This study aimed to describe the differences in students' creative thinking skills in a problem-based learning model with scaffolding in the biochemistry course. This study was designed using a quantitative explanatory research design with a sample of 113 students of the Jambi University Chemistry Education Study Program. In this study, the researcher used the experimental class and control class. The sampling technique used is total sampling and purposive sampling. The research data was taken by observation, test, and interview methods. The quantitative data analysis used was the ANOVA test and continued with the Post-Hoc Scheffe’s test. The findings of this study indicate that the results of the ANOVA test indicate a significant difference in the average creative thinking results in terms of psychomotor aspects with the acquisition of significance scores of 0.000. In addition, the results of this study indicate that class A students have higher creative thinking skills than class B and class C. This is because class A students use a problem-based learning model integrated with scaffolding in their learning.

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.

Problem-solving process requires information processing, and the information processing is related to working memory capacity (WMC). This study aims to determine the effect of WMC on students' mathematical abilities and to describe the ability of the students with high and low WMC in solving mathematical problems. This research used mixed method with Sequential Explanatory Design. The quantitative data were collected through the provision of OSPAN tasks and math tests to 58 students aged 15-17 years, while the qualitative data were collected through interviews based on mathematical problem-solving tasks. The results showed that WMC had a significant effect on students' mathematical abilities (R=0.536; p=0.000). Researchers found differences in students' mathematical problem-solving abilities with high and low WMC. Students with high WMC can remember and manage information well which supports the determination of more advanced problem-solving strategies and have better attention control so that they find varied appropriate solutions. Students with low WMC experienced decreased attention control as the complexity of the tasks increased, missed important information in problem solving strategies, and did not recheck their work, leading to wrong solution/answer. The mathematical performance of students with high WMC outperformed the mathematical performance of students with low WMC.

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.

This research aims to determine second-year university students’ understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of 112 student teachers of primary teacher education program at two private universities in Indonesia were involved in this research. A qualitative method with a holistic type case study design was used in this research. The results indicate that a significant percentage of the participants could not correctly interpret and represent fractions. In terms of interpretation, it is found how language could obscure the misunderstanding of fractions. Then, the idea of a fraction as part of a whole is the most widely used in giving meaning to a fraction compared to the other four interpretations, but with limited understanding. Regarding data representation, many participants failed to provide a meaningful illustration showing the improper fraction and mix number compared to the proper fraction. Improvement of fraction teaching at universities - particularly in primary teacher education programs - is needed so that students get the opportunity to develop and improve their knowledge profoundly. We discuss implications for teaching fractions.

This study was conducted following the initial stage of the transition to distance education necessitated by the onset of the COVID-19 pandemic and meeting the various challenges that came with it. At this point, countries and teachers have gained experience in preparing and delivering online education. Therefore, the study aimed to identify the beliefs of primary school mathematics teachers about teaching in synchronous virtual classrooms. It adopted a mixed methods approach, following a convergent parallel design. The overall study sample comprised 410 male and female teachers. A questionnaire was used to collect quantitative data across three dimensions (teaching efficiency, employing the philosophy of active learning, mathematical achievement). There were 31 items (verified for validity and reliability) comprising statements measured using a five-point Likert scale, together with open-ended options for further elaboration. In total, 130 teachers completed the questionnaire. Interviews were conducted with 10 teachers to collect qualitative data. The results show means in the range 3–5.75 for agreement with statements concerning the beliefs of mathematics teachers about teaching in virtual classrooms in the following order of importance: teaching competence; mathematical achievement; employing the philosophy of active learning. The study also found no statistically significant differences attributable to the variables of gender, qualification, or teaching experience, and also that many factors are considered to affect teaching in synchronous virtual classrooms related to the teacher, the family, and the student.

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.

The delivery of science, technology, engineering and mathematics (STEM) learning to improve an individual’s competence and future career interests has become a critical scientific undertaking for teachers and researchers alike. A plethora of research has proposed various hands-on robotics activities built on constructivist theories, thereby facilitating the development of knowledge based on reality for scientific and non-scientific stakeholders. Robotics may become an essential focus point within technology provision, which is an essential underlying characteristic for the seminal development of computational thinking (CT). However, despite the potential benefit of CT in developing an individual’s problem-solving skills, strategies for improving this ability through hands-on robotics activities largely remain underexplored. This paper highlights the constructs drawn from hands-on robotics activities in a STEM workshop designed for pre-service teacher students. The qualitative research design involved eight participants to investigate the responses of pre-service teachers to a hands-on robotics activity intended to provide STEM material. The research findings emphasise the correlations between the CT principles and STEM learning phases and underscore the roles played by educational robotics to enhance previous literature on learning experience.

This study aimed to investigate the impacts of enrolling in the creative teaching module in science, technology, engineering, and mathematics (STEM) education from high school students’ perspectives. This study applied a case study and qualitative research approach involving 26 Grade 11 students and 31 Grade 8 students. The creative teaching-STEM (CT-STEM) module, which comprised various activities related to energy literacy in real-world situations for the community’s well-being, involved outdoor STEM education activities with the assistance of two science teachers. The CT-STEM module was developed based on the directed creative process model by applying four creative teaching strategies: (i) constructivism learning, (ii) discovery inquiry, (iii) problem-based learning, and (iv) project-based learning. The theme of these out-of-classroom activities is sustainability education, focusing on energy sustainability. The results showed that the planned approaches could positively impact and build students’ creativity and create an exciting learning experience. Furthermore, the findings from the open-ended questionnaire instrument, observations, and analysis of the worksheets have shown enhancements in five themes: the development of problem-solving skills with an emphasis on the element of sustainability education, high-level thinking skills, active learning skills, communication skills, and humanity skills. The students also showed an increased interest in STEM as they learned using the CT-STEM module.

The longitudinal changes of the average grades in four study semesters before and during the COVID-19 pandemic and distance learning are presented in the current study. 11th grade students’ (n=586; age M=17.38, SD=0.53) average grades were assessed, as well as their verbal and non-verbal reasoning abilities, and self-evaluations of problem-solving and self-management skills. The main findings of the study are: 1) There is a general pattern for the grades to increase during the four semesters from the autumn 2019 to the spring 2021; 2) The general tendency of changes in the grades is similar to various students’ groups based on their level of skills; 3) Higher level of students’ skills and cognitive abilities determined that students’ grades were higher and were more likely to increase during the “second wave of the pandemic”, compared to the middle and low-level skill groups. Results of the current study show a tendency for the average grades to increase during the pandemic and distance learning, however, there are group differences in the findings, relating the grade level to the individual level of students’ skills and abilities.

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.

This study aims to analyze the characteristics of social skills, digital literacy disposition, and mathematical literacy abilities of 49 students; to analyze the theoretical model of the direct and indirect influence of digital literacy skills and social skills on mathematical literacy skills. The number of samples is 49 of the 12th-grade students at state high school #1 Southern Konawe. The research instruments consisted of a mathematical literacy ability test, a social skills questionnaire, and a digital literacy disposition questionnaire. The data were analyzed by descriptive statistics and structural equational models (SEM) with a Smart PLS 3.0 application. The results showed that students' mathematical literacy skills tended to be better on content and context indicators but they are weak on competency and process indicators. Students' social skills tend to be better on indicators of peer-relationship skills and self-management skills, but are also weak on indicators of academic skills and compliance skills. Mastery of the digital literacy disposition tends to be better on the internet searching, content evaluation, and information sharing indicators but is still weak on knowledge assembly. Furthermore, it was found that (a) social skills have a direct effect on digital literacy disposition but do not directly affect mathematical literacy skills; (b) the digital literacy disposition has a direct effect on mathematical literacy skills.

Metacognitive, critical thinking and opinion expression are in high demand. This study aimed to investigate the effects of the blended project- based literacy that integrates school literacy movement strengthening character education (literasi berbasis proyek terintegrasi GLS dan PPK: Li-Pro-GP) learning model on students' metacognitive skills, critical thinking, and opinion expression. A post-test experimental design was used to answer the research question. The study was conducted from August to October 2021 at Government Junior High School 23 Malang. Seventh-grade students were selected as research participants. The participants included 30 students from class VII-2. The research instrument was five essay questions to measure critical thinking skills. Material and assessment experts validated the essay questions developed by the researcher. The items that were declared valid were tested for validity. The result showed five valid items with high reliability of .670. Metacognitive skills were measured using the Metacognition Awareness Instrument (MAI), which consists of 40 items. The questions declared valid were tested for validity with a very high reliability of .953 for 37 items, and only three items were invalid. The ability to express an opinion was measured with an observation questionnaire validated by experts with a valid instrument score. Data analysis was performed by path analysis using the SmartPLS software. The results showed that the Li-Pro-GP blended learning model significantly strengthened students' metacognitive skills, critical thinking, and opinion formation.

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.

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.

The successful application of the problem-based learning (PBL) approach requires feedback from the tutor to the student to guide the latter's learning process. The aim of this study was to characterise the views of a group of Chilean undergraduate students of Primary Teaching and their tutors regarding PBL methodology, and the role of feedback in it. Qualitative research was carried out based on a case study that gathered the views of students and tutors through a focus group. The methods of analysis adapted to the needs of this study are those derived from discourse analysis and especially from discourse in interaction in its three dimensions: interlocution (framework of participation), thematic (topic of discussion) and enunciative (enunciative positioning). The results indicate that students' views emphasised the inter-student collaboration involved in PBL, while tutors emphasised the motivational value of the methodology. However, both recognised the important role that feedback plays in enhancing learning opportunities. Knowing the views of both tutors and learners is central to improving PBL and feedback practices.

Digital puzzle worksheet (DPW) is innovative teaching material designed using open-source software such as Canva and Liveworksheets. Subsequently, puzzle games in the form of questions can improve problem-solving skills by engaging in metacognitive processes. This research used a case study method to describe the impact of applying the DPW to identify the metacognition levels of students through the assignment of contextual maths problems. The source of informants was third-grade elementary school students in West Java, Indonesia. Test instruments, observation sheets, and interviews were used, while data analysis adopted an iterative model. Furthermore, the method and time triangulation increased confidence in the resulting conclusions. The results showed that male students were at the metacognitive level of ‘strategic use’ and ‘aware use’ for females, based on the characteristics of the observed metacognitive level. The most prominent feature was identifying and determining problem-solving strategies with metacognitive awareness. The reaction of students to the DPW improved problem-solving abilities, expanded conceptual understanding, and enhanced digital technology competence. Therefore, this experience was applied when solving contextual mathematical problem assignments.