Special educators’ knowledge of high-leverage practices: Construction of a pedagogical content knowledge measure

Teachers who draw upon specialized knowledge in their instructional practice can be drivers of positive student outcomes, especially for students classified as having special educational needs. Although there are generally agreed upon characteristics of high-quality instruction that can be measured with well-constructed instruments (e.g., Danielson, 2011), supporting the development of teachers with specialized credentials (e.g., special education teachers)—whose instructional practice is grounded in a qualitatively different professional expertise—necessitates measurement tools that reflect that unique practice. Given the field’s recent agreement that special educators should possess deep knowledge of 22 High-Leverage Practices, there is a need for well-constructed tests that can be interpreted to support teacher capacity building in this body of knowledge. This study describes the construction of the Teacher Knowledge of HLPs, an instrument that measures special educators’ knowledge of High-Leverage Practices, and initial validity evidence for instrument use.     

Developing preschool teachers’ knowledge of students’ number conceptions

This article describes a study that investigates preschool teachers’ knowledge of their young students’ number conceptions and the teachers’ related self-efficacy beliefs. It also presents and illustrates elements of a professional development program designed explicitly to promote this knowledge among preschool teachers. Results indicated that teachers’ knowledge of students’ number conceptions improved and that their related self-efficacy increased. Furthermore, prior to participating in the programs, a significant negative correlation between knowledge and self-efficacy was reported. However, no significant correlation was found after the program.     

Teachers’ acquisition of knowledge about English word structure

Previous research suggests that teachers’ knowledge about English word structure (e.g., the phonological structure of words and common orthographic patterns in English) may be limited, although this knowledge is important for effective teaching of word decoding. This study examined teacher education students’ knowledge about word structure, and improvements in their knowledge as a result of instruction, using three tasks: graphophonemic segmentation, classification of pseudowords by syllable type, and classification of real words as phonetically regular or irregular. Participants came from a special education certification program and included both preservice and inservice teachers. Results indicated that prior preparation to teach reading influenced participants’ initial performance on two of the three word-structure tasks (all but graphophonemic segmentation); however, prior experience in teaching reading did not influence word-structure knowledge. A subset of participants who received specific instruction about word structure improved their knowledge relative to a comparison group of teacher education students who did not receive word-structure instruction. Prior preparation did not influence participants’ responsiveness to instruction. Conclusions support the viewpoint that teacher education must include information about English word structure for educators who will teach reading and suggest that sufficiently intensive instruction may be important in developing word-structure knowledge.     

Scaffolding middle school students’ content knowledge and ill-structured problem solving in a problem-based hypermedia learning environment

This study investigated the effects of domain-general and domain-specific scaffolds with different levels of support, continuous and faded, on learning of scientific content and problem-solving. Students’ scores on a multiple-choice pretest, posttest, and four recommendation forms were analyzed. Students’ content knowledge in all conditions significantly increased from pretest to posttest. However, the continuous domain-specific condition outperformed the other conditions on the posttest. Although domain-general scaffolds were not as effective as domain-specific scaffolds on learning content and problem representation, they helped students develop solutions, make justifications, and monitor learning. Unlike domain-specific scaffolds, domain-general scaffolds helped students transfer problem-solving skills when they were faded. Several suggestions are discussed for making improvements in the design of scaffolds to facilitate ill-structured problem solving.     

When Teaching Makes a Difference: Developing science teachers’ pedagogical content knowledge through learning study

It is a common view that developing teachers’ competence to restructure or reframe their knowledge and beliefs is inevitably a complex challenge. This paper reports on a research project with the aim to develop science teachers’ pedagogical content knowledge (PCK) through their participation in a learning study. A learning study is a collegial process in which teachers work together with a researcher to explore their own teaching activities in order to identify what is critical for their students’ learning. During one semester, three secondary science teachers worked in a learning study together with a researcher in a cyclical process in order to create prerequisites and further identify conditions for students’ learning. During the learning study, data were collected from video-recorded lessons and stimulated recall sessions in which the teachers and the researcher reflected on the lessons to analyze their development of PCK, their students’ learning and the impact of that knowledge on their own teaching. The results provide an insight into how the teachers developed their self-understanding in which they questioned their own epistemological beliefs, aims and objectives of teaching and taken-for-granted assumptions about science teaching and learning. As such, the study provides an understanding of teacher professional learning through a careful investigation of how teachers’ PCK is enhanced through their participation in the learning study, and further, how students’ learning might be developed as a consequence.     

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.     

Assessing college students’ perceptions of a case teacher’s pedagogical content knowledge using a newly developed instrument

Ongoing professional development for college teachers has been much emphasized. However, previous research on learning environments has seldom addressed college students’ perceptions of teachers’ PCK. This study aimed to evaluate college students’ perceptions of a physics teacher’s PCK development using a newly developed instrument and workshop intervention. A mixed method design was employed incorporating both quantitative and qualitative techniques. The survey “Assessing Students’ Perceptions of College Teachers’ PCK” was adopted as the instrument of research. This survey was conducted twice in this study; with the pre-test carried out during the mid-term exam and the post-test given in the last week of the semester. The results indicate that only SMK and IRS showed significant difference in the four categories of the survey, while IOC and KSU did not. Furthermore, the organized workshops helped the case teacher to better understand students’ prior conceptions of the subject matter and learning difficulties, and further facilitated her adjustment of instructional strategies. The limitations of this study are discussed and suggestions for improvement are also provided.     

Teachers’work: Beginning teachers’ conceptions of competence

Worldwide, teachers’ work continues to be the subject of discussion and debate, especially in terms of teacher competence and its appropriate appraisal. Available literature offers a number of perspectives of beginning teacher competence, yet the voices of beginning teachers themselves are not represented. This paper outlines the findings of a phenomenographic study that sought to uncover the conceptions of competence held by beginning teachers. The results of this study suggest that beginning teachers believe that teaching competence requires demonstration of thorough preparation, a sound knowledge base, effective classroom management, professional communication with a range of stakeholders, and an accurate sense of self-awareness in the role of teacher. These conceptions will be compared to a selection of the available literature about teacher competence and associated teaching standards.     

The nature of prospective mathematics teachers’ pedagogical content knowledge: the case of multiplication of fractions

The purpose of this study was to investigate prospective mathematics teachers’ knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers’ knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions was examined. Data were collected from 17 Turkish prospective teachers at the end of the spring semester of the 2004–2005 academic year. A case study design was used in which data were collected through the Multiplication of Fractions Questionnaire and semi-structured interviews. The prospective teachers suggested many difficulties that elementary grade level students may have and stated that these difficulties stemmed from students’ lack of formal knowledge and rote memorization of the algorithms. In addition, the prospective teachers suggested many strategies that could be used to overcome these misconceptions or difficulties. These strategies could be grouped under three headings: strategies based on teaching methods, strategies based on formal knowledge of fractions, and strategies based on psychological constructs.     

The Lesson Preparation Method: a way of investigating pre-service teachers’ pedagogical content knowledge

Teacher education should build on the knowledge base that pre-service teachers already have on account of their lifelong learning in and outside of school. An international team of mathematics and science teacher educators developed a method of investigating the pedagogical content knowledge parts of this knowledge base. They asked pre-service teachers to prepare a lesson about a topic, e.g. area, as if they had to teach that lesson the next day. In this article the main aspects of the research environment are described and their effects on the research outcomes are evaluated.     

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.     

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...     

Primary school students’ strategies in early algebra problem solving supported by an online game

In this study we investigated the role of a dynamic online game on students’ early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10–12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students’ online working when solving the problems. Before and after the intervention a paper-and-pencil test on early algebra was administered. The data analysis revealed that the online working contributed to the students’ early algebra performance. There was a significant gain in performance across all grades. The highest effect was found in grade 6. Out of the three strategy profile clusters that could be distinguished in the whole sample, the cluster dominated by using extreme values and the cluster characterized by the trial-and-error strategy were most influential on the gain in early algebra performance. The students’ level of online working, which was defined as a combination of online involvement and strategy use, appeared to have a marginally significant effect on the gain score for the total sample. Per grade there was no significant effect, yet the levels of online working were significantly related to grade. Free playing was mostly performed in grade 4, looking for answers in grade 5, and exploring relations slightly more in grades 5 and 6. About 17 % of the effect of grade on the gain score was mediated by the level of online working.     

Teachers’ engagement with published research: addressing the knowledge problem

Despite the increased interest in research impact, there is very little empirical evidence that educational research can inform practice directly, and furthermore, a body of literature which suggests that this is, in principle, impossible. This paper reports on a study in which secondary school teachers were given research findings about teaching gifted and talented students, and were supported, over a 12-month period, to incorporate findings into action research projects of their own devising. A theoretical framework from the research literature was used to investigate the process by which knowledge generated from research, was transformed into teachers’ pedagogical knowledge, thereby influencing the curriculum, pedagogy and provision for these students. Evidence suggests that teachers transformed propositional knowledge into practical knowledge by developing their conceptual understandings; they transformed abstract, impersonal knowledge into context-specific, personal knowledge by using cases from their previous experiences, and they transformed narrowly focused knowledge into broadly focused knowledge by imaginatively diffusing it into areas beyond those in the original research. Implications for research and practice are discussed.     

Validation and profile of Chinese pre-service teachers’ technological pedagogical content knowledge scale

Researchers state that teachers in different contexts reported different technological pedagogical content knowledge (TPACK). This phenomenon may partially be explained by cultural differences. Based on this consideration, the development and validation of the Chinese pre-service teachers’ technological pedagogical content knowledge (CTPCK) scale is described in this article. The sample was split into two subsamples on random basis (n1 = 229, n2 = 207) for the purpose of conducting (1) exploratory factor analysis (EFA) and (2) confirmatory factor analysis (CFA), respectively. After the EFA, the CTPCK scale excluded six items and included eight factors with 42 items. Reliability and correlations were discussed. The findings revealed that the CTPCK scale was a valid and reliable instrument for measuring the TPACK of Chinese pre-service teachers’ knowledge with or without linking educational technology.     

Supporting teachers’ technological pedagogical content knowledge of fractions through co-designing a virtual manipulative

This study explores the impact that co-designing a virtual manipulative, Fractions Lab, had on teachers’ professional development. Tapping into an existing community of practice of mathematics specialist teachers, the study identifies how a cooperative enquiry approach utilising workshops and school-based visits challenged 23 competent primary school teachers’ technological, pedagogical and content knowledge of fraction equivalence, addition and subtraction. Verbal and written data from the workshops alongside observations and interviews from the school visits were analysed using the technological, pedagogical and content knowledge (TPACK) framework. The findings show that the assumptions of even experienced teachers were challenged when Fractions Lab was shared as an artefact on which they were asked to co-design and subsequently interact with, using it in subsequent phases of the cooperative inquiry process. Two original aspects of successful co-design of virtual manipulatives through communities of practice are identified and offered to others: (1) careful bootstrapping of the first design iteration that gathers intelligence about the content area and the technological affordances and constraints available; and (2) involvement of highly motivated teachers who perceive themselves as agents of change in the domain area.     

Teachers’ content knowledge about oral language: measure development and evidence of initial validity

Reading and Writing - Efforts to improve classroom language practices and children’s language learning, as a means of supporting reading comprehension, may depend on teachers’ knowledge...     

Exploring challenges of assessing pre-service science teachers’ pedagogical content knowledge (PCK)

The purpose of this paper is to report on the challenges we faced in designing an instrument aimed at measuring pre-service science teachers’ topic-specific pedagogical content knowledge (PCK). After the instrument was conceptualised and developed, it was administered to 30 pre-service chemistry teachers. The findings suggest that the instrument can be used as a teaching tool to enhance pre-service science teachers’ topic-specific PCK along with some limitations. The discussion focuses on the implications of the aforementioned PCK assessment tool for enhancing pre-service science teachers’ topic-specific PCK and the challenges associated with measuring and enhancing pre-service science teachers’ PCK. Finally, our discussion focuses on the ways in which science-teacher educators can engage in transforming the concept of PCK and its use for research and professional development.     

Developing biology teachers’ pedagogical content knowledge through learning study: the case of teaching human evolution

This work explores how pedagogical content knowledge (PCK) on evolution was modified by two biology teachers who participated in a professional development programme (PDP) that included a subsequent follow-up in the classroom. The PDP spanned a semester and included activities such as content updates, collaborative lesson planning, and the presentation of planned lessons. In the follow-up part, the lessons were videotaped and analysed, identifying strategies, activities, and conditions based on student learning about the theory of evolution. Data were collected in the first round with an interview before the training process, identifying these teachers’ initial content representation (CoRe) for evolution. Then, a group interview was conducted after the lessons, and, finally, an interview of stimulated recall with each teacher was conducted regarding the subject taught to allow teachers to reflect on their practice (final CoRe). This information was analysed by the teachers and the researchers, reflecting on the components of the PCK, possible changes, and the rationale behind their actions. The results show that teachers changed their beliefs and knowledge about the best methods and strategies to teach evolution, and about students’ learning obstacles and misconceptions on evolution. They realised how a review of their own practices promotes this transformation.