Early Mathematics Education Research Articles

日本の就学前算数教育のあり方の検討 ― ドイツの『数の本』シリーズの関連性が示唆するもの ―

日本の就学前算数教育のあり方の検討 ― ドイツの『数の本』シリーズの関連性が示唆するもの ―

Exploring the utility of assessing early mathematics intervention response via embedded assessment.

The provision of high-quality early mathematics instruction and intervention is critical to ensure that all students are on track for academic success. Given this, identifying and utilizing assessments that can enable the detection of nonresponse to mathematics instruction is a critical aspect of early intervention. To this end, the current study explored the extent to which there were distinct patterns of performance on embedded assessments for intervention participants within the context of a large-scale randomized control trial of the ROOTS intervention. This study also examined how performance on embedded assessments was associated with pretest mathematics scores and residual gains on mathematics measures, and how those associations differed based on (a) the point in the intervention when students demonstrated difficulty, and (b) intervention intensity. Findings from this study suggest that participants fell into 4 distinct performance categories and performance classifications were associated with pretest measures and gains in mathematics achievement. Study results also highlight the potential relevance of instructional intensity and timely monitoring of student performance. Implications for intervention and instructional planning in the context of tiered instructional delivery models are discussed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Early Mathematics Teaching Profiles

Responding to the scarcity of research on early mathematics teaching profiles, this article reports on
 a novel assessment approach to identifying characteristics of early mathematics teaching occurring
 in early childhood settings. The new approach uses the interplay between teachers’ content
 knowledge in mathematics, knowledge of students and learning, and knowledge of how to teach
 mathematics effectively during the course of early mathematics as a proxy to identify quality of
 mathematics instruction provided. In this study, 210 pre -kindergarten to 3rd grade teachers in a
 large public school system in the Midwest were observed as they taught mathematics. The
 descriptive results revealed that the quality of mathematics instruction varies considerably among
 early childhood teachers. Some teachers are identified as delivering high quality mathematics
 instruction because they provide students with opportunities to fully and purposefully engage in
 deepening their understanding of important mathematics concepts, whereas others are rated as far
 lower in quality, because their mathematics teaching is procedural in terms of content emphasized
 and instructional strategies used. As a whole, observed quality of mathematics teaching was
 revealed to be mediocre. Implications of results for early math professional development are
 discussed. 

Children';s Geometric Understanding through Digital Activities: The Case of Basic Geometric Shapes

Early mathematics education bases a foundation of academic success in mathematics for higher grades. Studies show that introducing mathematical contents in preschool level is a strong predictor of success in mathematics for children during their progress in other school levels. Digital technologies can support children’s learning mathematical concepts by means of the exploration and the manipulation of concrete representations. Therefore, digital activities provide opportunities for children to engage with experimental mathematics. In this study, the effects of digital learning tools on learning about geometric shapes in early childhood education were investigated. Hence, this study aimed to investigate children progresses on digital learning activities in terms of recognition and discrimination of basic geometric shapes. Participants of the study were six children from a kindergarten in Kırşehir, Turkey. Six digital learning activities were engaged by children with tablets about four weeks in learning settings. Task-based interview sessions were handled in this study. Results of this study show that these series of activities helped children to achieve higher cognitive levels. They improved their understanding through digital activities.

Individualized Instructional Delivery Options: Adapting Technology-Based Interventions for Students With Attention Difficulties

Students who demonstrate mathematics difficulties (MDs) in the early grades are at risk of poor educational outcomes. Fortunately, strategic early mathematics intervention programs can improve academic outcomes for students with MDs, and instructional technology has demonstrated promise in delivering targeted and individualized mathematics instruction. However, it is unclear whether instructional technology is effective for all students, and there is a dearth of research on adaptations to technology-based interventions for students with difficulties attending to instruction. To this end, the current study investigated functional relations between the use of targeted instructional cueing and self-regulation support features in an iPad-based mathematics program and improved response accuracy for kindergarten students. Results presented here suggest a functional relation between the provision of instructional cueing and self-regulation support features and improved response accuracy for students who participated in an iPad-based mathematics intervention program. Implications for early mathematics instruction and technology-based intervention development are discussed.

MathemAntics: a model for computer-based mathematics education for young children / MathemAntics: un modelo de enseñanza de matemáticas asistida por ordenador para niños

Computer-based early mathematics education, especially when implemented on a touchscreen device, can help young children learn basic concepts of number and operations in deep and engaging ways. We have developed MathemAntics — antic or playful mathematics — a software system that works on touchscreen tablets, to serve as a key aspect of mathematics instruction for children from age three to the early grades. This paper discusses the need for such software; describes and analyses currently available software; articulates the theoretical and design principles that form the basis of MathemAntics and can serve as the foundation for new software; presents a case study of a child using MathemAntics; and describes potential use of MathemAntics in a classroom setting. We invite readers to explore, investigate and use MathemAntics themselves.

A comparative study of variations in arithmetic fluency between Norwegian and Finnish third graders

ABSTRACTThe study aimed to investigate variations in addition and subtraction fluency by observing grade three students in Norway (n = 253, Mage = 8.38 y.) and Finland (n = 209, Mage = 9.35 y.) while controlling for their age and non-verbal reasoning. Gender differences were also examined. The focus of the study was on the performance of the low-achieving (LA) students in comparison to the typically achieving (TA) group, not neglecting differences in how early educational support was organised across the two countries. Two-minute speed tests in both addition and subtraction within the 1–20 number range were used to assess fluency. The Finnish students outperformed students in the Norwegian sample both in addition and subtraction fluency. There were more Norwegian students in the LA group (i.e. performance at or below the 25th percentile) in both addition (37.9% vs. 20.1%) and subtraction (39.1% vs. 15.8%). In comparison to the TA students, the LA students made more errors and skipped over more arithmetic tasks in an attempt to solve them. Observed differences are discussed in relation to both country characteristics concerning early mathematics education and early educational support.

Application of mathematical and machine learning techniques to analyse eye-tracking data enabling better understanding of children’s visual-cognitive behaviours

In this research, we aimed to investigate the visual-cognitive behaviours of a sample of 106 children in Year 3 (8.8 ± 0.3 years) while completing a mathematics bar-graph task. Eye movements were recorded while children completed the task and the patterns of eye movements explored using machine learning approaches. Two different techniques of machine-learning were used (Bayesian and K-Means) to obtain separate model sequences or average scan-paths for those children who responded either correctly and incorrectly to the graph task. Application of these machine-learning approaches indicated distinct differences in the resulting scan-paths for children who completed the graph task correctly or incorrectly: children who responded correctly accessed information that was mostly categorised as critical, whereas children responding incorrectly did not. There was also evidence that the children who were correct accessed the graph information in a different, more logical order, compared to the children who were incorrect. The visual behaviours aligned with different aspects of graph comprehension, such as initial understanding and orienting to the graph, and later interpretation and use of relevant information on the graph. The findings are discussed in terms of the implications for early mathematics teaching and learning, particularly in the development of graph comprehension, as well as the application of machine learning techniques to investigations of other visual-cognitive behaviours.

English

Pattern activities have a crucial role in supporting early academic and language skills related to cognitive development, as they play a key role in understanding mathematical ideas and relationships, and in understanding the order, logic and concepts of mathematics. From this point of view, the research was conducted to investigate the effect of the Pattern-based Mathematics Education Program on the early academic and language skills of 61-72-month- old preschoolers. Quasi-experimental design with pretest-posttest control group was used in the study. Forty children, 20 for the experiment and 20 for the control group, constituted the sample. In the experimental and control groups, there were 61-72-month-old children who had not received any special mathematics education and were showing normal developmental characteristics; while attending one of the pre-school education centers in two different campuses of a public university in Besiktas and Esenler districts in the city of Istanbul, Turkey. In the study, General Information Form and Kaufman Survey of Early Academic and Language Skills” were used as data collection tools. A total of eight weeks 'Pattern-based Mathematics Education Program' was applied to the children in the experimental group, five days a week. Kaufman Survey of Early Academic and Language Skills was administered as pre-test and post-test to the experimental and control groups. The same test was given to the experimental group as retention test three weeks after the post-test. In this study, which was limited to the activities presented in the Pattern-based Mathematics Education Program, it was determined that the Pattern-based Mathematics Education Program was effective in supporting the early academic and language skills of 61-72 month old preschoolers.   Key words: Pattern skills, early academic and language skills, early mathematics education, early childhood education.

Early childhood Teacher’s Perception and Current Status on Early Childhood Storytelling Mathematics Education

Early childhood Teacher’s Perception and Current Status on Early Childhood Storytelling Mathematics Education

Multiple pathways between affect and mathematical competence in young children—commentary on the studies in the Special Issue

Affect and mathematical competence are each multifaceted constructs. Accordingly, the studies in this Special Issue address multiple pathways between the two in young children. This commentary highlights the variability of these pathways and asks how affective variables are specifically related to core mathematical activities such as problem solving. One conclusion is that affective and cognitive variables seem to be related already in young children, but that there is also considerable variation in this relationship. Future studies should address inter-individual differences and use more content-specific measures of affect, to identify factors that cause early negative affect that is specific to mathematics. The studies further suggest that among the sources of children’s negative affect towards mathematics are the abstract nature of mathematics as well as the view of mathematics that young children experience in their classrooms. Creating fearless learning environments that allow for failure, and that enable children to make early experiences of success, is an important challenge for early mathematics education.

Critical Science and Mathematics Early Childhood Education: Theorizing Reggio, Play, and Critical Pedagogy into an Actionable Cycle

Young American children in today’s public schools live in a world in which tensions around about identity (i.e., ethnicity and race, gender continuums, language backgrounds and proficiencies, cultural values and beliefs, economic resources, schooled experiences, literacy, and im/migration history) are part of everyday conversation. However, many early childhood science and mathematics educators are reticent to engage deeply in dialogue around these identities, not only due to a common narrative where science and mathematics are interpreted as culturally-neutral, but also because few models within early childhood science and mathematics education exist on how to engage in these conversations. Given this, we ask, how can we prepare and support teachers in developing a positive awareness of culture, identity, diversity, and other critical tensions faced by our youngest learners? How can we prepare and support teachers in engaging in these critical conversations as connected to science and mathematics with young children?

Fostering Inquiry and Creativity in Early Years STEM Education: Policy Recommendations from the <i>Creative Little Scientists</i> Project

Creative Little Scientists was a 30-month (2011-2014) EU/FP7-funded research project focusing on the synergies between early years science and mathematics education and the development of children’s creativity, in response to increasing interest in these areas in European educational policy. Using a variety of methods, including desk research, a teacher survey and classroom-based fieldwork, the research provided insights into whether and how children’s creativity is fostered and appropriate learning outcomes, including children’s interest, emerge. Based on these and ongoing collaboration and dialogue with participants and other stakeholders the project proposed recommendations for policy and teacher education. This paper presents these recommendations and the research on which they were based. Throughout the study, mixed methods were employed, combining quantitative approaches used in surveys of policy and teachers’ views based on a list of factors, alongside qualitative approaches employed in case studies of classroom practice. A strong conceptual framework developed at the start of the project guided data collection and analysis, as well as the presentation of findings and the development of policy recommendations, thus ensuring the latter’s strong and consistent relationship with the relevant theoretical knowledge, the comparative research, analysis of classroom practices and the production of guidelines for teacher education.

Stability and instability in the co-development of mathematics, executive function skills, and visual-motor integration from prekindergarten to first grade

Correlational and short-term longitudinal studies both demonstrate significant associations between children’s executive function skills and visual-motor integration and their mathematics achievement in early childhood. Our current understanding of the development of these skills in early childhood is limited, however, by a lack of clarity concerning whether the associations between them are causal in nature or could be explained by other unmeasured stable characteristics shared among the constructs. Using a latent state-trait approach, we examined the development of executive function skills, visual-motor integration, and children’s mathematics achievement from the beginning of prekindergarten to the end of first grade (N = 1138). Findings of stability and instability in relative rankings in children’s skills across four time points suggest that children’s growth in mathematics skills is a product of both persistent unmeasured stable influences and time-specific effects of prior executive function skills and visual-motor integration. Specifically, visual-motor integration related to subsequent mathematics achievement and executive function skills in prekindergarten, and executive function and mathematics achievement were bidirectionally related through first grade, even when accounting for stability in each construct. These results suggest that future experimental research should consider executive function skills and visual-motor integration as well as specific mathematics skills as potential targets for early mathematics instruction.

Ecuadorian kindergartners’ numerical development: contribution of SES, quality of early mathematics education, and school type

Abstract This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numeracy test at both the start and the end of the Kindergarten year. In all classrooms, the quality of early mathematics education was assessed twice via the COEMET instrument. Results first showed rather low scores on the early numeracy test, with only 50% (at the start) up to 70% (at the end) of the items solved correctly, along with large inter-individual differences in these scores. Second, the quality of early mathematics education in the participating classrooms was also rather low. Third, children’s early numerical abilities at Kindergarten entry, SES, and school type predicted children’s early numerical abilities at the end of the school year. The quality of early mathematics education did not contribute to children’s numerical development. We critically discuss our findings in view of optimizing the quality of Ecuadorian early mathematics education as a stepping stone towards enhanced numerical development.

Understanding children’s reasoning in multiplication problem-solving

ABSTRACTThis article investigates two children’s intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given the same problems. The findings reveal a variety of intuitive thinking in solving the multiplication problems through addition beyond direct modeling and counting strategies. The authors also discussed how different educational backgrounds in early elementary mathematics education may affect children’s intuitive ideas and reasoning in solving multiplication problems. The study implies the importance of understanding children’s intuitive ideas of multiplication and highlights potential opportunities for developing children’s understanding of multiplicative thinking and algebraic thinking in earlier stages of arithmetic learning.

Enhancing and analyzing kindergarten teachers’ professional knowledge for early mathematics education

While early childhood mathematics education did not play an important role for many years, today the necessity to be attentive to children’s early mathematics learning is no longer in doubt. There is a broad consensus that mathematical learning in kindergarten is more informal than learning in school. To guarantee coherent mathematical learning in kindergarten, pre- and in-service education of kindergarten teachers in mathematics education is becoming more important. Therefore, a sound theoretical foundation and examination of professional knowledge to realize early mathematics education are necessary. We present a theoretically and empirically founded domain-specific model of kindergarten teachers’ professional knowledge. It serves as a framework to plan and realize professional development programs – as an example shows. A qualitative study – worked out in the German context – indicates that this structure can help to analyze kindergarten teachers’ professional knowledge. We indicate how our findings and interpretations connect to issues shared across national contexts.

Problem Solving in Early Mathematics Teaching—A Way to Promote Creativity?

This article presents results from a design research study where 145 six-year-old were taught mathematics through problem solving. In the article, the implementation of the first problem solving task within the study—“the tower task”—is explored together with interviews focusing on the children’s perceptions of the task as well as of problem solving in general. The results indicate that the children experienced the task as fun and accessible even though very few of them could solve it with ease. Further, the children seemed to make use of and develop their creativity by working on the problem-solving task. In the article, possibilities and limitations whit implementing problem solving in early mathematics education are discussed.

The Effect of Preschool Mathematics Education in Development of Geometry Concepts in Children

Given the fact that early mathematics education is important for further learning of mathematics, authors of this paper examine the effects that preschool mathematics education on development of geometry concepts in children. On a sample of 290 children, through a one-on-one interview, we studied the development of geometry concepts in children at the end of preschool education in Serbia. Research results show that the preschool mathematics education achieves significant effects developing geometry concepts in children. Preschool mathematics education does not achieve equal effects on the development of all geometry concepts covered by the curriculum of preschool education, that there are no differences in the development of these concepts depending on the location of the preparatory preschool institution and the gender of the child, but that the education level of the child’s parents has great impact on the development of these concepts.

Early Number Skills Gains and Mathematics Achievement: Intervening to Establish Successful Early Mathematics Trajectories

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for mathematics difficulties in a kindergarten intervention study. Results indicated strong relationships between formal number skills gains and mathematics achievement across kindergarten and Grade 1. Intervention participants demonstrated larger informal and formal early number skills gains compared with their control peers, and relations between early number skills gains and first-grade mathematics achievement were moderated by intervention participation. Importantly, these findings suggest that formal and informal number skills gains may be critical components of later mathematics achievement for at-risk students. Implications for special education and intervention in tiered instructional systems are discussed.