An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics

The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking.     

Understanding teachers as change agents: An investigation of primary school teachers’ self-perception

This study reports on a large-scale survey on primary school teachers’ perceptions of being change agents and the extent to which these perceptions are related to personality and contextual factors. A principal component analysis and confirmatory factor analysis revealed nine characteristics of teachers as change agents. Personality and contextual factors are related to teachers’ perceptions of being a change agent. Four teacher profiles were distinguished according to the varying degrees of teachers’ perceptions of themselves as change agents. This study adds to the further understanding of teachers as change agents, their characteristics and how these characteristics are related to personality and contextual factors.     

Higher educational impact on student objectives: Longitudinal change in Clark-Trow “educational philosophies”

This study explores the impact of higher education on 3,942 arts and sciences students as measured by change in their freshman and senior ratings of four Clark-Trow educational philosophies: vocational, academic, collegiate, and nonconformist (Clark and Trow, 1966). A repeated measures analysis of variance was applied to each of the four philosophies, controlling for sex, entering year, major, parents' educational background, scholastic aptitude, and academic motivation. As expected from Clark-Trow theory, students showed significant increases in academic and nonconformist philosophies, and decreases in vocational and collegiate philosophies. Relationships between independent variables and freshman-senior change suggested post hoc reinterpretation of the dimensions underlying the Clark-Trow phenotypes: i.e., from identification with the college and involvement with ideas to social interests and academic interests (the latter suggested by Terenzini and Pascarella, 1977).     

Is content knowledge pre-requisite of pedagogical content knowledge? An empirical investigation

Journal of Mathematics Teacher Education - Given the scarcity of studies explicitly exploring the often tacit assumption that teachers’ content knowledge (CK) is pre-requisite of pedagogical...     

Pre-service teachers’ experiences of ICT in daily life and in educational contexts and their proto-technological pedagogical knowledge

Many pre-service teachers are members of the net generation and are expected to be familiar with different ICTs, yet several studies have indicated that they are not necessarily able to use them for teaching and learning. The notion of teachers’ technological pedagogical knowledge (TPK) is central to this concern. In this study we use the responses of 146 pre-service teachers to open-ended questions about the experiences and knowledge of ICT and pedagogy they brought with them when they entered university teacher training. The data were analysed qualitatively with content analysis based on an integrative framework generated from a number of theoretical perspectives. Derived categories and subcategories were used to construct a framework for ‘proto-TPK’ as a basis for establishing a starting point for the coordinated development of TPK with students in their university training and early careers.     

Examining the impact of educational technology courses on pre-service teachers’ development of technological pedagogical content knowledge

The purpose of this qualitative study was to examine the impact of educational technology courses on pre-service teachers’ development of knowledge of technology integration in a teacher preparation program in the USA. The present study was conducted with eight pre-service teachers enrolled in the elementary teacher education program at a large university in the mid-western USA. Data sources included interviews, documents, and observations. The findings identified knowledge of technology integration the pre-service teachers developed and identified knowledge of technology integration needed in the technology integration courses. The present study provided a number of suggestions on different activities that could be built into educational technology courses to better prepare pre-service teachers to teach with technology.     

Vocational knowledge in motion: rethinking vocational knowledge through vocational teachers’ professional development

The paper presents empirical data to consider some of the current debates concerning the nature of vocational knowledge taught in Further Education colleges to students following craft, vocational and occupational courses. The concept of ‘knowledge in motion’ and workplace learning theories are employed as a conceptual framework to examine the continuing professional development (CPD) activities of vocational teachers. This is used to shed light on the ways in which teachers use CPD as a means of accessing and transporting vocational knowledge from occupations to classrooms. Empirical data were gathered through questionnaire, in-depth interviews and participant observation. The findings are presented around five themes: (1) the range of CPD engaged with by vocational teachers; (2) the limitations of propositional, explicit knowledge; (3) engaging with and capturing tacit knowledge; (4) managing the temporality of vocational knowledge; and (5) networking within and to the occupation. Findings suggests that vocational knowledge is distributed and networked and this conceptualisation makes visible some of the ways teachers are able, through CPD activity, to transport vocational knowledge from occupations to classrooms.     

Technological,pedagogical and content knowledge in one-to-one classroom: teachers developing “digital wisdom”

One-to-one (1X1) laptop initiatives become prevalent in schools aiming to enhance active learning and assist students in developing twenty-first-century skills. This paper reports a qualitative investigation of all 7th graders and their 15 teachers in a junior high-school in Northern Israel gradually implementing 1X1 model. The research was conducted during a second year of 1X1 implementation at the school level, which was a first year of teaching and learning with laptops for all study participants. The study triangulates non-participant lessons’ observations and semi-structured interviews with 15 teachers. The data were collected twice: at the beginning and toward the end of the 2011–2012 academic year – in total, 30 observations and 30 interviews were conducted. The results were examined through phenomenological research techniques and discussed in terms of the technological, pedagogical and content knowledge (TPACK) and “digital wisdom” approaches. The teachers showed significant increase of technological knowledge. However, only moderate connections between technology and pedagogy as well as between technology and content were found. Some of the teachers functioned as moderators, scaffolding students and supporting their individual or collaborative learning. However, many teachers struggled with effective management of 1X1 classroom. Neither conjunction of teacher TPACK nor facilitation of student digital skills was observed. The paper suggests an overlap of the TPACK framework and the digital wisdom approach and provides implications for curriculum developers and educational policy-makers.     

Facilitating growth in prospective teachers’ knowledge: teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants?? pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.     

The impact of educational development workshops on teachers’ practice

Abstract

Workshops are common practice as a staff and educational development tool in higher education around the world, yet while it is common to seek participants’ immediate reactions there been little attempt made to measure their impact. This paper reviews the available literature on the effectiveness of workshops and reports the findings of a study in to the effectiveness of 33 workshops delivered by the Oxford Centre for Staff and Learning Development over a four month period. The study used questionnaires at the end of the workshops and four months later, and these were followed up by telephone interviews with a sample of participants. The study demonstrates that workshops can lead to changes in practice, and that these changes are themselves deemed to be successful by those involved. In addition, where at the end of a workshop participants report that they are likely to make changes this can be used as a reasonably accurate predictor of subsequent change. The features of workshops identified in end‐of‐workshop questionnaires which are linked with likelihood of subsequent change are also reported.     

An investigation of factors impacting on mainstream teachers’ beliefs about teaching students with learning difficulties

The relationship between teacher experience, further professional development training, and beliefs and attributions about teaching students with additional learning support needs was studied in a sample of 199 mainstream general class primary school teachers. Using multiple regression, it was found that none of the teacher experience or professional training variables were significant predictors of locus of causality, stability, or controllability attributions, or of teacher self‐efficacy with students with difficulties in learning. Self‐efficacy, however, was a positive predictor of attributions, and sympathy a negative predictor. Multivariate analysis of variance found no relationship between teacher experience, further professional development training, and dependent outcome variables: self‐efficacy with learning difficulties, coping with learning difficulties, interactions with people with disabilities, or general optimism. Implications for continued professional development are discussed.     

Exploring elementary english teachers’ practical knowledge: A case study of EFL teachers in Taiwan

Teaching English in elementary schools has been an important educational policy in Asian countries over the past several decades. This study investigates how in-service teachers in elementary schools conceptualize their practical knowledge about English teaching in Taiwan. It provides examples of experiences and practical knowledge that English teachers have developed in their own contexts. The practical knowledge of teachers was investigated using a qualitative case study. Three in-service teachers participated in this study. Data include interviews, classroom observations, teachers’ reflective journals, and teaching materials. The study provides practical principles and rules of practice for elementary EFL teachers. It offers insights that policy makers need to consider in setting up a sound English teaching and learning program for elementary schools in EFL contexts.     

An analysis of prospective teachers’ knowledge for constructing concept maps

Background: Literature contends that a teacher’s knowledge of concept map-based tasks influence how their students perceive the task and execute the creation of acceptable concept maps. Teachers who are skilled concept mappers are able to (1) understand and apply the operational terms to construct a hierarchical/non-hierarchical concept map; (2) identify the legitimacy of the constructed concept map by verifying its graphical structure and its educational utility; and (3) determine the inherent ‘good’ and ‘poor’ qualities of the resulting graphical structure to reiterate the ‘good’ qualities and to coach and provide feedback to alleviate ‘poor’ qualities.

Purpose: The purpose of this study was to investigate the nature of prospective teachers’ knowledge underpinning the technique used to construct concept maps and thus, explicate their facility to construct concept maps.

Sample, Design and Methods: Data consisted of 200 concept maps constructed by prospective teachers in an elementary science methods course.

Results: Analysis revealed that the prospective teachers had predominantly constructed either hierarchical and/or non-hierarchical concept maps. It is likely that their maps reflect the teaching that they themselves would have experienced in their science classrooms during their own education. Additionally, most of these concepts maps only contained the root concept and subordinate concepts and lacked directional linking lines, linking phrases, labelled lines and propositions.

Conclusions: We argue that teacher educators need to assess their prospective teachers’ understanding of concept mapping in relation to the legitimacy (the nature and quality) of the end-products (graphical structures) of such practices. Prospective teachers also need to understand the educational utility of concept mapping in terms of how these end-products impact and/or effectuate learning.     

Being “chill” with teachers and “frozen” by peers in science: overcoming social and educational barriers in a learning community

This forum discusses the issue of ‘othering’ and how intersectionality is a useful analytical framework for understanding the students’ immigrant experiences in, and out of, the science classroom. We use a feminist perspective to discuss Minjung’s study because gender is a key aspect of one’s identity other aspects such as race, religion, socio-economic status, and age have assumed a significant status in gender studies. Lastly we examine the supports and barriers that cliques can produce and propose the importance of building a learning community in the science classroom to engage all students.     

The national in‐service courses for science teachers and their effect on educational reform in Mexico

The educational system in Mexico has undergone important changes in recent decades. One of the most important took place in 1993, when the compulsory character of secondary school (ages 12–15) was established. National In‐service Courses (NICs) were established as a way to bring curricular changes proposed in the reform near to the teachers. The results, according to the National Certification Exams, have not been satisfactory. In this paper, we describe the general context of education in Mexico, putting emphasis on teacher initial preparation and the reform that took place as well as the way in‐service courses are implemented, analyzing their possibilities to bring about real changes in science teaching and learning.     

Personal and Social-Contextual Factors in K–12 Academic Performance: An Integrative Perspective on Student Learning

Our extensive literature review in the fields of educational, social, and cognitive psychology has led us to identify about a dozen variables that demonstrate direct empirical links to academic achievement at the K–12 level. Those variables are grouped into four major categories: student engagement, learning strategies, school climate, and social-familial influences. We then categorize the first two variables as personal factors and the latter two as social-contextual factors. We document empirical findings that have shown particular relationships between the reviewed personal and social-contextual factors and academic achievement, mainly in the areas of reading and mathematics. Based on our conceptualization, we propose an integrated perspective that students’ personal factors in the domains of behavior, affect, attitude, and cognition as well as their social-contextual environment have to work in concert to produce optimal school performance. We conclude with a discussion on educational implications and future research to be addressed.