Specialized Content Knowledge Research Articles

Mental mathematics knowledge for teaching of ‘high gain’ pre-service teachers

Background: Initial teacher education (ITE) research in South Africa shows gaps in pre-service teachers’ (PSTs) primary mathematics knowledge.Aim: We study the mental mathematics understandings and teaching experiences of three PSTs who achieved high gains for learners they taught mental mathematics to using the Mental Starters Assessment Project (MSAP) jump strategy materials.Setting: The three PSTs, from one urban university, taught the jump strategy to Grade 3 classes in three different Gauteng schools.Methods: Learner pre- and post-tests around the taught unit provided the basis for categorising the three ‘high gain’ PSTs. Extended interviews with each PST were then transcribed. Initial grounded analyses of these data were subsequently overlaid with categories drawn from the mathematical knowledge for teaching literature.Results: All three PSTs indicated relatively strong common content knowledge of jump strategies and connected specialised content knowledge. They also exhibited strong awareness of the MSAP content. They differed in how they saw the relationship between fluency, calculation and equivalence tasks.Conclusion: The study’s findings indicate the need for more explicit attention to the connection between mental maths fluencies and strategic calculation in ITE.Contribution: The study points to ways in which mental mathematics can be understood and taught for strong learning gains.

How much C is in TPACK? A systematic review on the assessment of TPACK in mathematics

AbstractTeachers need technological pedagogical content knowledge (TPACK) for teaching with technology, and its assessment is crucial for research and practice. Previous literature reviews on TPACK assessment were not specific to a content area (e.g., mathematics), although, by definition, the TPACK framework includes content-specific knowledge facets. Consequently, requirements for TPACK assessment could differ depending on the content. Further, reliable assessment of mathematics-specific TPACK depends on the quality of the test instruments used, but there is no consensus on the type of instruments used in past studies. This systematic literature review adds to existing reviews by focusing on TPACK assessment in mathematics, investigating the study characteristics, the instrument characteristics, and the operationalizations of TPACK. Regarding study characteristics, the findings reveal an increase in the number of studies conducted across various countries worldwide. As for instrument characteristics, researchers frequently used self-developed instruments to assess TPACK, often without providing information on reliability or validity measures. Regarding operationalizations, more than half of the studies used self-report scales to assess mathematics-specific TPACK, followed by observations and material analyses, while knowledge tests were hardly used. Additionally, assessments typically referred to the domain of mathematics as a whole instead of subdomains of mathematics. The results raise questions regarding the validity of the instruments and the comparability across studies.

‘기둥’과 ‘뿔’에 대한 초등 예비교사의 교과 내용 지식 분석

The purpose of this study was to examine elementary preservice teachers’ subject matter knowledge (SMK) of prisms, pyramids, cylinders, and cones. The analysis of the preservice teachers’ SMK regarding the extension of each solid figure revealed that they had more difficulties with cylinders and cones compared to prisms and pyramids. Some of them classified cylinders and cones as solids of revolution based on the instructional sequence of the curriculum. This study also analyzed their SMK by dividing it into three categories: (a) mathematical definitions, (b) school mathematics, and (c) instructional sequence. The mathematical definitions group demonstrated a high overall level of specialized content knowledge (SCK). The school mathematics group, on the other hand, had mostly common content knowledge (CCK). The instructional sequence group often showed SCK only for cylinders and pyramids. Based on these analysis results, we proposed specific measures for preservice teacher education to develop their SMK and knowledge at the mathematical horizon (KMH).

To Praxis Test or Not? Mathematics Content Knowledge Tests for Teacher Licensure and Programmatic Considerations on Moving the Preparation Field Forward

ABSTRACT This study examined the relationships between recommended mathematics coursework for secondary mathematics teacher preparation, internal program measures, prior academic performance, and the Praxis-II testing requirement for initial teacher certification used in several states. Using structural equation modeling and path analysis, the research aimed to understand these relationships and their policy implications. Conducted over six years and holding the program measures and design constant for five cohorts, the study found strong support for specialized content knowledge courses, particularly for secondary mathematics teacher candidates who were not well-prepared in high school. Additionally, the findings suggest that the Praxis-II exam might not be necessary for all teacher candidates in mathematics, especially those who were well-prepared in high school and engaged in advanced mathematics coursework for teachers while meeting rigorous program requirements for teacher licensing. The study argues for reconsidering programmatic design in light of these findings while providing program faculty suggestions for program improvements. State Departments of Education and policy makers may consider the research methodology, validity of internal measures, and testing requirements for Praxis-II for future discussions.

Investigating Preschool Teachers’ Pedagogical Content Knowledge of Number Comparison

ABSTRACT Research Findings: The aim of this study was to investigate U.S. preschool teachers’ math pedagogical content knowledge in number comparison. Seventy-four in- and pre-service teachers completed a set of scenario-based questions from a researcher-designed questionnaire that is composed of learning scenarios. Through a mixed-method approach, the study revealed the following findings: a considerable portion of participants (89%) successfully identified the concept of number comparison embedded in a learning scenario, showcasing their specialized content knowledge. However, when it came to knowledge of content and students, only 24 participants (32%) were able to pinpoint both a child’s mathematical strength and area of need. In terms of knowledge of content and teaching, more than half of the participants (51%) recommended the utilization of hands-on materials and/or visual aids as part of their remediation techniques, while 49% did not reference these educational tools. Notably, no significant differences were observed between the pedagogical content knowledge of pre-and in-service teachers concerning number comparison. Practice or Policy: The findings indicate that teacher education and professional development should focus on helping teachers understand children’s learning trajectories on number comparison and include instructions on using concept specific developmentally appropriate strategies, and indicate that teaching experience cannot replace professional training.

Content Specific Pedagogical Knowledge and Teacher Knowledge Transfer

Pedagogical knowledge and in particular Content Specific Pedagogical Knowledge (CSPK) has been widely researched and discussed. Teacher training institutions globally have embraced knowledge bases proposed by researchers in their curriculum to prepare teachers for teaching. The transferability of CSPK has, however, received little attention. This article explores the transferability of CSPK by teachers. Using a literature review analysis method, the article raises the questions of why, and how, the need for CSPK transfer and addresses issues surrounding knowledge transfer. Focusing on a spiral curriculum, the transfer is seen more in relation to conceptual connection within a subject and across subjects, and integration of disciplines. The authors argue that teacher training should embrace aspects of knowledge transfer so that teachers are not rendered redundant when curricular changes and when some subjects which teachers have been trained are dropped from the curricular. Further research is recommended.

A microgenetic analysis of teachers’ learning through teaching

BackgroundWhat and how teachers learn through teaching without external guidance has long been of interest to researchers. Yet limited research has been conducted to investigate how learning through teaching occurs. The microgenetic approach (Siegler and Crowley, American Psychologist 46:606–620, 1991) has been useful in identifying the process of student learning. Using this approach, we investigated the development of teacher knowledge through teaching as well as which factors hinder or promote such development.ResultsOur findings suggest that teachers developed various components of teacher knowledge through teaching without external professional guidance. Further, we found that the extent to which teachers gained content-free or content-specific knowledge through teaching depended on their robust understanding of the concept being taught (i.e., content knowledge), the cognitive demand of the tasks used in teaching, and the lesson structure chosen (i.e., student centered vs. teacher centered).ConclusionsIn this study, we explored teacher learning through teaching and identified the sources leading to such learning. Our findings underscore the importance of teachers’ robust understanding of the content being taught, the tasks used in teaching, and a lesson structure that promotes teachers’ learning through teaching on their own.

Pre‐service middle school teachers' specialized content knowledge on sampling variability

AbstractThis study investigates a range of non‐normative ideas that pre‐service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre‐service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records of task‐based interviews has articulated fundamental facets of sampling variability that have not yet been fully explicated in the literature, especially with middle grade PSTs. With the content expectation of sampling variability for middle grade students as suggested by policy reports in the United States of America, this study is particularly fertile ground for designing curricula that can support middle grade PSTs' development of critical specialized content knowledge on sampling variability.

Training for conducting conversations professionally across domains – comparing communication training in biology teacher and medical education

ABSTRACT In higher education, the training of students’ communicative skills necessary for conducting professional conversations is gaining attention across domains – including medical and teacher education. Although teachers need communicative and content-specific knowledge for subject conversations on biological topics, biology-specific communication training is rare. Research on an interdisciplinary perspective on communication training, with the use of simulated conversations with standardised interlocutors, would close this gap. This study compares such training in medical and biology teacher education. We questioned pre-service biology teachers (n = 25) and medical students (n = 31) participating in communication training about their fear of failure in future professional conversations, and their perceived utility value of communication training. After some input, single participants in both groups simulated a conversation with a standardised caregiver or patient. Both training sessions ended with reflections on the simulation. Our results of t-tests and ANOVA indicate that training in subject conversations about sex education reduced the fear of failure, increased the perceived utility value, and indicate that future physicians and pre-service biology teachers benefit comparably from training. The findings and limitations of the study are discussed.

Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems

Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.

Designing TPACK-English Textbook for Economic Faculty Students

This study thoroughly investigates the educational needs of Economics students in English for Specific Purposes (ESP) and Technological Pedagogical Content Knowledge (TPACK), based on a survey of 292 students and 12 alumni from the Economics faculty. The study reveals nuanced linguistic preferences across six fundamental components: task, activity, language use, technology, pedagogy, and topic or content relevancy. The findings show that listening skills, particularly for information acquisition, were highly valued (mean score: 3.01), whereas speaking abilities such as explaining and knowledge elicitation were universally deemed critical (mean scores > 3.00), whereas activities such as making suggestions were deemed less important (mean score: 1.99). The study also identified important areas in economics education, highlighting significant topics such as Economics, Microeconomics, and Islamic Economics (mean scores > 3.00) and the impact of English proficiency levels in maximizing learning experiences. The findings demonstrate a variety of activity priorities, with a focus on collaborative instructional tactics and specific linguistic demands in economic communication. Furthermore, this study explored students’ educational needs and the design of English instructional material for economics faculty students. This design integrates technology, language skills, and economic theory to improve student learning and skill acquisition.

Insights into a Community of Inquiry that emerged during academics’ emergency remote university teaching of chemistry in response to concern for students

ABSTRACT Background Effective teaching of university chemistry in an online environment not only requires teachers to have specific discipline content knowledge; it also requires them to have knowledge and skills in technology-enhanced teaching practices. When transitioning from traditional face-to-face teaching into online contexts, teachers must learn new strategies and methods, along with a shift in their beliefs. Whilst online learning of chemistry is commonplace in many higher education institutions globally, the integration of computer and digital technologies in teaching chemistry in developing countries had been limited prior to the 2020 pandemic. Purpose In this study, the experiences, perceptions, and teaching strategies of university chemistry teachers in the Philippines have been explored during the transition of their instruction to emergency remote teaching at two timepoints during the COVID-19 pandemic. Sample Data were collected in the form of survey responses from 139 participants representing 35 universities and colleges across the nation. Results No strong relationships were found between participants’ experiences and their academic rank, length of service, or institution type, suggesting university chemistry teachers took similar approaches to quickly adopt and adapt available technologies to deliver the required curriculum. Since the Philippines continues to struggle to establish a robust infrastructure to promote online and technology-enhanced learning, participants had to devise pedagogies and practices that would allow accessible learning experiences for their students by curating online tools that would require minimal bandwidth and low internet data consumption. Using abductive methodology, the Community of Inquiry (CoI) framework was employed as a guide in interpreting university chemistry teachers’ experiences and perceptions about their implementation of emergency remote teaching using online technologies. Whilst participants had limited prior experiences in employing online learning pedagogies, key elements of the CoI framework became apparent through the new technologies and practices implemented by university chemistry teachers which fostered teaching presence, cognitive presence, and social presence.

The Effectiveness of Content Knowledge Instruction in Tennis and Badminton in Physical Education Teacher Education

Purpose: Our research examined the effects of a content course in a physical education teacher education program. Methods: Ten participants were recruited from a physical education teacher education content course to examine participants’ common content knowledge (CCK) and specialized content knowledge (SCK) in tennis and badminton. Descriptive and inferential statistics were used to investigate (a) participants’ pre–post gains in CCK and SCK, (b) the relationship between participants’ playing and teaching experience with CCK and SCK, and (c) the relationship among the dependent variables in both pretest and posttest. Results: Participants’ content knowledge variables increased significantly. Furthermore, the study revealed inconsistent relationships between participants’ self-reported playing, teaching, and coaching experiences with their CCK and SCK scores at the pretest. We found inconsistent relationships between CCK and SCK among pre- and posttests. Discussion/Conclusion: The primary finding is that preservice teachers can improve substantively their content knowledge through well-designed content courses, but in some domains, there is more work to do.

Toward proficiency: Developing a multiplication mathematical content knowledge test for pre-service mathematics teachers in Indonesia and Türkiye

This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.

Superior Performance Competencies Achieved Through Destination Imagination Experiences

Today’s workforce not only requires specific content-area knowledge and skills achieved through formal education but also, and most critically, superior performance competencies including distinguishable behaviors. While formal education prioritizes easily detectable and measurable content-specific knowledge and skills, superior performance competencies such as cognitive, affective, and motivational skills remain secondary unless students engage in extracurricular activities in real-world settings. This qualitative study investigated the phenomenon of achieving an array of superior performance competencies through learning by doing, at one of the 2023 Destination Imagination events. This study marked the first fieldwork in which the principal researcher directly observed the event in its natural setting. Data were collected, analyzed, and interpreted concurrently during the event by means of observations, ordinary conversations, and an informal interview. The inductive data analysis included analytic memos, and midway hypothesis coding which confirmed the significance of immersing in such activities and resulted in two major findings: 1) participating in such meaningful real-world activities cultivates distinctive behaviors that drive exceptional performance, positioning participants to stand out among their peers; and 2) this involvement also equips students with the capabilities to excel upon entering the workforce, ensuring superior employee performance in their roles.

The effect of specialized content knowledge in reciprocal peer learning in a university content class

ABSTRACT Background Teaching strategies using peers to influence student-learning outcomes are commonly used in physical education. Reciprocal peer learning is a teaching strategy where students work in pairs as tutor and tutee. Effective peer tutoring requires knowledge about the critical elements for correct performance (i.e. common content knowledge, CCK) and knowing how to detect and address common errors (i.e. specialized content knowledge, SCK). Research on training students for their task as tutor to increase peer learning effectiveness is limited. Purpose and research question This study documents an online approach to prepare students for their role as tutor during reciprocal peer learning. Also, it investigates the effect of online CCK + SCK-training versus online CCK-only training on (a) skill performance by tutees and error detection by tutors during peer learning; and (b) individual skill performance at a 1-week retention test. Methods Seventy-seven undergraduate students (25 female, 52 male) were randomly assigned to an online CCK + SCK (n = 37) or CCK-only (n = 40) training for learning Basic Life Support (BLS) as part of their curriculum. All participants learned online the correct procedure for BLS according to international guidelines (i.e. CCK). In the CCK + SCK condition, students additionally learned online to detect and correct four common errors related to chest compression. Following the online training all students learned BLS using reciprocal peer learning with manikins. For each student pair skill performance during practice by tutees was reported using digital manikins and error detection by tutors was collected using systematic observation of video recordings. One week following practice (i.e. retention), BLS-performance was assessed individually using a validated protocol. Findings During peer learning, SCK-trained tutees performed less unique errors (Mdn = 2 vs. 1, p < .05) and SCK-trained tutors detected a higher proportion of unique errors (Mdn 100% vs. 0%, p < .05) compared to CCK-only trained students. At retention, SCK-trained students outperformed the CCK-group for chest compressions with adequate rate (Mdn 91% vs. 69% p < .05) and complete release (Mdn 81% vs. 35% p < .05). Conclusions Teaching undergraduate students online to detect and correct errors positively impacted the quality of practice during peer learning and the performance at retention.

Pedagogical Content Knowledge in the Physical Education Field. A systematic review of the literature 2011-2022

Teaching of Physical Education, knowledge about what to teach, who to teach and how to teach must be considered; within the framework of these aspects, Pedagogical Content Knowledge arises, considered as an amalgamation between content and pedagogy. This study analysed the scientific production in the Scopus, Web of Science and Science Direct databases, regarding the development of Pedagogical Content Knowledge in the Physical Education Field, between 2011 and 2022 and was done systematically. Articles were included in English and Spanish, for a total of 32 articles. The results show that there was a peak of publications in the year 2020; the country in which more studies have been carried out is the United States; regarding the level of research, the vast majority are of an explanatory nature. The studies were classified into three categories: Pedagogical Content Knowledge in school Physical Education, in School Sports and in training programs for physical education teachers. It could be concluded that there is a need for Common Content Knowledge and Specialized Content Knowledge to be better taught in teacher education programs as they are a fundamental basis for Pedagogical Content Knowledge. Likewise, since this construct is dynamic and changing, it should also be considered in the professional development phase, since field experience and the relationships established in the field provide new knowledge and formative experiences. Keywords: Pedagogical content knowledge, physical education, teacher training, school sports, literature review.

Mathematical knowledge for teaching and mathematics didactic knowledge: a comparative study

AbstractThis paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: ‘mathematical knowledge for teaching’ and ‘mathematics didactic knowledge’. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical knowledge for teaching is viewed as a utilitarian-pragmatic approach rooted in English-speaking traditions as it focuses on its use in teaching and represents a practice-based conceptualization of knowledge domains required for mathematics teaching. Mathematics didactic knowledge, on the other hand, is considered normative-descriptive as it is formulated based on didactic principles and broader theoretical perspectives, providing a theory-driven conceptualization of knowledge domains rooted in traditions of German-speaking didactics of mathematics. The paper further highlights similarities and differences in these two constructs through an examination of two central knowledge domains: specialized content knowledge (part of mathematical knowledge for teaching) and subject matter didactic knowledge (part of mathematics didactic knowledge).

Reorganizing assessment questions to provide additional information on student understanding of specific course content.

Performance on exams and course letter grades are broad standards used to determine understanding of course content. To gain a different perspective on students' knowledge, we examined whether grouping exam questions based on the topic they assessed would provide additional information on students' comprehension. Assessment questions from our physiology course were organized into groups based on major physiology content categories. We created 10 content categories and calculated students' performance in each category. The average of the 10 scores was compared with the course grade. The scores in individual categories reflected student knowledge of specific physiology content. The average scores of the 10 categories correlated with course letter grades. Analysis of performance demonstrated that 65% of students with course grades between 70 and 73% answered less than 70% of assessment questions correctly in four or more content categories. Evaluation of performance in grouped assessment questions provided additional information on student understanding and identified specific course content in which students underperformed.

EXPLORING TEACHERS’ VIEWS ON THE PEDAGOGY OF WRITING SKILLS IN ENGLISH FIRST ADDITIONAL LANGUAGE

English writing proficiency in First Additional Language amongst Intermediate Phase learners has not reached satisfactory levels in South African schools. The aim of this paper was to explore teachers’ views on the teaching of writing skills in English First Additional Language specifically of grade 4 learners. The study sought to ascertain strategies used by teachers in teaching writing skills in selected EFAL grade 4 classrooms in uMkhanyakude District in the KwaZulu Natal province. A descriptive multiple case study design was adopted for this paper. Qualitative approach through semi-structured interviews and classroom observation were adopted, interpretive paradigm, purposive sampling, and thematic analysis were used. Findings revealed that teachers use various teaching strategies depending on the type of writing genre taught, needs of their learners, availability of resources and their context. Findings also indicated that teachers face challenges when teaching writing, they lack pedagogical knowledge on how to effectively teach writing and the support received is inadequate to enhance their pedagogy of writing skills especially for English First Additional Language. The paper concludes that there is a need for significant improvement on specific content and pedagogical knowledge that teachers possess to teach writing. Thus, this paper provides recommendations which emphasises the improvement of Initial Teacher Education in the writing domain by specifying the content and pedagogical knowledge to be taught, and ensuring adequate time dedicated to writing and writing instruction. Therefore, the paper advocates towards deep knowledge and understanding on how teachers can use a variety of strategies in trying to reinforce teaching of writing skills.