Development Of Number Sense Research Articles

Practical Pedagogical Approaches: Integrating Play-based and Experiential Learning at Pre-Primary Education as per NEP 2020 and NCF-FS 2022

Early childhood education in India is undergoing significant changes, guided by the National Education Policy (NEP) 2020 and the National Curriculum Framework for the Foundational Stage (NCF-FS) 2022. This paper explores practical pedagogical approaches for pre-primary and early childhood care and education (ECCE) in India, aligning with these policy recommendations. It examines key strategies for implementing play-based learning, developing language and literacy skills, building foundational numeracy competencies, and incorporating inquiry-based and activity-based learning approaches. The study emphasizes the importance of creating stimulating learning environments featuring well-equipped indoor and outdoor play areas to facilitate meaningful play experiences. It details methods for fostering oral language development, phonological awareness, and early literacy skills through various activities and a print-rich classroom setting. Strategies for developing number sense, basic operations, spatial awareness, and other core numeracy concepts are outlined. The paper also explores approaches for integrating inquiry-based learning to nurture scientific thinking and problem-solving skills. Additionally, the paper discusses the role of diverse activities in promoting holistic development across physical, cognitive, social-emotional, language, and aesthetic domains. It highlights integrating art and experimentation in ECCE to enhance creativity and self-expression. The role of educators is analyzed, focusing on their contribution to creating stimulating learning environments and facilitating meaningful experiences for children. Challenges in implementing these approaches include infrastructure and resource constraints, teacher training needs, parental engagement, and cultural relevance. However, the evolving policy landscape also presents opportunities for transformation through increased investment, flexibility in curriculum design, and an emphasis on developmentally appropriate practices. The paper concludes with recommendations for future directions, such as strengthening ECCE infrastructure, enhancing teacher professional development, fostering community engagement, conducting further research, and developing culturally appropriate resources. By synthesizing evidence-based practices aligned with policy directives, the paper provides a comprehensive overview of effective pedagogy for fostering young children’s holistic growth and development in early childhood education in India.

Using games to develop number sense in early grade maths clubs

Using games to develop number sense in early grade maths clubs

Unlocking numerical sense: An in-depth analysis of teaching practices among mathematics teachers in primary schools

Mathematics teachers face significant challenges in developing number sense among students. This study investigates the teaching practices of Saudi Arabian primary school mathematics teachers for fourth-grade female students. Using a descriptive-analytical approach and validated observation cards, the study sampled 20 teachers and analyzed data through statistical measures. Results revealed teaching practice levels as low in planning, moderate in implementation, and high in evaluation, with overall moderate effectiveness. No significant differences were found based on teaching experience, academic degree, class size, training programs, or teaching load. The study recommends the Saudi Ministry of Education enhance teaching practices via targeted professional development and suggests future research on instructional methods across different educational levels and the use of digital tools.

The relationship between family socioeconomic status and the young children's number sense development: The mediating role of parent-child activities.

This study examines the relationship between family socioeconomic status, parent-child activities, and young children's digital development. Using the Family SES questionnaire, the parent-child activities questionnaire, and the 5 to 6 year old children's number sense development scale as research instruments, 314 young children (M = 70.42, SD = 3.47). The results show that: (1) Family Socioeconomic Status can significantly positively predict the young children's number sense development; (2) Parent-child activities play a partial mediating role in the relationship between family socioeconomic status and the young children's number sense development. This study provides specific guidelines and recommendations for improving the young children's number sense development.

Developing Number Sense with Number Talks

The results of this study revealed students’ solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

Grade R Teacher Expressions of Themselves as Teachers of Early Numeracy Participating in an Intervention Programme

This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools participating monthly over 18 months. Inclusion of Grade R to schooling is relatively new following policy changes in Early Childhood Development. In-service support tends to be subsumed within the Foundation Phase without attention to the specialised nature of Grade R that emphasises learning through play. ENF focused on the development of specialised teacher knowledge to support the development of early number sense through play, particularly with conceptual manipulatives. Data sources include three pre-, during, and post-PD questionnaires. Findings reveal that participation in ENF, and access to multiple research informed numeracy resources, supported teachers in their relationship with numeracy and the teaching thereof. Questionnaire responses indicate greater confidence in themselves as knowledgeable teachers of numeracy and that belonging to the ENF community supported navigation of positive professional identities within the mixed messages of policy. The findings contribute to the community-supported field of Grade R PD research and early numeracy teaching and learning. In concluding we discuss implications of this research for Grade R PD and for policy.

Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

Development of number sense and numeration: a continuum hypothesis

This text focuses on the development of number sense, specifically addressing the challenges associated with understanding the number system, including the connections to and difficulties in early arithmetic learning. It provides a synthesis of the scientific literature related to this development. It concludes by proposing a hypothesis for the development of number sense, associated with the construction of dynamic and pictorial mental representations. This continuum proposes five key phases: perception of small quantities, additive thinking, multiplicative thinking and pre-place value, passage to tens and passage to hundreds and understanding place value.

The development of number sense and its conceptual nexuses in early childhood education

This article is the result of a Master's in Education research on the organization of teaching-learning numbers, in the context of Early Childhood Education. In the singularity of this text, bibliographical reflections and results are approached about the development of the numerical sense and the conceptual nexus of number, in a cultural-historical perspective. Authors from the Vigostsky school and their followers were used as a theoretical-methodological framework, in line with the defense of a childhood education that promotes children's development. The results show the importance of didactic intentionality in the organization of teaching-learning numbers in Early Childhood Education. They highlight the centrality of play in the appropriation of numerical sense, in order to understand the principles of counting, as well as the training of teachers who work in this educational segment.

How to Become a Numbers Person: Review of Making Numbers Count, by Chip Heath and Karla Starr (2022)

Making Numbers Count: The Art and Science of Communicating Numbers (2022), by Chip Heath and Karla Starr, is a practical guide to developing number sense. Full of useful tips and tricks, the book ends on a philosophical note that invites us to contemplate why each of us is simultaneously good and bad with numbers. The writing style is enjoyable, especially for a reference book, and it could generate fruitful conversation in numeracy courses as well as writing courses across disciplines and professions.

Number Sense Development During the Preschool Years: Relations Within and Between Key Skill Indicators

ABSTRACT Research Findings: This study examined age-based developmental trajectories of four key number sense (NS) skills within an accelerated longitudinal design. Using data from 408 preschoolers, ages 45 to 68 months, linear and latent basis growth curves were evaluated. Results indicated growth across NS skills was best represented as nonlinear for all but number naming. Significant variation in initial performance at 45 months was evident across skills, as was significant variation in growth for all skills but number naming. Practice or Policy: Mathematical skills at kindergarten entry have been supported as strong predictors of subsequent academic achievement as well as social emotional skills. Results of this study advance our understanding of the development of key skills in early mathematics during the preschool period and provide additional information about patterns of development of key NS skills across the preschool years. This information can be used to inform measurement development, consider timing of assessment practices, and promote targeted instruction in early education.

The Impact of a Summer Intervention Focused on Foundational Concepts of Number Sense for Early Learners

ABSTRACT This longitudinal quantitative study determined the impact of a summer mathematics academy for early learners on their number sense and how their number sense compared to that of their peers who did not attend the academy. The Texas Early Mathematics Inventory – Progress Monitoring (TEMI-PM) was used to measure students’ number sense. Results revealed that (1) all participants showed growth in their understanding of Number Identification in their first year of attending the academy, (2) participants who attended for two consecutive years grew in multiple areas of early number sense, and (3) participants who attended for one year demonstrated a decreased gap when compared to peers. The evidence supports the benefits of a mathematics-focused summer intervention to develop number sense for early learners.

Does this Answer Make Sense? Primary School Students and Adults Judge the Reasonableness of Computational Results in Context-Based and Context-Free Mathematical Tasks

This study investigates students’ and adults’ performance in judging reasonableness of computational results, namely reflecting on whether these results qualify as acceptable answers to mathematical tasks. Data was gathered via task-based questionnaires from 160 participants, evenly divided between fifth-graders and adults. Their responses to a systematically varied collection of context-free and context-based items shed light on their performance and strategies in relation to two interrelated aspects of reasonableness: number relationships and the effect of operations (internal reasonableness) and the practicality of answers (external reasonableness). The results revealed that students were better at utilising the former criterion compared to the latter, while for adults, the opposite was found. However, adults clearly outperformed students in both aspects. Task characteristics such as the involved numbers and operations, and the correctness or incorrectness of computation results, were found to be associated with fluctuations in performance, although the effect differed between context-free and context-based items. Algorithm- and rule-based strategies were more popular than sense-making ones especially among students, although only the latter type was correlated with increased correct response rates. Students often failed to obtain results that made sense considering real-life situations or the involved numbers and operations. Instead, they blindly trusted algorithms and rules, even when their use was inappropriate or insufficient. The findings highlight that to help students refine their ability to judge reasonableness, mathematics classrooms should prioritise the development of number sense and promote the search for connections between school mathematics and everyday life.

How the Number Line Can Be Used to Promote Students' Understanding of the Normal Distribution

A strong foundation in early number concepts is crucial for students’ future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or when problems about normally distributed random variables are presented in word questions which involve phrases that indicate inequalities. As a result, students shade wrong areas on the bell-shaped curve when they have to calculate probabilities for normally distributed variables. Visual representations such as the number line can support students’ development of quantitative literacy or number sense by helping them create a mental representation of the order and magnitude of numbers as well as inequalities. Based on a comprehensive investigation of evidence demonstrating this weakness, this experienced-based perspective proposes a framework that demonstrates how the number line can be used as a powerful teaching tool to promote students’ conceptual understanding about the normal distribution. The framework illustrates with authentic examples how the number line relates to the horizontal axis of the normal and standard normal curve and how it can be used to address erroneous quantitative reasoning when students are required to calculate probabilities for normally distributed variables. To determine if the number line teaching intervention affects student performance, the researcher adopted a non-equivalent pretest-posttest design with two intact classes. The results of the analysis show that students who received the intervention performed significantly better in the posttest.

Developmental Change of Approximate Number System Acuity (Keenness) Reveals Delay

Purpose: Major aim of the study was to investigate the development of mathematical thinking and processing in Pakistani sample. Particular focus of the study was to figure out whether Pakistani people across various age groups process numbers with similar sophistication as their western counter parts from developed countries. Mathematics plays huge role in the development of the society and research evidence in this context from Pakistan is scarce.
 Design/Methodology/Approach: 261 participants ranging from 5 to 72 years of age participated in the study. Panamath task being the robust measure of ANS acuity was administered.
 Findings: Results revealed that numerical acuity got precise with an increase in age. However, most sophisticated acuity has been shown around age 46-50 as compared to the western population showing its peak around 30 years of age. Delay in developing most sophisticated approximate number system acuity across the groups as compared to the trend reported in the western population raises many questions in terms of cultural variations and practices contributing to the development of number sense.
 Implications/Originality/Value: We need to improve our mathematical learning and teaching practices so that it could be helpful in economic growth in turn by better mathematical performance across various age groups. On a general note, economical practices, math related curriculum policies, lack in math related games, math practices at home and at educational institutions with varying level of curriculum and pedagogical practices might be a contributor for this trend. The study has important implications for understanding the development of number sense cross-culturally keeping in view the evidence from various cultures.

Purposeful Use of High-Leverage Practices to Teach Number Sense

High-leverage practices are essential components of specially designed instruction required by the Individuals with Disabilities Education Improvement Act. High-leverage practices such as explicit instruction and use of instructional and assistive technology have research evidence demonstrating their effectiveness when teaching students with learning and other disabilities. Although high-leverage practices are appropriate for many content areas, this article illustrates their use when teaching number sense. Number sense involves fluidity with (a) estimating and naming quantities, (b) evaluating accuracy of answers, (c) calculating mentally, and (d) drawing or representing problems. Development of number sense predicts later math achievement for students with and at risk for learning disabilities, making it an essential skill for teachers to address. Peppering common number sense activities with high-leverage practices enhances their impact for students with learning disabilities.

Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

Third Grade Students’ Use of Relational Thinking

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

Specialized Dynamic Technology:, Its Role On Developing Specialized Content Knowledge, And Developing Number Sense

Specialized Dynamic Technology:, Its Role On Developing Specialized Content Knowledge, And Developing Number Sense

Raise the (Proportion) Bar!

This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.