Educating the Young Mathematician: A Historical Perspective Through the Nineteenth Century

Educational programs for young children emerged reasonably early in the history of the United States of America. Its theoretical foundation was based on the thoughts and principles of various early European scholars who differed from one another in their educational theories and how they viewed experiences that would impact on young children’s education, including their mathematics experiences. The movements of Children’s Arithmetic, Mental Arithmetic, the infant school, and the Froebel kindergarten all influenced mathematics in early childhood education. This article reviews the history of mathematics education in relation to the history of early childhood education through the nineteenth century. It also discusses how research in mathematics education attempted to gain its own identity. Throughout history, researchers have identified issues in mathematics education and addressed them, defining the field, and generating a cadre of mathematics researchers.     

“Doing the Math”: Maternal Beliefs About Early Mathematics Versus Language Learning

Research Findings: Little is known about how parents approach preschoolers' mathematics learning and how this aligns with early mathematics education research and policy. This study examined these questions by contrasting parents' approaches to early mathematics and language and by exploring key themes in parents' talk about mathematics learning and education. Consistent with current research and policy, parents reported helping preschoolers learn mathematics and attempting to connect this learning to children's interests and everyday experiences. However, parents admitted to lacking goals for and knowledge about early mathematics. In addition, compared to language, parents reported that mathematics was taught less often at home, should be emphasized less in preschools, was less interesting to preschoolers, required more direct instruction, and was less of a personal interest and strength. Practice or Policy: Parent interventions could capitalize on parents' beliefs and practices by providing parents with concrete examples of what mathematics preschoolers learn through daily activities, how to maximize children's mathematics interests, and what the similarities are between early mathematics and language. These efforts will also need to help parents overcome their mathematics anxieties and show parents why early mathematics education is important. Similar strategies could be used to help early childhood teachers improve their mathematics practice.     

RETHINKING FOOD UTILIZED AS MATERIALS FOR ART

ABSTRACT

Teaching mathematics in an early childhood program requires mathematical content knowledge and teacher self-efficacy, yet research has shown that early childhood educators often have negative attitudes towards mathematics and feel underprepared to teach mathematical concepts. The study reported here documents the reconceptualization of a graduate, preservice teacher education program, a program designed to address teacher anxiety and increase capacity to teach mathematics in a play-based early childhood setting. The study aimed to investigate: (1) the effectiveness of the mathematics component of the course in equipping teacher candidates to teach mathematics in early childhood, and (2) whether participation in the mathematics component of the course changed teacher candidates’ self-efficacy regarding mathematics. Findings show that both self-efficacy and content knowledge improved when teacher candidates had the opportunity to engage with play-based learning experiences that embed mathematical concepts. Furthermore, the focus on a learning trajectories approach supports the identification of developmental progression points in children’s emerging mathematical understanding, assisting with teacher candidates’ fine-grained observations, assessment of children’s learning, and authentic, individualized planning for learning.     

Early childhood mathematics teaching: challenges,difficulties and priorities of teachers of young children in primary schools in Ireland

Issues of pedagogy are critical in all aspects of early childhood education. Early childhood mathematics is no exception. There is now a great deal of guidance available to teachers in terms of high‐quality early childhood mathematics teaching. Consequently, the characteristics of high‐quality early childhood mathematics education are clearly identifiable. Issues such as building on young children’s prior‐to‐school knowledge; engaging children in general mathematical processes; and assessing and documenting children’s learning are some of the key aspects of high‐quality early childhood mathematics education. The extent to which teachers of four‐ and five‐year‐old children in primary schools in Ireland incorporate current pedagogical guidance in early childhood mathematics education was explored in 2007 in a nationally representative questionnaire survey of teachers of four‐ and five‐year‐old children attending primary schools. This paper presents some of the findings of the study in relation to teachers’ self‐reported challenges, difficulties and priorities in teaching early childhood mathematics. Implications are drawn for professional development, curriculum guidance and educational policy.     

Revealing the research ‘hole’ of early childhood education for sustainability: a preliminary survey of the literature

In 2007, Environmental Education Research dedicated a special issue to childhood and environmental education. This paper makes a case for ‘early childhood’ to also be in the discussions. Here, I am referring to early childhood as the before‐school years, focusing on educational settings such as childcare centres and kindergartens. This sector is one of the research ‘holes’ that Reid and Scott ask the environmental education community to have the ‘courage to discuss’. This paper draws on a survey of Australian and international research journals in environmental education and early childhood education seeking studies at their intersection. Few were found. Some studies explored young children’s relationships with nature (education in the environment). A smaller number discussed young children’s understandings of environmental topics (education about the environment). Hardly any centred on young children as agents of change (education for the environment). At a time when there is a growing literature showing that early investments in human capital offer substantial returns to individuals and communities and have a far‐reaching effect – and when early childhood educators are beginning to engage with sustainability – it is vital that our field responds. This paper calls for urgent action – especially for research – to address the gap.     

HPM在教育中的实然困境与应然向度

研究表明教师教育的缺失,教育伦理学的迷失,理论和实践的脱离导致了数学教育中HPM的现实困境。分析了发生认识论是HPM的理论基础后,论述了数学教学中数学史的四种融入形态。并认为教师教育中增加HPM元素,理论研究者和实践者的合作,构建基于数学史的课堂教学模式是在数学教育中提升HPM的应然取向。其中,教师教育是HPM发展的内在逻辑,研究者和实践者合作是HPM持续发展的保障,构建基于数学史的课堂教学模式是HPM发展的核心表征。     

In good hands: Preparing research-skilled graduates for the early childhood profession

Recent developments in early childhood teacher education have seen the inclusion of curricula designed to serve the concept of continuous professional renewal through educating undergraduates in the interpretation, execution, and use of research. The challenge for educators is to “demystify” research and teach in ways that are professionally meaningful as well as intellectually acceptable. In this study, we follow three groups of early childhood students as they engage in a one-semester research subject. Focus groups and individual interviews showed considerable shifts in student attitudes about the value of research and in their development toward becoming active researchers who see research as a tool for answering questions in education.     

Whose Ethics? Toward Clarifying Ethics in Mathematics Education Research

The philosophical branch of ethics is foundationally concerned with the question of right or wrong, benevolent or harmful, and ultimately what is proper conduct. The present inquiry addresses two related questions: (1) How have theories of ethics been applied to mathematics education research? and (2) What alternatives have not been considered? What might the implications be if these alternative formulations were considered? To answer the first question, I offer a review of the philosophy of mathematics education literature, considering those articles which discuss ethics and mathematics education together. The ethical perspectives adopted within the literature span normative and non-normative, modern and postmodern orientations towards ethics. To answer the second question, I explored philosophy literature to identify which philosophical perspectives of ethics have (not) been adopted by philosophers of mathematics education research. The structure of this paper parallels these two questions: the first part considers the philosophy of mathematics education research and how researchers have defined ethics while the second part discusses additional philosophical approaches to ethics and puts those approaches into conversation with those identified in part one. I conclude by intertwining these two strands into my central thesis: ethics per se is construed too narrowly in the philosophy of mathematics education literature and considering additional ethical perspectives from philosophy can be generative of new ideas.     

我国学前教育政策研究的回眸与展望:价值取向、研究范式与核心主题

在我国学前教育事业不断走向科学化和规范化的过程中,学前教育政策研究发挥了非常重要的作用。回顾我国学前教育政策研究的历史,可以发现相关研究者在价值取向上始终坚持学前教育政策研究应呼应国家重大政策、服务时代与社会变革需求、关注事业发展中的关键问题,体现了对公平和质量的持续求索,日益关注弱势群体及精准扶贫,并从宏观探讨逐渐转向对关键政策点的研究,重视多元利益主体的诉求。在研究范式上,我国学前教育政策研究经历了从结构功能主义到批判性分析范式、从理论思辨到实证研究的转向,实现了多元研究范式的并存和互补,研究视野随之逐渐开阔,并积极引入了跨学科视角。学前教育管理与办园体制、财政投入与师资队伍保障机制,学前教育资源扩大与均衡配置、弱势群体扶助、普惠发展,学前教育政策规范、质量保障及立法等是今后一段时期内我国学前教育政策研究的核心主题。     

Understanding the Program Effectiveness of Early Mathematics Interventions for Prekindergarten and Kindergarten Environments: A Meta-Analytic Review

Research Findings: The early childhood years are critical in developing early mathematics skills, but the opportunities one has to learn mathematics tend to be limited, preventing the development of significant mathematics learning. By conducting a meta-analysis of 29 experimental and quasi-experimental studies that have been published since 2000, this study extends beyond prior evaluations of early mathematics programs for prekindergarten and kindergarten environments by quantifying program effectiveness in terms of effect sizes and examining 6 aspects of these programs. We found an overall moderate to large effect size. There was a tendency for programs to produce larger effects when they (a) targeted a single content strand, (b) presented content 120 to 150 min per week, (c) designed programs for the prekindergarten environment, (d) presented content individually to children, and (e) used researcher-made mathematics assessments. Practice or Policy: Early mathematics programs can be designed to be both developmentally appropriate and highly effective. The goal of this meta-analysis was to reveal these programs to early development and education professionals so that they understand some of the factors that might explain why some produced stronger effects than others.     

Exploring young children's (mathematical) thinking: preservice teachers reflect on the use of the one-to-one interview

One-to-one interviewing is one of the most powerful ways of exploring young children's thinking. While there are a few studies which report the use of this pedagogic strategy by preservice teachers, more are needed. This paper describes an early childhood mathematics education assignment which preservice teachers in a teacher-education college in Ireland undertake with four- and five-year-old children. It presents an analysis of data from a selected sample of 58 preservice teachers' reflections on their dialogues with individual children. It describes how the preservice teachers engaged with the process of interviewing the children; how they reflected on their interactions with the children; their reflections on the children's engagement; and their reflections on young children's mathematics generally. Some dilemmas faced by the participants in the course of the interviewing are highlighted. Findings demonstrate the integrated nature of the knowledge that early childhood teachers need to teach early childhood mathematics effectively. The learning arising from this assignment relates to early childhood mathematics thinking, to the psycho-social nature of learning in early childhood and to pedagogy in early childhood education.     

A Study Of Mathematics Anxiety in Pre-Service Teachers

The study investigated the changes in levels of mathematics anxiety among pre-service teachers in six different sections of a mathematics method courses for early childhood/elementary education pre-service teachers. The changes were a function of using Bruner’s framework of developing conceptual knowledge before procedural knowledge and using manipulatives and other activities to make mathematics concepts more concrete and meaningful. Data were collected using quantitative and qualitative measures. Two hundred forty-six pre-service teachers completed a 98-item Likert-type survey. Informal discussions, informal interviews, and questionnaire-guided narrative interviews were conducted with pre-service teachers. Data revealed a statistically significant reduction in mathematics anxiety in pre-service teachers (p < .001) who completed a mathematics methods course that emphasized Bruner’s model of concept development. Results of the study have implications for teacher education programs concerning how future teachers are trained, the measurement of mathematics anxiety levels among pre-service teachers, and the determination of specific contexts in which mathematics anxiety can be interpreted and reduced.     

Learning Stories – crossing borders: introducing qualitative early childhood observation techniques to early childhood practitioners in Saudi Arabia

Early childhood education has become a focus of government policy across the world. Part of the present increased interest in early childhood education has been a focus on curriculum frameworks and socio/cultural methods of assessment. Currently, New Zealand has emerged as a world leader in early childhood education, and observation and assessment techniques, developed in New Zealand, have become an international focus of research and pedagogic practice. One exemplar practice to have emerged from research in New Zealand is the assessment of children's learning. An assessment project, conducted at the instigation of the New Zealand Ministry of Education, was designed to recognise key outcomes from the New Zealand curriculum, Te Whāriki, and to provide practitioners with a tool that would assist in the development of assessment ideas and procedures. The result was Learning Stories. This present research explored the introduction of Learning Stories into Australia and investigated the potential of Learning Stories as an assessment tool for early childhood practitioners in the context of Saudi Arabia.     

An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood

The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics education, so too does the focus on teaching quality. This paper reviews nine instruments designed to measure mathematics teaching quality—their theoretical bases, foci, and psychometrics—and examines their appropriateness for administration in early childhood settings. Three of the nine measures are identified as having highly desirable characteristics, with one of them specifically designed for early childhood administration. The measures, our review process, and our recommendations for practice are presented. As school divisions and teacher educators examine teaching quality, they will be better able to support their teachers’ practice, and better able to reap the benefits in improved child outcomes.     

Inequities and lack of professionalisation of early childhood development practice hinder opportunities for mathematics stimulation and realisation of South African policy on quality education for all

White Paper 5's aim is to provide South Africa's children with a solid foundation for lifelong learning and development. Children need to be nurtured and developed holistically for them to participate efficiently in their democratic society. However, South African students continue to perform poorly in Trends in International Mathematics and Science Study compared to other African countries. Contributing factors highlighted by research on this poor performance include students' lack of foundational knowledge. Hence, mathematics stimulation for young children has been suggested as a prompt intervention towards improving mathematics performance. This paper therefore evaluates the preparedness of practitioners who work with 3–4-year-olds as resources for facilitating mathematics stimulation, availability of mathematics stimulating resources and daily planning for mathematics stimulation. The findings of this paper indicate that mathematics development of children younger than five years is loaded with many inequity factors and continue to exclude the majority of black children. This paper recommends professionalisation of the early childhood education with emphasis on quality provisioning that can be achieved through norms and standards that are monitored continuously in all formal and informal settings that provide early childhood education.     

Applying Technology to Inquiry-Based Learning in Early Childhood Education

Children naturally explore and learn about their environments through inquiry, and computer technologies offer an accessible vehicle for extending the domain and range of this inquiry. Over the past decade, a growing number of interactive games and educational software packages have been implemented in early childhood education and addressed a variety of subjects, including mathematics, science, reading, language, and social studies. However, most software packages have yet to integrate technology into inquiry-based learning for early childhood contexts. Based on existing theoretical frameworks, we suggest that instructional technologies should be used in early childhood inquiry education to (a) enrich and provide structure for problem contexts, (b) facilitate resource utilization, and (c) support cognitive and metacognitive processes. Examples of existing and hypothetical early childhood applications are provided as we elaborate on each role. Challenges and future research directions are also identified and discussed.