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It is well established that spatial reasoning skills (i) support mathematics achievement, (ii) are malleable, and (iii) can be improved through training. More recently, there has been interest in using spatial training to causally support corresponding improvements in mathematics achievement; however, findings so far appear to be mixed. The current study explores the effect of a spatial reasoning intervention on Year 11 students' spatial reasoning skills and mathematics achievement and considers the role of a pedagogical framework and the multidimensional nature of mathematics and spatial reasoning in the design of the intervention. The Experience-Language-Pictorial-Symbolic-Application (ELPSA) pedagogical framework was used to modify an existing spatial intervention program for delivery by high-school educators to Year 11 students (an important but understudied population). The spatial intervention involved training a range of spatial skills over an extended timeframe. Students were randomly assigned to the intervention condition or to a business-as-usual control (n = 73). Using a pre-/post-test design, we found the intervention was successful in improving participants' spatial reasoning skills and performance on measurement and geometry items compared to the control condition but not on number and algebra items. These findings demonstrate that spatial training can support mathematics achievement in certain contexts, highlighting the importance of identifying how individual spatial skills support specific mathematics tasks. Consideration was given for how to use strong pedagogical techniques to scaffold transfer, finding utility in the ELPSA framework. Implications for how to embed spatial training within real mathematics classrooms, as done in the current study, are discussed.

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.

This study aimed to develop a survey instrument to measure student attitudes towards mathematics teaching-learning processes that is appropriate for the Indonesian context. This study consisted of two phases: Phase 1 (n = 320) was a pilot study to assess the suitability of the instrument items for Indonesian students. Phase 2 (n = 1001) was conducted to examine the construct validity of the instrument. The data collected from Phase 1 were analysed using descriptive statistics (i.e., frequency counts, simple correlation, and one-way ANOVA for item analysis). Factor analysis was utilised to select items and for scale construction. The result of the screening process (44 items) was piloted to assess its reliability and validity. The instrument, consisting of 22 items, is a reliable and valid rating scale that measures three distinct factors: Teacher Presentation, Mathematics Interest, and Mathematics Value. The data from Phase 2 were analysed by employing confirmatory factor analysis (CFA) and the results confirmed that the three factors identified in the previous factor analysis underlie the student attitudes instrument.

The relationship between mathematics and spatial reasoning is well established and extensively researched. Certain mathematics content could be deemed explicitly spatial, for example within geometry. However, the link to spatial reasoning extends into other areas of mathematics, such as representations of the number line and reading and interpreting graphs. Correlational and training studies have tended to focus on mathematics either broadly (e.g., standardised test scores) or with specific measures (e.g., arithmetic) when examining the relationship between mathematics and spatial reasoning. In the present study, 455 students from grades 4 through 9 completed digital assessments of mathematics and spatial reasoning. The mathematics tasks reflected curriculum content with varying degrees of spatial intent. Separate assessments were developed for the primary and secondary cohorts. Relationships between mathematics task performance and spatial reasoning indicate distinctions in problem-solving between item types with different spatial skills influential for different content. The role of spatial reasoning in interactive forms of digital assessment is discussed.

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.

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.

Facebook groups (FGs) have been widely used by teachers/educators. However, the type of educational FGs they value most, and the reasons for their choices, are less clear. This paper examines the perspectives of 440 participants (86% mathematics teachers and 14% mathematics teacher educators) on their educational FGs. It identifies the types of FGs they value most, the reasons for their choices, and aspects they dislike. Data collected through an online survey suggests that FGs are used for professional engagement across Indonesia. Support for FGs included the perceived benefits of sharing information/resources about mathematics (as well as education in general), networking and communication with others, opportunities for teacher professional development sessions and announcements about/access to up-to-date information. However, limitations with the platform included occasional irrelevant posts/comments, unexpected member behaviour and the lack of responsiveness from FGs administrators. Commonly, most participants saw value in discipline-specific (i.e. mathematics) engagement, leading to professional learning/support. This study stimulated further discussion on ways to maximise benefits whilst simultaneously overcoming the identified challenges of these participant-driven online communities.

Spatial reasoning, the ability to mentally represent and transform objects and their relations, is considered so closely connected to mathematics that there is no longer a question of whether the two are related. Instead, there remains debate about how to answer the question of why. This paper explores the way the two fields of mathematics education and psychology define, assess and examine this important relationship. We find that both fields rely extensively on psychometric tests to define spatial reasoning skills and do not characterise spatial reasoning in context. We look at the points of connection and propose that the best way forward is to build on the complementary approaches currently undertaken. We suggest better alignment between the spatial and mathematics reasoning skills that have been identified (theoretically and for assessment development), and a focus on how spatial reasoning interventions influence how students think and learn. With the growing interest in spatial intervention for mathematics achievement, we analyse the different ways this has been undertaken and suggest directions for future research. For example, how might laboratory-based studies be scaled up within a range of classroom contexts, and how might classroom-based studies offer more control settings and systematic variation?

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.

This paper offers a framework for a mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning components, namely: Experience, Language, Pictorial, Symbolic and Applications. This framework has been used in developing lessons and teacher professional programs in Indonesia since 2012 in cooperation with the World Bank. This paper describes the theory that underlines the framework in general and in relation to each inter-connected component. Two explicit learning sequences for classroom practice are described, associated with Pythagoras theorem and probability. This paper then concludes with recommendations for using ELPSA in various institutional contexts.

Teachers should possess a robust knowledge of graph interpretation in a world that requires increasingly scientific citizens. This study aimed to investigate teachers' knowledge of interpreting a context-based line graph, by understanding the types of difficulties teachers have in interpreting such graphs. The study also sought to determine whether there were gender differences in teachers' graph interpretation skills and determine whether these interpretation skills were different among teachers with varying teaching experiences. Sixty-one teachers from ten districts in one Indonesian province participated in this study. Empirically derived items were developed to identify the teacher's conceptual understanding of line graphs with Curcio's ("Journal for Research in Mathematics Education," 18(5), 382-393, 1987) level of interpretation applied to explain the difficulties encountered. This study revealed that most of the teachers had difficulty answering questions that required 'reading beyond the data'. Specifically, these teachers interpreted the graph as an iconic representation of a real event rather than an abstract representation of data (i.e., speed vs. time). Performance differences in teachers' understanding of the graph were dependent on the grade level they taught, with differences especially evident in the interpretation of moderate and difficult items. There were no differences in teachers' understanding by gender or years of teaching experience. The results highlight the importance of focusing on teacher professional development centering on teachers' knowledge of graph comprehension.

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.

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.

Since the early 70s, there has been recognition that there are specific differences in achievement based on variables, such as gender and socio-economic background, in terms of mathematics performance. However, these differences are not unilateral but rather quite specific and relate strongly to spatial reasoning. This early work has paved the way for thinking critically about who achieves in mathematics and why. This project innovatively combines the strengths of the two Chief Investigators-Lowrie's work in spatial reasoning and Jorgensen's work in equity. The assumptions, the approach and theoretical framing used in the study unite quite disparate areas of mathematics education into a cogent research program that seeks to challenge some of the long-held views in the field of mathematics education.

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.

This project describes a way to help students recognise that the expressions on both sides of the equals sign are the same. It was developed to support teachers in disadvantaged communities to help their students make sense of mathematics.

Experience-Language-Pictorial-Symbolic-Application [ELPSA] is a learning framework that presents mathematical ideas through a cyclic design. The ELPSA framework which can be used to develop mathematics lessons and units of work that build students' concept understanding is described here.

This investigation examines school-family partnership relationships in rural and remote settings. The study highlights the teaching-learning relationships of classroom teachers, parents as instructors/supervisors, and students as they make sense of numeracy and literacy outcomes in distance education contexts. The case study data provide insights into how the distance education provider (the school) interacts with families to facilitate young students' learning experiences. At present, the school and the families they engage with have access to limited technological resources. This investigation considers learning engagement in these increasingly unusual settings and postulates the effect new technologies may have on pedagogical practices in the future.

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.

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.

Technological pedagogical content knowledge (TPACK) has been well accepted as a framework to understand and describe types of knowledge required by teachers to teach specific content with technology effectively. However, limited studies have used the framework in analysing the complexity of technology integration in mathematics classrooms. This study investigates, through examining critical instructional events, the most influential TPACK constructs in understanding and shaping teachers' pedagogical practices using digital technology. This case study was conducted in an early secondary mathematics classroom in Indonesia that used a web-based resource to support students' understanding of fractions. The finding suggests that the qualitative examination of the four intersected TPACK constructs assists in understanding the challenges and the opportunities to teachers when utilising an exploratory-based technology. It demonstrates that the combination of pedagogical stances and choice of technology significantly influence the visibility of other TPACK constructs. Implications of this study include the need of thoughtful planning prior to using web-based resources and the importance to utilise critical events in developing and assessing teachers' TPACK.

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.

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]

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three criteria, namely (1) equidistance, (2) congruence of sides and (3) "exactly opposite" as the intuitive counterpart of perpendicularity for performing reflection. On the other hand, the second participant, Sara, focused on perpendicularity and equidistance, as is the normative procedure. Brittany's inadequate knowledge of reflection shaped her actions and served as a validation for her solutions. Intuitively, her visual strategies took over as a fallback measure to maintain congruence of sides in the absence of a formal notion of perpendicularity. In this paper, we address some of the well-known constraints that students encounter in dealing with bilateral symmetry and reflection, particularly situations involving inclined line of symmetry. Importantly, we make an attempt to show how visual and analytical strategies interact in the production of a reflected image. Our findings highlight the necessity to give more explicit attention to the notion of perpendicularity in bilateral symmetry and reflection tasks.

This paper explores the relationship between social backgrounds and geographical locations with mathematical achievement. Using the national testing system in Australia, correlations between the variables were explored and it was found that students from rural and low SES backgrounds are still being marginalised in school mathematics--in terms of their success. This is despite 50 years since the first critical sociology of education noted the structural inequalities of education. For the authors this creates a challenge for researchers to consider better ways to understand the factors that may be impacting on mathematical achievement, particularly for those target groups within our study. The work of Bourdieu is used to frame the paper.

A critical incident is a situation or event that holds significance for learning, both for the students and teachers. This paper presents four examples of critical incidents from a Year 7 teacher's lesson excerpts in Indonesia involving teaching of fractions, to show how they shaped classroom situation, brought forward elements of conflict, and created learning opportunities. Three examples are drawn from the lesson using a web-based applet (Examples 1, 2 and 3). The illustration of these critical incidents will be followed by a discussion on how to harness them in order to develop students' understanding or be used as a challenge as well as a learning process for teachers. This paper highlights the effectiveness of a web-based applet for displaying pictorial representations in an interactive manner.

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.

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.