“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.     

Child developmental impact of Pittsburgh’s Early Childhood Initiative (ECI) in high-risk communities: first-phase authentic evaluation research

The national debate surrounding the issue of school failure has renewed interest in the quality, efficacy, and outcomes of early childhood intervention programs that can promote early school success for children at developmental risk. Moreover, researchers and policymakers report the need to document developmentally-appropriate models for assessing and evaluating early childhood outcomes. We report on the first-phase results of Pittsburgh’s early childhood initiative (ECI). ECI is a privately-funded effort by a consortium composed of the business, corporate, foundation, and community sectors to implement high-quality early care and education options for children in high-risk neighborhoods. The overarching objective of ECI is to ensure early school success for high-risk children. Our Scaling Progress in Early Childhood Settings (SPECS) Evaluation Team implemented an authentic assessment and program evaluation strategy and an enhanced “constructed comparison group” statistical model to conduct longitudinal research on the child developmental impact of the ECI model. First-phase results on 155 high-risk children indicate that those who participated in high-quality ECI programs for the longest periods of time demonstrated patterns of progress that exceeded maturational expectations. Weekly collaborative consultation to teachers and caregivers by consultants about program quality using the National Association for the Education of Young Children (NAEYC) standards as “best practice” benchmarks seemed to be associated with initial enhanced child outcomes and the particular impact of the ECI model.     

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.     

How Students Verify Conjectures: Teachers’ Expectations

Eight teachers were interviewed concerning how students verify conjectures. The study is a sequel to a previous study, “How Students Verify Conjectures” [Bergqvist, T. (2000). How students verify conjectures. Research reports in Mathematics Education 3]. Teachers’ expectations of students’ reasoning and performance are examined, and also how they wish students would work. The results indicate that the teachers tend to underestimate the students’ reasoning levels and that they believe that only a small group of students in each class can use higher level reasoning in mathematics.     

“To make the tacit explicit”: Teacher education, emerging discourse, and conceptions of teaching

The influence of teacher education on teaching is a problematic area, both in practice and in research. Often, because much research adopts a “first-order” perspective which focuses on teachers' behaviors, influences of teacher education are seen as temporary, negligible, or difficult to determine. The study reported here grew out of a general concern to document, via a “second-order” perspective which examines their thinking and perceptions, how teachers modify or improve what they do through formal teacher education. It addresses three important areas which have received little attention in recent research: foreign language teaching, in-service graduate education, and the role of a shared, professional discourse in developing teachers' conceptions of teaching. The paper presents a summary of the findings of an 18-month longitudinal study which examined how foreign language teachers' conceptions of their classroom practice developed as they took part in an in-service teacher education program. The paper discusses how the program's shared professional discourse contributes to increasing the complexity of the teachers' thinking about their teaching and suggests that as they learn to articulate their de facto ways of thinking in the shared discourse, the teachers gain greater control over their classroom practice and are thus more able to shape it to their own ends.     

Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and communicating in mathematics classrooms.     

Mathematics for teaching and deep subject knowledge: voices of Mathematics Enhancement Course students in England

This article reports an investigation into how students of a mathematics course for prospective secondary mathematics teachers in England talk about the notion of ‘understanding mathematics in depth’, which was an explicit goal of the course. We interviewed eighteen students of the course. Through our social practice frame and in the light of a review of the literature on mathematical knowledge for teaching, we describe three themes that weave through the students’ talk: reasoning, connectedness and being mathematical. We argue that these themes illuminate privileged messages in the course, as well as the boundary and relationship between mathematical and pedagogic content knowledge in secondary mathematics teacher education practice.     

“Bumpy moments” in teaching: Reflections from practicing teachers

During the complex teaching act, there are moments that require teachers to engage in reflection to make critical decisions about how to respond to particular problems in practice. The present investigation provides a stimulus for capturing these reflections as four elementary practicing teachers are asked to describe their “bumpy moments” in teaching. Analysis of the 19 “bumpy moments” identified offers insights into the thoughts, knowledge, and beliefs that these teachers are considering during their practice. Results have implications for capturing reflection during teaching, ongoing practicing teacher professional development, and preservice teacher education.     

Multiple representations as sites for teacher reflection about mathematics learning

This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.     

Early childhood teacher education: the case of geometry

For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and describe a series of research and development projects based on this body of knowledge. We conclude that research-based models hold the potential to make a significant difference in the learning of young children by catalyzing substantive change in the knowledge and beliefs of their teachers.     

Teachers attending to students’ mathematical reasoning: lessons from an after-school research program

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.     

Playing with maths: implications for early childhood mathematics teaching from an implementation study in Melbourne,Australia

The Early Years Learning Framework for Australia governs early childhood education in the years before school in Australia. Since this framework is not a curriculum, early childhood educators report uncertainty regarding what mathematical concepts to teach and how to teach them. This implementation study, positioned within the broader E4Kids study, explored the enactment of a suite of play-based mathematics activities by five early childhood educators in different settings over a seven-month period. The educators' approaches to incorporating the activities are discussed in light of the reported implementation frequency and the duration of activities. A regression analysis predicted significant changes in children's Fluid Intelligence/Reasoning associated with attending high-implementation programmes. Recommendations are made for further investigation of the enactment of mathematics activities in early childhood settings and for the provision of professional learning opportunities that focus on supporting children's concept development as well as their mathematical skills.     

A “top-down” analysis of high school teacher motivation

Classroom instruction may be affected by school contexts that are increasingly performance-driven because of legislative demands. Interpreting this as a need to investigate the relationships between school context and classroom practice, this study took a “top-down” approach by examining contextual elements of school goal structure and teacher community on teachers’ sense of self- and collective efficacy, and classroom goal structures. After collecting data from teachers in four Midwestern high schools, results indicated that teachers in highly performance-oriented schools reported significantly less adaptive motivational beliefs, lower community, and more performance-oriented instruction than teachers in a low performance-oriented school. Furthermore, a path analysis revealed that classroom goal structures were significantly and indirectly related to teacher community. We discuss how academic context may affect teachers’ motivational beliefs as well as classroom practices, and make recommendations for future research and practice.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project

Abstract

In the present study the relationship between teaching and learning was examined using a conceptual framework that links dimensions of instructional tasks with gains in student learning outcomes. The greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas, student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication.     

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.     

Introduction to the Special Issue: Developing a Relationship Perspective in Early Childhood Research

An interpersonal relationship perspective is gaining influence in early childhood practice and research. The research presented in this special issue, “Relationships in Early Childhood Programs”, focuses on adult-child, child-child, and adult-adult relationships as they develop in the context of early childhood programs. The authors address issues of importance to both practitioners and researchers: types and dimensions of early childhood program relationships; measurement of relationships; relationship processes that are central to program goals; and the importance of interpersonal relationships as a focus for practice, theory, and research.     

数学能力的脑与认知科学研究及其对早期数学教育的启示

数学能力是基础性的认知能力,包括数量、空间和逻辑推理等认知能力。早期数学教育有助于在儿童发育和发展的关键期为儿童奠定认知和神经基础,从而培养儿童抽象而精确的数学思维能力与问题解决能力。脑与认知科学研究表明,儿童生来具有数的概念,体现在两个独立的数的核心表征系统,一是大数系统,模糊估计、粗略表征物体的数量幅度;二是小数系统,精确计数、清晰表征每一个物体。早期数学教育可以借鉴当前丰富的脑与认知科学研究成果,将科学理论和教学实践相结合,利用儿童先天具备的数学潜质,逐渐深入而广泛地培养儿童的数学技能。培养儿童的早期数学能力需要家庭、学校和社会的共同努力。     

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for meaningful and developmentally appropriate mathematics experiences for young children in diverse early learning settings. Instructional and curricular methods inspired by the Reggio Emilia Approach are described as effective ways to teach number concepts to young children from preschool through primary age. Strategies for teachers of young learners are presented in order to strengthen the mathematics curriculum in contemporary early learning settings. The authors’ analysis and recommendations are informed by their extensive experiences including studies in Reggio Emilia early childhood settings (infant toddler, preschool, and primary schools) and their work in early childhood teacher education at their respective universities.