Exploring the Relationship Between Preschool Teachers’ Pedagogical Content Knowledge and Their Self-Efficacy Beliefs in Mathematics Education

This study attempts to identify preschool teachers' pedagogical content knowledge levels in mathematics and to examine its effect on preschool children's mathematics ability and their liking of mathematics. The study utilised the relational survey model, one of the general survey models. The working group was composed of 600 children aged 54-66 months old and a total of 150 teachers. The study employed three data collection tools: with the 'Preschool Teachers' Pedagogical Content Knowledge Scale regarding Mathematics' and the 'Mathematics Liking Scale for Children' developed by the researchers; 'Early Mathematics Ability Test' to determine children's mathematics ability. The data were analysed using IBM's SPSS 22 statistical package. The correlation analysis results suggested that there were no significant relationships between teachers' pedagogical content knowledge in mathematics, children's mathematics ability, and their liking of mathematics, while a positive and significant relationship was found between children's mathematics ability and their liking of mathematics.

The study investigated preschool teachers’ pedagogical content knowledge (PCK) in mathematics. The construct of PCK for teaching mathematics in preschool involves three components: (1) noticing mathematical situations in which children engage; (2) interpreting the nature of children’s math activity; and (3) enhancing children’s mathematical thinking and understanding. The research participants were 30 preschool teachers from a large city in South Korea. Teachers identified mathematical situations in a children’s play scenario, interpreted the nature of the mathematical situations, and identified how children’s mathematical thinking in the reported situation could be enhanced. The teachers’ responses were quantitatively scored. The results indicate that participants possessed higher levels of PCK about number sense, measurement, and classification than for patterning, operations, shapes, and spatial relationships. Teachers need knowledge to interpret mathematical situations in order to identify ways to enhance children’s mathematical thinking. Teachers with more teaching experience were more likely to have higher scores on the overall PCK measure. Teachers require greater knowledge to recognize specific mathematical concepts in use in children’s play in order to be able to extend and enhance preschool children’s mathematical thinking.

Teachers' pedagogical content knowledge (PCK) is pivotal for effective classroom instruction. Unfortunately, research on the acquisition of preschool teachers' PCK in the domain of early mathematics and how this knowledge relates to their mathematical classroom activities is scarce. The present contribution investigates (1) the acquisition of PCK in pre-service and in-service preschool teachers and (2) the association between preschool teachers' PCK and self-reported classroom activities in the domain of early mathematics. We offered a scenario-based questionnaire to 162 pre-service preschool teachers and 75 in-service preschool teachers to assess their PCK in the domain of early mathematics. Additionally, in-service preschool teachers fulfilled a questionnaire about their mathematical classroom activities. Our findings demonstrated that first-year pre-service preschool teachers scored significantly lower than second- and third-year pre-service preschool teachers. Furthermore, this latter group achieved a significantly lower PCK score than in-service teachers. Second, we observed a positive association between teachers' PCK and the classroom activities in the domain of early mathematics they reported to provide. Overall, our findings point to the interplay between PCK and effective classroom activities in preschool mathematics, and to the importance of teacher training and professional development programs, including opportunities to enhance the acquisition of this important knowledge.

본 연구는 현 과학교육의 개혁 운동에 기초하여 예비 교사들의 자기 효능감과 교과교육지식(PCK) 이해의 향상을 위하여 과학적 탐구를 실행하였다. 이를 위하여 과학교육 방법론 수업(Science Method Course)은 초등학교 교실에서 실행할 수 있는 효과적인 과학 탐구 모델링 수업과 과학적 실천 교수학습을 포함하도록 수정하였다(RSMC). 본 연구에서는 다음과 같은 연구 문제를 조사하였다: (1) 수정된 과학교육 방법론 수업(RSMC)의 처치 전후 예비교사들의 PCK 정도는 어떠한가?: (2) RSMC 이수 후 과학 교수학습에서 예비교사들의 자기 효능감의 정도는 어떻게 변화하였는가?: (3) 예비교사들의 자기 효능감과 PCK 수준의 변화는 어떤 상관관계가 있는가? 연구에 참여한 예비교사들은 미국 중부의 중간정도 규모의 대학의 교사교육 과정에서 제공하는 과학교육 방법론 수업에 등록한 76명이며, 분석을 위해서 STEBI-B 설문지와 PCK 평가지를 이용하였다. 본 연구의 결과로는 예비교사들이 RSMC 이수 후 개인적 과학교수 효능감(PSTE: Personal Science Teaching Efficacy)이 확실히 향상된 결과를 볼 수 있었다. 또한 PCK 평가지에 근거하면, RSMC 전과 후의 PCK 수준은 평균값이 현저히 상승하였으며, 예비 교사들의 자기 효능감과 PCK 수준의 변화 사이의 상관관계 분석에서는 긍정적인 상관관계를 보여주었다. 따라서 본 연구에서는 과학교육개혁 운동에 근거하여 설계된 과학교육방법론 수업(RSMC)은 예비 교사들의 오개념의 수정, PCK 수준의 향상 증진, 그리고 현장 학교에서 탐구수업의 모델링 등을 통하여 과학교수학습에서 자기 효능감의 향상에 긍정적인 영향을 미친다고 결론 내릴 수 있다. This study was designed to enhance preservice teachers' self-efficacy beliefs and pedagogical content knowledge (PCK) through scientific investigations based on current science education reforms. To do so, a science methods course was revised to include modeling effective scientific inquiry practices as well as designing and teaching scientific investigations in the K-5 practicum classrooms (Revised Science Methods Course). This study assessed the following research questions: (1) What level of PCK do preservice teachers have before and after the completion of RSMC; (2) To what extent do participants change their self-efficacy in science teaching after completing RSMC; and (3) Is there any correlation between participants' changes in self-efficacy and the level of PCK. Participants were 76 preservice teachers enrolled in a science methods course offered at a medium-sized university in the midwestern United States. This study employed the STEBI-B survey and the PCK rubric. There result of the study indicated that there was significant increase in Personal Science Teaching Efficacy (PSTE) of the participant preservice teachers after the completion of the course. Based on the PCK rubric analysis, there was a significant increase in mean scores of the post-RSMC lesson compared to those of the pre-RSMC lesson. The correlational analysis of participants showed a positive correlation between changes in self-efficacy and the level of PCK. Thus, it may be concluded that the reform-based science methods course had a positive impact on participants' self-efficacy in science teaching through correcting misconceptions, developing higher level of PCK, and modeling scientific investigation in their practicum schools.

This research aimed to determine the influence of Continuous Professional Development (CPD) training offered by Rwanda Quality Basic education for Capital Human Development Project (RQBEHCD) sub-component 1.2 on upper primary teachers’ Pedagogical Content Knowledge (PCK) in mathematics and science, and elementary technology (SET) subjects. The study adopted an explanatory sequential design to collect and analyze data. Quantitative data were collected from Mathematics and SET achievement tests while qualitative data were collected from semi-structured interview. Quantitative data were collected from 290 participants including 166 male and 124 female teachers. On the other side, the qualitative data were collected from 20 teachers including 12 males and 8 females selected randomly. Descriptive and inferential statistics (repeated measures Analysis of Variance were used to analyze quantitative data while interpretive and thematic analysis were used to analyze qualitative data. The results found high statistical significance in mean scores of mathematics teachers between pre and post-test, with a p < 0.001, medium learning gain of 0.37, and an effect size of 0.450. However, there were no significant differences found between male and female teachers (p > 0.05). Likewise, SET teacher's results showed a significant difference in mean score between pre and post-test with p < 0.01, learning gain of 0.20, and effect size of 0.432 but no significant difference was found between male and female teachers (p > 0.05). In addition, the qualitative results indicated that the CPD program enhanced engagement, interest, confidence, and self-efficacy in teaching Mathematics and Science. Thus, we recommended that the CPD program should be done nationwide to maintain teachers’ PCK in mathematics and science.

This study examined the relationship between preservice teachers' Educative Teacher Performance Assessment (edTPA) scores, the most widely implemented preservice teacher performance assessment in the United States, and the pedagogical content knowledge (PCK) levels reflected in their edTPA portfolios. PCK is a specialized form of teacher professional knowledge widely considered a paramount construct of teacher quality. Thirty‐six preservice science teachers' PCK levels were determined by analyzing their edTPA portfolios, including videos and written commentaries, with the PCK mapping approach, an enumerative analytical method capable of quantifying and visualizing the integration of PCK components. Data analysis indicates there was a significant positive correlation between participants' edTPA scores and their PCK levels (rs[36] = 0.949, p &lt; 0.0001). Through further analysis, this study also identified several key features of preservice teachers' PCK revealed in their edTPA portfolios: (1) preservice science teachers' Knowledge of Student's Understanding (KSU) and Knowledge of Instructional Strategies and Representations (KISR) were the most developed components of PCK; (2) accounting for over 50% of all connections between PCK components, KSU, KISR, and Knowledge of Assessments were among the most frequently integrated components of PCK; (3) Knowledge of Science Curriculum was the least frequently integrated, and therefore the weakest, component of preservice teachers' PCK; and (4) inquiry was the most frequently mentioned, and typically the only Orientation toward Teaching Science found in participants' edTPA materials. This study contributes to the growing body of scholarship on the characteristics of preservice science teachers' PCK and becomes one of only a handful of empirical studies that examine the edTPA's diagnostic abilities. Finally, potential implications regarding the edTPA in science teacher education, as well as directions for future research surrounding preservice science teacher PCK and PCK development, are discussed.

The focus on Pedagogical Content Knowledge (PCK) of pre-school teachers is a breakthrough point to promote teacher's professional development and quality of early childhood education. Based on an investigation of PCK of 161 pre-school teachers from Shanghai, this study described the level of PCK for early mathematics (PCK-EM) of pre-school teachers and examined the influence of their background on the level of PCK-EM. Further, the study put forward implications and suggestions on improving and promoting early mathematics education.

This study aimed to develop a measurement tool in order to assess preschool teachers’ pedagogical content knowledge regarding mathematics. The study was based on 300 preschool teachers working in formal independent kindergartens and nursery classes of primary/secondary schools in the Kahramanmaraş Province of Turkey. Among the participants, 150 were chosen for pre-application and 150 for the main application. The scale consists of five different case studies and a total of 35 items, including dialogues that focus on mathematical content and processes reflected in children’s talk during their play. In calculating the reliability of the scale, Cronbach Alpha was found to be .95 for the pre-application and .96 for the main application. For the validity of the scale, exploratory and confirmatory factor analyses were performed. The exploratory factor analysis results revealed the scale to be a single-factor structure. When the factor loads of each relevant item were examined, no item was found to exist with a factor load value of less than .30. After confirmatory factor analysis was performed, the model fit indices of CFI, TLI, RMSEA, and SRMR values were found to be .91, .91, .06 and .06, respectively. These results show the model to be reliable to an acceptable level. Based on the findings, it could be concluded that the scale is an instrument that produces valid and reliable measures, and that it can be used in order to determine the preschool teachers’ pedagogical content knowledge regarding mathematics.

Background: Education in mathematics and science is important at all school levels and should ideally start in the preschool, which implies that preschool teachers should have an adequate knowledge base in these subjects.Aim: This study aimed to investigate preschool teachers’ knowledge bases, including their subject matter knowledge (SMK) and pedagogical content knowledge (PCK) in mathematics and science.Setting: The study presents an account of preschool teachers’ knowledge bases in mathematics and science in Botswana and Sweden and how they influence their teaching choices and strategies.Methods: A pragmatic paradigm with a survey design and a mixed-methods mode with quantitative and qualitative approaches was used. Using a purposive sampling procedure, 64 preschool teachers from Botswana and 67 from Sweden participated in the study. Questionnaires and observation schedules were used to collect the data.Results: The findings showed that the Swedish preschool teachers had SMK and PCK in the two subjects. The Botswana teachers had SMK but lacked PCK. The early childhood educated preschool teachers from Sweden with developed PCK highlighted the daily routine situations as teaching or learning situations, whereas the primary school teachers from Botswana had SMK but found it difficult to teach at the preschool level.Conclusion: The preschool teachers’ knowledge bases included a play-based approach and knowledge about didactic considerations in spontaneous situations that made them teachable. The findings also showed the importance of a framework for specialised and professional early childhood education (ECE) training and acquiring SMK and PCK that contributed to the preschool teachers’ knowledge bases and practices in their teaching of mathematics and science. Early childhood education teachers’ educational experiences, their specialised and professional training profiles and the knowledge they acquired determined their knowledge bases and the SMK and PCK that minimised the constraints and challenges faced by them in the teaching of mathematics and science in ECE classrooms.

The purpose of this study was to assess 81 kindergarten teachers’ pedagogical content knowledge of mathematics on six subcategory areas such as number sense, pattern, ordering, shapes, spatial sense, and comparison. The data showed participants possessed a higher level of pedagogical content knowledge of “number sense” (M = 89.12) compared to other mathematics pedagogical content areas. The second highest scores among six subcategories of pedagogical content knowledge of mathematics was for the pedagogical content area of “pattern” (M = 82.33). The lowest scores among those six subcategories of kindergarten teachers’ pedagogical content knowledge were obtained from the subcategory of “spatial sense” (M = 44.23), which involved the means to introduce children to spatial relationships. The second lowest score was obtained for the subcategory of “comparison” (M = 50.40) which involved the means to introduce the concept of graphing and the use of a balance scale for measurement.

This study was carried out to examine the relationship between preschool teachers' mathematical pedagogical content knowledge (MPCK), their attitudes towards mathematics (ATM), and their attitudes towards mathematics teaching (ATMT). The research method was designed according to the relational survey model, one of the quantitative research methods. The study group consisted of 365 pre-school teachers working in pre-school educational institutions affiliated with the Ministry of National Education. The research data were obtained using the "General Information Form", "Knowledge Scale of Pedagogical Content in Preschool Mathematics" and "Scale of Attitudes for the Teaching of Mathematics". The obtained data were analyzed using the SPSS 22 package program. Firstly, as a result of the research, it was found that the ATM and ATMT levels of the teachers participating in the research were above average. In addition, findings showed that the levels of knowledge of mathematical pedagogical content were below average in some content areas (counting) and above average in some content areas (pattern, order, shape, spatial dimensions and comparison, and total score). Second, although the age of the teachers did not affect the levels of ATM and ATMT, on the contrary, it didaffect the levels of MPCK. Third, the seniority variable was found to affect ATM and MPCK levels but did not affect ATM. Finally, low positive correlations were found between the levels of MPCK, ATM, and ATMT. These research findings were discussed in light of the relevant literature and suggestions were made.

Teachers' pedagogical content knowledge (PCK) is pivotal for effective classroom instruction. Unfortunately, research on the acquisition of preschool teachers' PCK in the domain of early mathematics and how this knowledge relates to their mathematical classroom activities is scarce. The present contribution investigates (1) the acquisition of PCK in pre-service and in-service preschool teachers and (2) the association between preschool teachers' PCK and self-reported classroom activities in the domain of early mathematics. We offered a scenario-based questionnaire to 162 pre-service preschool teachers and 75 in-service preschool teachers to assess their PCK in the domain of early mathematics. Additionally, in-service preschool teachers fulfilled a questionnaire about their mathematical classroom activities. Our findings demonstrated that first-year pre-service preschool teachers scored significantly lower than second- and third-year pre-service preschool teachers. Furthermore, this latter group achieved a significantly lower PCK score than in-service teachers. Second, we observed a positive association between teachers' PCK and the classroom activities in the domain of early mathematics they reported to provide. Overall, our findings point to the interplay between PCK and effective classroom activities in preschool mathematics, and to the importance of teacher training and professional development programs, including opportunities to enhance the acquisition of this important knowledge.

Teachers' Sense of Efficacy: An Important Factor in School Improvement

In Indonesia, pre-service mathematics teacher education is strictly supervised so that Pedagogical Content Knowledge (PCK) becomes an important aspect to build the quality of learning. This study aimed to explore pre-service mathematics teachers’ PCK based on gender and academic skills. To obtain rich and in-depth data, a qualitative approach was used. A total of 70 subjects aged between 19 – 21 years old participated in this study. There were two subjects selected based on their academic skills and gender. Using a grounded theory approach, we conducted a preliminary analysis, open coding, axial coding to obtain the three PCK components, namely Knowledge of Subject Matter (KSM), Knowledge of Pedagogy (KP), and Knowledge of Student (KS). Research findings revealed that the pre-service teachers’ pedagogical content knowledge in terms of knowledge of subject matter was categorized as good in mathematics learning. As for their knowledge of pedagogy, the male subjects presented the concepts by employing the expository strategy, the female subjects with high skills used the guided discovery, and the female subjects with average skill also employed the strategy of expository. In the aspect of knowledge of students, the subjects with average skills overcame students’ misconception by explaining the procedures and using the strategy of asking, but the subjects with high academic skills did not only implement the two previous strategies but also used their reasoning behind every procedure of problem-solving that they carried out. These findings can be used as recommendations for the development of mathematics learning.

Aim: The purpose of this study was to provide insights into the specific ways in which teachers’ pedagogical content knowledge and self-efficacy impact the mathematics proficiency of senior high school students. Methods: The study employed positivism quantitative research approach and a descriptive design. The study sample size was 178 comprising 152 Home Economics students and 26 mathematics teachers. The sample members were chosen for the study using purposive sampling technique. A questionnaire and a test of mathematical proficiency were used to gather data. In this work, a basic linear regression model and descriptive statistics were employed as data analysis tools. Results: The study's findings indicate that teachers have a relatively high level of pedagogical content knowledge, with mean scores ranging from 2.88 to 3.69; 2). The study also discovered that teachers have a relatively high level of self-efficacy, with mean scores ranging from 2.88 to 3.69; 3). Additionally, the findings of the simple linear regression analysis did not show a significant correlation between the pedagogical content knowledge, self-efficacy, and students mathematics test performance. Conclusion: The study concluded that teachers’ pedagogical content knowledge and self-efficacy have no significant impact on senior high school learners’ mathematics proficiency. This therefore implies that other elements, such as student background variables, school resources, or educational practices, may have a greater impact on students' mathematical success. Recommendation: The study recommended that future studies use more complete measures of teacher dedication and other factors that may affect student outcomes to examine the association between teacher traits and student accomplishment in mathematics education.