“Mathematical knowledge for teaching” is a concept indicating the requirement for a specific kind of knowledge required to teach mathematics. Mathematical knowledge for teaching necessitates a more complex structure than what is required to carry out mathematical tasks and the knowledge to do that. The purpose of this study is to realize the adaptation of “Mathematical Knowledge for Teaching -Geometry (MKT-G)” Test that was initially conceived in English to Turkish (or to Turkish culture). During the adaptation process; after the translations of the items, focus group interviews were held with a group consisting of mathematics teacher educators and experienced mathematics teachers, and then the data from 243 elementary mathematics teachers was analyzed via  Item Response Theory (IRT). As a result of the analysis of the test items, psychometric values of the test items indicated that the items in the test performed well in Turkey. Besides, validity and reliability arguments were also tested. As a result, the Turkish version of the MKT-G test is highly reliable and valid to measure the teachers’ knowledge of teaching geometry.

In the current study, the problems posed by pre-service primary school teachers within the context of semi-structured problem formation were analyzed according to their type, cognitive structure, and content knowledge. A total of 134 pre-service primary school teachers attending a state university in Turkey participated in the current study designed in line with the case study design. The pre-service teachers were presented with a table and they were asked to establish a problem suitable for the elementary level using the data given in the table. The data were collected through the established problem statements and written explanations of the participants. The collected data were analyzed by using both content and descriptive analyses. The findings have revealed that the pre-service teachers less preferred real-life problems than routine type of problems and the problems at the level of reasoning than the problems at the levels of knowing and applying. Moreover, nearly half of the pre-service teachers erroneously expressed the grade level for which they established their problem. The results have shown that the pre-service teachers do not adequately use real-life problems and problems at the level of reasoning and that there are deficiencies in their mathematical content knowledge depending on their knowledge of the curriculum.

Kelley’s Discrimination Index (DI) is a simple and robust, classical non-parametric short-cut to estimate the item discrimination power (IDP) in the practical educational settings. Unlike item–total correlation, DI can reach the ultimate values of +1 and ‒1, and it is stable against the outliers. Because of the computational easiness, DI is specifically suitable for the rough estimation where the sophisticated tools for item analysis such as IRT modelling are not available as is usual, for example, in the classroom testing. Unlike most of the other traditional indices for IDP, DI uses only the extreme cases of the ordered dataset in the estimation. One deficiency of DI is that it suits only for dichotomous datasets. This article generalizes DI to allow polytomous dataset and flexible cut-offs for selecting the extreme cases. A new algorithm based on the concept of the characteristic vector of the item is introduced to compute the generalized DI (GDI). A new visual method for item analysis, the cut-off curve, is introduced based on the procedure called exhaustive splitting.

The article focused on the use of assessment for learning in promoting active learning and learner participation in mathematics. Assessment for learning (AfL) has been found to enhance learning and improve performance. However, teachers’ use of AfL to enhance active learning has not been clearly outlined. This study is part of the broader research study that explored mathematics teachers’ use of AfL to enhance mathematics teaching and learning in primary schools in Alexandra Township, Johannesburg. A case study research-type and a qualitative approach were used to collect data from mathematics teachers. Nine teachers were purposefully selected from whom data were collected using semi-structured interviews and non-participant observation. The findings revealed that teachers had limited pedagogical knowledge in using AfL to promote active learning in their classrooms. They failed to apply a learner-centred approach that promotes effective learner participation in mathematics classrooms. Therefore, it is recommended that teachers undergo ongoing continuous development on classroom time management and planning for the effective use of AfL.

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing proportional reasoning is not an easy task. In this study, we investigated how teachers give proportional reasoning about the concept of proportional and non-proportional situations, especially in making sense of them. The research subjects were mathematics teachers who had taught proportional-related material. Data was collected using task-based interviews outside the teacher's working hours. Data analysis and interpretation were completed using a framework meaning-based approach. The results of the data analysis showed that the teacher is careful in understanding information, is aware of multiple meanings, and knows key information in understanding the contextual structure of proportional and non-proportional situations. Furthermore, they are also able to identify additive and multiplication relationships, have flexibility in understanding proportional and non-proportional situations separately or collectively, and understand problem-solving systematics in detail.

The objective of this research was to assess the efficacy of project-based learning in enhancing the analysis of student worksheets in the domains of Science, Technology, Engineering, Arts, and Mathematics (STEAM) with the integration of the ecoprint technique, focusing on its influence on student motivation and creativity. This investigation was conducted as a quasi-experiment involving a sample size of 150 students selected through cluster sampling. Data collection was executed using standardized tests, with instrument validity ascertained through the Aiken index and instrument reliability determined via Cronbach's alpha coefficient. Data analysis was performed using multivariate analysis (MANOVA) and descriptive quantitative methods. The study's findings reveal a significant disparity in the mean scores of both learning motivation and student creativity. In conclusion, the implementation of project-based learning coupled with STEAM-based student worksheet analysis utilizing the ecoprint technique yields a substantial enhancement in learning motivation and student creativity. These findings underscore the success of employing STEAM-based worksheets in conjunction with the ecoprint method to foster students' motivation and creativity, as ecoprint inherently encompasses all STEAM components within the manufacturing process.