Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.

This research aims to describe secondary school students' functional thinking in generating patterns in learning algebra, particularly in solving mathematical word problems. In addressing this aim, a phenomenological approach was conducted to investigate the meaning of functional relationships provided by students. The data were collected from 39 ninth graders (13-14 years old) through a written test about generating patterns in linear functions. The following steps were conducting interviews with ten representative students to get detailed information about their answers to the written test. All students' responses were then analyzed using the thematic analysis software ATLAS.ti. The findings illustrate that students employed two types of approaches in solving the problem: recursive patterns and correspondence. Students favored the recursive patterns approach in identifying the pattern. They provided arithmetic computation by counting term-to-term but could not represent generalities with algebraic symbols. Meanwhile, students evidenced for correspondence managed to observe the relation between two variables and create the symbolic representation to express the generality. The study concludes that these differences exist due to their focus on identifying patterns: the recursive pattern students tend to see the changes in one variable, whereas the correspondence ones relate to the corresponding pair of variables.

Research on conceptual understanding is one of the first steps in designing materials to improve learning. Literature reports that students have difficulties analyzing and describing phenomena in electric circuits. This report contributes to students' conceptual difficulties regarding simple electrical circuits by systematically analyzing an open conceptual test answered by 531 first-year engineering students. We found students' reasoning that has not yet been reported in the literature as misconceptions or difficulties. To deepen our understanding of students' difficulties, we chose five students by convenience to interview. We present evidence that there are two main contributions to the taxonomy in this study: the Series Circuit Misconception, which is when students convey that the current through bulbs is the same because they are in series, using that as a mnemonic ignoring any change in the circuit; and the Inverse Parallel Circuit Misconception, that is when students mention that the resistance of the circuit decreases when disconnecting bulbs in parallel, neither are reported in the literature. The results of this study have implications for physics education research in electric circuits and educational practice in the classroom.

This study aims to produce a product to evaluate students' critical thinking skills that departs from physics content where students often have misconceptions. This research is a development research with research stages covering a) research and review literature; (b) planning chapter objectives; (c) developing a preliminary form; (d) field-testing the preliminary form; (e) Revise the preliminary form; (f) conducting a main field-test. The Waves Critical Thinking (WCT) test developed consists of 7 questions with 15 specific domains. Total percentage of content validity test was obtained 87.98% with appropriate criteria and based on the construct validity WCT test, the Goodness of Fit criteria were obtained which were classified as fit. The test instrument being tested consists of 15 objective items. The reliability of WCT test results 0.597 as a Cronbach's alpha score with the medium category and all the components have a good level of composite reliability. The outcome of the study was the WCT test with a valid state for measuring students' CT in a specific domain of physics wave material.

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM.

This study aimed to assess the geometric knowledge of student teachers from a university in the Eastern Cape province of South Africa. The study used a sample of 225 first-year student teachers who completed school mathematics baseline assessments on a computer- aided mathematics instruction (CAMI) software. The study adopted a descriptive cross-sectional research design, using quantitative data to measure student teachers’ geometry achievement level, and qualitative data to explain the challenges encountered. The results show that student teachers exhibited a low level of understanding of school-level geometry. The low achievement levels were linked to various factors, such as insufficient grasp of geometry concepts in their secondary school education, difficulty in remembering what was done years ago, low self-confidence, and lack of Information and Communications Technology (ICT) skills along with the limited time for the baseline tests. These results suggest that appropriate measures should be taken to ensure that student teachers acquire the necessary subject-matter knowledge to teach effectively in their future classrooms.

Children who are currently in primary schools are part of the generation that will be most affected by the current environmental trend of our planet in the future. They are the generation that will need to live in accordance with sustainable development and biodiversity protection. One of the key aspects of biodiversity education is to increase environmental literacy using appropriate and effective methods. Our aim was to assess the ecological literacy of a group of primary school students in Slovakia and to identify areas where additional support and clarification may be needed for effective biodiversity education. Our findings reveal widespread misconceptions regarding terms such as 'ecology,' 'community,' 'population,' and 'ecosystem.' The research emphasizes the importance of innovative pedagogical approaches to address and correct these misconceptions effectively. By incorporating exploration-oriented teaching methods, hands-on activities, and a constructivist approach, educators can engage students in experiential learning and facilitate a deeper understanding of ecological principles. Interdisciplinary and participatory research approaches focused on biodiversity education offer promising avenues to enhance ecological literacy. Moreover, increasing interest in environmental education can contribute to nurturing environmentally conscious individuals equipped to tackle ecological challenges effectively. This study underscores the urgency of prioritizing ecological education at primary schools and provides insights into strategies for fostering ecological literacy among young learners.

In an era where diversity and digitalization significantly influence higher education, understanding and adapting to various learning preferences is crucial. This study comprehensively analyzes 394 scholarly articles from 1984 to 2022 using bibliometric methods, providing a dynamic overview of the research patterns in learning styles within higher education. We identified four stages of development during this period: 1984–1995 (Low-interest), 1996–2005 (Early development), 2006–2018 (Development), and 2019–2022 (Intensification). Our analysis highlights that the United States, the United Kingdom, and Australia were the top three leading publishers of research on learning styles in higher education. The results reveal three main topics of publications: educational technology, learning environments, and subject behaviors. This research not only identifies emerging research topics but also underscores the importance of adapting instructional strategies to diverse learning styles to enhance educational outcomes in higher education.

School dropout intention and reduced academic achievement are two crucial indicators of school dropout risk. Past studies have shown that school performance plays a mediating role in the models explaining dropout intentions. School burnout and test anxiety have been identified as predictors of both academic performance and school dropout. However, their combined effects on the intention to leave school have not yet been investigated. We aimed to address this gap by exploring the predictors of school dropout intention in a sample of 205 French secondary school students. Structural equation modelling analyses have revealed the specific facets of school burnout (devaluation) and test anxiety (cognitive interference) that explained the school dropout intentions and academic performance. Grade Point Average (GPA) was a mediator of the effects of these variables on the intention to drop out of school. The findings highlight the need to acknowledge assessments as a school stress factor that could contribute to health problems and intentions to drop out of school.

The education of gifted students is often characterized by high expectations, ambitious goals, and significant effort invested in learning. Their experiences of success and failure are shaped by a variety of factors, including personal, family, school, cultural, and social influences. This article examines how gifted students perceive and experience their own successes and failures, as well as how these experiences are perceived and responded to by their peers. Using qualitative methods, the study involved semi-structured interviews with thirty gifted students from seventh to ninth grades across ten elementary schools in Slovenia. The findings indicate that gifted students experience a range of emotions in response to success, from satisfaction to anxiety, while their reactions to failure often involve frustration and self-criticism. Peer responses to their success and failure vary significantly, ranging from supportive encouragement to jealousy and social exclusion. These findings highlight the complex interpersonal dynamics at play within school environments. Understanding and addressing these dynamics is crucial for creating inclusive, supportive, and stimulating learning environments that nurture both the academic and social-emotional well-being of gifted students.

This study analyzes trends, collaborations, and research developments on augmented reality (AR) in mathematics education using a bibliometric approach. Data were collected from the Scopus database on July 31, 2024, identifying 542 documents published between 2015 and 2024. After screening, 194 journal articles were selected for analysis. Using VOSviewer, the study produced visualizations related to document types, publication trends, journal sources, research subjects, institutions, countries, keywords, and author collaborations. The results show that 88.7% of the documents are journal articles, indicating that this topic is predominantly published in scholarly journals. Publication trends reveal significant growth since 2016, peaking in 2024, reflecting increasing global interest. Education Sciences and IEEE Access are among the top journal sources. Subject-wise, social sciences and computer science are the main disciplines exploring AR in mathematics education. Chitkara University (India) and Johannes Kepler University Linz (Austria) are leading institutions, while the United States, Malaysia, and Spain contribute the most publications. Keyword analysis shows rapid growth in research using terms such as "augmented reality" and "mathematics education," emphasizing the role of immersive technology in enhancing student engagement and conceptual understanding through visual and interactive learning. Influential authors like Lavicza, Mantri, and Haas highlight the importance of global collaboration. Based on a thematic analysis of the most-cited articles, this study proposes the AI Mathematical Education Impact and Outcome Framework. In conclusion, although research on AR in mathematics education has significantly advanced, further studies are needed to evaluate its effectiveness across varied educational contexts.