Specialized Content Knowledge Research Articles

Mathematical modeling and discussions on knowledge for teaching: interactions towards the continuing education of mathematics teachers

In this article, we present our reflections on some of the interactions between Mathematical Modeling and the discussions concerning the professional knowledge of teachers. These interactions, as proposed through the continuing education of early years teachers, show that coordination between these two fields is beneficial to the training of educators, both facilitating the learning of mathematical content and contributing in various ways to the development of skills used to investigate and understand the role mathematics plays in society. Furthermore, the article highlights how these discussions have proved valuable in allowing teachers to understand the importance of possessing specialized content knowledge for teaching mathematics, as posited in the Mathematical Knowledge for Teaching model, developed by Ball, Thames and Phelps (2008).

INVESTIGATING PRESERVICE SECONDARY MATHEMATICS TEACHERS’ PEDAGOGICAL CONTENT KNOWLEDGE: A CASE STUDY IN MICROTEACHING COURSE

Effective teachers have a deep knowledge about the content of the subject matter they teach. As well as a deep knowledge of the material being taught, teachers must also have a deep knowledge about the processes and practices of teaching and learning. Pedagogical content knowledge is the intersection of discipline specific subject content knowledge and pedagogical knowledge. The purpose of this study is to examine Pedagogical Content Knowledge (PCK) of 30 preservice secondary mathematics teachers in microteaching course. The participants of this research are third-year preservice secondary mathematics teachers at Sanata Dharma University undertaking microteaching course. The data were collected in the form of observation, quesstionare, and written document. During the microteaching course, researcher observed preservice teachers’ comprehension of PCK components. The observation sheet is designed based on the conceptual framework for analysing PCK developed by Chick, Baker, Pham, and Cheng (2006). The findings revealed that many students have developed their PCK. However there were also some skills and knowledge that should be improved. Keywords : preservice secondary mathematics teachers, PCK, microteaching

Scaffolding excellence: Content-language integration and the development of Japanese ‘global leaders’

How does one develop advanced foreign language proficiency, specialized content knowledge, and a global intercultural perspective in the four short years of undergraduate study? This paper provides a descriptive case study of the Global Leaders Program, a broad-based curriculum renewal at a top-tier Japanese national university specializing in the social sciences. It focuses on content-language integration in the Faculty of Economics and the manner in which English language development is scaffolded for students through a progression from Content-based Instruction (CBI) and Content and Language Integrated Learning (CLIL) in the early years to English-medium Instruction (EMI) at advanced levels. Classroom instruction is further interwoven with multiple opportunities to apply theoretical knowledge and benchmark English proficiency through short-term field study tours and subsequent full-year student exchange experiences abroad. Following a description of the program, the paper discusses initial challenges in accommodating the additional English language instruction required by GLP and draws conclusions about a more fundamental hurdle that remains if an international excellence initiative such as the global leader’s program is to be successful in Japan. In addition, the paper offers insight about the contemporary educational practices of top-tier institutions in Japan and East Asia which may be instructive for receiving institutions that have a high intake of students from this region of the world on study abroad and longer-term student exchanges.

Using Lesson Study to Support the Teaching of Early Number Concepts: Examining the Development of Prospective Teachers’ Specialized Content Knowledge

Growing awareness of the importance of education in the early years has led professional organizations and policy makers to consider the effectiveness of mathematics education for young children. Factors such as educational environments, early years curricula and teacher education are some of the many aspects that have been examined. This paper describes the types of mathematical content knowledge that 25 prospective primary teachers developed as they designed, taught and reflected upon early number lessons. This Lesson Study approach involved two mathematics educators and 25 prospective primary teachers designing, teaching and re-teaching five early number lessons in two elementary classrooms with 4–5 year old children. The results suggest that effective teaching of early number concepts draws on mathematical knowledge that is specialized and unique to teachers; in other words Specialized Content Knowledge (SCK). The study found that engaging in Lesson Study promoted mathematics SCK development in two primary ways, notable by: (1) raising awareness of the complex relationships between early number concepts that contribute to developing robust early number understandings and (2) developing expertise in identifying the nature and source of children’s mathematical errors. The development of participants’ early number SCK is described and recommendations are made for the design of experiences in Initial Teacher Education (ITE) to support teachers in the provision of high quality mathematics experiences to young learners.

A first step toward a practice-based theory of pedagogical content knowledge in secondary economics

The purpose of this qualitative case study was to gain an in-depth understanding of how three award-winning secondary economics teachers demonstrated their pedagogical content knowledge (PCK), specifically horizon content knowledge, specialized content knowledge, knowledge of content and teaching, and knowledge of content and students. The teachers consistently connected economic content to other grades, subjects, and economic concepts and skills. Economic content was also regularly used to prepare students for citizenship, including casting more informed votes and understanding current events. However, authentic discussions, including ones about controversial issues, were mostly lacking. An emphasis was placed on developing students’ economic reasoning skills, including real-world applications of the economic way of thinking and decision-making models. Additionally, active learning instructional practices were frequently incorporated, and economic content was almost always related to students’ interests and experiences. A detailed description of a first step toward a practice-based theory of PCK in secondary economics concludes the article.

Identifying content knowledge for teaching energy: Examples from high school physics

Introducting a methodology for identifying content-specific teacher knowledge that shapes their in-the-moment decisions during interactions with students.

The effect of a specialized content knowledge workshop on teaching and learning Basic Life Support in elementary school: A cluster randomized controlled trial

BackgroundResearch investigating the effect of specialised content knowledge (SCK) on teaching and learning Basic Life Support (BLS) is lacking. PurposeTo investigate the effect of a specialised content knowledge workshop on teaching behaviour, lesson context and student learning of BLS. Specialised content knowledge comprises knowledge of content progressions, skill analysis, and how to correct common errors. MethodsA cluster randomized controlled trial. Ten elementary teachers from three schools were assigned to a common content knowledge (n=4) and specialized content knowledge condition (n=6). Common content knowledge teachers received a 50-min BLS workshop focused on learning BLS. Next to learning BLS, specialised content knowledge teachers also practised the teaching of BLS focussing on skill progressions, skill analysis and how to correct common errors children would likely make. Teachers then taught one BLS lesson and their behaviour together with lesson context was collected through direct observation. BLS performance of 203 children (mean age: 11.3 years) was individually assessed immediately after the lesson. ResultsStudents taught by specialised content knowledge teachers spent more time practising BLS (57% vs 30%), were less engaged in cognitive activities (29% vs 55%) and achieved a significantly higher BLS performance (62% vs 57%) compared to students taught by common content knowledge teachers, P<.05. Specialised content knowledge teachers on average gave more feedback (31 vs 19). Discussion and conclusionThis study demonstrates that a 50-min workshop with a focus on specialised content knowledge impacted teachers’ in-class behaviour, which in turn significantly improved students’ BLS performance.

Provoking contingent moments: Knowledge for ‘powerful teaching’ at the horizon

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research.Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.

Pharmacists' Knowledge and Practices Surrounding Expedited Partner Therapy for Chlamydia trachomatis, New York City, 2012 and 2014.

Health care providers in New York City can prescribe treatment for Chlamydia trachomatis (Ct) for a patient's partner without the partner having a medical evaluation ("prescription-expedited partner therapy" [EPT]), and use of prescription-EPT is common. However, there is little known about pharmacists' knowledge and practices surrounding EPT. Two cross-sectional surveys, in 2012 and 2014, were conducted with representative samples of supervising pharmacists in NYC neighborhoods with high rates of Ct infection. In both survey years, the majority of pharmacists who agreed to participate returned a survey (2012: 81% [83/103], 2014: 61% [106/173]), and pharmacist and pharmacy characteristics were similar across the 2 surveys. Pharmacists' EPT-related knowledge and practice was generally low, with little change between 2012 and 2014. In both years, fewer than half of pharmacists knew EPT was legal (2012, 46%; 2014, 42%). There were even decreases in specific content knowledge; in 2014, significantly fewer of the pharmacists who knew EPT was legal, knew that the initials "EPT" must be written in the body of the prescription (2012: 58%; 2014: 36%, P < 0.05). Most pharmacists in both survey years reported they had never received an EPT prescription, and those who had reported only infrequent receipt. NYC pharmacists had low levels of knowledge and familiarity with EPT law and reported infrequent receipt of EPT prescriptions. Pharmacists and providers should be further educated about EPT laws and regulations so that prescription-EPT use can be accurately monitored, and to assure the success of this partner treatment strategy.

Symbols, Symbolism and Significance in Yann Martel’s Life of Pi: Specific Content Knowledge for Teacher Development

Symbols and symbolisms across literary genres are powerful rhetoric devices used to enhance not only writers’ style, but to convey richness in meaning that transcends narrative descriptions. However, as its interpretations are context-bound, it causes anxieties for the under-proficient language teacher who, firstmost, requires deep specific content knowledge to drive instruction and enhance cognition amongst learners. Using qualitative descriptive case study, this paper aims to provide specific content knowledge by examining the literary use of symbols, symbolisms and significance in Yann Martel’s ‘Life of Pi’, which has been prescribed as a set book for Grade 12 school-exiting learners in South Africa, for the year 2017 onwards. The paper will – by analysing arbitrary, cultural and personal symbolisms and significances, mostly through psychoanalytical lens – unravel covert meanings and messages in cultural, religious and environmental contexts whilst simultaneously showing how these are pivotal to understanding major themes in the novel.&#x0D;

Investigating Chinese preschool teachers’ beliefs in mathematics teaching from a cross-cultural perspective

In China, preschool curriculum has undergone reform and profound changes. Much remains unknown, however, regarding preschool teachers’ teaching beliefs after 30 years of curriculum reform and adaptation. This study aimed to address the issue and investigate teachers’ beliefs concerning teaching mathematics. Twelve preschool teachers in China participated in the study: they watched videos of mathematics lessons conducted in the US and were interviewed with questions regarding the lessons. Qualitative analysis was then applied; themes were searched from the participants’ responses. The study revealed that Chinese preschool teachers acknowledged the features of (a) active learning, (b) involving every child, and (c) connecting lessons with everyday activities. However, they believed that their own teaching would be more purposeful: they would choose a specific content focus, use a series of steps, and make explicit summary at the end. The study also revealed Chinese preschool teachers’ solid specialized content knowledge in mathematics.

The preparation experiences of elementary mathematics specialists: examining influences on beliefs, content knowledge, and teaching practices

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (n = 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.

The effect of a specialized content knowledge workshop on teaching and learning Basic Life Support

The effect of a specialized content knowledge workshop on teaching and learning Basic Life Support

Effects of a Specialized Content Knowledge Workshop on Preservice Teachers’ Pedagogical Content Knowledge in Physical Education Teaching

It has been known that specialized content knowledge (SCK) is directly related to pedagogical content knowledge (PCK). However, little is known about the direct relationship between SCK and PCK. The purpose of this study was to examine the effects of a SCK workshop with knowledge packet on preservice teachers’ PCK in physical education teaching. A total of 18 preservice teachers, who were taking secondary methods class, were randomly divided by two different groups (i.e., control group and experimental group). Pedagogical content knowledge in physical education (PCKPE) tool and concept map assessment were used to examine preservice teachers’ PCK. A SCK workshop using knowledge packet was conducted only for the experimental group. A 2 X 2 (Group X Time) analysis of variance (ANOVA) with repeated measures was utilized and a significant interaction was found between group and time (Wilks’ ramda = .48, F (1, 7) = 7.68, p .05). The preservice teachers’ PCKPE scores significantly improved from pre-test (M = 29.54, SD = 3.17) to post-test (M = 40.95, SD = 3.37) in experimental group (p .001). The PCKPE scores were strongly related to the concept map scores in both pre- and post-test (r = .82 and .86, respectively, p .001). Results confirm that the PCKPE measurement tool can be used to accurately measure PCK as a direct observational tool.

Developing preservice elementary teachers’ specialized content knowledge: the case of associative property

Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching. This type of knowledge, although serving as a critical component for preservice teacher education, is often challenging to develop with preservice elementary teachers (PTs). The purpose of this study is to investigate PTs’ development of SCK for teaching fundamental mathematical ideas in a university methods course. Focusing on the case of the associative property (AP) of multiplication, the author as the course instructor identified three instructional opportunities (a formal introduction and two delayed revisits) to stress two SCK components, representations, and explanations. PTs’ learning progresses were assessed through three diagnostic tests (a pretest, a mid-term exam, and a final exam) and two prompts, which informed the upcoming lesson design. Meanwhile, the course instructor conducted ongoing reflections on PTs’ learning, which also informed the corresponding lessons. It was found that PTs initially generated abstract number sentences without reasoning about the contexts of word problems. This representational sequence indicates a symbol precedence view. When prompted for explanations, PTs focused on individual numbers rather than quantitative relationships, and they could not consistently apply the basic meaning of multiplication for reasoning. The methods course, when designed to address these issues, promoted PTs’ SCK development. At the end of the course, the majority of PTs were able to generate number sentences based on the word problem structures and provided reasonable explanations; however, the methods course also faced dilemmas due to PTs’ robust symbol precedence view and the tension between PTs’ learning and children’s learning. Very few studies have explored ways to support PTs’ knowledge growth in SCK, especially for teaching fundamental mathematical ideas. This study, by carefully documenting the successes and challenges in developing PTs’ SCK, contributes to the existing literature. Based on our findings, this study highlights the importance of stressing basic meanings so as to develop PTs’ explanation skills. Meanwhile, to develop PTs’ representation skills, university instructors should be aware of the tension between PTs’ and children’s learning as manifested by PTs’ symbol precedence view. Finally, to support PTs’ SCK growth, it is also important to emphasize the role of elementary textbooks.

Developing Elementary Content Knowledge in Physical Education Teacher Education

The purpose of this study was to investigate how curricular, content courses, and lessons are structured in ways to develop pre-service teachers' in-depth elementary content knowledge in physical education teacher education. Six elementary content course instructors' learning context data were collected from five physical education teacher education programs in the United States. Both qualitative and quantitative methods were adopted to analyze the collected data. The results of this study indicated: (a) the physical education teacher education programs offered fewer learning opportunities to learn K-12 content; (b) the elementary content courses were structured with different levels of content foci; (c) a primary tool for measuring in-depth elementary content knowledge was written exams or quizzes; and (d) three dominant instructional approaches--lectures, peer teaching, and modeling-- intended to develop specialized content knowledge were incorporated in the lessons. The research findings may guide teacher educators to reform their teacher preparation programs in ways to facilitate pre-service teachers' elementary content knowledge acquisition necessary for successful teaching.

Preservice teachers’ response and feedback type to correct and incorrect student-invented strategies for subtracting whole numbers

Despite the important role of teachers’ interpreting and responding to student ideas in teaching mathematics, there are many unanswered questions related to teacher learning and the role of errors in student-invented strategies. This study examined the reasoning and responses of 140 preservice teachers (PSTs) to students’ correct and incorrect strategies for whole number subtraction, as well as the PSTs’ perceived challenges in connecting student strategies to traditional methods. The study also investigated the role that PSTs’ specialized content knowledge plays in their ability to respond to correct and incorrect student-invented strategies, with respect to student-centeredness and feedback type. Results reveal that although some PSTs interpreted the validity and generalizability of the student methods incorrectly and justified them from the procedural aspect of each method, PSTs’ specialized content knowledge (e.g., the mathematical depth of the PSTs’ interpretation of student work) seemed to relate to their tendency to create student-centered approaches. However, specialized content knowledge did not seem to support PSTs’ feedback type in the domain of whole-number subtraction.

Developing Preservice and Inservice Teachers’ Pedagogical Content Knowledge in Economics

High school student achievement in economics has been predominantly characterized by low test scores, while secondary social studies preservice teachers have less formal training in economics than most other social studies disciplines. In this self-study, the instructional affordances and constraints of an experimental economics methods course are analyzed in terms of developing secondary social studies preservice and inservice teachers’ pedagogical content knowledge (PCK) in economics from both the instructor and pre and inservice teachers’ perspectives. Two course assignments appeared to most notably develop PCK in economics, the Analysis of Economic Events and the Active-Learning, Interdisciplinary Economic Lesson. Findings suggest interrelationships exist among common content knowledge, specialized content knowledge, and horizon content knowledge for teaching economics. Implications and instructional suggestions for social studies teacher education and professional development are discussed.

Controversy in Biology Classrooms-Citizen Science Approaches to Evolution and Applications to Climate Change Discussions.

The biological sciences encompass topics considered controversial by the American public, such as evolution and climate change. We believe that the development of climate change education in the biology classroom is better informed by an understanding of the history of the teaching of evolution. A common goal for science educators should be to engender a greater respect for and appreciation of science among students while teaching specific content knowledge. Citizen science has emerged as a viable yet underdeveloped method for engaging students of all ages in key scientific issues that impact society through authentic data-driven scientific research. Where successful, citizen science may open avenues of communication and engagement with the scientific process that would otherwise be more difficult to achieve. Citizen science projects demonstrate versatility in education and the ability to test hypotheses by collecting large amounts of often publishable data. We find a great possibility for science education research in the incorporation of citizen science projects in curriculum, especially with respect to “hot topics” of socioscientific debate based on our review of the findings of other authors. Journal of Microbiology & Biology Education

Teachers and their Educators - Views on Contents and their Development Needs in Mathematics Teacher Education

Finland has scored well in international assessments (e.g. PISA, TIMSS), and the pressure to attain excellent scores has activated a drive toward even more effective mathematics teacher education. This article presents the results of a qualitative assessment of the mathematics teacher education provided by the University of Eastern Finland. In this study, the views held by practicing teachers (N=101) and teacher educators (N=19) are compared so that the outstanding development needs of mathematics teacher education in terms of their contents can be revealed. The data was gathered via an electronic survey and was mainly analyzed using data-driven methods. In addition, framework provided by Mathematical Knowledge for Teaching (MKT) was used to categorize the respondents’ views regarding the contents of mathematics teacher education and to develop general guidelines for the reform of mathematics teacher education. The results indicate that mathematics teacher education should include pure mathematical content (Common Content Knowledge, CCK) and mathematical content that will have been designed only for future teachers (Specialized Content Knowledge, SCK). Teacher educators and practicing teachers both held the view that the relevance of CCK studies depend on the connections between university and school mathematics. Pedagogical studies should also be reformed because practicing teachers have realized that effective teaching (Knowledge of Content and Teaching, KCT) requires knowledge about learning mathematics (Knowledge of Content and Students, KCS) that is not offered in the current educational system on a sufficiently broad basis. In this study, suggestions for developing mathematics teacher education were mostly connected to four domains of MKT: (CCK, SCK, KCT and KCS). Interestingly those domains are the same domains which has been empirically tested and better conceptualized.