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Enhancing Children's Spatial and Numerical Skills through a Dynamic Spatial Approach to Early Geometry Instruction: Effects of a 32-Week Intervention
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This study describes the implementation and effects of a 32-week teacher-led spatial reasoning intervention in K–2 classrooms. The intervention targeted spatial visualization skills as an integrated feature of regular mathematics instruction. Compared to an active control group, children in the spatial intervention demonstrated gains in spatial language, visual-spatial reasoning, 2D mental rotation, and symbolic number comparison. Overall, the findings highlight the potential significance of attending to and developing young children's spatial thinking as part of early mathematics instruction.
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... Additionally, children become aware of the principles of measuring while learning spatial relations, geometry and time (Baroody, 2011;Battista, 2007;Clements & Stephan, 2011;Jones & Tzekaki, 2016). Geometrical awareness skills become more precise with age, such as the understanding of shapes (Clements, 2011;Hawes et al., 2017), conservation, mass and volume (Clements & Sarama, 2007;Clements & Stephan, 2011). Furthermore, as children age and their language develops, they gain skills to describe spatial qualities in a more sophisticated way (Clements & Sarama, 2007). ...
... Somewhat surprisingly, the age group of the children was not associated with the teaching frequency for STS. However, children acquire a more complex understanding of time (Lyytinen, 2014), spatial relations and shapes (Clements, 2011;Hawes et al., 2017) and measurement, and mass and volume (Baroody, 2011;Clements & Stephan, 2011) between the ages of three and seven. We expected this to impact the association between the age group of the children and the frequency at which STS are taught, irrespective of the broad learning objectives set in the Finnish curricula. ...
This study explored teaching early mathematical skills to 3- to 7-year-old children in early childhood education and care (ECEC) and pre-primary education. Teachers in ECEC ( N = 206) answered a web survey. The first aim was to determine whether teaching frequency or pedagogical awareness of teaching early mathematical skills varied according to the category of skills (numerical skills, spatial thinking skills and mathematical thinking and reasoning skills) and whether children’s age group moderated these differences. The second aim was to explore to what extent teacher-related characteristics and children’s age group explained variations in teaching frequency concerning early mathematical skills. Results from repeated MANOVAs demonstrated that the frequency and pedagogical awareness of teaching early mathematical skills depended on the skill category and that children’s age group moderated these differences. In 5- to 6-year-olds and 6- to 7-year-olds, numerical skills were taught more often than spatial thinking skills, whereas in 3- to 5-year-olds, they were taught as frequently. In all age groups, mathematical thinking and reasoning skills were taught the least. Pedagogical awareness was lowest in teaching spatial thinking skills in all age groups, but only in 6- to 7-year-olds was teachers’ pedagogical awareness in teaching numerical skills higher than in the two other categories. According to a univariate analysis of variance, pedagogical awareness and mathematics professional development programmes were strongly associated with teaching frequency in all skill categories. The results emphasise that children’s opportunities to learn early mathematical skills depend on teachers’ characteristics.
... However, the authors could not determine the impact of different spatial skills as most of the studies were focused on spatial visualization. More specifically, classroom-based spatial visualization instruction was found to lead to improvements in geometry, measurement, and word problems (Lowrie et al., 2019), and non-symbolic comparison tasks (Hawes et al., 2017). Hawes et al. (2022) concluded that the mathematical-spatial relationship is unique because of the links between content, strategies, and broad cognitive factors. ...
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.
... Duval, 2017;Seah & Horne, 2019;Van Hiele, 1959/1985, visualspatial thinking (e.g. Cohrssen et al., 2017;Hawes et al., 2017;Lowrie et al., 2017), geometric shapes (e.g. Hallowell et al., 2015;Roth & Gardener, 2012), and geometric proofs (e.g. ...
The mathematical construct of dimension is one of the fundamental ideas for developing a sound understanding of two-dimensional (2D) and three-dimensional (3D) shapes. Yet, research in mathematics education has rarely explored children’s understanding of dimension in primary education. This paper explores how year 5/6 (9 to 11 years old) children construct and negotiate their meanings about dimension while engaging in classroom interactions about 2D and 3D shapes during geometry lessons in a New Zealand (NZ) English-medium multilingual primary classroom. Transcribed data of two key moments selected from six audiovisually recorded geometry lessons are presented. The findings suggest that children may use different discursive constructions—“another world”, “different ways to go”, and “flat vs fat”—to display their meanings about dimension. The findings also suggest that children and teacher participants may use prosodic features of their languages to interactionally construct the meanings of these discursive constructions. The paper discusses these findings in light of current research literature and offers a few implications for curriculum development and future research.
... These concrete materials included objects such as tiles, blocks, multi-link cubes and magnetic shapes. For example, in one classroom-based intervention with 5-to 7-year-olds, training, which targeted intrinsic skills using materials such as multi-link cubes and magnetic shapes, was found to be effective at improving both spatial and mathematics ability (Hawes et al., 2017). Block building and puzzle training in pre-school children has also been shown to be effective (Schmitt et al., 2018) and appears to be particularly beneficial for pre-school children from disadvantaged backgrounds Schmitt et al., 2018) and thus might go some way to closing attainment gaps when children start school. ...
Background:
There is a growing evidence base for the importance of spatial reasoning for the development of mathematics. However, the extent to which this translates into practice is unknown.
Aims:
We aimed to understand practitioners' perspectives on their understanding of spatial reasoning, the extent to which they recognize and implement spatial activities in their practice, and the barriers and opportunities to support spatial reasoning in the practice setting.
Sample:
Study 1 (questionnaire) included 94 participants and Study 2 (focus groups) consisted of nine participants. Participants were educational practitioners working with children from birth to 7 years.
Methods:
The study was mixed methods and included a questionnaire (Study 1) and a series of focus groups (Study 2).
Results:
We found that whilst practitioners engage in a variety of activities that support spatial reasoning, most practitioners reported little confidence in their understanding of what spatial reasoning is.
Conclusion:
Informative and accessible resources are needed to broaden understanding of the definition of spatial reasoning and to outline opportunities to support spatial reasoning.
... These concrete materials included objects such as tiles, blocks, multi-link cubes and magnetic shapes. For example, in one classroom-based intervention with 5-to 7-year-olds, training, which targeted intrinsic skills using materials such as multi-link cubes and magnetic shapes, was found to be effective at improving both spatial and mathematics ability (Hawes et al., 2017). Block building and puzzle training in pre-school children has also been shown to be effective (Schmitt et al., 2018) and appears to be particularly beneficial for pre-school children from disadvantaged backgrounds Schmitt et al., 2018) and thus might go some way to closing attainment gaps when children start school. ...
Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomised, controlled, pre-post, follow-up, training design (N=182; mean age 8years; 49%female; 83.5% White). We show that both embodied and non-embodied spatial training approaches improve spatial skills compared to control. However, we conclude that embodied spatial training using physical manipulatives leads to larger, more consistent gains in mathematics and greater depth of spatial processing than non-embodied training. These findings highlight the potential of spatial activities, particularly those that use physical materials, for improving children’s mathematics skills.
... Cheng & Mix, 2014;Hawes et al., 2017;Lowrie et al., 2018; ...
... Although it is seldom that spatial thinking is explicitly taught in schools, spatial vocabulary and principles like rotation, visualization, identification, and translation are indeed often employed in math disciplines like geometry and calculus. Researchers have developed a strategy for providing explicit spatial instruction that involves collaborating with classroom instructors to create spatial interventions [5,6]. Such instruction typically focuses on developing selected aspects of spatial reasoning skills through the use of up-to-date methods and processes that are helpful for solving nuanced math classroom problems. ...
Children can connect with and grasp complex geometric concepts when we harness and integrate spatial thinking into learning situations. In this chapter, we’ll look at a couple warm-ups and a few classroom exercises that show how thoughtful resources and unique geometry assignments may help students enhance their understanding in the complex context of the K-12 classroom. Throughout the class, students used a number of spatial abilities, such as visualization and mental rotations, while building and working with polyominoes.
... Although spatial language is important for children's early spatial development, there is variation in how much families engage in talk about spatial concepts (e.g., Pruden et al., 2011). Since spatial reasoning is important for math achievement (Geer et al., 2019;Gilligan et al., 2017;Gunderson et al., 2012;Verdine et al., 2017), and interventions targeting spatial knowledge have also led to increases in math knowledge (Cheng & Mix, 2014;Hawes et al., 2022;Hawes et al., 2017;Lowrie et al., 2019;Lowrie et al., 2017;Mix et al., 2020), facilitating high quality early spatial experiences has potential for supporting children's later mathematical success. In the present study, when playing with a shape puzzle like those typically available to families, parents and children engaged in very little shape talk beyond labeling shapes. ...
Shape puzzles offer opportunities for families to talk about geometric concepts, which supports early spatial reasoning. However, puzzle features (i.e., similarity of shapes) may influence the nature of parent-child talk about shapes (e.g., labeling shapes vs. elaborating on shape properties). In this study, 128 dyads of parents and children (ages 30–47 months) completed both Typical and Highly Alignable (HA) shape puzzles. Compared to the HA puzzle, there was more shape labeling during the Typical puzzle; the HA puzzle elicited more elaborative shape talk (particularly comparing and contrasting shapes). Further, the HA puzzle elicited more elaborative shape talk when similar shapes were distributed on different rows rather than arranged side-by-side. Follow-up analyses found the HA puzzles were more difficult for children to complete. Findings suggest that including similar shapes and manipulating the arrangement of shapes may increase the difficulty of puzzles and elicit increased parent support and enhanced parent-child spatial language during puzzle play.
In this handbook, the world's leading researchers answer fundamental questions about dyslexia and dyscalculia based on authoritative reviews of the scientific literature. It provides an overview from the basic science foundations to best practice in schooling and educational policy, covering research topics ranging from genes, environments, and cognition to prevention, intervention and educational practice. With clear explanations of scientific concepts, research methods, statistical models and technical terms within a cross-cultural perspective, this book will be a go-to reference for researchers, instructors, students, policymakers, educators, teachers, therapists, psychologists, physicians and those affected by learning difficulties.
In Taking Shape, spatial reasoning is greeted and treated as integral to and foundational of all mathematics understanding - present in every action, influenced by and influencing every movement through our structured world, and impacting the language used to make sense of experience. To that end, spatial reasoning is not presented as yet another curriculum topic that teachers should incorporate into their practice, nor as a subcomponent of mathematics instruction that might be absorbed inside geometry and measurement. Readers are provided with focused introductions to such key issues in cognition as visualization, mental manipulation, working memory, gesture, and motivation. At the same time, they are given entry points to key themes in spatial reasoning such as symmetry, manipulating shapes, and situating forms - all formatted in tasks, games, and challenges that involve ready-at-hand materials.
Sensitivity to numerical magnitudes is thought to provide a foundation for higher-level mathematical skills such as calculation. It is still unclear how symbolic (e.g. Arabic digits) and nonsymbolic (e.g. Dots) magnitude systems develop and how the two formats relate to one another. Some theories propose that children learn the meaning of symbolic numbers by scaffolding them onto a pre-existing nonsymbolic system (Approximate Number System). Others suggest that symbolic and nonsymbolic magnitudes have distinct and non-overlapping representations. In the present study, we examine the developmental trajectories of symbolic and nonsymbolic magnitude processing skills and how they relate to each other in the first year of formal schooling when children are becoming more fluent with symbolic numbers. Thirty Grade 1 children completed symbolic and nonsymbolic magnitude processing tasks at three time points in Grade 1. We found that symbolic and nonsymbolic magnitude processing skills had distinct developmental trajectories, where symbolic magnitude processing was characterized by greater gains than nonsymbolic skills over the one-year period in Grade 1. We further found that the development of the two formats only related to one another in the first half of the school year where symbolic magnitude processing skills influenced later nonsymbolic skills. These findings indicate that symbolic and nonsymbolic abilities have different developmental trajectories and that the development of symbolic abilities is not strongly linked to nonsymbolic representations by Grade 1. These findings also suggest that the relationship between symbolic and nonsymbolic processing is not as unidirectional as previously thought.
This chapter discusses the close connection between numbers and space. First, it demonstrates the automaticity of numerical-spatial interactions via the spatial numerical association of response codes (SNARC) effect. It then reviews recent behavioral, patient, and transcranial magnetic stimulation (TMS) studies that suggest that numerical manipulations are dependent upon intact spatial representations. Studies that support the role of the parietal cortex in number processing are also examined.
There are many continuous quantitative dimensions in the physical world. Philosophical, psychological, and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time and mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, and density) and number can be conceptualized discretely or continuously (i.e., natural vs real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability, and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions. For further resources related to this article, please visit the WIREs website.
The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In this article we discuss what we mean by mental rotation, why it is important, and how it can be developed with young children in classrooms. We feature results from one team of teacher-researchers in Canada engaged in Lesson Study to develop enhanced theoretical understandings as well as practical applications in a geometry program that incorporates 2D and 3D mental rotations. Children in the Lesson Study classrooms (ages 4–8 years) demonstrated large gains in their mental rotation skills during 4 months of Lesson Study intervention in the Math for Young Children research program. The results of this study suggest that young children from a wide range of ability levels can engage in, and benefit from, classroom-based mental rotation activities. The study contributes to bridging a gap between cognitive science and mathematics education literature.
Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children. © 2009 by the National Academy of Sciences. All rights reserved.