Early Mathematical Concepts Research Articles

ATTITUDES OF PARENTS AND TEACHERS TOWARDS MATHEMATICS EDUCATION IN THE CONTEXT OF STEAM EDUCATION

The pre-school period is valuable in itself. It is at this age that the child's most important personality traits, his or her perception, thinking, communication, etc., develop. STEAM goes hand in hand with the development of 21st century skills and should be included as early as possible in the curriculum. Children's early experiences with science, technology, engineering and mathematics and the arts influence their future success in these areas. When teachers give children early opportunities to learn maths and science in an interactive environment that builds communication and collaboration skills, children are more confident and competent in these subjects. This not only makes higher education more accessible to children but also contributes to a well-prepared society. Survey of 116 teachers and 104 parents identified that parents of pre-school children are more accurate in identifying the disciplines that STEAM education integrates, they perceive that the teacher's background in mathematics and science influences children's mathematical and science education, and that young children can apply early mathematical concepts. Parents identified advantages and barriers to the successful implementation of STEAM in pre-school education.

Improving Children's Cognitive Abilities with Playing Simple Math and Science

Playing with math and science for children are not only interesting but also can increase creativity and increase cognitive skill. Playing math to childhood are introduce beginning basic math concept by interesting playing. In daily life, the childhood can introduce and study math very simple. Starting from look their finger than learn to count its. When the children share the cake with their friends, it’s also introduce math concept. In daily, the children are nearing from the world of mathematics, but almost of us, understanding math only about number, summary, reduction, multiplication, arithmetic, etc. even though many early mathematical concepts are close to the world of children. By introducing the basic concept of mathematics from an early age will be able to have life skills for their future, because almost of human life are related to mathematics concept. In addition to basic math concepts, early childhood also needs to know about the world of science. Playing science in early childhood is an effective learning to recognize the world around him with the five senses of them.

Exploration of Teaching Methods in the Implementation of Early Mathematics Teaching and Learning (PdP)

The National Standard Preschool Curriculum (NSPC) (Revised 2017) describes the disciplines of knowledge that provide Early Mathematics learning experiences encompassing the concepts of pre-numbers, numbers, number operations, money values, time, shape and spatial for preschool children. The implementation of teaching and learning (PdP) of Early Mathematics is mandatory based on the importance of each conceptual scope with 40 minutes time allocation for teaching in a week. The goal of Early Mathematics PdP is to foster children's interest in math skills through various activities and daily experiences. In addition, children are also expected to master basic math skills and improve thinking and problem solving skills. However, there are various challenges and obstacles faced by preschool teachers in implementing Early Mathematics PdP. Among the main challenges underlined by previous researchers are the teacher’s attitude, knowledge level of Early Mathematics concepts, teacher’s mastery of pedagogy and knowledge of children’s development. Thus, this concept paper explores the practices and challenges faced by preschool teachers in rural areas. Based on the review, several suggestions for improving Early Mathematics PdP were also identified to overcome the challenges of preschool teachers; for example, participation in workshops and competency training for preschool teachers. It is expected that this concept paper contributes ideas to overcome teacher problems as well as intensify studies in the field of Early Mathematics at the preschool level.

EduGame Maru: Application for Early Mathematics Learning as an Alternative for Optimizing Cognitive Ability for 4-6 Years Children

Mathematics teaching process in kindergarten must adapt to the pandemic situation which requires learning from a distance. This research develops an Android-based application for learning mathematical concepts, named EduGame Maru, consisting of five types of games: recognizing numbers, algebra, statistics, geometry, and probability. This research aimed to create an interactive, innovative, and practical application as a digital medium. The method used in this research was the RD model, with 4D development (define, design, develop, and disseminate). The EduGame Maru application received a validation result of "very feasible for use," with 3.36 points from media expert validators and 3.64 points from material expert validators, so the average was 3.50. Meanwhile, during the testing at Kindergarten Labschool, Universitas Pendidikan Indonesia, Serang Campus, the EduGame Maru application got 3.56 points from the teacher's assessment. In this case, the EduGame Maru application not only trains cognitive abilities but also helps children to understand early mathematical concepts by applying the NCTM (National Council of Teachers of Mathematics) principles. Therefore, it can be concluded that EduGame Maru can help teachers and parents optimize the cognitive aspects of children aged 4-6 years, especially early mathematical concepts during online learning.

Exploring environmental factors affecting assistive technology strategies in mathematics learning for students with physical disabilities

Purpose To explore the environmental facilitators and barriers affecting K-12 students with physical disabilities when using two assistive technology (AT) strategies, LEGO Mindstorms robots and a computer, in mathematics lessons. Materials and methods A qualitative multiple case study with three students with physical disabilities was conducted. The participants did five lessons in concepts they were studying in school with each AT strategy in a controlled environment. Observations of the lessons, and parent and teacher interviews after the last session were collected. Results The AT strategies acted as facilitators because they were easy to use, participants could participate actively, and parents and school staff wanted to implement them. However, the strategies presented some barriers since the students required more time to complete the lessons with the robot, and some computer programs were not compatible with the students’ skills. Also, barriers such as lack of technical knowledge on the part of parents and teachers, distractions in the environment, and funding issues were reported. Conclusion This study may be useful for rehabilitation staff and teachers who are considering implementing AT to support the participation of students with disabilities. Personnel needs to be trained to use the AT strategies, and several modifications may be necessary for the satisfactory use of the devices. IMPLICATIONS FOR REHABILITATION Hands-on manipulation promotes the active learning of early mathematical concepts. Students with disabilities may have the opportunity to participate in active learning through assistive technology (AT). Knowledge about environmental factors that may facilitate or limit the use of AT in the classroom will help teaching staff make decisions when implementing these strategies with students with disabilities. The use of an AT strategy may depend on the objectives the rehabilitation staff and teachers want to achieve during a task. For instance, the robot could be used for tailoring a task according to the student’s needs and abilities. On the other hand, computer programs could be considered if time and ease of use are important factors.

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Booked on Math: Developing Math Concepts in Pre-K Classrooms Using Interactive Read-Alouds

This paper outlines the development and implementation of a ten-week micro-curriculum, Booked on Math, designed to introduce preschool children to foundational mathematics concepts through interactive read-alouds. The Booked on Math curricula includes ten book readings and associated inquiry-based lesson plans. Booked on Math read-alouds and lesson plans were implemented across six preschool classrooms over a ten-week period in a university-based early childcare center. A total of 74 pre-kindergarten students participated in the project with four classrooms receiving the Booked on Math intervention and two classrooms serving as the control group. Pre- and post-test data on student learning outcomes were collected across seven Teaching Strategies GOLD (TS GOLD) mathematical constructs (counts, quantifies, connects numerals with quantity, spatial relationships, shapes, compares and measures, and knowledge of patterns). Results indicated statistically significant differences in treatment group post-test data for three TS GOLD constructs: (1) quantifies, (2) shapes, and (3) spatial relationships. Additional regression analyses indicated two TS GOLD constructs: (1) quantifies and (2) knowledge of patterns were significant predictors of children’s post-test outcomes after controlling for covariates (e.g., age and gender). To conclude, implications of the study and future research opportunities related to leveraging interactive read-alouds to teach early childhood mathematics concepts are discussed.

Limited trial on origami construction as mathematics learning strategy for early childhood on kindergarten teachers

The aim of this study is to do a limited trial on the hypothetical learning strategy for early childhood mathematics concepts using origami construction. Using the training devices designed for the limited trial, 17 early childhood education teachers in Bandung and its surrounding areas were trained on the learning strategy. The trial pre-test and post-test scores and it shows an improvement in the knowledge of participating teachers of early childhood mathematics learning using origami. The significance of the improvement had been proven using t-paired test. The improvement might be caused by the fact that most of the participants only have high school diploma as education background with lack of training on early childhood mathematics learning, and also with the fact that origami is mainly used for fine motor skills improvement in early childhood education. Thus, the origami construction can be used as an alternative strategy to learn mathematics concept in early childhood.

Preferences for tactile and narrative counting books across parents with different education levels

Counting books are a potential source of input for children’s learning of early mathematics concepts. However, little is known about the factors that affect the counting books parents choose for their children. Parents (N = 696) of preschoolers (ages 2;6–4;11) were surveyed about their preferences for two specific counting book features, tactility and narrative quality. These two features were studied both covertly, by experimentally manipulating the types of books parents saw and asking parents why they would choose particular books, and explicitly, by asking parents to rate the importance of various factors when choosing counting books for their children. The a priori hypotheses were that parents would prefer tactile over non-tactile counting books for boys and narrative over non-narrative counting books for girls and that education level would be positively associated with counting book reading. Results did not support these hypotheses. Instead, parents’ preferences for the features depended on their education level. Higher education levels were generally associated with decreased preference for tactility and increased preference for narrative quality. Results raise the question of whether the books parents choose for their children may be one way parent education shapes children's early learning environments.

Recombinant Enaction: Manipulatives Generate New Procedures in the Imagination, by Extending and Recombining Action Spaces.

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based learning-particularly how actions generate new internal structures that support problem-solving-are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action-traces recombine during problem-solving. This model is based on a study of two groups of sixth-grade students solving area problems. Before problem-solving, one group manipulated a tangram, the other group answered a descriptive test. Eye-movement trajectories during problem-solving were different between the groups. A second study showed that this difference required the tangram's geometrical structure, just manipulation was not enough. We propose a theoretical model accounting for these results, and discuss its implications.

Computational Thinking Concepts for Grade School

Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding “computational thinking” as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of early education. Computational thinking does not come naturally and requires training and guidance. This paper argues for the inclusion of computational thinking in tandem with mathematics. As an example, the paper demonstrates spreadsheet applications that can be utilized concurrently with early mathematical concepts. It demonstrates that at this time, spreadsheets are the best medium for inculcating computational thinking but recognizes that advances in technology may favor other digital approaches in time.

From Seeberg to Colmar: early mathematical concepts in prehistoric Europe at the interface between material culture, technology and metaphors

Im Mittelpunkt dieses Artikels stehen Vergleichsanalysen von Kupferperlen der Cortaillod-Kultur sowie einleitend das Depot von Seeberg Burgäschisee-Süd. Dieses Depot war für eine lange Zeit ein isolierter Fundkomplex, sodass vonseiten der Forschung Thesen zu dessen metrologischer Struktur als wenig überzeugend angesehen wurden. 2008 jedoch kam es zu einem Durchbruch für die Forschung, konnte doch in Colmar in einem äneolithischen Grab eine für die Cortaillod-Kultur charakteristische Perlenkette geborgen werden, deren Platzierung in der Bestattung eine Bewertung der Stellung und Bedeutung jener Perlen während des Äneolithikums erlaubte. Für die hier vorgelegten Analysen sind diese Perlen von großer Bedeutung, vergleichbar etwa mit dem „Stein von Rosette“ für die Entzifferung der Hieroglyphen, tragen sie doch dazu bei, die archaischen und wenig abstrakten Methoden mathematischen Denkens und verwendeter Zahlbegriffe zu verstehen und beides mit dem damals neuen Ansatz der Metallurgie zu verknüpfen.L’article ci-dessous est une étude comparative de perles de cuivre appartenant à la culture de Cortaillod. Le célèbre dépôt de Seeberg Burgäschisee-Süd est resté unique pendant de longues années, ce qui amena certains archéologues à douter de la validité d’une hypothèse d’une structure métrologique. Suivant un aperçu sur cette trouvaille, notre article présente une analyse basée sur la méthode statistique de Kendall. De plus, nous disposons maintenant d’une nouvelle découverte de la plus haute importance : un autre dépôt de perles, mis à jour lors de fouilles à Colmar en Alsace. Ces perles, d’un type caractéristique de la culture de Cortaillod, furent retrouvées dans une tombe énéolithique. La répartition de ces objets dans la sépulture lève enfin le doute sur la valeur que l’on plaçait sur ces perles. L’étude comparative de ces deux dépôts, qui fait appel à des méthodes tant statistiques que conventionnelles, constitue le noyau de cet article; elle nous permet d’approfondir nos connaissances dans le domaine problématique des notions mathématiques et métrologiques existant en Europe à l’époque préhistorique. Les perles de la culture de Cortaillod se trouvent à l’intersection de méthodes plus archaïques et moins abstraites dans le domaine des mathématiques et du dénombrement et des nouvelles notions liées à l’apparition de la métallurgie.This article presents a comparative analysis of copper beads of the Cortaillod culture. The famous deposit from the site of Seeberg Burgäschisee-Süd remained isolated for a long time, and hence the hypothesis of its metrological structure seemed unbelievable to some archaeologists. This article begins with a reminder of this find and presents a new analysis based on Kendall’s statistics. In addition, we present a breakthrough discovery of another deposit of beads. During excavations of the site of Colmar in Alsace, an Eneolithic grave was discovered; it produced copper beads of a type that is characteristic of the Cortaillod culture. The distribution of these objects in a grave finally removes doubts as to how beads were valued. The comparison of the deposits of Seeberg and Colmar, using both statistical and conventional methods, is at the core of this article; it allows us to gain a deeper insight into the problematic area of early mathematical and metrological concepts in prehistoric Europe. The beads lie at the interface between traditional, more archaic and less abstract methods of perceiving mathematical relations based on the concept of linear measure and the new approach brought about by the arrival of metal technology.

The Math Gap: A Description of the Mathematics Performance of Preschool-aged Deaf/Hard-of-Hearing Children

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures were used to assess understanding in number, geometry, measurement, problem solving, and patterns, reasoning and algebra. Results present strong evidence that d/hh students' difficulty in mathematics may begin prior to the start of formal schooling. Findings also show areas of strength (geometry) and weakness (problem solving and measurement) for these children. Evidence of poor foundational performance may relate to later academic achievement.

Improving Algebra Preparation: Implications From Research on Student Misconceptions and Difficulties

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of the arithmetic content they teach can dramatically, and sometimes negatively, impact their students' ability to transition to algebra. The purpose of this article is to bring awareness of some common algebra misconceptions, and suggestions on how they can be averted, to those who are teaching students the early mathematical concepts they will build upon when learning formal algebra. Published literature discussing misconceptions will be presented for four prerequisite concepts, related to symbolic representation: bracket usage, equality, operational symbols, and letter usage. Each section will conclude with research‐based practical applications and suggestions for preventing such misconceptions. The literature discussed in this article makes a case for elementary and middle school teachers to have a deeper and more flexible understanding of the mathematics they teach, so they can recognize how the structure of algebra can and should be exposed while teaching arithmetic.

Measurement of Kindergartners' Understanding of Early Mathematical Concepts

.Early measures of mathematics skill and development have focused on early numeracy skills like counting, number identification, and sequencing of numbers. This study attempted to expand early mathematics assessment. Six new measures of early mathematics skill competence were developed and evaluated. Four existing measures also were examined. Measures were developed to directly assess kindergarten children’s understanding of concepts including number sense (ordinality, subitivity, cardinality), shape recognition, and patterning. Technical adequacy estimates were examined including test–retest reliability, concurrent and longitudinal correlation with criterion measures, and sensitivity. The Pattern Completion, Set Comparison with Unequal-Sized Items, and Subitivity measures performed best. Existing early numeracy measures performed comparably to or better than the new measures.

Mediators of preschoolers’ early mathematics concepts

The purpose of this study was to extend existing research relative to the predictors of early mathematics skills. Using Vygotskian theory as a framework, our primary goal was to determine whether social skills or letter awareness skills served as better mediators between receptive language and early mathematics concepts. The secondary goal was to examine possible differences in children’s early mathematics, language, letter awareness, and psychosocial skills for two different childcare settings, centre and family childcare. Participants included 109 children (48 girls) all of whom attended out‐of‐home childcare at least 13 hours each week and who would be attending kindergarten the following year. Sixty‐one children were enrolled in out‐of‐home family childcare and 48 in out‐of‐home centre childcare. Relative to our first goal, letter awareness fully mediated between receptive language and early mathematics (Sobel z‐value = 2.92, p = .003). This suggested that when children are able to understand a system of symbols for sounds and if they have sufficient receptive language skills, they are able to understand a system of symbols for number. Teaching early mathematics skills as frequently as letter awareness skills might reinforce more efficient acquisition of both. Relative to our second goal, children in centre‐based care outscored children in home‐based childcare on early mathematics and letter awareness skills. This suggested that some differential trainings for centre childcare providers versus home care providers might be appropriate so as to provide the highest quality environment for both groups of children.

Families With Young Deaf Children and the Mediation of Mathematically Based Concepts Within a Naturalistic Environment

A qualitative study is described that sought to examine the relationship between young deaf children's level of mathematics ability ("more successful" and "less successful" as defined by scores on the Test of Early Mathematics Ability-3, Ginsburg & Baroody, 2003) and the opportunities available to develop early mathematics concepts during daily life with their families. Findings indicate substantial differences between the two groups of children. Children who demonstrated higher levels of mathematics ability were found to spend a larger percentage of their day interacting with the adults around them and to experience more frequent and purposeful exposure to mathematically based concepts (number/counting, quantity, time/sequence, and categorization) at home. The findings suggest the need for an early intervention program to facilitate parents' use of early mathematics concepts within naturalistic environments with their young deaf children to promote readiness for formal schooling.

Mathematics Intervention for First- and Second-Grade Students With Mathematics Difficulties

This study sought to examine the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. A regression discontinuity design was utilized. Participants included 126 (Tier 2, n = 26) first graders and 140 (Tier 2, n = 25) second graders. Tier 2 students received 15-min intervention booster lessons for 18 weeks in early mathematics skills and concepts. Results showed a significant intervention effect for second-grade Tier 2 students on the Texas Early Mathematics Inventories—Progress Monitoring (TEMI-PM) total standard score. The effect was not significant for first-grade Tier 2 students.