Mathematics Teachers’ Approaches to Computer‐based Instruction

Schon (1987) has criticized the normative curriculum of professional schools including technical colleges: at first basic science (mathematics, physics, etc.), then applied science, and finally technical skills of day‐to‐day practice. In Schön's opinion, the tradition of professional education is an obstacle to changing teaching methods from drill and practice to open‐learning environments. Solomon (1986) presents the different approaches which teachers take in computer‐based instruction in stages from drill and practice to open‐learning environments. This paper reports a six‐year case study, inspired by the work of Schön and Solomon, on the impact of, and the teachers’ role in, the use of computers and Mathcad in the mathematics instruction of technical colleges. The teaching experiment was started with 51 first‐year students during the academic year 1988‐1989 at the Technical Institute of Jyvaskyld. The class of mechanical engineering had 162 and the class of electrical engineering 206 lessons of mathematics during the first experimental year. Two senior lecturers of mathematics taught the classes. Before the experiment, computers had never been used in mathematics instruction at the institute. The various ways of using Mathcad were classified on the basis of the forms filled and files saved by the teachers, as well as on the notes made by the researcher. The teachers’ ways of using computers in our experiment during the years 1988‐1995 clearly showed the existence of stages. Some of the stages were the same for both teachers, but there were also some differences. Both teachers started by fitting an open computer‐based environment into the traditional instruction.     

Professional Communities in the Context of Teachers’ Professional lives: A Case of Mathematics Specialists

We describe an urban school initiative aimed at teachers’ professional development with the goal of increasing their mathematics content knowledge and helping them improve their practice. In the lowest performing schools, mathematics specialists were employed to teach only mathematics in upper-elementary grades (ages 9–12). One aspect of this initiative was a provision of time and space for the formation of site-based professional communities that were intended to support teachers in trying to implement changes in their practice. Teachers’ professional communities developed at some sites and not at others. In this analysis, we explore the conditions that afforded or constrained the development of teachers’ professional communities. Using two contrasting school sites as examples, we describe five aspects of the teachers’ individual and collective professional lives that influenced the emergence of teachers’ professional communities.     

Shifting Pre-Service Teachers’ Beliefs About Mathematics Teaching: the Contextual Situation of a Mathematics Methods Course

For pre-service teachers (PSTs) who have been exposed to traditional approaches, teacher education courses can be a revelatory experience in their development as educators. This study explores if Canadian upper elementary/lower secondary (grades 4–10) PSTs change their beliefs about mathematics teaching as a result of taking a mathematics methods course and how the course influenced these beliefs. Surveys were used to measure participants’ mathematics beliefs, and results show that PSTs’ beliefs moved to favor reform-based approaches. Qualitative data complemented the survey results, suggesting that experiencing new approaches and having the opportunity to apply them into practice are important to their development as mathematics teachers.     

Preschool Teachers’ Understandings of the National Preschool Curriculum in Greece

In 2003, a new curriculum was enacted in Greek preschool education, replacing the previous one of 1989 and following the development of new curricula for the other rungs of compulsory education. Within this context, the new curriculum development policy aimed at an equal integration of preschool education into the unified design of primary and secondary education. A basic issue in any such educational change is how teachers make sense of the new curriculum and what impact it has on their thinking and daily practice. Considering the need to better understand the relationships between curriculum and parameters that shape practice, the study examines preschool teachers’ perspectives of the new early childhood curriculum and its implementation, as well as the extent to which the new curriculum has influenced preschool practices.     

Teachers’ Unions on the Defensive?: How Recent Collective Bargaining Laws Reformed the Rights of Teachers

Between 2011 and 2013 lawmakers in every state proposed, and often enacted, laws intended to impact codified state provisions related to teachers and teachers’ unions (author calculation). These new laws either worked against union interests (e.g., by prohibiting collective bargaining) or they aligned with union positions (e.g. by providing enhanced compensation benefits to teachers). In recent years scholars have paid more attention to the impact of teachers’ unions and collective bargaining. Few researchers have made an effort to understand state-level attempts to legislatively modify traditional union-protected rights. This paper is the first to explore these changes in detail. Using a self-collected dataset, I track the proposal and enactment of legislation related to teachers’ unions and their collective bargaining agreements in state legislatures between 2011 and 2013. I find that while large-scale attacks on public sector bargaining rights dwindled after 2011, smaller, more focused legislative proposals concerning the rights of teachers continued. Lawmakers succeeded in removing several job protections for teachers in ways that left both teachers and unions more vulnerable to the actions of school and district administrators. However, contrary to the popular media narrative, teachers actually made legislative gains, particularly in the area of compensation and benefits following 2011.     

School Teachers’ Experiences of Science Curriculum Reform

We examine teachers’ experiences of a major reform of the school science curriculum for 14–16-year olds in England. This statutory reform enhances the range of available science courses and emphasises the teaching of socio-scientific issues and the nature of science, alongside the teaching of canonical science knowledge. This paper examines teachers’ experiences of the reform and the factors that condition these experiences. A designed sample of 22 teachers discussed their experiences of the reform within a semi-structured interview. Our analysis considers how the external and internal structures within which teachers work interact with the personal characteristics of teachers to condition their experiences of the curriculum reform. In many cases, personal/internal/external contexts of teachers’ work align, resulting in an overall working context that is supportive of teacher change. However, in other cases, tensions within these contexts result in barriers to change. We also explore cases in which external curriculum reform has stimulated the development of new contexts for teachers’ work. We argue that curriculum reformers need to recognise the inevitability of multiple teaching goals within a highly differentiated department and school workplace. We also show how experiences of curriculum reform can extend beyond the learning of new knowledge and associated pedagogies to involve challenges to teachers’ professional identities. We argue for the extended use of teacher role models within local communities of practice to support such ‘identity work’.     

Teachers’ and Pupils’ Perceptions of Technology and the Implications for Curriculum

The recent explicit inclusion of technology into the science component of the school curriculum in Western Australia necessitates changes in both curriculum materials and the nature of classroom teaching. This paper reports an investigation of the perceptions of technology of senior teachers who are heads of the science department in their schools, and relates these perceptions with those of a sample of 13‐year‐old pupils in this state. The investigation reveals that many teachers have a restricted view of technology which may be interpreted as a view that technology is dependent upon science. Such a view may neglect the historical aspects and societal influences on science and technology. Further, the available evidence indicates that local pupils have a low level of awareness of technology. The paper discusses the implications of these findings for curriculum change and suggests a starting point for achieving a successful balance in the teaching of technology, science and society issues in the classroom.     

A Mile Wide or an Inch Deep? Improving Elementary Preservice Teachers’ Science Content Knowledge Within the Context of a Science Methods Course

Since the beginning of the reform movement in science education, there has been concern that elementary teachers lack the science content knowledge (SCK) needed to engage students in authentic scientific inquiry. This study included 19 preservice elementary teachers and examined the development of their SCK within the context of a uniquely designed elementary science methods course. A project-developed science knowledge test was administered at the beginning and the end of the science methods course, before and after science content was covered concurrent with modeled pedagogy. The preservice elementary teachers had adequate knowledge of low difficulty science content on the pretest, but demonstrated improvement on moderate and difficult science content, especially on topics emphasized in the methods course. Data analyses conducted on change in SCK using analysis of variance were statistically significant and demonstrated a large effect size. Details are discussed, along with large-scale implications and recommendations for elementary science teacher education.     

Teachers’ Understanding of Interactive Approaches in Special Education

This paper considers the adoption of interactive approaches in the history of special education and addresses teachers’ use and conceptualisation of interactive approaches. Teachers in special schools and units in the United Kingdom were asked whether they used interactive approaches and, if so, what this meant in their context. Interactive approaches were reported to be used by two-thirds of the sample and what this meant to the 58 respondents, from different areas of special education, varied considerably. Their responses are compared with the central elements of interactive approaches in the literature. Areas of consensus are discussed and a relative lack of emphasis on process amongst the teachers is identified.     

The Connection Between Forms of Guidance for Inquiry-Based Learning and the Communicative Approaches Applied—a Case Study in the Context of Pre-service Teachers

Research in Science Education - Recent research has argued that inquiry-based science learning should be guided by providing the learners with support. The research on guidance for inquiry-based...     

Pre-service Mathematics Teachers’ Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

This study examined pre-service mathematics teachers’ knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4–8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males’ knowledge scores are significantly higher than females’ scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers’ knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers’ positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.     

Elementary Teachers’ Mathematics Subject Knowledge: the Knowledge Quartet and the Case of Naomi

This paper draws on videotapes of mathematics lessons prepared and conducted by pre-service elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A grounded approach to data analysis led to the identification of a ‘knowledge quartet’, with four broad dimensions, or ‘units’, through which mathematics-related knowledge of these beginning teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised and analyses one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson. We claim that the quartet can be used as a framework for lesson observation and for mathematics teaching development.     

Assessing Teachers’ Beliefs to Facilitate the Transition to a New Chemistry Curriculum: What Do the Teachers Want?

In this article, we describe the results of a study of chemistry high school teachers’ beliefs (N = 7) of the chemistry curriculum and their roles, their beliefs on the teacher as developer of materials, and their beliefs about professional development. Teachers’ beliefs influence the implementation of a curriculum. We view the use of a new curriculum as a learning process, which should start at teachers’ prior knowledge and beliefs. The results reveal that it is possible to develop a new curriculum in which teachers’ beliefs are taken as a starting point. Promising approaches to prepare teachers for a new curriculum is to let them (co)develop and use curriculum materials: It creates ownership, and strengthens and develops teachers’ pedagogical content knowledge (PCK).

Elementary School Teachers’ Use of Technology During Mathematics Teaching

Various educational technologies have been advanced as potential vehicles to transform teaching and learning. Still, research studies have documented that primary school teachers struggle to integrate technology in meaningful ways. This article presents the findings of a year-long study in which the author frequently observed three primary school teachers’ enactments of technology into their mathematics teaching. Each teacher was observed between 25 and 30 times during the school year. The types of technologies used as well as the types of mathematical tasks and problems that participants posed while teaching with technology were inductively analyzed. Inductive qualitative analyses indicated that participants’ technology use focused on presentation technologies such as the document camera or interactive whiteboard more than computer-based technologies or interactive activities. Further, teachers varied widely in their enacted pedagogies while integrating technology, and two participants demonstrated more frequent enactments of learner-centered pedagogies toward the end of the school year. Implications for researching teachers’ use of technology in the future are also shared.     

Exploring the Complexity of Students’ Scientific Explanations and Associated Nature of Science Views Within a Place-Based Socioscientific Issue Context

Science & Education - In addition to considering sociocultural, political, economic, and ethical factors (to name a few), effectively engaging socioscientific issues (SSI) requires that...     

Prospective and In-Service Mathematics Teachers’ Attention to a Rich Mathematics Task While Planning its Implementation in the Classroom

International Journal of Science and Mathematics Education - This study explores secondary mathematics teachers’ attention to the three components of Jaworski’s (1992) “teaching...     

Investigating Teachers’ Skills in Interpreting Evidence of Student Learning

This study measured and explored the relationships among elementary mathematics teachers’ skill in (a) determining what an item measures, (b) analyzing student work, (c) providing targeted feedback, and (d) determining next instructional steps. Twenty-three elementary mathematics teachers were randomly assigned to one of three conditions: analyzing items and student responses without rubrics, analyzing items and student responses with rubrics, or analyzing items and student responses with rubrics after watching a professional development program on providing feedback to students. Findings show there is a moderate to strong relationship between teachers’ abilities to analyze student responses to infer what a student knows and can do and their abilities to take action based on that information through either providing the student feedback or making appropriate instructional adaptations. Findings show it was relatively more difficult for teachers to provide feedback that was likely to move students forward in their learning than it was for them to analyze a student's response or to determine next instructional steps. No teacher skill differences associated with the different treatment conditions were found.     

Quantitatively Investigating Inservice Elementary Teachers’ Nature of Science Views

Research in Science Education - Many nature of science (NOS) studies have demonstrated that teachers can improve their understandings of NOS with explicit and reflective instruction; however, the...