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[English]: This quantitative study with n = 206 participants (mathematics pre-service teachers from Indonesia) investigates the effect of two factors on pre-service teachers’ beliefs: (1) contexts related to students’ achievement as well as (2) the differences between school mathematics and university mathematics. The results of this quantitative study show that the participants (1) have different beliefs about teaching and learning of mathematics in different contexts of students’ achievement (a class dominated by high-achieving students vs. a class dominated by low-achieving students) and (2) have different beliefs about school mathematics and university mathematics. Interestingly, compared to their beliefs about school mathematics, the pre-service teachers’ beliefs about university mathematics correlate better with their beliefs about teaching and learning in different contexts of students’ achievement. The implication of the better correlations for the pre-service teacher education are further discussed. [Bahasa]: Penelitian kuantitatif dengan 206 calon guru matematika ini bertujuan untuk menginvestigasi efek dari dua faktor yang mempengaruhi keyakinan para calon guru: (1) konteks yang berhubungan dengan capaian siswa dan (2) perbedaan karakteristik antara matematika sekolah dan matematika universitas. Hasil penelitian menunjukkan bahwa para calon guru tersebut (1) memiliki keyakinan yang berbeda tentang bagaimana mengajar dan belajar matematika di dalam konteks yang berbeda, yaitu antara kelas yang didominasi oleh siswa-siswa capaian tinggi dan kelas yang didominasi oleh siswa-siswa capaian rendah, dan (2) memiliki keyakinan yang berbeda antara matematika sekolah dan matematika universitas. Menariknya, jika dibandingkan dengan keyakinan tentang matematika sekolah, keyakinan para calon guru tentang matematika universitas ternyata lebih baik korelasinya terhadap keyakinan mereka tentang bagaimana mengajar dan belajar di dua konteks kelas tersebut. Selanjutnya, artikel ini akan mendiskusikan implikasi dari korelasi yang lebih baik tersebut terhadap pendidikan para calon guru matematika.

The research presented in this article is a systematic review of the literature on the assessment of mathematical modeling in the setting of mathematics education published in the previous five years. This research has compiled the current best information from around the world to offer an overview of the assessment of mathematical modeling for pre-service mathematics teachers or mathematics teachers. We followed the approach used in Joklitschke et al. (2021), which involved 10 steps in systematic literature review (SLR). We accessed using Web of Science (WoS), Scopus, and mathematics education journals that are ranked 1-10. Based on a full-text analysis of 18 peer-reviewed papers published in English, most of the research was conducted among pre-service mathematics teacher and most of the studies were conducted in Turkey, United States, and Germany. The future trends and opportunities were also discussed. We also found that most test types employed for measuring modeling competency were project, cognitive dimension, holistic approach, and the tests utilized more qualitative approach.

Pre-service mathematics teachers (PSTs) may hold different beliefs about school mathematics and university mathematics and different beliefs about teaching mathematics between high-achieving (HA) vs. low-achieving (LA) classes. Because of the differentiation, the beliefs relationship is complex. This quantitative study administered a questionnaire on 508 PSTs for secondary school from five Indonesian universities to investigate the differentiation and the complex relationship in beliefs considering the year of study. The data analyses reveal a differentiation of beliefs about university mathematics and school mathematics. Despite this differentiation, those beliefs correlate significantly and positively, indicating the tendency of seeing school mathematics and university mathematics with the same view. Similarly, although PSTs may hold different beliefs about teaching and learning in HA and LA classes, the beliefs in HA and LA classes correlate significantly and positively. Furthermore, we found that beliefs about university mathematics correlate with beliefs about teaching and learning in both HA and LA classes. We also found significant correlations between PSTs' beliefs with the year of study, but, unexpectedly, the correlations are very small. Reflecting on the results of this study, we discuss the necessity of designing courses related to university mathematics and mathematics education during university education carefully.

The use of Likert scale items for measuring teachers' beliefs quantitatively is criticized. In this study, two quantitative methods to measure teachers' beliefs, a Likert scale instrument as well as a new instrument employing rank-then-rate items, are each compared with a qualitative approach at obtaining beliefs, i.e. interviews along with observations. In the first comparison, teachers' responses to the Likert scale instrument seem to not fit the beliefs interpreted from the qualitative approach, particularly regarding beliefs about teaching and learning. Further analyses show that a tendency to respond according to social desirability as well as unspecific teaching contexts seem to be responsible for these inconsistencies. In the second comparison, since the rank-then-rate instrument also takes students' abilities as a teaching context into account, we observed a better fit between teachers' responses to the instrument and the qualitative approach. The results of both comparisons indicate the importance of considering teaching contexts as well as alternatives to Likert scale items because of social desirability in order to have a better prediction about teachers' beliefs.

The aim of this pseudo-longitudinal study is to investigate pre-service teachers' beliefs about (1) the nature of mathematics and (2) mathematics teaching and learning and the development of both beliefs over the course of their studies. A quantitative belief questionnaire was completed by 142 participants divided into three groups based on their years of studies: Beginning, Middle, and End. Additionally, five pre-service teachers from the End group were interviewed to explore the influence of different university courses on the development of their beliefs. The data analyses show a significant difference between the Beginning and the End group regarding beliefs about mathematics favoring a problem-solving view. The difference is an indication related to the development of beliefs about mathematics during teacher education. Courses dealing with university mathematics seem to be responsible for the development. Further, the data analyses also show significant differences between the Beginning and End group regarding beliefs about teaching and learning, also favoring a problem-solving view in a class dominated by low-achieving students. The differences indicate that beliefs about teaching and learning develop during teacher education. However, no evidence supports the hypothesis that courses related to mathematics education contribute to the observed differences. Instead, experiences during an internship semester in observing as well as teaching in real classes by applying what has been promoted in the courses may contribute to the development. Possible explanations regarding the development of beliefs and the contribution of courses in teacher education as well as the implication of the findings are discussed.

Studies measuring teachers' beliefs quantitatively by using self-report Likert scale instruments often face methodological difficulties. Such difficulties might be due to the fact that those instruments often provide less or no contexts. Whereas, several studies have shown that contexts at school, particularly contexts related to students' abilities, may influence teachers' beliefs. To overcome such difficulties, we offer an approach by using rank-then-rate items instead of Likert scale items and by explicitly taking into account students' abilities within a questionnaire. In this study, we had 43 Indonesian teachers answering this questionnaire to investigate how students' abilities influence teachers' beliefs about teaching and learning of mathematics and problem solving as well as the interrelation between these beliefs with their beliefs about mathematics. The results suggest that teachers may elicit different beliefs about teaching and learning in the context of students' abilities. Furthermore, we found that teachers' beliefs about mathematics correlate with their beliefs about teaching and learning in the context of low ability students, but not in the context of high ability students.

The results of international comparative studies like PISA and TIMSS attract researchers to conduct studies comparing math contents of curricula directly to each other. Unlike those studies, we compared math contents of Indonesian and Singaporean curricula based on math contents tested in PISA 2012 items. We also enrich the comparison with the examination of the role of problem solving in the intended learning processes of the two curricula. The results of the comparison of math contents show that there are differences in the breadth of the math contents of the two curricula. The results also indicate that the Singaporean curriculum covers math contents tested in the PISA 2012 items which are missing in the Indonesian curriculum. However, it is still difficult to identify possible reasons for the distinct performances between Indonesia and Singapore in the PISA 2012 study from the comparison. Enriching the comparison with the examination of the role of problem solving in the intended learning processes of the two curricula gives us additional insight into a possible reason. The results show that the intended learning process of the Singaporean curriculum highlights problem solving much more than does that of the Indonesian curriculum. These results are suggestive of the need for further research.