Research on instructional quality has been of great interest for several decades, leading to an immense and diverse body of literature. However, due to different definitions and operationalisations, the picture of what characteristics are important for instructional quality is not entirely clear. Therefore, in this paper, a scoping review was performed to provide an overview of existing evidence of both generic and subject-didactic characteristics with regard to student performance. More precisely, this paper aims to (a) identify both generic and subject-didactic characteristics affecting student performance in mathematics in secondary school, (b) cluster these characteristics into categories to show areas for quality teaching, and (c) analyse and assess the effects of these characteristics on student performance to rate the scientific evidence in the context of the articles considered. The results reveal that teaching characteristics, and not just the instruments for recording the quality of teaching as described in previous research, can be placed on a continuum ranging from generic to subject-didactic. Moreover, on account of the inconsistent definition of subject-didactic characteristics, the category of ‘subject-didactic specifics’ needs further development to establish it as a separate category in empirical research. Finally, this study represents a further step toward understanding the effects of teaching characteristics on student performance by providing an overview of teaching characteristics and their effects and evidence.

The study aims to find out the influence of Mistake-Handling Activities to determine mathematical definitions knowledge, which can be regarded as a component of mathematics content knowledge, of teachers on the development of teachers in providing mathematical definitions. Within this framework, Mistake-Handling Activities were carried out with five volunteer mathematics teachers. Written opinions and semi-structured face-to-face interviews were used as data collection tools. During the application, focus group interviews were carried out, and the application was enhanced with discussions. The data were analyzed using the document review method, and codes, categories, and themes were also determined. The results revealed that Mistake-Handling Activities yielded certain emotional advantages such as increasing teachers’ interest and curiosity, critical thinking, self-confidence, awareness, and offering different viewpoints as well as yielding cognitive advantages such as recognizing their shortcomings, acknowledging the importance of knowing the definition of a concept, and using the definition.

Numerical thinking is needed to recognize, interpret, determine patterns, and solve problems that contain the context of life. Self-efficacy is one aspect that supports the numerical thinking process. This study aims to obtain a numerical thinking profile of Mathematics pre-service teachers based on self-efficacy. This study used descriptive qualitative method. The data obtained were based on the results of questionnaires, tests, and interviews. The results of the self-efficacy questionnaire were analyzed and categorized (high, moderate, and low). Two informants took each category. The results showed the following: informants in the high self-efficacy category tend to be able to interpret information, communicate information, and solve problems with systematic steps. Informants in the moderate self-efficacy category tend to be able to interpret and communicate information, but tend to be hesitant in choosing the sequence of problem-solving steps. Meanwhile, informants in the low self-efficacy category tend not to be able to fully interpret the information. As a result, the process of communicating information and solving problems goes wrong. Another aspect found in this study is the need for experience optimization, a good understanding of mathematical content, and reasoning in the numerical thinking process.

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students’ common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students’ understanding of the wrong concepts to the correct ones. A research design was used to achieve this goal. It identified and solved the errors in the definition of angle and triangle among first-year students in the Department of Mathematics Education at an excellent private college in Mataram, Indonesia. The steps were as follows: A test instrument with open-ended questions and in-depth interviews were used to identify the errors, causes, and reasons for the students’ misconceptions. Then, the MDWI approach was used to identify a way to correct these errors. It was found that students generally failed in interpreting the concept images, reasoning, and knowledge connection needed to define angles and triangles. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features.

This study aimed to determine the effect of cognitive and affective factors on the performance of prospective mathematics teachers. Cognitive factors include cognitive independence level and working memory capacity, while affective factor include math anxiety. Mathematical performance was then assessed as basic math skills, advanced math skills and problem-solving ability. This research combined quantitative and qualitative research methods. In order to determine the effects of cognitive independence, working memory capacity, and math anxiety on math performance, multiple regression tests were used. To then see the effects of these three factors on problem-solving ability, a qualitative approach was used. Eighty-seven prospective math teachers participated in this study. Based on the results of the multiple regression, it was found that the level of cognitive independence affects basic math skills but has no effect on advanced math skills. Working memory capacity was seen to positively affect math performance (basic and advanced math skills, problem-solving skills), while mathematics anxiety demonstrated negative effects on advanced math skills and problem-solving skills.

Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with the use of digital learning resources like dynamic geometry programmes and applets, which foster visualisation. Students explore geometric concepts through the manipulation of interactive virtual representations. This study aims to explore whether learning of geometry with digital resources is reflected in higher student achievements in solving geometric problems. This study also aims to explore the role of graphical representations (GRs) in solving geometric problems. The results of the survey show a positive impact of the model of teaching on student achievement. In the post-test, students in the experimental group (EG) performed significantly better than students in the control group (CG) in the overall number of points, in solving tasks without GR, in calculating the area and the perimeter of triangles and quadrilaterals than the CG students, in all cases with small size effect. The authors therefore argue for the use of digital technologies and resources in geometry learning, because interactive manipulatives support the transition between representations at the concrete, pictorial and symbolic (abstract) levels and are therefore important for understanding mathematical concepts, as well as for exploring relationships, making precise graphical representations (GRs), formulating and proving assumptions, and applying different problem-solving strategies.

Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT). However, many still find it challenging to solve this problem. The subjects in this study were twenty-one prospective mathematics teachers who took number theory courses, and then two research samples were selected using the purposive sampling technique. This study uses a qualitative descriptive method to describe the thinking process of prospective teachers in solving Diophantine linear equation problems. The results showed that the first subject's thought process was started by turning the problem into a mathematical symbol, looking for the Largest Common Factor (LCF) with the Euclidean algorithm, decomposition process, and evaluation. The second subject does not turn the problem into symbols and does not step back in the algorithm. The researcher found that teacher candidates who found solutions correctly in their thinking process solved mathematical problem used CT components, including reflective abstraction thinking, algorithmic thinking, decomposition, and evaluation. Further research is needed to develop the CT components from the findings of this study on other materials through learning with a CT approach.

Geometric thinking affects success in learning geometry. Geometry is studied from elementary school to university level. Therefore, in higher education and basic education, it is necessary to carry out a systematic review in order to obtain tips for improving geometric thinking skills. A systematic review of geometric thinking was done in this study. In this study from 2017 to 2021, geometric thinking was investigated in the form of a synthesis review of the effect size of the given treatment. This is a comprehensive discussion of theories, models, and frameworks on the topic of geometric thinking from 36 articles. The research findings revealed that the interventions used were predominantly effective, with effect sizes ranging from "small" to "very large," with the "very large" effect obtained in the intervention of van Hiele's learning phase and various technology-based-media and concrete manipulative media. The research trend was reflected through twelve clusters of interrelated keywords. The results of this literature review suggested that it is necessary to carry out a specific study on how to achieve the highest level of geometric thinking, a more detailed form of scaffolding, and concrete manipulative media and technology that can be explored for a certain level of the participants’ geometric thinking.

The government has imposed social restrictions during the COVID-19 pandemic, affecting the education sector, including the early childhood school. Distance education offers different methods from the conventional methods, as the students are expected to gain the same skills, including critical thinking skills. Therefore, teachers must provide distance learning innovations using relevant learning media, such as multimedia-based learning. This research aims to assess the efficacy of multimedia learning in early childhood distance learning. This research is a quantitative model with a quasi-experimental pretest and posttest design. The data collection technique utilized questionnaires given to 30 samples of early childhood children. The data were statistically analyzed using SPSS software. The results confirmed that multimedia-based learning for distance learning could develop critical thinking skills in early childhood children during the COVID-19 pandemic. The results of this study offer exploration of learning strategies to improve children’s critical thinking.

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The impact of structured steps that students need to take during the process of solving stoichiometric problems was explicitly analyzed. A total of 108 eighth-grade students participated in the study. Of the overall number of students, half of them were included in the experimental classes, whereas the other half were part of the control classes. Before and after the intervention, contextual problems were administered twice to all the student participants. The study results indicate that the students of the experimental classes exposed to structured steps in solving algebraic problems and the procedural transformations scored better results in solving problems in mathematics for chemistry compared to their peers who did not receive such instruction. Nevertheless, the result shows that although the intervention was carried out in mathematics classes, its effect was more significant on students' achievements in chemistry. The findings and their practical implications are discussed at the end of the study.

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.

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.

Development research demands a improvement in the implementation of learning by developing products based on learning needs. The products of this development are teacher book and student book based on the realistic mathematic education (RME) approach for package A in statistics material. Validity testing in this study includes instrument validation, self-evaluation, expert validation, one-to-one evaluation. Aiken's V and Intraclass Correlation Coefficient (ICC) are used to determine the validity and reliability of the product. The result of research shows that the instruments and prototype are valid and feasible. Then, the ICC obtained moderate stability, it also categorize reliable. In terms of context and hypothetical learning trajectory (HLT) developed, the products should be revised to achieve meaningful learning.

The aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.

This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.

Under the influence of neo-liberalism and marketization, education is increasingly becoming more content-focused than character one. Ignoring the fact that money, science, and technology may take a person to the moon, these are ethical and moral values that take him/her to the even loftier heights of humanity. Recent COVID-19-driven focus on information and communication technology (ICT) and digital learning have further added to these woes by focusing more on human-machine interaction than human-human ones. Traditional models for inculcating these values through education which heavily rely on the physical presence of teachers do not seem to work in these circumstances. This demands a model for inculcating these values in learning management systems/ e-learning platforms. This study contributes in this regard by first identifying key players and factors, and then proposing a model for it. Using the Delphi model, it gathers opinions from 59 experts in two rounds. Academic institutions, society and online community members, teachers, and e-contents were identified as key factors and players. It suggests a holistic approach-based model through which all of them play their role and collaborate through an e-learning platform. That platform can be used to disseminate information, create awareness, monitor, and report the e-learners. It uses pull and push strategies to help the e-learners to develop those values.

The actions, processes, objects, and schemas (APOS) theory is a constructivist learning theory created by Dubinsky based on Piaget's epistemology and used to teach math worldwide. Especially the application of APOS theory to the curriculum of a mathematics class helps students better understand the concepts being taught, which in turn contributes to the formation and development of mathematical competencies. With the aid of the APOS theory and the activity, classroom discussion, and exercise (ACE) learning cycle, this study sought to ascertain the effect of teaching derivatives in Vietnamese high schools. In this quasi-experimental study at a high school in Vietnam, there were 78 grade 11 students (40 in the experimental and 38 in the control classes). As opposed to the control class, which received traditional instruction, the experimental class's students were taught using the ACE learning cycle based on the APOS theory. The data was collected based on the pre-test, the post-test results and a survey of students' opinions. Also, the data that was gathered, both qualitatively and quantitatively, was examined using IBM SPSS Statistics (Version 26) predictive analytics software. The results showed that students in the experimental class who participated in learning activities based on the APOS theory improved their academic performance and attitudes. Additionally, it promoted the students' abilities to find solutions to problems about derivatives.

Lesson study, observation and analysis are relevant to professional development and initial teacher education. As a strategy, it helps to bridge the gap between theory and practice. The health conditions brought on by the COVID-19 pandemic forced the restriction of the tutors’ direct observation of preservice teachers at school. This study analyses preservice teachers’ performance through video observations to evaluate their professional activity at school during the COVID-19 pandemic. The Fifteen Items Revised Tsang-Hester Observation Rubric (FIR-THOR) was administered to a sample of 166 preservice teachers in their internship schools and their video recordings each one of 45-minute teaching lessons were analysed. The results show that the FIR-THOR appears as a robust instrument, which allows us to conclude that the instrument works well in the three five-items dimensions that compose it - Instruction, Management, and Assessment - proving to be reliable for assessing teacher intervention in the classroom. Among the three dimensions, the preservice teachers’ performance stands out in the Management of the classroom, as well as in the classroom Instruction. This contribution is relevant considering the potential of lesson analysis in learning and professional development during initial teacher training.

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.