Development Of Number Concepts Research Articles

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as “motion along a path” and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

SOME IDEAS FOR DIGITAL SUPPORT OF STUDENTS’ ACTIONS IN PRESCHOOL AND FIRST-GRADE COUNTING

The use of digital support for preschool and fi rst-grade education is an urgent and disputable question. It is thus even more important to analyse the content of actions, which we expect students to acquire. In this case it is possible to assign the appropriate functions to the software. In our study we used Davydov’s analysis of the action of counting as a prerequisite for the wholesome Maths curriculum design. Our research aim is to study the psychological conditions for preschool and fi rst grade students to acquire and appropriately perform a possible procedure of counting, required for the number-concept formation. We exploit the context of adding or removing some tokens to the “hidden” amount, signed with the corresponding number - so that the students cannot count each object directly. We have devised the general comprehensive view of the necessary support for mediated “counting up” and “counting down” and the series of tasks, varied according to modifi - cations suggested in Galperin’s theory of planned step-by-step formation. We have conducted two cycles of experimental teaching (over  hours each,  participants in total,  years of age). The data collected (video-taped classroom discussions, students’ drawings, pre- and post-tests) showed signifi - cant progress and allowed us to consider our hypothesis on the content of students’ actions as a feasible perspective for future research. Moreover, the analysis of the action content, which will presumably provide children with a solid basis for number-concept development, defi nes particular requirements for the digital support design. The computer is to provide the place to work with suitable tokens and special modelling means, as well as the “unbiased” feedback on whether the calculated answers suffi ce, and the opportunity for teachers to vary task conditions as planned.

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence.

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the "Groupitizing" ability in 1209 third to eighth graders (mean age at first timepoint=10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d=3.29), is a central predictor of math achievement (beta weight=.30), is linked to conceptual processes in mathematics (minimum d=0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight=.11) in ways that explicit symbolic measures may miss.

Associations between early numeracy and mathematics-specific vocabulary

Background: Early numeracy development is supported by linguistic features such as mathematics-specific vocabulary. Researchers have established a link between the amount and quality of children’s exposure to mathematics-specific vocabulary and their numeracy learning. Studies have also shown that children from low socio-economic status are less exposed to mathematics-specific vocabulary and also tend to underperform on mathematics assessments. South African children consistently perform poorly on local and international mathematics assessments.Aim: To describe associations between numeracy and mathematics-specific vocabulary of the sample who participated in the study.Setting: Participants in this study are from Quintile 1 schools and receive social grants from the South African government.Method: 133 Grade 1 and 2 children completed assessments for (1) early numeracy (MARKO-D SA), (2) mathematics-specific vocabulary (MMLT) and (3) early reading (EGRA). Correlation analyses were conducted to investigate associations between variables and developmental continuity of number concept development and reading skills were described.Results: An association between numeracy and mathematics-specific vocabulary was found. The data confirm that number concepts and reading skills develop hierarchically. Although English-speaking children performed better on the numeracy assessment, isiZulu and Sesotho speakers performed better on the reading test.Conclusion: Mathematics-specific vocabulary is a key tool for early number concept development, also in isiZulu and Sesotho. Teachers’ pedagogical content knowledge (PCK) should include how number concept development intersects with mathematics-specific vocabulary. Explicit teaching of mathematics-specific vocabulary should be included in the Foundation Phase curriculum.

The intersect of early numeracy, vocabulary, executive functions and logical reasoning in Grade R

The current quantitative study, a naturalistic field experiment, was conducted in a public primary school in Soweto, Johannesburg, with the objective to examine how children’s achievement on four assessments at the beginning of Grade R, namely their numeracy, their mathematics-specific vocabulary, their executive functions, and their logical reasoning capabilities, predicted their performance on a numeracy assessment at the beginning of Grade 1. A purposive intact group of 59 participants was assessed at the beginning of their Grade R year and again when they entered Grade 1. The results of the study indicate that, apart from existing or prior numeracy knowledge at the beginning of Grade R, mathematics-specific vocabulary was the strongest predictor for numeracy attainment at the beginning of Grade 1. We suggest that early grade teachers consider young children’s number concept development as a cognitive, developmental psychology phenomenon and that they help learners build a lexicon of mathematics-specific qualifiers in their teaching with words that represent concepts of, among others, space, position, comparison, inclusion, sequence and magnitude.

Children’s development of an understanding of number: A model for Grade R teachers

Background: Teachers teach mathematics by focusing on procedural knowledge (what steps to follow when doing mathematics) and pay scant attention to the conceptual understanding that underlies these procedures such as double-digit addition or subtraction and overall additive and multiplicative relations. They teach concepts in a haphazard way instead of looking at them from a convergent perspective of concepts that a child builds, one after the other.Aim: This study explores what Grade R teachers know about young children’s specific developmental numerical cognition and if they infuse their understanding of number concept development in their pedagogy.Setting: Samples of 15 female Grade R teachers were purposefully selected from five schools in what was previously a racially segregated living area in South Africa.Methods: This research design is a descriptive case study. Data were collected using semi-structured interviews and observation notes documented during workshops and when the teachers implemented their learnings in their classrooms.Results: The main finding was that although teachers could reflect on the model of number concept development they had learned, they found it hard to infuse their knowledge into a strictly structured curriculum.Conclusion: Despite the Meerkat Maths programme offered to the teachers, they could not rely on their intuitive pedagogy, coupled with the model of number concept development that they had learned because of the strict demands of the school curriculum content with which they had to comply.

The development and assessment of counting-based cardinal number concepts

The development and assessment of counting-based cardinal number concepts

Development of an instrument to assess early number concept development in four South African languages

A recently published interview-based test, known by its partly German acronym, MARKO-D SA, is introduced in this article by way of a narrative of its development through various cycles of research. The 48-item test, in 4 South African languages, captures number concept development of children in the 6 to 8-year age group. The authors present their argument for the South African versioning and translation of the test for this country, where there is a dearth of suitable assessment instruments for gauging young children’s mathematical concept development. We also present the findings of the research that was conducted to standardise and norm the local version of the test, along with our reasoning about the theoretical strength of the conceptual model that undergirds the test.

A Proposed Instructional Theory for Number in Preschool

Background: research has revealed that young children’s development of early number concepts is critical for their long term success. Students who are more skilful with small numbers are much more likely to perform well in mathematics five and even more years after they leave preschool. Objectives: to develop an instructional theory for number in preschool, which is intended to be a resource with the potential for informing and guiding preschool teachers in supporting their students’ development of early number concepts. Design: a preliminary version of an instructional theory was formulated and then tested in a classroom setting. Context and participants: a classroom design experiment was conducted in a public preschool classroom with 22 five-year-old students. Data collection and analysis: The research team assumed the role of a classroom teacher and used a preliminary version of the instructional theory to support the mathematical learning in class during 21 instructional sessions. This work analysed how participation and learning evolved. The analysis was used to assess the suitability of the instructional theory as a teaching resource and adjust it. Results: the results of the classroom design experiment indicate that the proposed instructional theory can be a useful resource for preschool teachers. Conclusions: the developed resource can help preschool teachers enhance their pupils’ opportunities for long-term educational success in mathematics.

Musical activities for enhancing number concepts in preschool children

A concept is the basic unit of all types of learning. Young children generally form concepts through the use of senses. Number concept is defined by McIntosh et al. (1992), as a person’s general understanding of numbers and operations. Research studies suggest that children construct basic number and arithmetic concepts gradually from experiences that involve numbers and difficulties in counting might hinder in mathematical progress (Baroody and Coslick, 1998). Therefore, attention should be given to assess and understand the number concepts formed during preschool age. Music is considered to play an important role in stimulating young children in learning. Hetland (2000) described that using songs and different music components can help in teaching numbers because of the high association between music and spatial-temporal reasoning skills. The study was carried out on twenty four numbers of pre-school children belonging to the age of 3- 4 years, selected through purposive sampling method. Pre and post-intervention design was used to assess the influence of musical activities on the development of number concepts in children. The number concepts were assessed in the categories of Number sense, Number representation and Number relation based on the principles of counting proposed by Gelman and Galistell (1978). It was found from the study that most children could name numbers but the concept of cardinality was not attained by many of the children. Findings revealed that children improved in all the areas of number concepts after the musical intervention. However, it was also observed that all the concepts are not mastered at the same time by all the children.

Supporting Learning Trajectories for the Development of Number Concept: Digital Games

The aim of this study is to examine the games in ABCya (https://www.abcya.com/) based on the learning trajectories for the development of number concept. To achieve this aim in the study it was examined which ABC educational game application support the learning trajectory and the development level related to number concept of games. This research was designed in qualitative research methodology based on content analysis method. The ABCya application, which includes a dynamic structure, is suitable for manipulation and includes digital game features with mathematical content which make it appropriate to support the mathematical development of pre-school students. It is seen that the games mostly support the trajectories of the “recognition of number and subitizing” and “verbal and object counting” for the children aged between 4-6. For the trajectory of the “comparing, ordering and estimating numbers” there are games supporting the perceptual and counting comparison and ordinal numbers, but games supporting the estimation skills are limited. It is very important to introduce the digital platforms that include educational game activities to both teachers and families and to inform them about their contribution to academic development of the children.

Developing Number Concepts in Young Children through Educational Games

Many children appear to experience low motivation towards learning mathematics, which may negatively impact on their performance and engagement in further learning. More recently, educational games have been presented as a way of improving student motivation and performance in mathematics. The current study aimed to explore the impact that educational games had on the development of number concepts in kindergarten children aged between 5 and 6 years in Amman, Jordan. Employing purposive sampling techniques, fifty-five (N=55) kindergarten children (25 males and 30 females) in private kindergartens participated in the study. The sample was randomly distributed into two groups: twenty-nine (29) in the experimental group and twenty-six (26) in the control group. Researchers developed an innovative Mathematical Educational Games Program (MEGP) and an achievement test for children. Results indicated a significant difference between the control and experimental groups in favour of the experimental group with no significant difference being attributed to gender. In addition, the results showed no interaction between gender and the MEGP. This paper will therefore discuss the implications of these findings on the development of number concepts with kindergarten-aged children.

Study on the Features and Strategies of Number-Concept Development of Rural Children in Early Primary School Years: Study of Number-Concept Development of Rural Children

The development level of children’s number-concept is a critical element in measuring the development of children's thinking. Previous studies have shown that preschool is an important stage of development and that vocabulary can help promote children’s number-concept development. This study aims to explore the characteristics of the development of rural children’s number-concept in their early years, and propose teaching strategies suitable for rural children based on the research results. This research method is based on a one-to-one standard test, supplemented by a self-designed structured interview for teachers. The research object is the early school-age children in rural areas. The impact of gender, age, school, and language on children’s number-concept development is discussed. By describing and studying the characteristics of their number-concept development, educational strategies and suggestions are put forward. This research can contribute to the literature theoretically, pedagogically and practically.

통합적 요리활동을 통한 유아의 수 개념 발달에 관한 연구

통합적 요리활동을 통한 유아의 수 개념 발달에 관한 연구

The Impact of a Varied Field Experience on Preservice Teachers’ Perceptions of their Personal Growth: A Summer Mathematics Academy for Early Learners

This study was organized to examine the impact of a field experience for elementary preservice teachers working with young children enrolled in a summer academy focusing on early mathematics. The academy was designed to provide engaging learning experiences to support the development of early number concepts for pre-K students from an elementary school with low socioeconomic populations. Using a qualitative case study, the researchers examined the experiences of the preservice teachers through pre- and post-focus groups, daily and weekly reflections, and a follow-up interview. The results revealed an increased confidence in preservice teachers’ ability to teach early number concepts when supported by a lead teacher. The preservice teachers also demonstrated growth in supporting student learning through differentiation in instruction. As teacher educators must consider the types and timing of field experiences offered to elementary preservice teachers, findings have implications for teacher preparation programs with varied field experiences.

The Effect of Early Numeracy Program on the Development of Number Concept in Children at 48-60 Months of Age

This study investigates the effect of Early Numeracy Program on the development of number concept in children at 48-60 months of age. The study was carried out in the central district of a province (Mugla/ Mentese) in the Aegean region of Turkey. The study group of the research included 78 children (40 in experiment group, 38 in control groups) attending two different kindergartens in the central district of the aforementioned province. In this study in which quasi-experimental design with pre-test-post-test control group was used the data were collected with Early Numeracy Assessment and Number Development Assessment Tool. SPSS was used for data analysis and whether there was a significant difference between the mean scores of the experimental and control groups in terms of pretest, post-test, and follow-up test was checked using Independent Samples t-Test and Dependent Samples t-Test. Early Numeracy Program supported with educational material was applied to children for 2 days a week over a period of 12 weeks. In the statistical analysis, it was found that the mean post-test scores of the children in the experiment group were significantly higher than the mean scores of the children in the control group. As a result, it was determined that the applied Early Numeracy Program significantly increases the level of development of number concept for children at 48-60 months of age.

Diagnostic test for number concept development during early childhood

Background: This article presents the Afrikaans translation of an originally German diagnostic test for early number concept development. The process of ‘importing’ a test to South Africa by considering linguistic-, functional-, cultural and metric equivalence is outlined. A theoretical model describes five levels of young children’s hierarchical number concept development which collectively contribute to early mathematical understanding. The five-level hierarchical structure has previously been confirmed by testing the theoretical model in a one-dimensional Rasch analysis in Germany. Aim: The current study aimed to determine whether the individual items, allocated to test the concepts of each level of the Afrikaans translation of the diagnostic test, confirm the hierarchical structure of the theoretical model. Setting: A Rasch analysis indicated that the model was fit for the Afrikaans translation. A sample of 165 Afrikaans-speaking grade one children was tested in six Afrikaans medium primary schools in Gauteng. Methods: Analysis of fit values, person and item reliability and a person–item map was used as part of a Rasch analysis. Results: The theoretical model of hierarchical number concept development holds for the Afrikaans MARKO-D. Five levels were clearly distinguishable on a Write map and the individual items tested the concepts according to the levels of the theoretical model. Conclusion: The Afrikaans MARKO-D can now successfully be used to describe young Afrikaans children’s number concept development. A five-level theoretical model is a useful tool for teachers using the MARKO-D to assess young children’s numerical competence.

Stimulating numbers: signatures of finger counting in numerosity processing.

Finger counting is one of the first steps in the development of mature number concepts. With a one-to-one correspondence of fingers to numbers in Western finger counting, fingers hold two numerical meanings: one is based on the number of fingers raised and the second is based on their ordinal position within the habitual finger counting sequence. This study investigated how these two numerical meanings of fingers are intertwined with numerical cognition in adults. Participants received tactile stimulation on their fingertips of one hand and named either the number of fingers stimulated (2, 3, or 4 fingers; Experiment 1) or the number of stimulations on one fingertip (2, 3, or 4 stimulations; Experiment 2). Responses were faster and more accurate when the set of stimulated fingers corresponded to finger counting habits (Experiment 1) and when the number of stimulations matched the ordinal position of the stimulated finger (Experiment 2). These results show that tactile numerosity perception is affected by individual finger counting habits and that those habits give numerical meaning to single fingers.

Enhancing Established Counting Routines to Promote Place-Value Understanding: An Empirical Study in Early Elementary Classrooms

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding. Faced with competing demands, teachers may resist abrupt, disruptive, or time-intensive changes to existing practices. In this study, we explore ways of introducing changes in pedagogical supports that minimally disrupt existing classroom routines that nonetheless offer potential gains in children’s understanding of base-ten number concepts. Specifically, we examine the impact of modifying how teachers demonstrate and discuss representations of the ten-for-one structure during the familiar “Days in School” counting routine on young children’s place-value understanding. We report on a 2-year longitudinal study of a cohort of students beginning in grade one, conducted in nine classrooms across a control school and a treatment school. We describe the modifications in the counting routine and report the results of children’s development of base-ten number concepts. The percentage of children who identified base-ten number concepts was three times higher for the children in the treatment group than for the children in the control group. Moreover, nearly twice as many children in the treatment group as compared with the control group advanced beyond a concatenated single-digit conception by the end of second grade when counting two-digit quantities. We conclude with a discussion of the implications of our findings for early elementary mathematics education more generally.

The relationship between non-verbal systems of number and counting development: a neural signatures approach.

Two non-verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here we used an individual differences approach to test for a relationship between the spontaneously evoked brain signatures (using event-related potentials) of PI and the ANS and initial development of symbolic number concepts in preschool children as displayed by counting. We observed that individual differences in the neural signatures of the PI system, but not the ANS, explained a unique portion of variance in counting proficiency after extensively controlling for general cognitive factors. These results suggest that differences in early attentional processing of objects between children are related to higher-level symbolic number concept development.