Prospective Secondary Teachers Research Articles

Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news

AbstractEducating students to apply probability literacy and reasoning in out-of-school contexts requires the previous preparation of teachers, which should include the assessment of their mathematical and didactic knowledge. Consequently, we investigated three research questions concerning the probabilistic reasoning and literacy of 66 prospective secondary school teachers when solving probability questions related to a report taken from the media news, their ability to identify the fundamental stochastic ideas needed to solve the task, and their capacity to predict their students’ potential difficulties. The participants needed to compute the probability of a complementary event, several conditional probabilities, and perform critical reading of the information in the report. Despite the participants’ good mathematical knowledge, a high percentage showed reasoning biases, such as the fallacy of the transposed conditional, confusion between conditioning and causation, and few identified the information missing to solve a question. There was a poor capacity to determine the stochastic ideas needed to solve the questions, beyond probability, sample space, conditional probability, and sampling. The participants quoted a few potential errors of their students, mainly conceptual mistakes with scarce recognition of interpretation errors. These results reveal the need to reinforce teachers’ probabilistic literacy, reasoning, and related didactic knowledge.

Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development

AbstractResearch has shown that there is a need to examine prospective teachers’ development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16–18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing their noticing of students’ mathematical thinking of this concept in teacher education programs is crucial to achieve high school student mathematics achievement. This study examines how prospective secondary school mathematics teachers (PTs) notice students’ mathematical thinking about the limit concept as they participated in a teaching module. PTs had to anticipate and interpret students’ mathematical understanding and make instructional decisions to support students’ conceptual progression using information about high school students’ understanding of the limit concept. We examined PTs changes related to how they anticipated, interpreted and made instructional decisions during the teaching module. We identified a change in how PTs conceived the understanding of the dynamic limit concept: from all-or-nothing dichotomy to progression; and a change in the instructional decisions they made: from decisions focused on changing the type of discontinuity to conceptual decisions. These changes allow us to characterise development noticing pathways. Our findings also help to identify the teaching module characteristics that support the development of PTs noticing.

예비중등음악교사의 국악지식 형성배경이 국악 수업 설계에 미치는 영향

Objectives The purpose of this study was to specify the relationship between variables related to Korean Traditional Music Class Design, such as pre-service teachers’ Background of Traditional Korean Music Knowledge Formation, and their general characteristics of demographic.
 Methods For this purpose, an online survey was conducted on 80 students majoring in music education at graduate schools of education located across the country to measure the general characteristics of the research subjects, the Background of Korean Traditional Music Knowledge Formation and Pedagogical Content Knowledge(PCK) shown in Korean traditional music class design. First, an independent samples t-test and one-way ANOVA were conducted to confirm differences in Pedagogical Content Knowledge according to general characteristics such as gender, marital status, and number of graduate schools attended, etc. Next, the sub-factors of general characteristics that showed significant differences as a result of the independent sample t-test and one-way analysis were set as control variables, and each sub-factors of the background of Korean traditional music knowledge formation(KTM); intra-personal formation background, contextual formation background) was set as an independent variable. Hierarchical multiple regression analysis was conducted to confirm the influence of variables on the design of Korean traditional music classes.We surveyed 80 graduate students majoring in music education located across the country and measured their general characteristics of demographic, PCK(the teaching content knowledge) that appear in the design of Korean traditional music classes, the Background of Korean Taditional Music Knowledge Formation, Statistical analysis, correlation analysis, independent samples t-test, one-way ANOVA, and Hierarchical regression analysis were performed.
 Results First, in terms of differences in the level of Korean traditional music class design according to the general characteristics of prospective secondary music teachers, the experience of taking Korean traditional music courses and Korean traditional music training experience, which were mentioned as important in previous studies, did not appear statistically significant. Second, this study examined the effects of pre-secondary music teachers' backgrounds on the design of Korean music lessons and found that among the sub-factors of teaching content knowledge measured through lesson design, the effects of contextual backgrounds on curriculum knowledge and intrapersonal backgrounds on content knowledge were statistically significant.
 Conclusions The results showed that there was a difference in scores among the sub-elements (pedagogical knowledge, curriculum knowledge, and content knowledge) of the Korean traditional music class design designed by prospective secondary music teachers, and it was confirmed through research that the background of Korean traditional music knowledge formation had an influence on the Korean traditional music class design.

Teachers’ noticing of proportional reasoning

AbstractThe importance of understanding what and how mathematics teachers notice is well documented, but more research is needed on content-specific noticing. In particular, knowing how teachers notice proportional reasoning, a vital topic spanning all grades of mathematics, could inform measures that support students’ proportional reasoning. We examined how teachers noticed when responding to two prompts (one student-focused and one teacher–student-interaction-focused) after watching a video of a middle grades proportional reasoning lesson. We analyzed the proportional reasoning reported from 13 elementary and 20 secondary prospective teachers and used cooccurrences along with noticing practices to describe how teachers noticed proportional reasoning and what aspects of proportional reasoning they noticed. Results indicate: (a) the two prompts resulted in differences in what and how participants noticed proportional reasoning, (b) participants were primarily descriptive and not interpretative when describing the proportional reasoning they noticed, and (c) the elementary and secondary prospective teachers both noticed similar aspects of proportional reasoning but showed differences in how the proportional reasoning cooccurred with the noticing practices. These findings reiterate the importance of the prompts used with teachers, the potential of using video to advance teachers’ noticing of proportional reasoning, and the methodological potential of using cooccurrences to examine teachers’ content-specific noticing.

Prospective secondary science teachers conceptions of the methodology of teaching

Prospective secondary science teachers conceptions of the methodology of teaching

A Comparative Glance At Teaching Practice of Mother Tongue Teacher Candidates in Türkiye and United Kingdom

This research aimed to determine how prospective secondary school language teachers conduct their teaching practicum in the United Kingdom and Türkiye. The study was designed using a multiple-case holistic design. Accordingly, data for the research were collected through document analysis and interviews. Data related to the teaching practicum in the Turkish Language Teaching program at Kırşehir Ahi Evran University Faculty of Education in Türkiye were obtained through document analysis. Data regarding the teaching practicum in the Postgraduate Certificate in Education program for secondary English teaching at the University of Reading Faculty of Education in the United Kingdom were obtained through document analysis and interviews with faculty members at the institution. It is evident that while the instructional content of teaching practicums in both nations exhibits substantial similarities, a notable disparity emerges with regard to the temporal extent of the practicum experience afforded to prospective secondary school language educators. As a result, the process of teaching practicums for secondary school language teacher candidates differs between Türkiye and the UK in terms of practicum hours, school diversity, and assessment methods.

생성형 인공지능 리터러시 활용 교육에 대한 인식 및 지원 방안 탐색: 예비중등교사를 중심으로

Objectives The study was conducted to explore the future directions for the implementation of a generative AI literacy education program for pre-service secondary teachers. Methods A survey was conducted among 94 pre-service secondary teachers from A University. The purpose of the survey was to assess their level of interest in understanding and utilizing generative artificial intelligence, their requirement for relevant education, and the assistance plans they might need. Additionally, in-depth interviews were conducted with 6 pre-service secondary teachers. Results 79.8% of pre-service secondary teachers reported having experience with AI programs, and 46.8% indicated that their knowledge of AI-related topics was at an introductory level. To support education in AI literacy, a practical space was provided where technologies related to AI could be used and AI literacy education should encompass both specialized majors and general liberal arts education. In-depth interviews revealed that the intention to enroll in AI literacy courses stemmed from the desire to enhance the capabilities of prospective secondary teachers, a personal interest in AI literacy, and curiosity about the courses themselves. Furthermore, the importance of adapting to societal changes and integrating AI-related subjects into the curriculum was emphasized. Conclusions It was suggested that the AI subject for pre-service secondary teachers should be taught as a practical-oriented regular course, focusing on enhancing the ability to critically analyze and embrace the information provided by artificial intelligence, rather than focusing on coding. It was also recommended to provide disciplinespecific education tailored to each subject area.

메타버스 플랫폼 젭(Zep) 활용 영어수업 설계에 대한 예비중등영어교사의 인식

메타버스 플랫폼 젭(Zep) 활용 영어수업 설계에 대한 예비중등영어교사의 인식

Exploring Pre-Service STEM Teachers’ Capacity to Teach Using a Gender-Responsive Approach

Teachers’ perceived efficacy of their ability to teach using a gender approach is key for future generations to become more gender-sensitive and respectful towards gender inequities. However, little is known about graduate training for gender-responsive STEM (science, technology, engineering, and mathematics) teaching. In this study, after exploring the measurement invariance across countries (Greece and Spain) and sexes (male and female) of the TEGEP (Teacher Self-Efficacy for Gender Equality Practice) scale, a total of 222 prospective secondary school STEM teachers (136 Greek, 86 Spanish) from seven public universities were surveyed. Results showed that (1) the TEGEP has acceptable measurement invariance across countries and among sexes allowing comparison between groups and (2) that Greek and Spanish STEM students finish their master studies without sufficient confidence in gender knowledge, skills, and attitudes to practice a gender-sensitive teaching. The ability to teach gender knowledge was significantly higher in Greek than in Spanish students (4.52 vs. 4.03), while the latter felt more competent than the Greek students in conveying values/attitudes in regard to gender (4.54 vs. 4.83). The study calls for reflection, and considering that gender mainstreaming in STEM is anecdotal and not aligned with existing curricula, seeks to raise awareness and institutional compromise in implementing a gender-responsive approach in STEM. The TEGEP could be utilized to assess and monitor the gender competencies required of graduates in order to provide a more equitable and gender-sensitive STEM education in Greece and Spain.

An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education

This study endeavors to illustrate how research on the professional development of mathematics teachers can help to enhance and nurture the professional knowledge of mathematics teacher educators (MTEs), thus becoming a potential source of professional growth for MTEs. To achieve this, a professional task was administered to 38 prospective secondary teachers from two Spanish public universities to explore their level of development in professional noticing. Specifically, the study focused on their skill of attending to children’s strategies in relation to transformations between semiotic representations as well as their awareness of the role of the semiotic register in task design. Drawing from the responses provided for the task, we offer a range of insights regarding expected or desirable Pedagogical Content Knowledge (MTEPCK) aimed at fostering the development of professional noticing, such as several challenges to be overcome by pre-service teachers or the identification of three potential levels of progression in their skill to attend to children’s strategies.

Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone course Mathematical Reasoning and Proving for Secondary Teachers and systematically studied its effect on PSTs’ content and pedagogical knowledge specific to proof. This paper focuses on one course module—Quantification and the Role of Examples in Proving, a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs’ content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs’ responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs’ learning and their applicability beyond the study context.

Prospective secondary school teachers’ knowledge of sampling distribution properties

The aim of the work was to assess prospective Spanish secondary school mathematics teachers’ knowledge of sampling representativeness and variability. To achieve this goal, a questionnaire with four items taken from our previous research with secondary education and high school students was proposed to 66 prospective teachers. In each item, participants were asked to provide four values of a binomial distribution, varying the parameters of the distribution in each item. The analysis of the mean and range of the sample of four values provided by the participants, and its comparison with the theoretically normative and acceptable values of the sampling distribution suggests a good knowledge of the sample representativeness, except for one item and an overestimation of the variability for large values of the number of trials in the binomial distribution. The study of the participants’ arguments serves to identify some reasoning biases related to sampling distribution. The results are better than those obtained with students in our previous studies.

Enhancing prospective secondary teachers’ potential competence for enacting core teaching practices—through experiences in university mathematics and statistics courses

Enhancing prospective secondary teachers’ potential competence for enacting core teaching practices—through experiences in university mathematics and statistics courses

Prospective Secondary Teachers’ Emergent Knowledge and Beliefs: Inquiry-Oriented Differential Equations Contributing to Teacher Preparation

This article reports on the evolution of prospective secondary teachers’ knowledge (meanings for frac{dy}{dt}) and beliefs (about teaching and learning mathematics) in a semester-long inquiry-oriented differential equations class. Students entered the course with limited, primarily procedural, meanings for frac{dy}{dt}. Throughout the semester, they engaged in collaborative mathematical inquiry using a research-based curriculum. As viewed through the emergent perspective, students’ meanings for frac{dy}{dt} and their beliefs about teaching and learning mathematics co-evolved with community norms and practices through the classroom discourse. Students’ end-of-term portfolios and portfolio presentations were analyzed for evidence of meanings for frac{dy}{dt} and beliefs about students’ roles, instructors’ roles, and the general nature of learning mathematics. In these, students expressed rich, multifaceted meanings for frac{dy}{dt} and beliefs about learning as an active process of meaning-making. While many prospective teachers do not see the relevance of advanced mathematics coursework to their career, these students reflected on their experiences in the course and volunteered ways in which their emerging knowledge and beliefs would influence their future practice. We emphasize that the classroom norms supported students in pursuing connections themselves, and conjecture that similar norms would support the development of reflective practitioners in other contexts.

Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in the work of teaching. We argue that the dimensions of Rowland's (2013) Knowledge Quartet, especially Foundation and Contingency, form a fruitful framework for this purpose. We contribute an analytic framework to characterize the quality of mathematical knowledge observed in the Foundation and Contingency dimensions, developed using a purposive sampling from over 300 representations. These representations all featured geometry teaching. We showcase the framework with examples of "high" and "developing" Foundation and Contingency.Then, we compare our coding along these dimensions with performance on a measure of mathematical knowledge for teaching geometry. Finally, we describe the potential for generalizing this framework to other domains, such as algebra and mathematical modeling.

Music Teacher Role Stress: A Structural Equation Model

Teaching music can be very stressful. The music education literature includes investigations of sources of stress and suggestions for stress relief, although it lacks a consistent underlying conceptual framework for stress. Role stress—a framework for understanding stress related to workplace dynamics—has the potential to provide structure while accounting for the nuance and complexity of organizations. The purpose of this study was to adapt and develop psychometrically sound questionnaires and then collect data to test a model to determine relationships among role stressors, role stress, and other variables of interest. Participants ( N = 1,576) responded to items related to six hypothesized role stressors, specialization and teaching loads, holding multiple jobs, years taught, job satisfaction, organizational commitment, and intent to leave the current job. I analyzed the data using descriptive statistics, factor analysis, and structural equation modeling. Key findings included (a) strong relationships among role stress and negative occupational outcomes, (b) confirmation of four known role stressors but nonseparation of role conflict and role ambiguity in statistical models, and (c) weak relationships between role stress and model covariates (years teaching, within-specialization teaching, and having multiple jobs). These results have implications for current and prospective secondary music teachers, music teacher educators, and school administrators.

Investigating how secondary prospective teachers plan to launch cognitively demanding tasks

Investigating how secondary prospective teachers plan to launch cognitively demanding tasks

Mathematical Specialized Knowledge of a Mathematics Teacher Educator for Teaching Divisibility


 
 
 The knowledge of Mathematics teachers has been a very prominent focus of attention in the last decades. However, it leaves aside one of the dimensions involved in the development of this type of knowledge, specifically the knowledge of Mathematics teacher educators. In this paper, we discuss a mathematics teacher educator’s knowledge in the context of classes on Euclid’s division algorithm theorem in a Number Theory course for prospective secondary teachers. Some indicators of this specialized knowledge of mathematics teacher educators are presented and discussed.
 
 

Prospective Secondary Math Teachers Encountering STEM in a Methods Course: When Math is More Than “Just Math”

Education reforms in the United States and abroad have increased efforts to improve student interest and capacity in STEM (science, technology, engineering, and mathematics). Despite these attempts, students still have little opportunity to engage in STEM learning in K-12 education. This qualitative case study was designed to investigate how incorporating STEM into teacher education can promote STEM teaching as well as enhance math instruction. The study took place in the fourth year of an undergraduate teacher education program spanning a secondary math and science Methods course and student teaching. Guided by the framework of sensemaking, individual interviews, teaching artifacts, and written reflections for four teachers were analyzed to identify moments of dissonance that pushed participants to reach new understandings about the learning and teaching of math. Findings indicated that learning to teach math through the lens of STEM shifted pre-service teachers’ instructional emphasis in two ways: 1) figuring out math vs. learning about math; and 2) teaching math through authentic STEM contexts as opposed to focusing purely on mathematics. However, experiences in student teaching can either enhance or stifle these gains. Findings suggest the role of teacher education in promoting STEM education by shifting prospective teachers’ mindsets about mathematics and teaching.

Metacognitive Awareness on Teaching and Teaching Competence of Secondary Prospective Teachers

Metacognition is the individual’s awareness of how he learns and what he does, employment of proper knowledge to gain his ends; the ability to employ cognitive skills that are required in an ordinary test, the knowledge of which strategies be employed with which goals, and the assessment of individual processes before and after the performance” (Flavell, 1997). Here, an attempt was made to investigate the relationship and differences of metacognitive awareness on teaching and teaching competence of prospective secondary teachers. The main objective of the study was to compare the significant mean differences and relationship of of metacognitive awareness on teaching and teaching competence of male and female secondary prospective teachers. A sample of 100 secondary prospective teachers consisted of 50 males and 50 females from Dr. PMIASE, Sambalpur, and Panchayat College, Bargarh, were selected randomly. For this study, both correlational and causal-comparative method was employed by the researcher. To collect data, the researcher used the Inventory of Metacognitive Awareness for Teachers (MAIT) developed by C. Balcikanli (2011) and the General teaching Competence scale (GTC) developed by B.K. Passi and Lalitha (1994). The obtained data were analyzed using”t” test and Pearson correlation coefficient “r.” It was that found the mean scores of male teachers are significantly better than the female teachers when metacognitive awareness was compared with teaching and teaching competence. Lastly, the result indicated there existed a strong positive correlation of metacognitive awareness on teaching and teaching competency concerning male and female student teachers.