Pattern discernment and pseudo-conceptual development in early childhood mathematics education

In this empirical study, we investigate an early childhood education activity in mathematics on the concept of ‘pattern’. The children participating in the study attend an intermediate form of schooling in Sweden called ‘the preschool class for six-year-olds’, intended to facilitate their transition from preschool to school. Following a prolonged activity over 45 minutes, we analyse for what the children are supported in discerning and what they give as evidence of having discerned in and about patterns. The theoretical point of departure is variation theory, conceptualising learning as increased discernment. The results show that in terms of the important Vygotskian distinction between ‘pseudo concepts’ and ‘concepts (proper)’, the children's discernment and what they are supported in discerning are of the former kind. Pseudo concepts are discussed as integral to the institutional form of the preschool class and premised to be important to the child's further conceptual development.     

Providence talks: A citywide partnership to address early childhood language development

Early research has shown that there may be inconsistencies in how parents in different socioeconomic classes prepare their children to learn to read. Previous research has highlighted a “word gap” between children from low-income families and high-income families. Effects of this “word gap” are evident at the start of kindergarten and contribute to the current nationwide achievement gap in educational outcomes for low-income children. Providence Talks (PT) is a city-wide initiative launched in 2014 in an effort to close this gap. PT helps caretakers learn about the importance of speaking with their children at an early age and supports them in their ability to improve the language environments within their home. We uncover positive results for the efficacy of a citywide intervention dedicated to improving outcomes for vulnerable children across the urban landscape.     

Expanding the instructional triangle: conceptualizing mathematics teacher development

As mathematics educators think about teaching that promotes students’ opportunities to learn, attention must be given to the conceptualization of the professional development of teachers and those who teach teachers. In this article, we generalize and expand the instructional triangle to consider different interactions in a variety of teacher development contexts. We have done so by addressing issues of language for models of teachers’ professional development at different levels and by providing examples of situations in which these models can be applied. Through the expansion of our understanding and use of the instructional triangle we can further develop the concept of mathematics teacher development.     

Looking through the lens of a teacher's life: The power of prototypical stories in understanding teachers' instructional decisions in mathematics

The focus of this narrative inquiry was to examine how teachers describe influences on their instructional decisions in mathematics. Using a lens provided by pivotal or prototypical stories teachers told about their past experiences, connections were suggested between these past experiences and their instructional decisions. These connections helped to illustrate how instructional decisions may be shaped by priorities and beliefs established earlier in life, as well as by current contexts. Further research on the use and characteristics of prototypical stories is suggested.     

Continuing professional development in the Greek early childhood education system

Over the past years, Greece has been undergoing a severe financial crisis. The main purpose of this study was to examine how early childhood teachers perceive continuing professional development (CPD) under such societal turmoil. More specifically, this study examined the perceptions of 45 in-service kindergarten teachers attending the ‘Didaskaleio’ training institute. Results showed that although Greek early educators express a positive attitude towards CPD, there are certain contradictions in their views regarding the way they perceive CPD and their expectations regarding CPD activities. Results indirectly reflect the changing context, the systemic weaknesses and the antinomies of Greek early childhood education.     

Policy-to-practice contexts for early childhood mathematics in England

This article considers the relationship between policy and practice in the early childhood mathematics curriculum for reception-class (RC) children of five years in England. It explores what the policy requires RC teachers to do in terms of curriculum implementation; what RC teachers’ views and understanding of the early childhood mathematics curriculum are; how RC teachers implement early years mathematics policy; and how RC children respond. A case study design included interviews with elite participants who influenced the policy-making process, survey of RC teachers and a detailed investigation of RC classes on three school sites. As elite interviews underlined, international comparison studies have had an important influence on early childhood mathematics policies by creating top-down pressure for standards. Elites and practitioners drew attention to a tension between a play-based pedagogy and a standards agenda. Tensions in policy text were reflected in mixed and ambivalent views and reported practices by elites and practitioners. RC teachers did not merely receive and implement policy expectations but brought their own values and understandings to practice. The study reveals interplay between local and global influences in a context of changing views of early childhood, early learning and early years pedagogy.     

Exploring the relationship between teacher enjoyment of mathematics,their attitudes towards student struggle and instructional time amongst early years primary teachers

In this study we explored the relationship between teacher enjoyment of teaching mathematics, their attitudes towards student struggle, and the amount of time teachers spent teaching mathematics. Ninety-eight primary educators were surveyed regarding their attitudes and behaviors towards mathematics instruction. Hierarchical regression analyses revealed that teacher enjoyment of teaching mathematics explained variance in both teacher attitudes towards student struggle and instructional time spent on mathematics, even after relevant educator characteristics were accounted for. Findings suggest that teacher enjoyment of teaching mathematics in the early primary years has important implications for both the quality and quantity of mathematics instruction students receive.     

Interactive TV as an option in early childhood teacher education

Abstract

The qualitative study examined the processes and approaches to collaboration, reflection, and dialogue of preservice and mentoring teachers who were engaged in a yearlong internship experience. Within the context of a university course grounded in constructivism, social constructivism, and the concept of teacher as researcher, the study explored the social interactions of the teachers throughout the course of the school day. Teachers were observed in the process of planning and reflecting on daily classroom activities through collaborative meetings with a focus on the teaching and learning process. The preservice teachers were educated in the use of the main principles described by the Reggio Emilia Approach ‐ collaboration reflection, and dialogue (Edwards, Gandini &; Forman, 1998) and thus, served as a guide for the collaborative interactions with the mentoring teachers.     

Continuing evolution: The Rhode Island early childhood summer institute

Abstract

This narrative chronicles the continued evolution and development of the Rhode Island Early Childhood Summer Institute, an intensive 5‐day inservice professional development program designed for educational leaders from various sectors of the early care and education field. The goal is to review the continued use of successful practices implemented in the 1993 through 1997 programs and to highlight new programmatic features that were introduced in the most recent 2000 and 2001 programs. The Rhode Island Early Childhood Summer Institute program may serve as a model to others responsible for designing inservice professional development experiences to enhance the capacity of the early childhood workforce.     

The indirect effect of children's gender on early childhood educators' mathematical talk

The purpose of this study is to examine how teachers might engage in mathematical talk differently with boys and girls within an early childhood classroom setting; therefore, possibly building and maintaining the stereotype of mathematics as a male domain. Utilizing a multi-model approach, results suggests minimal differences in the extent in which teachers in this study engaged in mathematical talk with girls and boys in class. However, any noted differences in mathematical talk and questions seem dependent upon the classroom contexts (i.e., whole-class, small group, and center time). Implications and future research will be discussed.     

The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice

Case studies were conducted to investigate the conceptions of mathematics and mathematics teaching held by three junior high school teachers. Examination of the relationship between conceptions and practice showed that the teachers' beliefs, views, and preferences about mathematics and its teaching played a significant, albeit subtle, role in shaping their instructional behavior. Differences among the teachers in their conceptions and practices are explained followed by a discussion of properties of their conceptual systems.This paper is based on the author's doctoral dissertation which was directed by Professor Thomas J. Cooney of the University of Georgia and was partly supported by a grant from San Diego State University. I wish to express my appreciation to the teachers who participated in the study and their administrators.     

谈数学教育中学生思维品质的培养

阐述了数学思维品质的概念，并根据素质教育的要求，从创调教学环境，优化教学方法，挖掘教学内容，设计教学过程等方面，提出了引发学生数学思维，培养其数学思维品质的途径和方法。     

Understanding variation in classroom quality within early childhood centers: Evidence from Colorado's quality rating and improvement system

This study examines variability in quality across classrooms within early childhood centers and its implications for how quality rating systems (QRSs) capture center-level quality. We used data collected for administrative purposes by Qualistar Colorado which includes the environmental rating scale (ERS) collected in all classrooms in the 433 centers participating in Colorado's QRS between 2008 and 2010. We conducted variance components analysis for the ERS and found that between 26% and 28% of the variation in quality captured by the ERS occurred across classrooms within the same center serving children in the same age range. This finding reveals that capturing center-level quality based on average ERS will often miss important within-center quality differences and points to the merits of using “no score below” rules along with rating tier cutpoints in determining center-level ERS. Most QRSs assess center-level quality for a randomly selected subset of classrooms. To test the implications of cross-classroom quality variation for this practice, we simulated four classroom selection strategies in current use: selecting 50% of the rooms, 33% of the rooms, two rooms, or one room. In general, the larger the share of classrooms measured under a selection rule, the lower the chance that a center's rating tier will be misclassified. The error rates under each selection rule also depend on the extent of cross-classroom quality variability, how centers are distributed by size, and the QRS structure. QRS designers, therefore, need to consider the tradeoff between the costs of measuring more classrooms in each center versus the costs of misclassifying centers. The paper quantifies the magnitude of these tradeoffs using the Colorado data and two illustrative QRSs. The implications of our findings for QRS designers, parents, and other stakeholders are discussed.     

Effects on the technological pedagogical content knowledge of early childhood teacher candidates using digital storytelling to teach mathematics

This study aimed to present early childhood teacher candidates' experiences preparing digital stories and to reveal the resulting changes, if any, in self-reported technological pedagogical content knowledge (TPACK). This study was quasi-experimental and indicated that teacher candidates' evaluations of digital storytelling were affected by their preparation experiences. Moreover, results showed a shift from dual intersections of technology, pedagogy, and content knowledge to the triple intersection of TPACK.     

Using video to promote early childhood teachers' thinking and reflection

This article examines findings from a qualitative study employing group stimulated-recall interviews using video-recordings of early childhood teachers to elicit their thinking and reflections about their teaching interactions. It focuses on the value of video to enable teachers to reflect on their practices and the extent to which collectively viewing recorded episodes allows negotiated understandings of their own and other teachers' practices. Whilst these findings suggest that video and collective dialogue are useful professional learning tools for teachers to examine and improve their teaching, structural and relational challenges exist that may impact on how effectively such tools are used.     

将素质教育思想融入数学教学之中

高等数学是电大开放教育财经、理工专业的一门基础必修课。在开放教育数学教学中,必须充分发挥数学课程的实用、思维、德育、美育等功能,注重数学思想方法教学,运用多种教学方式,培养学生思维能力和自主学习的能力。     

Preschool teachers' beliefs about children's print literacy development

Beliefs have often been considered important because of their relation to practice. Little is known about the literacy beliefs of preschool teachers, particularly their print literacy beliefs, even though young children's experiences with print have implications for formal schooling. Therefore, this study explored the print literacy beliefs of preschool teachers in a large multicultural area of central Canada. Interviews were conducted with eight preschool teachers based on a previous study in Australia. There were five themes that emerged from this research: uncertainty and variation in beliefs about how and when children learn to read and to write; isolation from other preschools and limited access to professional literacy knowledge; the importance of parent involvement in children's literacy development and the need to inform; increased literacy knowledge required; and variation in practices for fostering print literacy development. This study has important implications for preschool teaching as well as for educators of preschool teachers.     

More than a shortage of early childhood teachers: looking beyond the recruitment of university qualified teachers to promote quality early childhood education and care

In Australia and internationally, government policies aim to increase the supply of early childhood teachers and thus improve the quality of early childhood education and care services. In this paper, we suggest that such a policy-quality trajectory in Australia is not as straightforward as policy discourses suggest. From industrial relations and broader policy contexts, we argue that the early childhood profession is a profession on the margins and that this marginalisation complicates efforts to enhance numbers of early childhood teachers. Mindful of this marginalisation, we draw upon preliminary findings from a study exploring the motivations, beliefs and expectations of mature age postgraduate students to highlight practical issues pertaining to students and early childhood teacher education programs that further complicate policy drives to increase the supply of early childhood teachers. We propose that the success of such policy drives is dependent on a comprehensive addressing of the complexities raised in this paper.     

Purposeful pauses: teacher talk during early childhood mathematics activities

This paper describes how early childhood teachers' incorporation of pauses raises the quality of talk-in-interaction during play-based mathematics activities. Responses of both children and teachers are shown to be more contingent and expansive when conversations include protracted pauses than during interactions in which pauses are largely absent. Pauses provided children with opportunities to initiate topics and facilitated more equitable access to discourse moves for children. By pausing before responding to a child's conversational gambit, teachers gained opportunities to assess children's demonstrated numeracy-related skills and understanding, and could thus provide authentic, individualised scaffolding. Pauses were not necessarily silent: a pause in an interaction with one child could be used strategically to model the learning interaction with a second child before returning to the first child in order to continue the discourse sequence.