Pre-service secondary teachers’ pedagogical content knowledge for the teaching of mathematical modelling

Educational Studies in Mathematics - The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help...     

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.     

Predictors of primary school teachers’ knowledge about developmental dyscalculia

Developmental dyscalculia is a specific learning disability that is described as a heterogeneous and persistent cognitive disorder. Given the need to detect and intervene as early as possible to minimise its effects, teachers’ knowledge about symptoms, characteristics and effective intervention strategies in dyscalculia is essential. Given the lack of research about this topic and measures to evaluate teachers’ knowledge, this study aims to present a literature-based measure to evaluate knowledge about developmental dyscalculia and to investigate the predictors of this type of knowledge. Data were collected from a sample of 175 primary school teachers. The measure presented adequate psychometric properties. Teachers’ personal characteristics such as age and gender did not predict their knowledge about dyscalculia. Being a Special Education teacher predicted a higher knowledge of intervention strategies in dyscalculia and having heard about dyscalculia predicted higher knowledge about not only intervention strategies but also dyscalculia characteristics. The data are discussed, and suggestions for further studies are presented.     

Student teachers’ pedagogical content knowledge for teaching systems thinking: effects of different interventions

ABSTRACT

Systems’ thinking has become increasingly relevant not only in education for sustainable development but also in everyday life. Even if teachers know the dynamics and complexity of living systems in biology and geography, they might not be able to effectively explain it to students. Teachers need an understanding of systems and their behaviour (content knowledge), and they also need to know how systems thinking can be fostered in students (pedagogical content knowledge (PCK)). But the effective development of teachers’ professional knowledge in teaching systems thinking is empirically uncertain. From a larger study (SysThema) that investigated teaching systems thinking, this article reports the effects of the three different interventions (technical course, didactic course and mixed course) in student teachers’ PCK for teaching systems thinking. The results show that student teachers’ PCK for teaching systems thinking can be promoted in teacher education. The conclusion to be drawn from our findings is that a technically orientated course without didactical aspects seems to be less effective in fostering student teachers’ PCK for teaching systems thinking. The results inform educators in enhancing curricula of future academic track and non-academic track teacher education.     

An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking

Using algebraic habits of mind as a framework, and focusing on thinking about functions and how they work, we examined the relationship between 18 pre-service middle school teachers’ ability to use the features of the algebraic thinking (AT) habit of mind “Building Rules to Represent Functions” and their ability to recognize and interpret the features of the same AT habit of mind in middle school students. We assessed the pre-service teachers’ own ability to use the AT habit of mind Building Rules to Represent Functions by examining their solutions to algebra-based tasks in a semester-long mathematics content course. We assessed the pre-service teachers’ ability to recognize and interpret students’ facility with the AT habit of mind Building Rules to Represent Functions by analyzing their interpretations of students’ written solutions to algebra-based tasks and their ability to plan and analyze AT interviews of middle school students during a concurrent field-based education course. The data revealed that the pre-service teachers had a limited ability to recognize the full richness of algebra-based tasks’ potential to elicit the features of Building Rules to Represent Functions in students. The pre-service teachers’ own overall AT ability to Build Rules to Represent Functions was related to their ability to recognize the overall ability of students to Build Rules to Represent Functions, as exhibited during one-on-one interviews, but not to their ability to recognize the overall ability to Build Rules to Represent Functions exhibited exclusively in students’ written work. Implications for mathematics teacher education are discussed.     

The impact of instruction in enhancing teachers’ knowledge of teaching mathematics in some Lesotho primary schools

The quality of mathematics teaching in Lesotho primary education remains one of the vexing problems in the education system. The study investigated how teachers viewed the impact of instruction on enhancing their knowledge of teaching. Data for the study were elicited from the second-year students enrolled for a Bachelor of Education in the 2009/10 academic year at the National University of Lesotho. Questionnaires and interviews were used for data collection. The findings show that before instruction, the teachers operated with limited knowledge of teaching. At the end of the course the teachers’ knowledge of teaching was enhanced. Significant change was apportioned to engaging in reflection and teaching for relational understanding. Implications of the findings for the course, teacher education and professional development are also discussed.     

Prospective primary teachers’ self-efficacy and emotions in science teaching

The self-efficacy of prospective primary teachers was studied, considering in particular the relationship of that construct with the emotions they expect to experience as future science teachers, differentiating between when they will be teaching the content of the ‘nature sciences’ (biology and geology) and that of the ‘hard sciences’ (physics and chemistry). The study instrument was a questionnaire completed by 188 prospective primary school teachers in their initial education at the University of Extremadura during the academic year 2009/2010. The results showed them to mostly have positive emotions towards nature sciences and negative towards the hard sciences. While their beliefs concerning their self-efficacy are significantly related to their emotions about their future teaching of the hard sciences, high self-efficacy was significantly correlated with more positive emotions and fewer negative emotions towards physics and chemistry.     

Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory

In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues’ mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers’ prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.     

Are teachers teaching for a knowledge society?

Many countries whose economies are in transition have initiated ambitious education reforms intended to modernize their education systems to better respond to the needs of new social and economic realities. Albania is a good example of a society that is emerging from a closed planned socialist system and moving fast to an open society and knowledge‐based economy. As an essential tool in transforming people's knowledge and skills to promote a knowledge society, teaching must reflect, among other things, an active role for students and multilateral communication to support productive learning in classrooms. The aim of this study was to generate scientific evidence for policy‐makers about whether teaching in the first grade of upper secondary schools meets these criteria. Based on our observation data from 303 classrooms in 34 schools in Albania, analyzed using the categories of Flanders' interaction analysis, we found that teacher talk occupies more than 70% of all lesson time and that student‐initiated talk constituted less than 30 seconds within a typical 45‐minute lesson. We conclude that unless education policies give a high priority to supporting teachers in transforming teaching in schools to promote productive, interactive learning, students will not be able to acquire the knowledge and skills they need within a modern knowledge society.     

Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking

In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.     

Subject knowledge for primary teaching: the influence of the personal dimension on beginning primary teachers’ conceptualisations and interpretations

This paper argues that professional discourse relating to subject knowledge for primary teaching is less than coherent in the context of initial teacher training (ITT). This study explored the ways in which the term subject knowledge was conceptualised and interpreted by beginning primary teachers. The research was conducted across two ITT partnerships with final-year undergraduate trainees. Data were collected via questionnaires, semi-structured interviews and participatory visual methods. The findings indicated that conceptualisations of subject knowledge were highly individualised and dependent on personal factors, rather than reflecting a shared understanding of a critically distinct concept.     

Preservice teachers’ knowledge of proof by mathematical induction

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.

Teachers’ knowledge and confidence for promoting positive mental health in primary school communities

This paper reports an investigation into Australian primary school teachers’ knowledge and confidence for mental health promotion. Questionnaires were delivered to 1397 teachers. In-depth interviews were held with 37 teachers. Quantitative results showed that half to two thirds of teachers felt efficacious and knowledgeable about selected components of mental health promotion. Independent judgments by staff about students’ mental health status concurred with students’ scores on the Strengths and Difficulties Questionnaire in about 75% of cases, indicating a good level of staff awareness about students’ mental health status. Exposure to the KidsMatter Primary mental health promotion initiative was associated with improvements in teachers’ efficacy, knowledge and pedagogy, with small to medium effect sizes. Qualitative analysis indicated that teachers’ subject-matter and pedagogical knowledge were heavily reliant on curriculum resources. Implications of the findings for the implementation of school-based mental health promotion initiatives are discussed.     

The role of subject knowledge in primary prospective teachers’ approaches to teaching the topic of area

The relationship between primary teachers?? subject knowledge and their approaches to teaching is an ongoing concern. This study reviews the relationship between prospective teachers?? subject knowledge in the topic of area and their approaches to teaching that topic. The research presents case studies of four primary prospective teachers on a 1-year postgraduate teaching course. The strengths and limitations of their subject knowledge are examined, in relation to their selection of teaching activities. The results suggest connections between these strengths and limitations, in relation to espoused teaching activities and pedagogical orientations. This questions the assumption that secure subject knowledge is necessarily transformed into effective teaching and concurs with other research that suggests other factors may be involved, such as knowledge of learners.     

Basic school teachers’ perspective to digital teaching and learning in Ghana

This study proposes a model for describing the situation of Digital Teaching and Learning (TD-TaL) in Ghanaian schools using the perspectives of basic school teachers. The Digital Teaching and Learning model was developed based on the theories of Valsiner’s Zone of Free Movement (ZFM) and Zone of Promoted Action (ZPA) and Vygotsky’s Zone of Proximal Development (ZPD). The model proposes to look at the effects of ZFM in schools (comprising Digital environment factors and Personal attitudinal and Digital Culture factors) and ZPA (comprising Teacher Training factor) on the Teachers’ Digital Knowledge, Competence and Action ( TDKCA) factors to influence teachers in their Zone of Proximal Development. The model was tested in Ghana’s case using the survey data collected from 256 teachers from 45 schools across six districts in the Western Region of Ghana. The findings from Regression path analysis revealed that Personal and Digital Culture factors, but most of all teachers’ Digital Attitudes effected directly on Teachers’ Digital Activities they claimed to be doing, whereas from Environmental factors only Schools’ Digital Agenda was impacting Teachers’ Digital Action both directly and indirectly through Teachers’ Digital Training (ZPA). The model specifically highlighted that in observed Ghanaian schools the ZFM factors Digital Infrastructure and Digital Support to Digital Teaching did not associate with the ZPA factor Digital Teacher Training and overall to Teachers’ Digital Knowledge, Competence and Action factors.