Mathematics Pedagogical Content Knowledge Research Articles

The relationship between opportunities to learn in teacher education and Chinese preservice teachers’ professional competence

ABSTRACT Although research on the relationship between opportunities to learn (OTL) in teacher preparation and preservice teachers’ learning outcomes, including aspects of their knowledge, has significantly increased in recent years, the relationship between OTL and preservice secondary school teachers’ cognitive competence and, particularly, the situated aspect of competence, in Mainland China remain poorly understood. This paper examines this association based on a study involving 583 preservice teachers chosen from four preservice teacher education institutions. The results revealed that the preservice teachers received adequate OTL in various domains, such as tertiary-level mathematics and mathematics education pedagogy. However, mainly due to the influence of academically oriented teacher preparation models in Mainland China, there were quite weak overall connections between OTL and the four examined aspects of teachers’ professional competence (mathematics content knowledge, mathematics pedagogical content knowledge, a mathematics instruction-related perspective on noticing, and a general pedagogy-related classroom perspective on noticing). Comparatively speaking, relatively strong associations existed between OTL in teaching methods, school-based teaching practicums, and the situated aspect of competence (e.g. noticing). These findings show that, to a great degree, initial teacher preparation in Mainland China does not relate closely to preservice teachers’ professional competence.

Blurring the lines to promote access and equity in 2‐ and 4‐year Hispanic serving institutions

AbstractPartnerships between two‐ and four‐year Hispanic Serving Institutions (HSI) can provide high‐quality, in‐depth learning experiences for traditionally underserved students. Blurring the lines between these institutions allows for more seamless transitions for prospective teachers (PTs), and maximum collaboration and program impact. This article contributes to the growing literature on such partnerships and collaborations. We describe how our partnership between Northwest Vista College (2‐year institution) and University of Texas at San Antonio (4‐year institution) supported PTs and their development of mathematics pedagogical content knowledge and skills to facilitate in diverse settings (i.e., mathematics sensemaking, questioning, teaching through problem solving, soft teaching skills). To describe the nature of our partnership, in this article we (1) explain some of the main elements of the partnership between the two‐ and four‐year campuses, (2) review the unique, collaborative nature of the Community Mathematics Project, and (3) discuss outcomes that have resulted among Mathematics Fellows who have gone through the program.

유아교사의 수학적 상호작용에 대한 수학지원지식의 영향

Objectives In this study, it was verified whether the moderating effect of teaching creativity on the effect of early childhood teachers' play teaching efficacy and mathematics pedagogical content knowledge on mathematical interaction was significant.
 Methods For this purpose, 300 nursery class teachers working at daycare centers and kindergartens in the metropolitan area were selected. As a measuring tool for the mathematical interaction of early childhood teachers, Kim and Kwon (2022)'s tools and early childhood teachers' mathematics subject pedagogical knowledge tool developed by Hong and Jeong (2012) were used to find out mathematics pedagogical content knowledge. In order to measure teaching creativity, the ‘teacher's creative teaching-learning test tool’ developed by Cropley (2004) was modified and adapted by Baek and Kim (2008) and validated and verified. For data analysis, frequency, percentage, average, reliability analysis, partial correlation analysis, multiple regression analysis for moderating effect analysis, and moderating effect analysis were conducted using the SPSS 22.0 program. At this time, a hierarchical multiple regression analysis was conducted after injecting the status of tenure and training, career, number of times of use of study materials, and the number of homeroom teachers as control variables.
 Results The effect of mathematics pedagogical content knowledge on the mathematical interaction of early childhood teachers was regulated by teaching creativity.
 Conclusions This study found that the early childhood teacher's teaching creativity plays a role in regulating the effect of mathematics pedagogical content knowledge on mathematical interaction, and thus the role of teaching creativity is important in the variables that affect mathematical interaction. Therefore, it was revealed that educational and institutional support for improving teaching creativity is needed first.

Effectiveness of the continuous professional development training on upper primary mathematics and science and elementary technology teachers’ Pedagogical Content Knowledge in Rwanda

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.

Relationship between mathematical pedagogical content knowledge, beliefs, and motivation of elementary school teachers

Pedagogical content knowledge (PCK) is one form of teachers’ professional knowledge in subject teaching, and teachers’ rich PCK enables effective instruction and improves students’ academic performance. However, there has been limited research on the relationships of individual difference characteristics of teachers to PCK among in-service elementary school teachers. Therefore, in addition to the demographic variables (gender and years of teaching experience) and psychological variables (beliefs about teaching and learning and teacher efficacy) examined in previous studies, this study attempted to clarify whether motivation for teaching is related to PCK. We conducted a web survey of in-service elementary school teachers in Japan (n = 267). The results showed that the traditional beliefs that students are to be controlled by their teachers and indifference, which describes a state of lack of motivation to prepare for class, were negatively associated with two elements of mathematical PCK (knowledge of learners and knowledge of instruction). Furthermore, multiple regression analysis revealed that traditional beliefs about teaching and learning were negatively associated with the knowledge of learners and indifference to subject instruction with knowledge of instruction. This suggests that teachers’ motivation for teaching is related to PCK, in addition to the variables that have been previously examined.

Prospective mathematics secondary teachers’ perceptions of their pedagogical content knowledge: an approach in the educational context of Zambia

ABSTRACT The purpose of the current study was to contribute to a better understanding of Zambian prospective mathematics secondary teachers’ pedagogical content knowledge of mathematics (M-PCK) as part of a larger project aimed at characterising their subject matter and pedagogical content knowledge (PCK) related to the function concept. K-means Cluster analysis was used to derive profiles based on M-PCK perceptions. Three profiles related to M-PCK perceptions of prospective teachers emerged from the clustering process namely (i) self-doubting (cluster 1), (ii) anti-M-PCK (cluster 2) and (iii) confident and enthusiastic (cluster 3). A One-way ANOVA test was performed to determine the existence of differences in prospective teachers’ perceptions between Clusters based on the five M-PCK sub-factors. The test revealed significant differences between Clusters of prospective teachers’ perception of all sub-factors. Prospective teachers in Clusters 1 and 2 showed low confidence in their M-PCK perceptions while those in Cluster 3 generally showed moderate confidence.

A promising approach to scaling up professional development: intelligent, interactive, virtual professional development with just-in-time feedback

AbstractThe scalability and accessibility of quality professional development (PD) is an ongoing concern in the teacher education community, yet little research has been conducted on potential solutions. We aimed to address this gap by developing an interactive, virtual PD program that uses intelligent tutoring systems and provides instant feedback to teachers. We then explored the role of this program in developing teachers’ content and pedagogical content knowledge of mathematics. We collected data from 60 teachers located across the USA and found that those who completed the program increased their content and pedagogical content knowledge.

Teachers’ mathematics pedagogical content knowledge and quality of early mathematics instruction in Turkey

It is a well-known fact that societies today need to provide quality mathematics education to individuals from their early years in order to compete on a global scale. Although there is a growing interest in early mathematics, there are still some obstacles regarding quality mathematics instruction. Two of the most important obstacles are the mathematics pedagogical content knowledge (MPCK) and early mathematics teacher qualification of pre-school teachers. The purpose of this study was to evaluate the relationship between pre-school teachers’ classroom mathematics practices and their MPCK. The study included 55 pre-school teachers. Classroom Observation of Early Mathematics – Environment and Teaching (COEMET) was adapted into Turkish. The teachers’ MPCK was assessed using the Survey of Pedagogical Content Knowledge in Early Childhood Mathematics (SPECKECM). The results show that the teachers’ MPCK was at a medium level, being most successful regarding shapes and least in patterns. The COEMET scores were positively and statistically significantly correlated to the total score of the SPECKECM. Moreover, teachers’ pedagogical content knowledge (PCK) scores successfully predicted the total COEMET scores.

Keyakinan dan mathematics pedagogical content knowledge calon guru matematika: fokus pada domain bilangan

The purpose of this study was to identify and describe the beliefs and mathematics pedagogical content knowledge (MPCK) of pre-service mathematics teachers. This research is a type of quantitative research with a descriptive design. This research involved 29 final year mathematics pre-service teacher at a college in Southeast Sulawesi, Indonesia. The instruments used in this study were a confidence questionnaire and the MPCK test based on the TEDS-M indicator. The data analysis technique used in this research is descriptive analysis technique. The results showed that the pre-service teacher's belief in mathematics and teaching mathematics was in the high category. Meanwhile, the MPCK of pre-service teachers is in the less category. This shows that pre-service teachers still have difficulties in planning appropriate activities, appropriate methods, predicting student responses, evaluating student mathematical solutions, identifying student misconceptions and representing mathematical concepts or procedures. Future research may consider expanding the focus on the predictive relationship between belief and MPCK pre-service teachers.

Exploring mathematical pedagogical content knowledge of pre-service teachers

The purpose of this cross-sectional study was to examine pre-service teachers’ perceptions of their mathematical pedagogical content knowledge and to determine effect of demographic variables (Gender, year of study) on their mathematical pedagogical content knowledge. A Likert scale questionnaire was used to collect data from 104 pre-service teachers. Descriptive statistics and Mann-Whitney U-test were used to examine pre-service teachers’ perceived knowledge of teaching strategies, mathematical language and symbols, misconceptions, curriculum, and their perceived knowledge of learners. Results show that in general, majority pre-service teachers have strong perceptions of their mathematical pedagogical content knowledge. They consider lesson planning, purpose of the mathematics curriculum and assessment tools used in a mathematics classroom as important aspects of their perceived knowledge of the curriculum. It was also revealed that their perceived knowledge of misconception would enable them to know and anticipate their learners’ misconceptions. However, results also indicated that there was no statistically significant difference in pre-service teachers’ mathematical pedagogical content knowledge based on gender and year of study. Study implications are also discussed.

Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?

Scaling up teacher professional development (TPD) struggles with spreading TPD while considering individual contexts. The presented study examines connecting these aims by using a cascade approach and taking a perspective on scaling up that acknowledges the need for adaptations by local facilitators. Teachers’ learning gains in a TPD course enacted by facilitators (group B) are compared to those in the same TPD course enacted by the program developers (group A). Results indicate that teachers in group B achieved comparable learning gains regarding mathematical pedagogical content knowledge and beliefs as teachers in group A. Implications for scaling up TPD are discussed.

Validierung eines Tests zur Erfassung des mathematikdidaktischen Wissens von Lehramtsstudierenden der Primarstufe

ZusammenfassungMathematikdidaktisches Wissen stellt eine zentrale Komponente der professionellen Kompetenz von (angehenden) Primarstufenlehrkräften im Bereich Mathematik dar, die mit situationsspezifischen Fertigkeiten zusammenhängt und, vermittelt über das professionelle Handeln, Effekte auf die mathematischen Leistungen von Schüler:innen haben kann. Um mathematikdidaktisches Wissen im Zusammenhang mit anderen Komponenten professioneller Kompetenz (z. B. Emotionen, Überzeugungen, Handlungsplanung, Instruktionsqualität) untersuchen zu können, bedarf es eines ökonomischen und frei verfügbaren Tests, welcher gängige Gütekriterien hinreichend erfüllt. Der vorliegende Beitrag stellt die Validierung eines solchen Tests vor. Entsprechend der Teststandards werden Grundnahmen in den Evidenzkategorien Inhalt, Struktur und Beziehungen zu anderen Variablen untersucht, um zu prüfen, ob die Testscores Schlussfolgerungen zum Konstrukt mathematikdidaktisches Wissen von Lehramtsstudierenden der Primarstufe zulassen. Die Ergebnisse liefern Validitätsargumente, die auf eine hinreichend hohe Reliabilität des Tests hinweisen und für theoriekonforme Schlussfolgerungen basierend auf den Testwerten sprechen. Der Beitrag schließt ab mit einer integrativen Betrachtung der Validierungsevidenzen, die für den Test bisher vorliegen.

Using natural language processing to analyze elementary teachers’ mathematical pedagogical content knowledge in online community of practice

This study focuses on how teachers’ pedagogical content knowledge (PCK) of mathematics may differ depending on teacher interactions in an online teacher community of practice (CoP). The study utilizes data from 26,857 posts collected from the South Korean self-generated online teacher CoP, ‘Indischool’. This data was then analyzed using natural language processing techniques; specifically, text classification with word2vec, BERT, and machine learning classifiers was used. The results indicate that the texts of posts can predict the level of teacher interactions in the online CoP. BERT embedding and classifier exhibited the best performance, ultimately achieving an F1 score of .756. Moreover, topic modeling utilizing BERT embedding is used to uncover the specific PCK of teachers through high- and low-interaction posts. The results reveal that high-interaction posts with numerous likes and replies demonstrate more in-depth reflections on teaching mathematics and refined PCK. This study makes two significant contributions. First, it applies a data science framework that allows for the analysis of real data from an actual online teacher community. Secondly, it sheds light on the intricacies of knowledge management in an online teacher CoP, an area that has to this point received limited empirical attention.

Examining the Dynamics of Teaching Algorithms of Fractions – A Case Study of Grade 3 Rural Schools in South Africa

This article emanates from a study that sought to establish teacher experiences in the effective teaching of Mathematics, especially when dealing with teaching algorithms of fractions in their schools. Fraction algorithms is a section of algebra in mathematics that deals with quantities as wholes and sub-constructs. In grade 3, learners seem to be unable to comprehend the meaning and this leads to teachers being frustrated. The authors posit that despite the teacher’s dilemmas about teaching fractions in grade 3, there still exists effective teaching in schools. The study adopted an interpretivism paradigm in which thematically analysed data was collected through interviews from 8 purposely selected participants. The researchers noticed that examining the dynamics in teaching algorithms of fractions involves significant development of the idea through prominent learner participation, handling of tangible materials by learners and learner inclusivity. The study reveals that teachers need to compatibly reflect on Mathematics Fundamental Knowledge (MFK) and Mathematics Pedagogical Content Knowledge (MPCK) to have the option to adequately teach their learners. Overall, it was found that teachers worked very hard to strive for excellence in teaching grade 3 learners and that they did their best irrespective of overcrowding, inadequate training and resources and other challenges they faced to achieve effective teaching fraction algorithms for their grade 3 learners. Keywords: Constructivist Theory, Effective Teaching, Community, Pedagogy, Collaboration, Fractions Algorithms

What About Early Childhood Mathematics Education in Early Childhood Teacher Education?

From existing research, it is known that early childhood teacher education provides few opportunities to learn mathematical content or mathematics pedagogical content knowledge. Furthermore, little is known about the extent to which teacher educators are qualified to teach early childhood mathematics within teacher education programs. This study investigates the frequency of opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge. Additionally, we investigate some characteristics of teacher educators, namely the sources they use for professional development with respect to early mathematics education. We report descriptive results as well as correlations. The results indicate that opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge have increased over time. Moreover, the results indicate that teacher educator professional development formats that encourage professional exchange among teacher educators, experts in early mathematics education and in-service teachers may increase teacher educators’ competence in early childhood mathematics and thereby the frequency with which this topic is addressed in teacher education.

What About Early Childhood Mathematics Education in Early Childhood Teacher Education?

From existing research, it is known that early childhood teacher education pro-vides few opportunities to learn mathematical content or mathematics pedagogical con-tent knowledge. Furthermore, little is known about the extent to which teacher educators are qualified to teach early childhood mathematics within teacher education programs. This study investigates the frequency of opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge. Additionally, we investigate some characteristics of teacher educators, namely the sources they use for professional development with respect to early mathematics education. We report descriptive results as well as correlations. The results indicate that opportunities to learn mathematical con-tent knowledge and mathematics pedagogical content knowledge have increased over time. Moreover, the results indicate that teacher educator professional development for-mats that encourage professional exchange among teacher educators, experts in early mathematics education and in-service teachers may increase teacher educators’ compe-tence in early childhood mathematics and thereby the frequency with which this topic is addressed in teacher education.

Knowledge of Mathematics Content and its Relation to the Mathematical pedagogical content knowledge for Secondary School Teachers

Knowledge of Mathematics Content and its Relation to the Mathematical pedagogical content knowledge for Secondary School Teachers

Identifying and dealing with student errors in the mathematics classroom: Cognitive and motivational requirements.

Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students' knowledge and skills. Mathematics teachers need to be highly attentive to students' thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students' errors. To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers' ability to identify students' errors was assessed based on (a) a digitalized speed test showing different students' solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson's mathematical content. Teachers were asked to analyze students' thinking and to determine how best to react. In addition, teachers' mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers' abilities to identify, analyze, and deal with students' errors. The results indicate that all components are interrelated. However, path analysis reveals that teachers' ability to deal with students' errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students' errors is largely dependent on their mathematics content knowledge. The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.

Pre-school Teachers' Attitudes towards Mathematical Pedagogical Content Knowledge, Mathematics, and Mathematics Teaching

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.

An Examination of Related Factors of Mathematical Pedagogical Content Knowledge in Elementary School Teachers: Focusing on Conceptions of Teaching and Learning and Test Utilization Strategy

We examined the relationship between pedagogical content knowledge (PCK) test scores and elementary school teachers’ psychological variables, conceptions of teaching and learning and test utilization strategy, for mathematics. Through a web-based survey, participants responded to a six-item descriptive PCK test and to inventories of conceptions of teaching and learning and test utilization strategy. Data from 297 elementary school teachers were analyzed for associations with PCK scores. The results showed that constructivist conceptions and test utilization strategy were positively correlated with PCK test scores, and traditional conceptions were negatively correlated. In addition, the results of multiple regression analysis showed that traditional conception and test utilization strategy each showed unique associations with the PCK test. These results suggest the importance of teachers’ beliefs and test utilization strategies as related variables of teachers’ PCK.