This study compares experts' and teachers' conceptualization of pedagogical content knowledge (PCK). The study participants included teachers (n=20) enrolled in a graduate mathematics education course on PCK. Participants responded to two open-ended questions: a) describe in your own words what PCK is; b) provide an example of PCK. The responses were collected, qualitatively and quantitatively analyzed, and then compared to those suggested by experts to identify and describe the similarities and differences between teachers’ and experts’ conceptualizations using the Pareto analysis. Experts’ and teachers’ PCK components ranking was analyzed using the nonparametric Mann-Whitney U test. Even though the results of the quantitative analysis were not significant (e.g., the observed U-value is 32 whereas the critical value of U at p < .05 is 13), the qualitative discussion on the differences between expert and teachers’ ranking suggests insightful interpretation of priorities among PCK components across the two groups.

Scaffolding dialogue is a concept in learning that refers to the support or assistance given to individuals during the dialogue process. The main objective of this research is to create a basic structure of dialogue to help and support students during the learning process in improving their algebraic reasoning skills. Algebraic reasoning is a process in which students generalize mathematical ideas from a certain set of examples, establish these generalizations through argumentative discourse, and express them in a formal and age-appropriate way. The study was designed using the grounded theory qualitative model method, which used three sequential steps: open coding, selective coding, and theoretical coding. The research was conducted on students of the mathematics education department at Universitas Islam Sultan Agung. Data collection methods include algebraic reasoning ability tests, questionnaires, and interviews. Data analysis in grounded theory is an iterative and non-linear process that requires researchers to constantly move back and forth between data collection and analysis. This process aims to produce a theory that is valid and can explain phenomena well based on empirical data obtained during research. The dialogue scaffolding strategy framework in improving students' algebraic reasoning abilities includes instructing, locating, identifying, modeling, advocating, exploring, reformulating, challenging, and evaluating.