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.     

The Impact of an Ongoing Professional Development Program on Prekindergarten Teachers' Mathematics Practices

Mathematics is a natural part of daily life for young children as they explore and investigate the world around them. To build on these experiences, and to begin establishing a mathematical foundation, early childhood educators must not only be knowledgeable about mathematical concepts, they must also be aware of the most developmentally appropriate ways in which to teach these concepts to young children. After participation in an ongoing professional development program, specifically targeting teachers of prekindergarten children in public school, Preschool Programs for Children with Disabilities (PPCD), Head Start, and child care settings, teachers reported positive changes in math practices. Specifically, teachers reported a stronger alignment to national mathematics standards and increased awareness pertaining to developmentally appropriate mathematics practices as they apply to early childhood classrooms. Teachers reported a shift towards more hands-on activities and a shift away from the use of worksheets in their prekindergarten classrooms. Implications from this study suggest that ongoing professional development that is designed to meet the specific needs of early childhood educators can have a positive impact on reported mathematics content knowledge and instructional practices.     

GENDER DIFFERENCES IN THE RELATIONSHIP BETWEEN TAIWANESE ADOLESCENTS' MATHEMATICS ATTITUDES AND THEIR PERCEPTIONS TOWARD VIRTUAL MANIPULATIVES

This study explored gender differences in the relationship between young people's mathematics attitudes and their perceptions toward virtual manipulatives. Seven hundred eighty junior high school adolescents who participated in the problem-solving activity using virtual manipulatives were selected for examination. The study found the male adolescents' views on motivation and enjoyment of mathematics could explain many aspects of their perceptions toward virtual manipulatives. The female adolescents' views on the importance of mathematics and freedom from fear of mathematics could explain many aspects of their perceptions toward virtual manipulatives. However, motivation, enjoyment, and importance of mathematics were more prominent than freedom from fear of mathematics in predicting male adolescents' perceptions toward virtual manipulatives, and freedom from fear and importance of mathematics were more prominent than enjoyment and motivation of mathematics in predicting female adolescents' perceptions toward virtual manipulatives. Two implications can be drawn from this study. First, teachers could provide males with appealing problem contexts not only to be used to remove the fear of mathematics, but also to be used for enjoyment and as motivation to see the importance of mathematics. Then male students could be encouraged to have more confirmed positive perceptions toward virtual manipulatives when engaging in the activities of computer-based mathematics. Second, teachers could provide females with interesting teaching activities, not only to be used for motivation and the enjoyment of mathematics, but also to be used to remove the fear of mathematics and for experiencing the importance of mathematics. Then female students could have positive perceptions toward virtual manipulatives when technology was integrated into the classroom to enhance learning and to support effective mathematics teaching.     

Are We Having Fun Yet? How Teachers Use Manipulatives to Teach Mathematics

Teachers often comment that using manipulatives to teach mathematics is ‘fun!’ Embedded in the word ‘fun’ are important notions about how and why teachers use manipulatives in the teaching of mathematics. Over the course of one academic year, this study examined 10 middle grades teachers’ uses of manipulatives for teaching mathematics using interviews and observations to explore how and why the teachers used the manipulatives as they did. An examination of the participants’ statements and behaviors indicated that using manipulatives was little more than a diversion in classrooms where teachers were not able to represent mathematics concepts themselves. The teachers communicated that the manipulatives were fun, but not necessary, for teaching and learning mathematics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Developing Number Sense in Pre-K with Five-Frames

Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students’ mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant evidence of teacher use and a lack of systematic research we know little to nothing about both the developmental and pedagogical implications of using five frames and related instructional manipulatives in early childhood mathematics classrooms. In this paper, we provide an overview of five-frames and specifically demonstrate ways that five-frames, if used in conjunction with concrete manipulatives, can support pre-kindergarten (pre-K) children’s development of Gelman and Gallistel’s (1978) three basic counting principles: the stable-order principle, one-to-one correspondence, and cardinality. We conclude by discussing the developmental and instructional implications of using five-frames, as well as offer a set of teaching tips designed to help teachers maximize the potential advantages of integrating five-frames in the pre-K classroom.     

Approaches to teaching in thematic work: early childhood teachers’ integration of mathematics and art

Thematic work that integrates different knowledge areas is considered suitable for developing young children’s knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers’ work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive mathematics learning and teaching integrated with art. Data for analysis were collected from a questionnaire answered by 27 early childhood teachers from Finland and Sweden. Influenced by a sociocultural theoretical framework, the analysis concerns the teachers’ expressed goals for learning and their strategies for achieving these goals. The analysis reveals qualitatively different approaches to the learning goals addressed by the teachers – process-oriented, product-oriented, development-oriented and providing awareness – which, respectively, seem to generate different meanings of mathematical learning integrated with art. This study offers an overview of teachers’ approaches to teaching mathematics and art in thematic work, and of how different approaches may influence what mathematical meaning is offered to children to explore.     

Female Preservice Teachers and Mathematics: Anxiety,Beliefs, and Stereotypes

The purpose of the current study was to examine if preservice teachers’ (PSTs) mathematics anxiety decreased and if their beliefs and stereotypes changed after they completed their early childhood mathematics methods course. It was hypothesized that by using and modeling concrete materials or manipulatives (Thompson, 1992; Vinson, 2001) and placing a greater emphasis on conceptual understanding (Bursal & Paznokas, 2006), two strategies identified as reducing PSTs’ mathematics anxiety, negative beliefs, and stereotypes that are associated with math anxiety, would diminish. Thirty preservice teachers, all female, participated in this study. Using a qualitative research approach, measures included midcourse evaluations, a draw-a-mathematician task (Mewborn & Cross 2007), the Abbreviated Math Anxiety Scale (Hopko, Mahadevan, Bare, & Hunt, 2003), and anecdotal notes. Although we were encouraged that the math anxiety experienced by our preservice teachers slightly decreased by the end of the semester, it was discouraging to find minimal change of beliefs and stereotypes of mathematicians. This confirms that many preservice teachers enter teacher education programs with well-established images of how to do school, along with entrenched beliefs about mathematics and their ability to do math (Vacc & Bright 1999) and these beliefs are very difficult to change.     

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.     

Practices more likely to occur in kindergarten mathematics teachers’ instruction when English learners are present

Considering the rising proportion of English learners (ELs) in general education, little is known about how this change in classroom composition relates to the frequency of instructional activities and skills. This study uses a multimodal perspective on learning mathematics in a multilingual context, which recognizes the diverse modes of communication that students draw on in mathematics classrooms. We examined national data using quantitative analyses and investigated the mathematics practices that were more likely to occur in kindergarten classrooms that did and did not have ELs. We found teachers reported greater frequency of manipulatives and count/calendar activities in mathematics instruction when there were EL students in the classroom. Teachers in classrooms with ELs also reported a greater frequency of mathematics content that involved teaching shapes and practical skills. The findings indicate that teachers tended towards a supportive multimodal approach to instruction when ELs were present.     

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.     

A Study of Early Childhood Mathematics Teaching in the United States and China

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts. Specifically, 27% of the U.S. participants did not set any goals for mathematics, and 20% did not use a curriculum or any resources. In contrast, 3% of the Chinese participants fell into each of these categories. Second, early childhood mathematics content in the United States appears to be broader and less differentiated by age group than in China. Lastly, emerging curriculum (mathematics learning that emerges from children's play, activities, and routines) is the prevailing approach for 3- and 4-year-olds in the United States. In comparison, mathematics-specific teaching is the primary, but not sole, form of instruction in China. Practice or Policy: These findings have important implications for implementing the Common Core mathematics standards in the early years.     

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.     

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.     

Effects of a Pre-Kindergarten Mathematics Intervention: A Randomized Experiment

Abstract

Research indicates that a socioeconomic status-related gap in mathematical knowledge appears early and widens during early childhood. Young children from economically disadvantaged families receive less support for mathematical development both at home and in preschool. Consequently, children from different socioeconomic backgrounds enter elementary school at different levels of readiness to learn a standards-based mathematics curriculum. One approach to closing this gap is the development and implementation of effective mathematics curricula for public preschool programs enrolling economically disadvantaged children. A randomized controlled trial was conducted in 40 Head Start and state preschool classrooms, with 278 children, to determine whether a pre-kindergarten mathematics intervention was effective. Intervention teachers received training that enabled them to implement with fidelity, and a large majority of parents regularly used math activities teachers sent home. Intervention and control groups did not differ on math assessments at pretest; however, gain scores of intervention children were significantly greater than those of control children at posttest. Thus, the intervention reduced the gap in children's early mathematical knowledge.     

Teacher characteristics and contextual factors: links to early primary teachers’ mathematical beliefs and attitudes

This study examines how various teacher characteristics and contextual factors are related to early primary teachers’ beliefs about mathematical teaching and learning and teachers’ attitudes toward their own learning of mathematics. A total of 396 early primary teachers across Nebraska participated in the study. Teacher characteristics and contextual factors were grouped into four sets: teacher professional background, teacher mathematical knowledge for teaching, teaching contexts, and students’ experiences. Multiple regression analyses were conducted with each set of predictors separately, as well as with all four sets together. The results showed significant relationships between teachers’ mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics. Teacher certification level, the number of college math courses taken, and perceived support from colleagues and administrators were also related to some aspects of teachers’ mathematical beliefs and attitudes. The findings suggest the potential role of teachers’ mathematical knowledge for teaching in improving teachers’ mathematical beliefs and attitudes.     

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.     

Role of teacher characteristics and school resources in early mathematics learning

The authors investigated the degree to which school-level teacher characteristics and resources are related to the mathematics learning of kindergarten children using a sample drawn from a large US database. Kindergarten-level teacher characteristics were operationalised as collective teacher efficacy, teacher experience and teacher preparation; kindergarten resources were operationalised as efforts that schools make to reach out to parents, classrooms with mathematics manipulatives, and classroom technology. Kindergarten students learned more in mathematics over a year in schools where teachers’ collective efficacy was high. School resources yielded a range of significant yet mixed results in young children’s mathematics achievement. Notably, younger students and students entering kindergarten with lower levels of mathematical skills benefited greatly from classroom resources. Overall, the presence of classroom technology as a school-level resource was positively related with older kindergarten students’ learning. Based upon the findings, organisational and policy implications are discussed.     

Using manipulatives to support an embodied approach to learning trigonometry in a South African school: A case study

ABSTRACT

Multiple Intelligence Theory suggests that individuals perceive knowledge in eight different ways. This article reports on a study that explored the role of manipulatives in the teaching and learning of trigonometric ratios in grade 10. The approach attempts in addressing three domains of the Multiple Intelligence Theory (linguistic/verbal intelligence, logical/mathematical intelligence and spatial intelligence). The foundation of this research was a case study contained in the interpretative paradigm involving five grade 10 mathematics pupils at a high school in South Africa. The data was collected from: (1) activity sheet containing written responses of pupils; (2) observations; and (3) semi-structured interviews. The data was analysed and it was found that the use of manipulatives in teaching and learning mathematics played a positive role in leaners understanding of trigonometric ratios at grade 10 level. In general the findings of this study supported other research findings that confirm that manipulatives were important mediating tools in the development of conceptual and procedural understanding of mathematical concepts. Besides these pedagogical implications the study proved that the manipulatives effectively consolidated the features of Lesh's model.     

The influence of perceptually rich manipulatives and collaboration on mathematic problem-solving and perseverance

We conducted a two-part study to examine how the use of different manipulatives, levels of instructional guidance, and collaboration among college-aged students influenced their mathematics performance and perseverance. In Study 1, we manipulated different types of manipulatives (no manipulative, bland, and perceptually rich), and different contextual factors of instructional guidance (high vs. low) to identify how they influenced students’ ability to complete mathematical problems as well as impact students’ perseverance. Findings showed that participants’ use of bland manipulatives positively impacts their ability to complete word problems. Study 2, grounded in findings from Study 1, incorporated collaborative learning to lessen the negative effects of using perceptually rich manipulatives and enhance students’ perseverance in mathematics. The results from Study 2 aligned with the findings from Study 1 concerning the negative effect of perceptual richness for problem-solving and perseverance. Moreover, the collaboration of participants had a positive effect on students’ perseverance during problem-solving as students who collaborated with perceptually rich manipulatives persevered as much as those who collaborated with bland manipulatives as well as those who worked individually with bland manipulatives.