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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., (© 2020 The British Psychological Society.)

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.

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.

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 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.

A survey ("n" = 410) revealed statistically significant gender differences between middle school students' preference for playing particular types of games. Subsequent instrumental case studies theorised the "within-game" and "out-of-game" experiences of two middle school students as they played a digital hand-held game. These two case studies comprised stimulated recall sessions and subsequent follow-up, open-ended interviews. The analysis described the influence digital game playing can have on a participant's mathematics sense making. Findings included distinct differences in both the approach and the strategies employed by the respective participants to not only engage with the game, but contextualise it within their own knowledge and experiences. Furthermore, the study demonstrated the extent to which game playing can be a catalyst for further learning outside the game experience.

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. (Contains 4 tables.)

One way of providing middle-school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. Students are expected to learn serious, substantive mathematics in classrooms in which the emphasis is on thoughtful engagement and meaningful learning. Lesh and Harel (2003) have indicated that the kind of problem-solving situations that should be emphasised in the classroom are simulations of real-life experiences where mathematical thinking is useful in the everyday lives of the student or their family and friends. Such problems are worthwhile since they tend to reflect the nature of "real" problems because they are complex, ill-structured, contain multiple perspectives, and offer multiple pathways or solutions. In the investigation presented here, the authors consider the influence a genuine artifact has on students' spatial reasoning. They have found that middle-school students' are more likely to utilise a range of spatial skills to complete mathematics tasks when they are deeply engaged in an activity. They use artifacts that the students can readily relate to in everyday situations in order to enhance the authenticity of the classroom activity. Activities such as these allow students to embed themselves in the situation and thus help them make sense of mathematical ideas through spatial reasoning. Such skills and processes include building and manipulating mental representations of objects, perceiving an object from different perspectives, and interpreting and describing physical environments. (Contains 5 figures.)

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. (Contains 4 figures.)

Describes the types of problems young children generated in problem-posing situations as they worked, on a one-to-one basis, with a student teacher. Indicates that problem-posing actions of students can be nurtured by teachers' actions. (Author/KHR)

Investigated problem-solving methods used by 3 sixth-graders working on a variety of mathematics problems over the school year. Found that the students used different strategies: one used visual strategies, one a more verbal approach, and the third a combination of the two. Over time, all three moved toward more nonvisual, verbal/analytic forms of reasoning as task familiarity increased. (JPB)

Describes the range of processes used by year 3 children engaged in solving non-routine mathematics problems. Discusses how it can be told when children are thinking mathematically. (ASK)

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. [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 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: 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.

• 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]