportunities (Experience and Apply). Importantly, the tablets provided affordances for the children to utilise User Generated Content (UGC) to support active engagement when using the tablets. [ABSTRACT FROM AUTHOR]

Over three decades of research has shown that spatial reasoning and mathematics performance are highly correlated. Spatial visualization, in particular, has been found to predict mathematics performance in primary and middle school children. This research sought to determine the effectiveness of a spatial visualization intervention program on increasing student spatial reasoning and mathematics performance. Participants were 327 students from 17 classrooms across ten schools with nine experimental and eight control classes. The intervention program was delivered over a three-week period by classroom teachers, while the control classes received standard mathematics instruction. When compared to the control group, participants in the intervention group improved significantly on their spatial reasoning performance, and specifically on spatial visualization and spatial orientation. The intervention group also significantly improved on their mathematics test performance, with those in the intervention group outperforming their control group peers on geometry and word problems but not on mathematics questions requiring the decoding of graphics (non-geometry graphics tasks). These results add to evidence that a spatial reasoning enrichment program implemented by teachers in their own classrooms can enhance both spatial reasoning and mathematics performance. Moreover, the study provides new insights about the aspects of mathematics performance that are most affected by spatial visualization training. [ABSTRACT FROM AUTHOR]

Most large-scale summative assessments present results in terms of cumulative scores. Although such descriptions can provide insights into general trends over time, they do not provide detail of how students solved the tasks. Less restrictive access to raw data from these summative assessments has occurred in recent years, resulting in opportunities for data to be analysed at a deeper level. This article examines longitudinal data on students’ performance on spatial numeracy tasks, with a specific focus on gender differences. Using an adapted Knowledge Discovery in Data (KDD) research design, data from a nationally-representative cohort were analysed over a five-year period. Results highlighted distinct differences in how males and females processed many of the spatial tasks. The opportunity to analyse summative assessment instruments at a deeper level offers more scope for worthwhile curriculum and classroom implications. [ABSTRACT FROM PUBLISHER]

Background Although spatial ability and mathematics performance are highly correlated, there is scant research on the extent to which spatial ability training can improve mathematics performance. Aims This study evaluated the efficacy of a visuospatial intervention programme within classrooms to determine the effect on students' (1) spatial reasoning and (2) mathematics performance as a result of the intervention. Sample The study involved grade six students (ages 10-12) in eight classes. There were five intervention classes ( n = 120) and three non-intervention control classes ( n = 66). Methods A specifically designed 10-week spatial reasoning programme was developed collaboratively with the participating teachers, with the intervention replacing the standard mathematics curriculum. The five classroom teachers in the intervention programme presented 20 hr of activities aimed at enhancing students' spatial visualization, mental rotation, and spatial orientation skills. Results The spatial reasoning programme led to improvements in both spatial ability and mathematics performance relative to the control group who received standard mathematics instruction. Conclusions Our study is the first to show that a classroom-based spatial reasoning intervention improves elementary school students' mathematics performance. [ABSTRACT FROM AUTHOR]

This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is acquired; and (3) the applicability of mathematics. These factors were used in subsequent multivariate analyses to determine whether teachers' mathematics competence influenced their personal mathematics viewpoints and perspectives. There was no difference between those students who had studied advanced and standard mathematics at school on the three belief and attitude measures, despite distinct differences in their MCK. [ABSTRACT FROM AUTHOR]

This investigation examined Singaporean and Australian students' performance and strategy use when solving mathematics tasks. Half of the questions in the 24-item test were drawn from the national Singaporean Grade 6 test, with the other 12 items sourced from the Australian national assessment. 1187 grade 6 students solved graphic and non-graphic mathematics tasks and reported their solution strategies later classified and coded as symbolic, pictorial or imagistic. Results revealed performance differences in favor of the Singaporean cohort on three of the four task categories. There were distinct differences between the types of strategies employed by the students across these task categories. The Singaporean students were more likely to use conditioned heuristics to solve the tasks, especially the non-graphic tasks, whereas the Australian students were reluctant to use these heuristics. Cultural differences were also found in the way students solved the tasks, especially when encountering unfamiliar tasks. [ABSTRACT FROM AUTHOR]

The article discusses how to harness critical incidents for the development of students and teachers. Topics include an excerpt of a lesson in Indonesia which involve teaching of fractions in a classroom environment, accessing the website www.bbc.co.uk/skillswise/game/ma17frac-game-fractions-side-by-side in which symbolic and pictorial forms of fractions are presented, and explaining a question about non-negative integers.

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10-12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low. [ABSTRACT FROM AUTHOR]

This study describes Singapore students’ ( N = 607) performance on two tasks in a recently developed Mathematics Processing Instrument (MPI). The MPI comprised tasks sourced from Australia's NAPLAN and Singapore's PSLE. This study also examines students’ use of the model method to solve the two tasks. The model method is a visual problem-solving heuristic prevalently used in Singapore classrooms. The study found that students who solved the tasks using a visual method predominantly used the model method as a visual problem-solving strategy. Another interesting observation was the hindrance of successful problem solving caused by the persistence of prototypical images of model drawings. Implications include encouraging teachers to get their students to identify problem situations where the model method will both work and not work well, and making the role of the generator in the model method explicit in the mathematics textbooks. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Tracy Logan and Tom Lowrie argue that while little attention is given to visual imagery and spatial reasoning within the Australian Curriculum, a significant proportion of NAPLAN tasks require high levels of visuospatial reasoning. This article includes teaching ideas to promote visuospatial reasoning in the primary classroom. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The investigation monitored the digital game-playing behaviours of 428 primary-aged students (aged 10–12 years). Chi-square analysis revealed that boys tend to spend more time playing digital games than girls while boys and girls play quite different game genres. Subsequent analysis revealed statistically significant gender differences in terms of the types of mathematics-rich games students prefer to play. Girls preferred to play games that required problem solving, quantitative computations and the interpretation of graphs. Boys preferred games that required visual/spatial engagement. Given the fact that boys outperform girls on spatial tasks and mathematics assessment items that contain graphics, this study has implications for the development of students'' mathematics sense making. [Copyright &y& Elsevier]

The graphics-decoding proficiency (G-DP) instrument was developed as a screening test for the purpose of measuring students’ (aged 8–11 years) capacity to solve graphics-based mathematics tasks. These tasks include number lines, column graphs, maps and pie charts. The instrument was developed within a theoretical framework which highlights the various types of information graphics commonly presented to students in large-scale national and international assessments. The instrument provides researchers, classroom teachers and test designers with an assessment tool which measures students’ G-DP across and within five broad categories of information graphics. The instrument has implications for a number of stakeholders in an era where graphics have become an increasingly important way of representing information. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The capacity to solve tasks that contain high concentrations of visual–spatial information, including graphs, maps and diagrams, is becoming increasingly important in educational contexts as well as everyday life. This research examined gender differences in the performance of students solving graphics tasks from the Graphical Languages in Mathematics (GLIM) instrument that included number lines, graphs, maps and diagrams. The participants were 317 Australian students (169 males and 148 females) aged 9–12 years. Boys outperformed girls on graphical languages that required the interpretation of information represented on an axis and graphical languages that required movement between two- and three-dimensional representations (generally Map language). [ABSTRACT FROM AUTHOR]

The article offers information on the success on structured number line of primary students. It says that the structured number line is a type of number line which constitutes mathematical information by placing marks in vertical and horizontal line. It states that students need to understand the conventions used for the creation of structured number lines to bring out the use of number line. It adds that the students who made errors in the solution process are unsuccessful on the number line.

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 Australia's 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. [ABSTRACT FROM AUTHOR]

The article provides insights to the six main types of graphics applied in mathematics including axis graphics and opposed position graphics and suggestions to allow students developed their capacity to understand the types of graphics. Axis graphics work by providing information through by marking a point on a line. Bar and plot charts are included in opposed position graphics. It states that one crucial way for students to understand graphics is to gain knowledge regarding kinds of graphics.

The article considers the influence a genuine artifact has on students' spatial reasoning. The task was given to Grade 5 students which required them to plan a family outing to a theme park by locating rides and attractions and subsequently indicating a sequence of events. A scenario was presented that was set within a context that the students could identify with and one in which they could apply personal experiences in order to make mathematical connections.

The authors investigated the performance of 172 Grade 4 students (9 to 10 years) over 12 months on a 36-item test that comprised items from 6 distinct graphical languages (e.g., maps) commonly used to convey mathematical information Results revealed (a) difficulties in Grade 4 students' capacity to decode a variety of graphics, (b) significant improvements in students' performance on graphical languages over time, (c) gender differences across graphical languages, and (d) influence of spatial ability on decoding performance. Implications of this study include the need for supporting development of students' ability to decode graphics beyond activities usually investigated in mathematics curricula. [ABSTRACT FROM AUTHOR]

Abstract: This investigation describes the way in which a case study participant (aged 7) represented, posed and solved problems in a technology game-based environment. The out-of-school problem-solving context placed numeracy demands on the participant that were more complex and sophisticated than the type of mathematics experiences he encountered in school. The participant used maps (including large- and small-scale maps, dynamic and static maps) to represent, interpret and solve problems. The participant demonstrated the capacity to decipher graphical information when simultaneously moving between maps with different representations, orientations, perspectives and scales as he played a Pokemon Game Boy. This paper outlines the strategies and mathematical ideas he used to make sense of the problem context, and describes the problem-solving processes he used to make sense of an open-ended task. [Copyright &y& Elsevier]

Gives pieces of advice to teachers about teaching problem solving tasks to children. Common element among all approaches to authentic teaching and learning; Factors to consider in teaching problem solving; Implications of the task in the classroom.

Explores the conversational nature of the word pedagogy. Implications of pedagogy for classroom learners of mathematics; Definition of pedagogy; Consideration of pedagogy as conversation.

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. [ABSTRACT FROM AUTHOR]

• Diagrams are one type of external representation for solving mathematics problems. • Participants included 1187 grade 6 students. • Task success was linked to effective use of diagrams during problem-solving. • Instruction in effective diagram use may help when solving new or complex problems. This investigation examined the strategies students employ to solve graphic and non-graphic mathematics tasks. The students' strategies were classified in terms of representation, specifically whether or not they used self-decoded diagrams to solve the tasks. The study involved 1187 Grade 6 students (from Singapore and Australia) solving graphic- and non-graphic mathematics tasks typically encountered in national tests. Data from these students provided solution strategies to mathematics problems; the strategies were classified as diagrammatic or analytic solutions. Data analysis was confirmatory in nature, which sought to analyze students' solutions to understand more fully the extent to which task representation relates to task difficulty, understanding and success. There was a strong association between task success and representation for items with moderate level of difficulty—with the employment of diagrammatic solutions more likely to lead to correct solutions. [ABSTRACT FROM AUTHOR]

Spatial visualisation is an essential component of geometric thinking and measurement sense. It is a particular type of spatial skill that involves manipulation of spatial images and may not be naturally occurring for students. However, research shows that it is malleable and can be developed through instruction. This article presents an open-ended activity to foster spatial visualisation as students explore the relationship between the surface area and volume of cube blocks. [ABSTRACT FROM AUTHOR]

The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students' representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative task analysis. Task solutions were analyzed as a function of spatial visualization skills and links were made between student solutions on tasks with different goals (i.e., non-metric and metric). Findings suggest that strong spatial visualizers solved the tasks with relative ease, with evidence for conceptual and procedural understanding. By contrast, Low and Average Spatial students more frequently produced errors due to failure to correctly determine linear measurements or apply appropriate formula, despite adequate procedural knowledge. A novel finding was the facilitating role of spatial skills in the link between metric task representation and success in determining a solution. From a teaching and learning perspective, these results highlight the need to connect emergent spatial skills with mathematical content and support students to develop conceptual understanding in parallel with procedural competence. • Spatial visualization training can support mathematics achievement. • Spatial skills influence the way students engage in measurement of area. • Spatial skills may facilitate the link between task representation and success. • Error patterns provide insight into differences in procedural compared with conceptual understanding. [ABSTRACT FROM AUTHOR]

Highlights issues on teaching mathematics in primary schools in the U.S. as of October 2003. Focus of mathematics lessons in primary schools; Main responsibility of teachers of mathematics; Measures that must be taken by teachers to illuminate the importance of the structure of arithmetic.

Introduces a series of articles about ways of engaging students mathematically and reflecting the practice of mathematics educators.

Introduces a series of articles on teaching and learning space and geometry.

Introduces the articles featured in the March 2003 issue of 'APMC.' Conference held by the Australian Association of Mathematics Teachers in Brisbane, Queensland; Aspects of mathematics and mathematics teaching; Importance of using children's natural language as they play with mathematical concepts.

Editorial. Discusses advances in the entertainment and technology industries and their impact on education. Evolution of technology; Adaptation of students to an array of multimodal communications; Importance of numeracy play in preschool settings.

Editorial. Presents an overview on the articles published in the 2002 issue of the 'APMC' magazine. Theme of the articles; Aspects of the pedagogical process; Link between teaching and learning.

Introduces a series of articles on ways of teaching mathematics to children.

Editorial. Introduces a series of articles on numeracy and the pedagogy of mathematics.

This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms of words and actions, the analysis focused on identifying the types of mathematical engagement promoted through the intended lesson and performed by students during the lesson. Using modified Watson's analytical tool (2007), students’ engagement was captured from what the participants’ did or said mathematically. We found that teachers’ enacted practices had an influence on student mathematical engagement. The teacher who demonstrated content in explicit ways tended to limit the richness of the engagement; whereas the teacher who presented activities in an open-ended manner fostered engagement. [ABSTRACT FROM AUTHOR]

This study aimed to identify the role and nature of spatial visualization in the problem solutions of pre-service teachers solving school-mathematics tasks requiring measurement reasoning. The nuances in the pre-service teachers' strategies were examined for the role of spatial visualization in the solution process. The findings suggest that inadequacies in visualizing the spatial configurations of the tasks led to incorrect numerical solutions despite the presence of conceptual knowledge. Furthermore, the tendency to rely on formula-based approaches appeared to have suppressed the preliminary spatial processing of the configurations. Theoretically, the paper offers insights into the mechanism that may be involved in the solution of spatially-related mathematical tasks. The findings imply that pre-service teachers need to be sufficiently engaged in spatial reasoning activities. • Spatial manipulation on mathematical tasks influences numerical solutions. • Spatial visualization is an enabler in solving spatially-related mathematical tasks. • Formula-based thinking may suppress the preliminary spatial inspection of the tasks. • Spatial reasoning needs to be explicitly taught to pre-service teachers. • Pre-service teachers should be empowered to analyze spatially-related tasks. [ABSTRACT FROM AUTHOR]