USING CHILDREN'S WORK TO REFLECT ON TEACHING: ONE EARLY CHILDHOOD STUDENT TEACHER'S REFLECTIONS

Abstract

The purpose of the study was to examine the engagement of preservice teachers in the kind of authentic experiences that provided the modeling needed to make high‐quality instruction in mathematics a reality for young children. Inasmuch as these preservice teachers had not yet received any formal methods classes in mathematics, the authors theorized that classroom teachers whose practices and dispositions were congruent with the National Council of Teachers of Mathematics standards and the State of South Carolina Mathematics Standards could model effective teaching instruction for young children using the project approach. These same teachers could then provide mentoring and encouragement to preservice teachers as they became involved in this high‐quality program for 4‐year olds, deepening the knowledge base of the preservice teachers regarding developmentally appropriate ways to teach numeracy to 4‐year olds. © 2005 Elsevier Inc. All rights reserved.     

The Impact of First Computer Encounters on Mathematics Teachers’ Computer Competence

ABSTRACT

Twenty‐seven United Kingdom teachers of secondary mathematics were interviewed about information technology (IT) and its influence on their teaching of mathematics. A common factor to emerge was the nature of their first experience of computers and the impact it had on their subsequent professional activity. The analysis identified four ways in which teachers first encountered computers; as learners at school, university or colleges of education, as teachers undertaking in‐service training, as self‐taught adult learners, or as employees or researchers engaged in computer‐based activity prior to becoming teachers. A significant issue to emerge was that similar initial encounters are likely to have different and lasting professional consequences depending on the persons involved and their perceptions of mathematics, computers, the relationship between the two, and a range of other personal and institutional factors. Some implications for both pre‐service and in‐service training are discussed.     

Toward a constructivist perspective: The impact of a mathematics teacher inservice program on students

A constructivist-oriented inservice program provided teachers of mathematics (K-12) with intensive two-week summer institutes and weekly classroom follow-up. Pre- and post-program data on student outcomes indicate that, along with transformations in the nature and quality of mathematics activity in the classroom, students' beliefs about learning mathematics changed and elementary students' attitudes toward mathematics improved. Although the instruction they now received focused more on conceptual understanding and less on computational skill, students' scores on standardized tests assessing routine knowledge were maintained.An earlier version of this paper appeared in R. Underhill (ed.),Proceedings of the Thirteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education 1, 43–49, Backsburg, VI.     

RELATIONSHIPS BETWEEN TEACHING SELF‐EFFICACY,WORK ENVIRONMENT AUTONOMY,AND TEACHER COMPETENCY AMONG EARLY CHILDHOOD PRESERVICE TEACHERS

Abstract

In this article, we examine the integration of science and mathematics teaching in early childhood education. We explore the meaning of integration and offer a rationale for integrating science and mathematics methods classes for pre‐service teachers. The case is made that pre‐service teachers should develop an understanding of the connections between mathematics and science so that they can be better prepared to teach with an emphasis on the connections between these two content areas.     

EARLY CHILDHOOD TEACHER EDUCATION FOR THE 21ST CENTURY: NOT BY CHANCE

Abstract

This study examined correlations between teachers’ attitudes toward mathematics/teaching mathematics and the practice of developmentally appropriate mathematics. This study tested two independent variables: (1) kindergarten teachers’ attitudes toward mathematics; and (2) kindergarten teachers’ attitudes toward teaching mathematics; and their relationships with the practice of developmentally appropriate mathematics.

The researcher designed a survey questionnaire by cross‐referencing several instruments and the review of related literature. A sample of 200 kindergarten teachers was randomly selected from the Indiana Department of Education website directory. Of the 200 kindergarten teachers, 81 teachers participated in this study by returning the survey questionnaire to the researcher via the postal service, e‐mailing, or posting the response over the Internet.

Each independent variable was tested to determine the level of its statistical significance by using multiple linear stepwise regression procedures. The results of this study revealed that kindergarten teachers’ attitudes toward teaching mathematics were found to be a significant variable correlating with the practice of developmentally appropriate mathematics, but kindergarten teachers’ attitudes toward mathematics were not a significant variable.     

Teacher education and LEA perspectives on disruptive behaviour: initial teacher training

From an examination of documents obtained from forty‐nine local education authorities (LEAs), a research suggested as useful by a project on disruptive behaviour (Lawrence, Steed & Young, 1978), an account was obtained of the expectations of LEAs as to how initial teacher training, programmes should introduce teachers to the skills required for coping with disruptive behaviour. This paper reports the findings derived from these LEA documents and examines their implications for initial teacher training.

LEAs are asking colleges to provide factual information about facilities, discussion of major related concepts and training in observational skills, and in a problem solving approach. These requirements are modest and feasible, but require staff who are up‐to‐date vis‐a‐vis disruptive behaviour.     

Improving Mathematics Instruction and Learning in the Junior High School: An Israeli Example

Abstract

A 4‐year project is described which was designed to improve mathematics instruction and achievements in two Israeli junior high schools. Project activities focused on the individual teachers, the mathematics staff, and the organization of instruction at the school level, under the assumption that more efficient teaching would lead to greater pupil learning.

Evaluation data gathered from classroom observation, questionnaires and tests indicated a general positive impact: many teachers improved their teaching strategies, more curricular material was being covered in class, a school‐wide program for mathematics instruction was established, teamwork among teachers was formalized, and pupil achievements improved.     

‘Come in with an open mind’: changing attitudes towards mathematics in primary teacher education

Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics.

Purpose: This paper reports on an investigation into student teachers’ self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been developed by the authors in response to a new, reformed four-year undergraduate initial teacher education (ITE) for primary teachers in Ireland. The authors aimed to use the feedback to evaluate and develop the course further.

Sample: We report on the attitudes of 345 pre-service primary teachers enrolled in a four-year undergraduate ITE programme. 281 of these participants had matched survey data before and after participating in the mathematics education programme.

Method and Design: Four evaluation criteria were used as a conceptual framework for the evaluation of the mathematics education programme. A multi-method approach was taken in investigating the students’ attitudes to mathematics by using a scale as a quantitative measure of attitude alongside open-ended survey items that provided qualitative insights into changes in attitudes.

Results and conclusions: Results from the survey data suggested overall that the participants’ attitudes towards mathematics were more positive after they had experienced the mathematics education programme. Overall, the written responses suggested that according to self-reportage, participants perceived that participation in the mathematics education programme had affected their attitudes towards mathematics positively. Comments indicated that the ‘small group’ tutorial structure was particularly well received and was associated with opportunities to actively engage, explore, interact and reflect. Suggestions offered by the participants will be used to inform planning and development of the mathematics programme.     

Evolution or Revolution: dilemmas in the post ERA management of special educational needs by local authorities

Abstract

The management by local education authorities (LEAs) of provision for special educational needs has long proved problematical, especially in mainstream schools. In the period following the 1981 Education Act, many LEAs sought to develop a ‘continuum of provision’ by the central direction of resources into the mainstream, but with limited success. In the wake of the 1988 Education Act, LEAs will need to pursue a more collaborative approach to the development of special needs policy. Examples of such approaches are studied and a model of an interactive relationship between schools and LEAs is proposed. Finally, the implications for LEA support services are discussed together with suggestions of a distinctive role for institutions of higher education.     

Preparing Mathematics Teachers to Teach English Language Learners: What We Know and What We Can Do

Abstract

A recent issue of The Educational Forum contained eight articles theming the preparation of teachers for linguistically-diverse classrooms. This article extends that discussion, and in it this scholar introduces practicalities for mathematics teachers in linguistically-diverse classrooms, and provides suggestions for teacher educators whose target audience is prospective mathematics teachers. The author’s intention is to contribute to the discussion of supporting ELLs in mathematics classrooms, and to advance the praxis for teachers and teacher educators.     

Teaching students with Down syndrome in regular classrooms in Ghana: views of secondary school mathematics teachers

ABSTRACT

The recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Significantly, mathematics is one of the core areas that the Ghanaian government has prioritised, and it has institutionalised mechanisms to encourage participation by many students. Accordingly, this qualitative study aimed to document the level of preparedness of mathematics teachers to support the teaching of students with Down syndrome in secondary school classrooms. Twenty-seven mathematics teachers from 14 schools, made up of 18 males and nine females, took part in the study. We found that participants were in favour of implementation of inclusive education. However, regarding the prospect of teaching students with Down syndrome, most of the participants thought that the regular secondary school classroom is not a suitable environment for these students to access education, especially due to a number of challenges. The need for the government to support schools with appropriate teaching materials and facilities is discussed extensively.     

When the black box springs open: practical work in schools and the nature of science

The aim of this paper is not to bury practical work in school science but to (once again) reconsider it. We draw on three main areas of discussion: accounts of science and ‘school science work'; teachers and others’ views of the nature of science; and our own data on teachers’ reactions to ‘critical incidents’ and practicals which go wrong. We use this as a basis for re‐thinking the role of practicals. An account of practical work is suggested which has as its main feature diversity rather than a single model or template. Within this diversity we believe that teachers should be open and honest with pupils about which type of practical work they are doing and why. We advocate that students should be made aware of the different kinds of practical work they do and the purposes of this practical work. In short, teachers should explain to students what type of practical work they are doing and why. Our second message is that teachers’ views about the nature of science both inform and are informed by their classroom practices and experiences‐‐especially during lab‐work. To encourage, promote and support critical reflection of these classroom practices and experiences is therefore a vital part of teacher professional development; this in time will promote science curriculum development.     

Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.     

The Growth and Nature of Research Interest in Arithmetic and Reading

ABSTRACT

The author examined whether mathematics instruction provided by kindergarten teachers is related to children's mathematics learning during the kindergarten year based on the children's socioeconomic status and race. Hierarchical linear modeling was employed using a large sample of kindergarten students to estimate relationships between the teacher's instructional approach (e.g., concrete-spatial, interpersonal, linguistic) and children's mathematics skills. Results showed that the teacher's instructional approach was selectively related to children's mathematics learning. Students in classrooms where teachers frequently employed a concrete-spatial instructional approach learned more during the kindergarten year. Students from lower socioeconomic backgrounds benefitted more from teachers who often employed an interpersonal approach, and Black/African American students benefitted less from classrooms where teachers relied more on a linguistic approach. The findings suggest that kindergarten teachers’ instruction needs to employ varied methods that take into account students’ mathematics skills and background characteristics.     

Competence,Confidence and Inservice Education for Mathematics Teachers

Abstract

Confidence in subject matter knowledge, in teaching ability and actual subject matter competence of 157 Grade 7–9 teachers, who participated in three summer inservice courses for mathematics teachers was measured. Results were consistent across courses: (1) inservice participation strengthened both mathematical competence and feelings of self‐confidence; (2) teachers lacking confidence in knowledge were those who lacked confidence in teaching ability; and (3) self‐confidence and actual subject competence were only partially interrelated.