Assessing student mathematical knowledge is an important factor in the mathematics learning process because students obtain important feedback to improve their knowledge and learning. Despite the importance of student assessment, several researchers have shown that student grades comprise noncognitive and metacognitive factors and teachers’ prejudices and beliefs. One method to obtain a more objective view of student mathematical knowledge is through standardized assessments. In this paper, we analyze two methods of assessing student mathematical knowledge by considering their written and oral grades and achievements on the Italian National Assessment of Knowledge (INVALSI). The final grade was produced using the fuzzy logic inference system. It was tested on a sample of 2279 Grade 13 Italian high school students, who had both an oral and written grade in mathematics and who took the INVALSI assessment in the school year 2020–2021. Both tested fuzzy-logic-based assessment methods lowered the mean grades.

In spring 2020, the COVID-19 pandemic forced a rapid shift to distance learning worldwide. Although recent research has focused on the impact that this transition had on students’ education and well-being, little has been done in particular on math education and on math anxiety (MA). Since MA is believed to be linked to the teaching methods, it could be hypothesized that the new learning environment affected MA levels. Thus, this study investigated whether students’ levels of MA evaluated before and during the first wave of the pandemic changed as a consequence of the distance learning implementation. Moreover, we were interested in investigating whether students’ satisfaction with the teaching methods, their effort in math, and their academic achievement were correlated to MA before and during the COVID-19 distance learning. Participants were 117 Italian middle and high school students. No significant differences between pre- and mid-pandemic MA were found when considering the entire sample. Analyzing separately, results indicated that high-MA students reported significantly lower MA levels during distance learning, however no difference was observed for moderate- and low-MA individuals. Furthermore, satisfaction with the teaching methods, effort in math, and math achievement were negatively correlated with MA, both before and during distance education.

Although the idea of evaluating students’ mathematical knowledge with fuzzy logic is not new in the literature, few studies have explored the possibility of assessing students’ mathematical knowledge by combining teacher-assigned grades (i.e., school grades) with students’ achievements on standardized tests (e.g., national assessments). Thus, the present study aims to investigate the use of fuzzy logic to generate a novel assessment model, which combines teacher-assigned mathematics grades with students’ results on the Italian National Assessment of Mathematical Knowledge (INVALSI). We expanded the findings from previous works by considering a larger sample, which included more than 90,000 students attending grades 8, 10, and 13. The results showed that the tested model led to a lower assessment score compared to the traditional grading method based on teacher’s evaluation. Additionally, the use of fuzzy logic across the examined school levels yielded similar results, suggesting that the model is adequate among different educational levels.

In the present study, we were interested in the appraisal by teachers who have had experience with an individual form of differentiation of the efficiency of grouping learners into homogenous or heterogeneous groups. In the study, seven aspects were thus considered: (1) the learning performance and motivation of learners, (2) the learners’ activity, (3) didactic ways of adapting teaching to diverse learners, (4) the impact on the formation of learners’ personality, (5) cooperation among learners, (6) opportunities for professional development, and (7) cooperation with parents. The research has shown that there is a statistically significant difference between the teachers who teach in homogeneous groups and the teachers who teach in heterogeneous groups in all the seven aspects of the appraisal of the efficiency of grouping learners into homogenous or heterogeneous groups. Regarding most of the assertions, teachers belonging to both groups perceive the way of teaching they perform as having the most advantages.

The question of grouping students into homogeneous and heterogeneous groups is not new, but it does not find an unambiguous answer in the literature, especially in mathematics. In this paper, we address the question of whether grouping students into homogeneous and heterogeneous groups in mathematics improves their knowledge. The quasi-experiment involved 126 8-grade (i.e., 13-14 years old) Slovenian primary school students, who were divided into two equal groups: the control group worked in homogeneous groups, and the experimental worked in heterogeneous groups. The results of the post-test show that the students from the experimental group had better results in mathematics, which indicates that heterogeneous groups should be preferred in mathematics. Lesson observations have identified differences in teacher behavior: educators working in homogeneous groups tend to give students with lower competencies tasks from lower taxonomic levels, and teachers favor abler groups. Such differences have not been observed among teachers working in heterogeneous groups. The implications for educators are also discussed.