Children's Mathematical Learning Research Articles

An Investigation of Teachers’ Perception on Parental Involvement in Teaching and Learning Mathematics

Parental involvement is the foundation stone of academic success. When parents interact with teachers and with their children to encourage mathematics learning, it builds a positive relationship that leads to better teaching and learning. Previous studies indicated that parental involvement affects learners' achievement. However, less is known about the effects of teacher perceptions of parental involvement on learners' mathematics achievement in primary school. The critical problem to be explored is teachers' perceptions toward parental involvement in learning mathematics. This paper investigates teachers' perceptions of parental involvement in teaching and learning mathematics. This study was guided by the following main question: What are teachers' perceptions of parental involvement in teaching and learning mathematics? The study used a qualitative exploratory case study design. Purposive convenience sampling is used to select research participants. Participants in the study are 18 Junior Primary teachers in Windhoek, Khomas Region-Namibia. Questionnaires and semi-structured interviews were administered to eighteen (18) teachers from selected schools located in Windhoek to explore teachers' perceptions of parental involvement in teaching and learning mathematics. The study's findings revealed that lack of parental support is one factor affecting the learners' achievement in mathematics, and the teachers need training on effectively involving the parents in learning mathematics. The anticipated contribution of the study is to motivate teachers and parents to collaborate in developing appropriate mathematical knowledge in children to understand mathematics concepts, to apply them in solving everyday problems and to encourage parents to support their children's mathematics learning, to equip parents with the necessary resources and skills for mathematics should we be faced with another disruption like the Covid-19 pandemic or exist in the future and for them to develop appropriate mathematical knowledge.

Cognitive Foundations of Early Mathematics: Investigating the Unique Contributions of Numerical, Executive Function, and Spatial Skills.

There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathways. The present study tests this hypothesis. One-hundred and eighty 4- to 9-year-olds (Mage = 6.21) completed a battery of numerical, EF, spatial, and mathematics measures. Factor analyses revealed strong, but separable, relations between children's numerical, EF, and spatial skills. Moreover, the three-factor model (i.e., modelling numerical, EF, and spatial skills as separate latent variables) fit the data better than a general intelligence (g-factor) model. While EF skills were the only unique predictor of number line performance, spatial skills were the only unique predictor of arithmetic (addition) performance. Additionally, spatial skills were related to the use of more advanced addition strategies (e.g., composition/decomposition and retrieval), which in turn were related to children's overall arithmetic performance. That is, children's strategy use fully mediated the relation between spatial skills and arithmetic performance. Taken together, these findings provide new insights into the cognitive foundations of early mathematics, with implications for assessment and instruction moving forward.

Pengaruh Pendekatan Permainan dalam Kartu Pinmat Math Hero terhadap Pemahaman Matematika di Tingkat Sekolah Dasar

This qualitative research investigates the use of the Math Hero Flashcards in elementary school children's mathematics education. Math Hero Flashcards are specially designed learning tools aimed at enhancing mathematical understanding, accuracy, and mastery of arithmetic operations for numbers 1-10 through interactive games. The study involves direct observation, interviews, and interactive play with children with the aim of understanding the effects of Math Hero Flashcards on children's mathematical understanding, learning motivation, and interest. The results of the research indicate that the use of Math Hero Flashcards enhances elementary school children's mathematical understanding, fosters motivation for learning, and creates a more enjoyable learning experience. However, some interview participants mentioned that they had found alternatives in the form of math game apps on their phones. Therefore, this research underscores the need for integration between physical learning tools like Math Hero Flashcards and learning technology to achieve holistic and engaging mathematics education for children.

A cultural-historical study of how a conceptual playworld creates conditions for personally meaningful mathematics in the Chinese kindergarten context

ABSTRACT Previous studies have emphasised that play can promote children’s learning of mathematics. However, little research has been directed towards understanding how collective imaginary play motivates children's mathematical learning. Informed by the cultural-historical conception of play and motives, this paper examines how Conceptual PlayWorld (CPW) creates conditions for Chinese children's meaningful mathematical learning using the concept of repeating patterns as an example. Video observations of teachers interacting with children (4–5 years) during the CPW implementation (8.54 h), as well as children's interviews (5.75 h), were gathered and analysed. Following the focus child Zeng's motives and intentions but all children's experiences in the CPW, the findings show CPW appears to create mathematical conditions that promote thinking, imagining and play. Zeng's motives for mathematical learning are stimulated by his play motives which are amplified through his active participation and problem-solving in a CPW, and this creates conditions for his personally meaningful learning of mathematics in the Chinese kindergarten context.

Parents' experiences of mathematics learning at home during the COVID-19 pandemic: a typology of parental engagement in mathematics education.

The COVID pandemic disrupted the schooling of students worldwide resulting in many having had a period of at-home learning. Many parents found themselves assuming responsibility for supporting their children's at-home learning. Parents often find it difficult to support their children's mathematicslearning compared with other curriculum areas. There has been limited research exploring parental engagement in mathematics education generally, and little into parental engagement in mathematics education during the COVID pandemic. This paper examines how parents supported their child's mathematics education during the school closures and identifies the factors that impacted this engagement. The Ecologies of Parental Engagement (EPE) model was used to help describe the engagement of different parents in mathematics education during the school closures and to examine the way the home space and available capital shaped parental engagement. Eight parents were selected from a larger Australian study that explored the impact of the pandemic-induced period of at-home schooling on primary school mathematics and science. One-on-one narrative interviews were conducted online with participants. Analysis identified three categories of parental engagement: monitors, facilitators, and enhancers. Parents in each category responded to their role in at-home learning differently, and accessed and activated different capital to support their child's at-home learning in mathematics during the pandemic. Results highlight the value of emotional capital, as well as knowledge of mathematics and mathematics education, with implications for schools hoping to engage parents in mathematics learning. The study offers a typology to be explored in future research concerning parental engagement in mathematics education.

Spatial configuration of hundreds charts influences children's knowledge of base‐ten concepts

AbstractThe hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base‐ten concepts. Kindergarten and first‐grade students were assigned to three instructional conditions in which they worked with a researcher to solve arithmetic word problems. The charts used in the conditions differed by the spatial configuration of the numbers: (a) top down, with numbers increasing from top to bottom; (b) bottom up, with increases from bottom to top; and (c) explicit bottom‐up, with a bottom‐up chart and an explicit visual cue that prompted a comparison between the “up‐is‐more” structure to a cylinder filling with water. Participants were more likely to count by tens than by ones to solve problems when the numbers in the chart increased from top to bottom than when they increased from bottom to top. No effects of spatial configuration on place‐value knowledge was observed. One account of the findings is that participants were more accustomed to the movements in the top‐down chart because they matched the direction in which children learn to read. The role of spatial affordances of instructional materials in children's mathematics learning is discussed.

Mimicking tracing actions enhances young children's mathematical learning

AbstractLearning mathematical concepts and procedures typically requires extended cognitive effort, presenting a challenge for many children. People can make tracing actions with the index finger, as well as mimic another's movements, with little or no conscious effort. From the perspective of cognitive load theory, such biologically primary actions may facilitate learning biologically secondary concepts and skills requiring extensive cognitive effort, such as mathematics. The present study investigated effects on learning processes and outcomes of students mimicking a teacher's tracing actions from the perspective of an evolutionarily informed cognitive load theory. One hundred and thirteen Grade Two children learned about number lines, either observing a teacher tracing out elements of worked examples with her index finger, or mimicking the teacher's tracing actions with their own index finger. In accord with hypotheses, results indicated enhanced performance due to mimicking on cognitive load, motivation, and post‐test performance. Directions for future research are discussed.

Translanguaging, multilingualism, and multimodality in young children's mathematics learning

The purpose of this qualitative research study is to portray the complex language practices of multilingual children when learning mathematics. To do so, I draw on data collected as part of a three-year research study that was designed to understand the relationship between young children's language use and mathematics learning, focusing on students’ work as well as interactions collected through research journal entries and audio recordings. I center the practice of thick description as a path to advance disruptive understanding of multimodal representations of children's language use while learning mathematics. I then consider the necessary movement from a preconceived understanding of language to enacting an understanding of language that is responsive to the experiences and diverse language practices of children. I argue that a disruptive understanding and enactment of language can foster meaningful mathematics learning by dismantling hierarchical power structures.

The benefits of a metacognitive lesson on children's understanding of mathematical equivalence, arithmetic, and place value.

Metacognition is theorized to play a central role in children's mathematics learning. The primary goal of the current study was to provide experimental evidence in support of this role with elementary school students learning about mathematical equivalence. The final sample included 135 children (59 first-graders and 76 second-graders) who participated in the study across three sessions in their classrooms. They completed a pretest during session one, a lesson and posttest during session two, and a two-week delayed retention test during session three. For session two, children were randomly assigned to receive a lesson on mathematical equivalence with or without integrated metacognitive questions. Relative to the control lesson, children who received the metacognitive lesson demonstrated higher accuracy and higher metacognitive monitoring scores on the posttest and retention test. Further, these benefits sometimes extended to uninstructed items targeting arithmetic and place value. No condition effects were observed for children's metacognitive control skills within any of the topics. These findings suggest a brief metacognitive lesson can improve children's mathematics understanding.

Contextual influences on children's mathematical understandings

In order to maximise children's mathematical learning opportunities in school, we need to take account of what they have already learned about mathematics in their out-of-school contexts. Children's representations provide one such mechanism for gaining insight into their everyday mathematical experiences and understandings. This study utilises an ecological theoretical framework to examine the ways in which children's everyday experiences in a range of contexts influence their early mathematical understandings. Data is presented from a study of 100 four to six-year-old Australian children as they entered and experienced their first year of primary school. Throughout the study, the children completed a series of drawing tasks related to different mathematical concepts, and were invited to provide either verbal or written narratives to accompany their drawings. These data were analysed using an ecological theoretical framework in order to explore the individual components of each context, as well as the relationships between these contexts. Findings demonstrate that children come to school with rich understandings of mathematics which have been shaped by their experiences in a range of contexts. The activities and relationships within children's home settings appear to be the most profound in terms of developing mathematical understandings, with very few children representing mathematics learning within a school context.

A video-based approach to investigating intentional teaching of mathematics in Chinese kindergartens

This video-based study investigates the extent to which Chinese teachers intentionally teach mathematics knowledge to kindergarten children. Evidence revealed that intentional teaching with the key practice of sustained shared thinking occurred more in group activities than in learning centers; however, there was insufficient intentional teaching in both learning contexts. Counting/calculation was the mostly taught mathematics knowledge in the kindergartens, followed with shapes, comparing, measurement, and space/position. These findings show how the everyday curricular practices experienced by children afford evidence of their acquisition of mathematics knowledge. This study also informs how intentional teaching can be productive in facilitating children's mathematics learning.

Above, below, or equal? Exploring teachers’ pedagogical positioning in a playworld context to teach mathematical concepts to preschool children

This research forms part of a larger study to investigate how early childhood teachers can use “Mathematical Playworld” to shift their pedagogical positions to improve children's mathematical learning. We analysed video-recordings of an imaginative play scenario involving two teachers and 11 children in an early learning centre. We found that early childhood teachers could use a Mathematical Playworld model to allow them inside children's play and align their learning intentions with children's imaginative play actions. This study frames how early childhood teachers can create the conditions for intentional mathematical teaching opportunities within play-based contexts by dynamically shifting their pedagogical positions.

Konzeptualisierung und Messung der Qualität der adaptiven Lernunterstützung in Lernsituationen mit mathematischen Regelspielen im Kindergarten. Eine Studie in Deutschland und der Schweiz

ZusammenfassungDie Qualität der adaptiven Lernunterstützung ist wichtig für die Förderung des mathematischen Lernens von Kindergartenkindern. Entsprechend bedarf es geeigneter Instrumente zur Bewertung der Planung, Durchführung und Reflexion von mathematischen Lernangeboten im Kindergarten. Bestehende Instrumente berücksichtigen vor allem die mikro-adaptive (mathematische) Lernunterstützung, die den Fokus auf die Interaktion zwischen der Fachkraft und den Kindern legt. Die Qualität der makro-adaptiven (mathematischen) Lernunterstützung (Planung und Reflexion von Lernsituationen) wurde im Kindergarten bis jetzt noch nicht umfassend untersucht. Sie gewinnt jedoch im Hinblick auf die zunehmende Bedeutung von Bildungsplänen im Kindergarten und der damit verbundenen Förderung von fachbezogenen Kompetenzen an Bedeutung.Im Artikel wird erstens die Qualität von (mathematischer) Lernunterstützung in Regelspielsituationen im Kindergarten konzeptualisiert. Dabei wird die Qualität der makro-adaptiven von der mikro-adaptiven Lernunterstützung unterschieden. Letztere wird getrennt in fachunabhängige Unterstützungsqualität (Gruppenmanagement, emotionale Wärme) und in instruktionale, mathematikbezogene Unterstützungsqualität (Lernanregung, Verwendung Fachsprache). Zweitens wird ein Messinstrument (Rating) zur Analyse der Qualität der Lernunterstützung in mathematischen Lernsituationen vorgestellt. Dieses wurde zur Analyse von videografierten Regelspielsituationen und anschließenden Leitfadeninterviews von 145 pädagogischen Fachkräften aus Deutschland und der Schweiz eingesetzt. Pro Fachkraft standen zwei Videosequenzen und zwei Interviews zur Verfügung. Auf der Basis dieser Daten wird das Messinstrument hinsichtlich verschiedener Gütekriterien sowie des Einflusses der Ausbildung der Fachkräfte (akademisch, nicht akademisch) und des Bildungskontextes (Deutschland, Schweiz) analysiert. Die theoretisch angenommene Unterscheidung von Gruppenmanagement, emotionaler Wärme und instruktionaler Unterstützungsqualität lässt sich durch eine konfirmatorische Faktorenanalyse stützen. Die Ergebnisse bestätigen die Bedeutung des Einbezugs von Planung und Reflexion als Dimensionen von adaptiver Lernunterstützungsqualität.

Linking Chinese mothers’ and fathers’ scaffolding with children's initiative and mathematics performance: a moderated mediation model

Many studies have shown a positive link between mothers’ scaffolding and children's mathematics performance. However, the mechanism driving the link, and whether mothers’ and fathers’ scaffoldings relate to children's mathematics performance similarly or differentially are currently not well understood. This study examined whether child initiative mediated the association between parental scaffolding and children's mathematics performance, and whether the co-parent's scaffolding moderated the mediating effect of child initiative on the associations. Participants were 96 two-parent Chinese families with children aged 5–6 years (47 girls). All children completed 2 math-related activities with their mothers and fathers, separately. Mother-child and father-child interactions in math-related activities were videotaped. Parental scaffolding was coded from the aspects of parents' cognitive, emotional, and autonomy support. Occurrences of children's self-starting, metacognition, or persistent behaviors were coded as children's initiative. Children's mathematics performance was assessed individually with the Test of Early Mathematics Ability–Third Edition (TEMA-3). Results showed that children's initiative only mediated the relationship between fathers’ scaffolding and children's mathematics performance. Mothers’ scaffolding was found to be a moderator in the relationship between fathers’ scaffolding and children's initiative in father-child interactions. This suggests that high levels of maternal scaffolding function as a facilitator, improving the positive link between paternal scaffolding and children's initiative, which in turn contributes to children's mastery of mathematics. These results highlight the important roles of both parents’ scaffoldings and child initiative in children's mathematics learning.

The Affective Being of Multilingual Children’s Language Use for Mathematics Learning

This article investigates how young multilingual children's mathematics learning is connected to their language use, lived experiences, contexts, and emotions. To this end, we consider the experiences of children who used both Spanish and English to learn mathematics. We center on two instances of kindergarten children counting and use Systemic Functional Linguistics (SFL) as our theoretical framework to reflect on how words become meaningful in multiple ways as a result of context, particularly when used in more than one language. From this perspective, we pose that children's language use is affective and made meaningful through social relationships. We consider how the understandings of multilayered meanings uncovered using an SFL lens affords a substantial path to interpret and think about the language use of multilingual children during mathematics learning. We argue that careful attention to and interpretation of children's language can help counteract pervasive ideas of neutrality in education.

Parental Involvement in Children's Mathematics Learning Before and During the Period of the COVID-19

The pandemic of coronavirus disease 2019 (COVID-19) has led to sudden and unexpected circumstances in education for all the involved people (pupils, teachers, education policymakers, parents). International organizations have paid attention to their responses in crises by using alternative modes of teaching. The typical teaching methods had to be replaced by e-learning processes and all the participants needed to adjust themselves and adapt innovative methods. Most studies concentrated on teachers' and students' difficulties, barriers and new challenges. However, a different role was given to parents as well, especially in the case of primary and the first grades of secondary education, as they were asked to facilitate their children to use the e-learning processes and support them during the learning process. The present study examined the change of parental involvement during the pandemic in comparison to the previous situation in the case of mathematical subject. A questionnaire was constructed and administered to parents from Cyprus at the first days of the school year 2019-2020 in order to examine their beliefs and self-efficacy beliefs about their parental role and involvement during homework at their children's mathematical understanding and the development of their children's perseverance strategies during mathematical problem solving. The same questionnaire was administered to them at the end of the e-learning teaching processes in May 2020, after they had alternative experiences in order to identify any differences at their respective beliefs. Only the sample of parents who took part at both phases of the study was used for the comparative analyses. Results indicated that parents, especially in primary education, had the willingness to support their children's learning under the different teaching and learning processes; however they needed training in order to develop appropriate knowledge, relevant experiences, positive beliefs and self-efficacy beliefs.

Manifestations of Mathematics within the Power Dynamics in a Pre-K Classroom

Background/Context Young children's engagement with mathematics is occurring in a context in which school transition and readiness concerns that invoke increased institutional rules and disciplinary practices involving power dynamics are coming into play. These trends made us curious to undertake an in-depth investigation of the different ways children and their teachers engage in mathematics in preschool classrooms today. Purpose/Focus of Study In our video-ethnography study we explored the ways mathematics manifested itself in a Pre-K setting and how mathematics functioned in different ways throughout the school day. The question guiding our research was: Recognizing the context of current transition and readiness concerns in early childhood education, in what ways is mathematics manifested in the interactions of teachers and children in a Pre-K classroom? Setting The study took place in a childcare center, accredited by the National Association for the Education of Young Children, in the United States. Participants Participants in this study were four 4- to 5-year-old children and their teachers in an ethnically diverse classroom. Research Design The study drew on a video-ethnographic method through semester-long observations and video-recordings in a Pre-K classroom. The analysis began with (a) labeling manifestations of mathematics in the video data through open coding, proceeded to (b) the examination and the categorization of the various manifestations of mathematics, was followed by (c) the identification of the key scenes which best represented each category, and ended with (d) the multimodal analysis of the key scenes. Findings This research illustrated that formal mathematics teaching and learning contexts included the kinds of disciplinary and bodily control practices that have been evident in studies of children at the preschool level transitioning into school. The study demonstrated the ways that mathematics, with its authoritative and classificatory nature, became a disciplinary tool itself during the course of the day. Also evident were the ways in which all actors in the classroom drew on mathematics for problem-solving in real-life situations within a power/resistance dynamic. Conclusions/Recommendations This research raises questions of how disciplinary practices might limit children's mathematics learning. The finding that mathematics was implicated in the practices of power dynamics among teachers and children and among children opens up possibilities for teachers to recognize how mathematics is being used informally and creatively by children. Teachers can then use this knowledge to build on young children's identities as powerful and competent mathematicians, using mathematics in problem solving during day-to-day interactions.

Mapeamento sistemático das pesquisas realizadas nos programas de mestrado profissional que versam sobre a aprendizagem matemática na educação infantil

A proposta deste artigo é apresentar um panorama das dissertações, realizadas em programas de mestrado profissional, que versam sobre a aprendizagem matemática na Educação Infantil. A pesquisa é qualitativa e utiliza como procedimento inventariante o mapeamento sistemático, em que a preocupação central é a caracterização dos estudos e não a realização de análise e inferências de qualidade. O cenário da pesquisa foi constituído pelos trabalhos disponibilizados no catálogo de dissertações e teses da Capes, no recorte temporal de 2013 a 2018. A busca inicial ocorreu no mês de julho de 2019, e após a adoção dos critérios de exclusão e inclusão, totalizou-se em 84 trabalhos. Destes, após o processo de parametrização, com o estabelecimento de 11 descritores, restaram-se 12 estudos sobre a temática em tela. Após este processo, realizamos a leitura flutuante dos textos e o fichamento. Em alguns casos os trabalhos foram lidos na íntegra. As pesquisas foram categorizadas em três focos e seis subfocos temáticos. Os resultados apontam a relevância das pesquisas realizadas, pois apresentam contribuições efetivas para a aprendizagem matemática das crianças. Apesar disso, a maior parte dos trabalhos estão centrados na realização de metodologias diversificadas e alguns textos não destacam de forma evidenciada o produto educacional, critério essencial em programas stricto sensu profissional. Por fim, destacamos que a metodologia adotada não é rígida, podendo ser adaptada por outros pesquisadores, permitindo a obtenção diversificada de dados.

Entering Aladdin's cave: Developing an app for children with Down syndrome

AbstractTablets have much to offer children with learning difficulties, but evidence of their effectiveness to teach academic skills is limited and cannot be easily separated from the quality of the software. This paper analyses data from 3 iterative cycles of designing an app for children with Down syndrome to support their awareness of quantity through an inclusive game. Research with neurotypical children suggests that representation of quantity (or magnitude) is an area with considerable potential in supporting the foundations for children's mathematical learning. It has received little attention as an aspect for intervention for children with Down syndrome. Data collected in this study illustrate the need to carefully align the game mechanic to the target skills, strengthen levels of access, and introduce gradations of attentional demand. They also signal the interrelationship between children's cognitive and affective responses to the game, making it essential to find the optimal level of challenge. Children's strategies in response to mistakes indicate the importance of creating an agile responsive system. The data also suggest that developers routinely extend the number of features that are optional, enabling a greater level of personalization and a more inclusive game.

Mathematics at Your Fingertips: Testing a Finger Training Intervention to Improve Quantitative Skills

Previous research indicates that the use of fingers as representations of ordinal and cardinal number is an important part of young children's mathematics learning. Further to this, some studies have shown that a finger training intervention can improve young children's quantitative skills. In this article, we argue that fingers represent a means for children to bridge between different external representations of number (including verbal, symbolic and non-symbolic representations). Therefore we predicted that an intervention that combined finger training with experience playing games involving multiple representations would lead to greater increases in quantitative skills than either aspect of the intervention alone. One hundred and thirty-seven children aged between six and seven years old took part in an intervention study over the course of four weeks. The study tested the impact of five different conditions on participants' quantitative skills, their finger gnosis, and their ability to compare magnitudes of two non-symbolic representations of number. Relative to a control group, those children receiving a finger training intervention saw gains in finger gnosis skills (the ability to differentiate fingers when touched, without visual cues). Those children who played number games saw an increase in their non-symbolic magnitude comparison skills. However, only those children who experienced both aspects of the intervention saw increases in quantitative skills, which were assessed using an instrument informed by Gelman and Gallistel's (1978) five principles of counting. The findings show that a finger training intervention, when combined with intensive exposure to multiple representations of number, can support young children's development of quantitative skills. This adds to evidence in the literature regarding the role of fingers in children's mathematics learning, and may have implications for pedagogical approaches.