We developed a Quantum Mechanics Conceptual Understanding Survey (QMCUS) in this study. The survey was conducted using a quantitative methodology. A multiple-choice survey of 35 questions was administered to 338 undergraduate students. Three experienced quantum mechanics instructors examined the validity of the survey. The reliability of our survey was measured using Cronbach's alpha, the Fergusson delta index, the discrimination index, and the point biserial correlation coefficient. These indices showed that the developed survey is reliable. The statistical analysis of the students' results using SPSS shows that the scores obtained by the students have a normal distribution, around the score of 7.14. The results of the t-test show that the students' scores are below the required threshold, which means that it is still difficult for the students to understand the concepts of quantum mechanics. The obtained results allow us to draw some conclusions. The students' difficulties in understanding the quantum concepts are due to the nature of these concepts; they are abstract and counterintuitive. In addition, the learners did not have frequent contact with the subatomic world, which led them to adopt misconceptions. Moreover, students find it difficult to imagine and conceptualize quantum concepts. Therefore, subatomic phenomena are still explained with classical paradigms. Another difficulty is the lack of prerequisites and the difficulties in using the mathematical formalism and its translation into Dirac notation.

Mathematics teachers’ instructional strategies lack in-depth knowledge of algebraic systems and hold misconceptions about solving two algebraic equations simultaneously. This study aimed to gain an in-depth analysis of teachers’ knowledge and perceptions about the promotion of conceptual learning and effective teaching of algebraic equations. The main question was, ‘How do junior secondary school mathematics teachers manifest their pedagogical practices when teaching algebraic equations? This article reports on a qualitative, underpinned by the knowledge quartet model study, that sought to explore how junior secondary school teachers’ pedagogical practices manifested in the teaching of algebraic equations. Data were collected from observations, semi-structured interviews, and document analysis of two mathematics teachers purposely selected from two schools. The collected data were analysed using a statistical analysis software called Atlas-ti. (Version 8) and triangulated through thematic analysis. The study revealed that teachers’ choices of representations, examples, and tasks used did not expose learners to hands-on activities that promote understanding and making connections from the underlying algebraic equation concepts. The study proposed Penta-Knowledge Collaborative Planning and Reflective Teaching and Learning Models to enable teachers to collaborate with their peers from the planning stage to lesson delivery reflecting on good practices and strategies for teaching algebraic equations.

Learning activities are conducted to help students achieve optimal academic achievement. This research aims to optimize student academic achievement through a learning process that integrates comprehensive formative assessments, including formative tests, self-assessment, peer assessment, and the initiator of creating summaries or concept maps that are given to students in a structured manner at the end of every lesson. The research method used was a quasi-experimental method with a 2x2 factorial design. Students enrolled in the biology education program of the basic physics course for the 1st semester of the 2019 academic year participated in this study. The participants were 66 undergraduate students divided into two classes. Thirty-four students in the experimental group were in class A, while 32 students in the control group were in class B. Data were collected using a learning outcome test instrument to measure academic achievement, which was tested at the end of the semester. Data were analyzed using a two-way ANOVA. This study concluded that a learning process that includes comprehensive formative assessment significantly affects students' academic achievement. These findings support the theory that formative assessment provides feedback, correction, and improvement in student learning.

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.

Although the central role of classical mechanics in physics teacher education is undisputed, divergent interests and perspectives from different disciplinary cultures might exist when thinking about how to best support pre-service teachers' professional development. In this article, we report the results of an exploratory mind map study to investigate which classical mechanics topics are regarded essential for physics teacher education according to N = 29 experts from different physics disciplines. The participants’ mind maps were analyzed using a category system and frequency analysis was applied. The results hint at similarities and differences in terms of key topics to be addressed in physics teacher education on classical mechanics according to experts from different physics disciplines, e.g., in terms of the depth of mathematics considered relevant for physics teacher education.

This study aimed to explore the implementation and impact of the Flipped Learning Model (FLM) and STEM Approach in elementary education. The advancement of technology and the Covid-19 pandemic has increased the importance of e-learning, including in elementary schools. The literature review analyzed 193 academic works published in the past six years using NVivo, Mendeley, and VOSviewer software. The validity of the data was verified through the analysis of five online databases. The results showed that STEM research has been well-developed with innovative approaches that improve learning outcomes, while FLM research in elementary schools is limited. The study suggested that combining FLM with STEM Approach (FLM-SA) can optimize learning in the technological era. By integrating FLM-SA, students can engage in active learning experiences in class and acquire fundamental knowledge outside of class, offering a solution to e-learning challenges. The study emphasized the strong connection between FLM and STEM Approach and how they can support each other to enhance student learning.

Teachers' learning styles are a crucial part of the learning process as they determine how teachers' brains capture and integrate information linked with the senses. Kurnia, identified as an auditory teacher, was expected to capture written information in a provided numeracy problem. Nevertheless, she prefers to capture visual information, like tables or figures, and utilize them to develop thought-provoking questions. Thus, this study intends to investigate her reasons and the factors affecting Kurnia's decision to utilize visual information as a reference in developing questions. This research adopts a qualitative design covering a case study. Kurnia was selected from 32 teachers from 28 schools; roughly 43% were from public schools, and 57% from private schools. Kurnia placed more emphasis on pictorial information before proposing questions, which was caused by situational factors: the subject matter, the grade level, the student's engagement in the class, the teacher's experience, the teaching experience, and the diversity of students' learning styles. This article recommends that teachers recognize their learning styles to know their strengths and weaknesses in teaching mathematics, and that they convey understandable information utilizing effective instructional methods that represent each learning style of students in the classroom.

Students in mathematics classes do not understand the importance of sociomathematical norms in learning mathematics. This causes sociomathematical norms not to be teachers' focus when learning mathematics. Besides, there is no standardized instrument for assessing this norm, so developing this instrument is necessary to measure socio-mathematical norms in learning mathematics. This study aims to create and verify the psychometric validity of the sociomathematical norm scale. This research used a survey method with 505 senior high school students from Jakarta and West Java as respondents. The results showed that 25 items had convergent validity, with a loading factor value of > 0.700, meaning they could be declared valid. Concurrent validity indicates that each sociomathematical norms indicator is valid as a whole. Discriminant validity shows that the average variance extracted value on the diagonal is higher than the other values, so each item is declared valid. It was concluded that each item of the sociomathematical norms instrument has accuracy in its measurement function. The reliability test shows that each sociomathematical norms item is declared reliable. The reliability value of the sociomathematical norm item is .99, and the person's reliability is .86. Thus, the instruments developed can measure sociomathematical norms in learning mathematics.

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.

<p style="text-align:justify">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&rsquo; 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.</p>