Connecting Teacher Beliefs to the Use of Children’s Literature in the Teaching of Mathematics

This article presents examples that illustrate how teachers use childrens literature in the teaching of mathematics. The examples are related to four curriculum ideologies that have influenced mathematics education in the USA for the last 75 years. It discusses why it is relevant to help teachers understand the ideological positions that influence their use of childrens literature during mathematics instruction, summarizes the four ideological positions, and presents results of a study of how teachers ideological positions relate to their use of childrens literature in the teaching of mathematics. The study examines two research questionsCan an instructional tool be developed that will highlight for teachers the different ways in which they and others use childrens literature to teach mathematics? and Can that instructional tool stimulate teacher discussion and reflection about their own beliefs and the ideological nature of the instructional environment in which they learned (as students) and teach (as teachers)? Study results indicate that both questions can be answered in the affirmative.     

Exploring the Development of Student Teachers’ PCK of the Multiple Meanings of Chemistry Topics

In chemical education, many secondary school students experience difficulties in understanding three mutual related meanings of topics, that is, the macroscopic meaning, the microscopic meaning, and the symbolic meaning. As a consequence, student teachers should be prepared carefully to learn how to teach this difficult issue. This article presents a naturalistic case study of the development of eight student teachers pedagogical content knowledge (PCK) of the multiple meanings of chemistry topics. The student teachers (all M.Sc.) participated in a teacher education program of which the initial phase focused on learning from teaching instead of learning of teaching. They were asked individually to choose and teach a chemistry curriculum topic with a focus on the macro-micro-symbolic issue. Research data were obtained by interviewing the student teachers individually before and after the lessons. The outcomes indicated a development of student teachers knowledge of teaching difficulties, for instance, too fast and mainly implicit reasoning between macro- and micro-meaning, and a dominant orientation towards the micro-meaning of topics. A development of knowledge of students difficulties was also indicated, for instance, difficulties in understanding the macro- and micro-meaning of reaction equations. Implications for the follow-up phases of the program are presented.     

Principled Teaching for Deep Progress: Improving Mathematical Learning Beyond Methods and Materials

This paper contributes to knowledge about principled action which makes a difference to learners attainment. We report on the Improving Attainment in Mathematics Project,¹ a project focusing on low-attaining secondary students. The purpose of the project was to introduce innovations in practice through action research with 10 teachers over 2 years, and evaluate the effect on students learning using national test scores, teachers reports, non-routine tasks and other performance indicators. However, this is not a study which shows how certain methods lead to better results. While it was found that learning improved, the methods and strategies the teachers used were not always generalisable across the project, indeed some were contradictory. Continued searching led to the identification of common underlying principles of teaching which different teachers manifested in different ways. Overt methods were less important than the collection of beliefs and commitments which underpinned teachers choices. There was, however, a convergence of practice around a focus on long-term development, the process of becoming a learner of mathematics, rather than short-term gains. In addition, we had to deal with some of the realities of authentic collaborative research with practitioners.     

Impact of science-technology learning environment characteristics on learning outcomes: pupils’ perceptions and gender differences

Science and technology are connected to each other and are mutually inspiring. The science-technology curriculum for junior-high school in Israel suggests that teachers integrate these subjects. In addition, this curriculum calls for infusing thinking competencies into the learning subjects and for implementing alternatives in assessment methods in the classes. The current research included three stages: field research, pilot research and expanded research. In the field research, an intervention program was planned and implemented. The intervention program included a three-year inservice training workshop consisting of 224 hours each year. Quantitative and qualitative tools were used to assess teachers implementation of the intervention program. The findings revealed the characteristics of the science-technology learning environment and various learning outcomes. The pilot research enabled the development and validation of a questionnaire called the Science-Technology Learning Environment Questionnaire (STLEQ). The STLEQ was aimed at assessing teachers and pupils perceptions of learning environment. The conclusions from the pilot research showed differences between teachers and pupils perceptions towards the impact of learning environment characteristics on learning outcomes.In the expanded research, two cohorts of pupils participated, namely, the 2002 cohort (N = 207) and the 2003 cohort (N = 159). These cohorts had studied science-technology in junior-high school. The findings of the expanded research partly match the findings from the pilot research, leading to insight into the pupils perspective of the science-technology learning environment. No gender differences were found in pupils scoring of learning outcomes. On the other hand, boys scored higher than girls on Computer Usage. This research enables researchers and teachers to use the questionnaire in order to investigate pupils perceptions of their learning environment.     

A Reinvented Union: A Concern for Teaching, Not Just Teachers

The current school reform movement, with its emphasis on teacher professionalism, teacher empowerment, and shared decision making, has challenged teachers unions to develop more collegial relations with school boards. Bob Chase, president of the National Education Association, has called for the union to reinvent itself and to assume responsibility for improving school quality and the quality of the teaching force. This article discusses the development of teachers unions in the 1960s as adversaries of school boards. From the beginning the unions adopted an industrial model of labor relations, one tailored for factories and assembly lines rather than school environments. Today, there are signs that teachers unions are accepting Bob Chases vision of a more professional union, one in which union leaders and school leaders can become public allies in the struggle to improve schools.     

Awareness of the backwash effect of assessment: A phenomenographic study of the views of Hong Kong and Swedish lecturers

An effective way to change student learning is to change the form of assessment. This has become known as the backwash effect of assessment. However, academic teachers ways of understanding the role of assessment in student learning are also important. This paper reports a phenomenographic study of the views of the role of assessment amongst Swedish and Hong Kong university teachers. The results are described in eight categories of conceptions, placed within a two-dimensional outcome space. The two dimensions are (1) the relation between teaching and assessment, and (2) the focus of the backwash effect. The results indicate that two features of the described conceptions are critical for changing teachers views of the role of assessment. One is the way one understands the significance of basic knowledge in ones discipline while the other is whether one looks upon the relation between teaching and assessment as being of an internal or external nature. As much research literature points out, to bring about changes in approaches to teaching and learning you must first bring about changes in conceptions of teaching and learning. To utilize assessment to improve student learning, teachers need to be made aware of the need of such improvement and of the role assessment can play in this process. On the basis of research such as that reported in this paper, staff developers could develop workshops or other strategies, which can accomplish this task.     

Authority and Authority Relations in Mathematics Education: A View from an 8th Grade Classroom

Compared to studies in general education, authority has received little attention in mathematics education, despite an increasing interest in sociological perspectives in mathematics classroom research. The subject of authority is particularly important in mathematics education, on the one hand, because of the immense authority mathematics itself seems to possess and pass on to its practitioners, but also, on the other hand, because of the anti-authoritarianism present, to some degree, in many trends in mathematics education such as cooperative learning approaches and constructivist pedagogies. Such an anti-authoritarian stance appears justified by data from an 8th grade mathematics classroom (supplemented with data from a second 8th grade classroom) which suggest that teachers possess immense authority in the eyes of the students and that this and other authority relations are strongly evident in the students non-reflective ways of interacting not only with their teachers but also among themselves. However, theoretical considerations on authority show that the problem may not be authority per se but the way one conceives the notion of authority, that there exist kinds of authority, such as Bennes anthropogogical authority, which can encourage reflective and also fruitful collaborative work.     

Safe Discussions Rather Than First Hand Encounters: Adolescents Examine Racism Through One Historical Fiction Text

summary This article presents a case study class response to Mildred Taylors now classic and widely read novel, Roll of Thunder Hear My Cry. Through data collected during one school year, the ways urban, adolescent students use their contemporary lenses to interpret the literary theme of confronting, overcoming and challenging racism are discussed. The participants responses are organized into four reader response categories that explicate the complex and interactive interpretations developed by the children while reading the novel. In addition to providing insights about the participants textual understanding, pedagogical findings indicate that the book can also be used to explore the nature of racism while creating a safe space to confront and more deeply understand racisms impact on the past as well as the students current reality.     

A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology

This paper reports on a study that investigated the pedagogical practices and beliefs of pre-service and beginning teachers in integrating technology into the teaching of secondary school mathematics. A case study documents how one teachers modes of working with technology changed over time and across different school contexts, and identifies relationships between a range of personal and contextual factors that influenced the development of his identity as a teacher. This analysis views teachers learning as increasing participation in sociocultural practices, and uses Valsiners concepts of the Zone of Proximal Development, Zone of Free Movement, and Zone of Promoted Action to offer a dynamic way of theorising teacher learning as identity formation.     

Orson Scott Card’s Ender and Bean: The Exceptional Child as Hero

Orson Scott Cards school stories in outer space, Enders Game and Enders Shadow, purportedly occur at the same time and tell the same story, but from the perspectives of two different child protagonists. Scenes in Enders Shadow even reproduce text from Enders Game. Nevertheless, 14 years elapsed between the publications of the two books. This essay brings child studies and exceptionality research to bear on the two novels, analyzing the development of Cards ideology regarding his view of the exceptional child and his view of the nature of heroism in a post-modern world.     

Action Research Aiming at Improving High School Science Teachers’ Teaching Proficiencies through the Development of Instructional Modules

The new Science and Technology Curriculum Framework recently issued in Taiwan advocates the teaching of integrated science and technology with greater emphasis on basic skills. Science teachers are not used to teach in this way, they need different abilities and skills in order to do so. Using various effective professional development strategies, including a collaborative action research approach, the aim of this study was to help science teachers develop professionally through the development of instructional modules on integrated science and technology. A research team was formed consisting of science educators/researchers, graduate assistants and science teachers from six junior high schools in the central area of Taiwan. In order to involve teachers collaboratively over an extended period of time, the entire study went through preparatory, elaborative and disseminative stages for three consecutive years. Various professional development opportunities were built-in. The instructional modules developed were discussed by participants of this study and evaluated by external experts before they were tried out in actual classroom settings. Both qualitative and quantitative methods, including field notes, interviews, observations, video-taping, audio-taping, document analysis, and surveys of students and teachers opinions were used to collect data for a closer examination of the effectiveness of the instructional modules and of the increase in teachers instructional proficiencies. Overall, teachers interdisciplinary experiences and knowledge increased. They were more flexible and resourceful in using instructional strategies that best fit the instructional settings. Their knowledge and skills in using information and communication technologies in science classrooms also increased considerably.     

Structuring Occasions

Within the mathematics education literature, the term constructivism has been subject to a diversity of interpretations, many of which are trivializations of original theoretical work. We suggest that trivialized versions of constructivism continue to be promulgated due, in large part,to misunderstandings of some of the vocabulary adopted by its advocates. This situation has been the source of considerable frustration in our ongoing efforts to communicate the insights and implications of radical and social constructivist theories to preservice and practicing teachers. We discuss some of the specifics of these frustrations along with strategies intended to flag and circumvent them in our work with teachers. The writing is structured around a set of recursively elaborated interpretations of a classroom episode. Developed around varied understandings of the terms structure and construct, these interpretations are intended to show how we have worked with teachers to foster a deep appreciation of how learning might be reframed as dependent on, rather than determined by, teaching.This revised version was published online in September 2005 with corrections to the Cover Date.     

A Review of Solution Chemistry Studies: Insights into Students’ Conceptions

This study has reviewed the last two decades of student conception research in solution chemistry pertaining to aims, methods of exploring students conception, general knowledge claims, students conceptions and difficulties, and conceptual change studies. The aims of solution chemistry studies have been to assess students understanding level of solution chemistry and in some studies compare understanding based on age and year at school or college. The methods of exploring students conceptions consisted of interviews, paper and pencil surveys (open-ended questions and multiple-choice questions), free writing and drawings and the validity of these methods have been highlighted. The general knowledge claims synthesized in this study are students (a) attending to mechanical events, (b) preference for everyday language usage over chemical language, (c) confusing solution chemistry with non-related concepts, (d) lack of sub-microscopic explanation for macroscopic observation, (e) difficulty with visualizing and representing sub-microscopic ideas, (f) difficulty with symbolic representations, (g) inconsistent explanations, (h) development of student understanding with age, and (i) development of conservation reasoning with age. To incorporate students conceptions, conceptual change studies have used strategies such as worksheet, analogy, collaboratively working with a teacher, hypermedia, and group exploration. The results of conceptual change studies generally have had a positive impact enabling students to consider their ideas and develop plausible models of solution chemistry. For improvement of student learning in chemistry, this review of solution chemistry studies sheds light on teacher thinking and capacity building with respect to explicitly incorporating students conceptions into chemistry curriculum; practicing research-based strategies; forging links among types of chemical knowledge; collaborating for experimental teaching; and conducting further research.     

Confidence is Everything” – Perspectives of Teachers and Students on Learning Mathematics

This paper problematises confidence as a frequently used explanation for performance in the mathematics classroom. I report on an interview-based study of how some English Advanced level (16+) students who have chosen to study mathematics, and their teachers, speak about confidence with respect to the learning of mathematics. I outline what constitutes confident learners for these teachers and, differently, for their students and what the students feel teachers could do to improve the students confident state. I discuss the implications of this for the education of prospective teachers of mathematics.     

Visions for ICT, Ethics and the Practice of Teachers

The failure of educational computing is often attributed to deficiencies of practice: resisting teachers and lack of will, competence and sincerity on behalf of the teaching profession. But the complexity of school life and teachers work has been underestimated by the entrepreneurs of educational computing. Theoretically there is a need to approach this area from a different angle. We will suggest there is a need to reframe the issue of ICT in schools with educational policy and discourse with education, rather than with technology in mind. In order to reach that goal there is a need to inculcate technology as an ordinary part of teachers vocabulary about their own work and as a part of their professional ethos. Teachers need to examine the moral values inherent in their practices and use those values as bases for debate. Not taking up these issues and instead adopting defensive stances is dangerous to the profession. The danger is that defensiveness can be seen by others outside the school as rigidity and play into the hands of those who are impatient with teachers. It would serve teachers well if they had a more robust ability to communicate the nature of the difficulties they face and how they deal with them.     

Focusing Improvement and Quality Assurance: Work Samples as Authentic Performance Measures of Prospective Teachers’ Effectiveness

The authors suggest that the gap between common evaluation practice in teacher preparation and the consensus reform goal of high levels of student learning for all students is an impediment to reinventing teacher preparation, professional development, and the professionalization of teaching. In the context of Oregons six-year-old educational transition to a standards-based design for schools and schooling, prospective teachers in Oregon have, since 1989, been required to design, develop, and implement teacher work samples as credible evidence of their effectiveness in fostering student learning as a condition for recommendation for an initial teaching license. This article describes teacher work sample methodology and evidence for its reliability and validity in evaluating the performance of prospective teachers. In short, this article describes a methodology that responds to one critical part of the National Commission on Teaching and Americas Futures challenge to reinvent teacher education and improve student learning.     

‘‘O Bottom,Thou Art Translated’’: Directing a Bilingual <Emphasis Type="Italic">Dream</Emphasis> in the Marshall Islands

A unique production of Shakespeares A Midsummer Nights Dream was staged in early 2004 by students of the Marshall Islands High School, Majuro, in the Central Pacific. The plays director, Andrew Garrod, describes the rehearsal process and performance of the play, in which the school students were supported by undergraduates from the Education Department of Dartmouth College, New Hampshire, spending a term teaching in the islands schools. The nature and worth of the learning experienced by the young actors, and their community, are considered in a context where Shakespeare and any kind of dramatic production are little known.