This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical Knowledge and Applying Mathematical Knowledge. The sections were cross-analyzed with students’ responses to provide a comprehensive analysis of how teachers use various techniques to support students. It is proposed that teachers can use this framework to create an environment that promotes learning with open-ended as well as other open problems in their mathematics classroom. The OPA framework can contribute to teacher education, the design of mathematics curricula and to educational research.

Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature over the past two decades, this is not the case among African policy-makers and political leaders. Drawing mainly from our professional experiences as mathematics educators and from the international research literature, our primary intent in this paper is to answer this question: How does the learning of mathematics in English at the basic school level help or hinder students’ mathematical proficiency? To answer this question, the paper is organized as follows. The first part, the introduction, gives a brief overview of the language of learning and teaching in Africa. The second part describes the method and conceptual framework undergirding the research. In the third section, we have analyzed the effects of mathematics learning and teaching through English for basic students whose mother tongue is a Ghanaian language. The conclusion offers four recommendations for developing and improving the mathematics proficiency of students in basic schools.

The purpose of this study was to investigate how mental rotation strategies affect the identification of chemical structural formulas. This study conducted event-related potentials (ERPs) experiments. In addition to the data collected in the ERPs, a Chemical Structure Conceptual Questionnaire and interviews were also administered for data collection. Eighteen university students majoring in chemistry were recruited. In the ERP experiments, the participants were required to identify 2D figures, 2D chemical structural formulas, 3D objects and 3D chemical structural formulas. The contours of 2D figures are similar to those of 2D chemical structural formulas, but they contain no content knowledge. Likewise, the contours of 3D objects are similar to 3D chemical structural formulas without content knowledge. The results showed that all students used similar strategies of mental rotation in identifying 2D figures, 3D objects and 3D chemical structural formulas. However, the high-achieving students used different strategies in identifying 2D figures and chemical structural formulas, while the low-achieving students tended to use similar strategies of mental rotation in identifying both 2D figures and chemical structural formulas. The results indicate that some of the difficulties in identifying 2D chemical structural formulas that students encounter are due to their inappropriate strategies of mental rotation.

The aim of this study is to reveal the benefits gained from “Special Training Methods II” course and the problems prospective mathematics teachers encountered with it. The case study method was used in the study. The participants in the study were 34 prospective mathematics teachers studying at a Primary School Mathematics Education Department. The data collection tools were a form composed of open-ended questions and semi-structured interviews. Descriptive analysis of the quantitative data was carried out. In the “Special Teaching Methods II” course, beginning in the spring term of the 2015-2016 academic year, teaching activities on “multiple intelligences”, “discovery”, “group work”, “problem-solving”, “history of mathematics” and “computer-assisted teaching” were developed and implemented. It was concluded that these activities helped students like mathematics more, understand the importance of helping each other and cooperation and have more enjoyable lessons, as well as aiding their cognitive, social and emotional development. It was also found that through these activities participants improved their belief in themselves and increased their confidence regarding teaching mathematics. The participants also faced with some difficulties during the application process. They mostly mentioned that preparing worksheets was time-consuming, finding a school to perform the activity was hard and students were reluctant.

Advanced technology helps educational institutes to improve student learning performance and outcomes. In this study, our aim is to measure and assess student engagement and collaborative learning in engineering classes when using online technology in solving physics problems. The interactive response system used in this study is a collaborative learning tool that allows teachers to monitor their students’ response and progress in real time. Our results indicated that students have highly positive attitude toward using the interactive response system as a tool in education in order to improve collaborative learning and student engagement in classes. Consequently, student-learning performance has been improved considerably, and technology was successfully incorporated in engineering classes.

It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to analyze the multiplication and division of fractions problems posed by pre-service elementary mathematics teachers and to investigate how the problems posed change according to the year of study the pre-service teachers are in. The study employed developmental research methods. A total of 213 pre-service teachers enrolled in different years of the Elementary Mathematics Teaching program at a state university in Turkey took part in the study. The “Problem Posing Test” was used as the data collecting tool. In this test, there are 3 multiplication and 3 division operations. The data were analyzed using qualitative descriptive analysis. The findings suggest that, regardless of the year, pre-service teachers had more conceptual difficulties in problem posing about the division of fractions than in problem posing about the multiplication of fractions.

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these problems and the groups’ reflective diaries regarding their problem posing and solution processes. The data were analyzed by using content analysis and the codes were constructed according to the problems’ contents. The participants' diaries were examined in terms of generated codes and the expressions supporting/relating the codes were determined. While designing the problems, the participants considered the factors such as being interesting, understandable, appropriateness to real life and modelling process, model construction, and usability of different mathematical concepts. Their solutions were generally handled in terms of usage of the mathematical statements, appropriateness to the modelling process and being meaningful for real life. Modelling training should be provided to enable the student teachers to develop modelling problems and their designs should be examined and the feedbacks should be given.

In Turkey, as in all countries of the world, education is regarded as the sole means of modernization, progress, civilization, productivity, and sustainability of all these things. The aim of the Turkish education system is to raise students with the national, moral and cultural values of the Turkish nation, to educate them as citizens of a social law state, and solve the existing or potential problems that may arise in the future. The most important document that shows how this aim will be achieved in the country is the curriculum. The purpose of this study is to reveal the frequency of the social issues included in the current curriculum at the elementary education level. Within the scope of the study, social issues presented by sociologists were established through e-Delphi panels, coded under seven titles by researchers, those who were thought to bring solutions to these problems were counted by descriptive analysis method in the specific aims, themes and achievements of the curriculum used at elementary level. Results show that curriculum adopted at the elementary education level include mostly issues related to individual life and individualization, socialization, democratic life and democratization while economic issues, and issues related to family, environment and urbanization are emphasized less. These findings are discussed with other research results.

This study is conducted to develop the diagnostic test, which can be used to measure the higher-order thinking skill (HOTs) of students of first-grade senior high school in Bima district, West Nusa Tenggara. The step of developing instruments such as test which using modification model of Oreondo which include two activities such as test designing and test trials. The analysing technique of validity of content used Aiken formula, classical test theory used software Iteman 4.3, the model of Rasch used software Winstep and analysing reliability used software SPSS. The conclusion which can be taken are developing instrument has the characteristics as a useful instrument and fulfil requirement used to measure. This case proved from the data of analysis result which confirm that the instrument has been achieved the content of validity by expert judgment and obtained the empirical evidence, both as classical test theory or Rasch model.

Environmental learning in the 21st century requires students to have Higher Order Thinking Skills (HOTS). The purpose of this study was to measure HOTS students using Higher Order Thinking Skills Assessment based on Environmental Problem (HOTS-AEP). The research method used in this study was descriptive method with a total sample of 248 students consisting of Elementary School (ES), Junior High School (JHS), Bachelor Program (BP), and Master Program (MP). The results showed that students overall have a very low HOTS category. HOTS scores scale of 0-100 on ES (22.3) are still higher than JHS (20.2). Whereas at the university level, BP scores (19.9) are lower than MP (21.4). This showed that learning must be oriented towards increasing HOTS through various media development learning, learning materials, learning models, and strategies. This study concludes that the HOTS score of students was still very low and needs to be improved.

The industrial revolution era 4.0 has now become a major topic in every country. Various sectors respond quickly to this problem, including education. In response to this, there are several aspects of skills that students must master. One of them is problem-solving skills. One of the aspects that influence the students’ problem-solving skills is the context and problem-based learning model. The purpose of this study is to describe the effect of the model on students' skills to solve physics problems. The research method used is a quasi-experimental research design with non-equivalent control group design. The data analysis technique used Independent Sample T-Test by PASW 18 with a significance 5%. Based on the results of the Independent Sample T-Test can be concluded that there is an effect on the model that was applied with a significant gain of 0,00. The results showed that the context and problem-based learning (C-PBL) model affected the physics problem-solving skills. The C-PBL model is able to improve the students’ physics problem-solving skills, communication skills, the students’ confidence in learning, as well as improving students’ understanding of physics lessons conceptually.

The article analyzes the evolution of pedagogical systems and the practice of universities in the world. The work reveals the essence and main structural components of the university education, as a special institution of higher education, designed to become a systemic solution to the problem of management and development of teacher education. The model presented by us includes the following components: education, as a platform for transferring innovative solutions into practice; Mega-Science -a system of research collaborations that provides advanced solutions to global problems; technologies -research constructs according to the Lego principle, generating local problem-solving based on a cluster; implementation -a system of investment decisions on the implementation of developments in the practice of activity; innovation is a system for the formation of products open to use that stimulate the development of education. The paper presents the main results of these developments, conclusions are made about the need to form a university of education as a special system operating within the framework of the concept of open pedagogical education and aimed at creating a federal scientific and educational hub of global importance for reproduction and the formation of human capital in scientific, engineering activities, the generation of new solutions in the field of training and development of teaching staff in.

Studies have acknowledged computational thinking (CT) as an efficient approach for problem-solving particularly required in digital workplaces. This research aims to identify indicators for a holistic CT assessment instrument for undergraduate students. A three-round fuzzy Delphi study has been conducted to gain comprehensive opinions and consensus from undergraduate lecturers of computer science disciplines and experts from the information technology industry. In round 1, the experts judged a set of predefined indicators describing CT skills and attitudes identified from the literature, while rounds 2 and 3 focused on variables selection. The consensus was achieved on holistic CT, and the indicators are teamwork, communication, spiritual intelligence, generalization, problem-solving, algorithmic thinking, evaluation, abstraction, decomposition, and debugging. Results demonstrate the importance of attitudes in the process of solving a problem and suggest higher education institutions to consider holistic CT in preparing qualified future graduates. Many CT studies focused only on the skills of CT. This study outlines the assessment indicators that consider both CT skills and attitudes, particularly at the undergraduate level.

This study investigated the development of problem-solving strategies demonstrated by 42 elementary pre-service mathematics teachers in problem-solving mathematics classes. The study used a mixed methods approach of quantitative and qualitative research by analyzing the collected data.. The quantitative portion calculates the frequencies and percentage of the participants’ responses to the problems posed in three different phases of the intervention: before, during, and after receiving the mathematics lessons. The qualitative approach was used for in-depth investigation to describe various mathematical problem-solving strategies demonstrated by participants across the three different research phases. Findings of the study indicated a limited number of problem-solving strategies present during the first phase of research such as “use arithmetic operation strategy,” and “make a drawing strategy,”. During the implementation of the problem-solving lessons and classroom discussion, the participants began to develop more strategies such as  “use logical reasoning,” “solve a simpler problem,” “guess and check,” “organize data in a table or a list,” “look for a pattern,” “work backwards,” and “solve an equation,”. However, the research findings nonetheless revealed participants’ weakness in applying the variety of skills required for success in problem solving, such as interpreting information, mathematical working, and logical thinking. Results also demonstrated a limited and incorrect use of mathematical terminology, as well as a lack of problem comprehension. The discussion of the study addresses different features and issues related to mathematical problem-solving strategies. In light of its findings, this study presents recommendations and suggestions for the future development of pre-service teachers’ problem-solving strategies.

The purpose of this study is to evaluate the psychometric and structural instruments of the Physics Metacognition Inventory (PMI) developed by Taasoobshirazi, Bailey, and Farley (2015). The PMI consists of 26 items in six factors. The English and Indonesian versions were tested on an English course (N = 37) in the Geophysics study program at Tadulako University. The trials were conducted separately within a two-week interval. The data collected from 364 students of the Physics Education Department, University of Tadulako were analyzed using the Exploratory Factor Analysis (EFA). Later, data were collected from 351 students of some Indonesian universities which have physics education study programs, and the data were analyzed using the Confirmatory Factor Analysis (CFA). The EFA result reveals six factors based on the rotation result with the maximum loading factor. The CFA result shows the RMSEA values of .018, 2 (284) = 316.32 (χ2 / df = 1,11), GFI = .93, CFI = .99, AGFI = .92 and NFI = .93 which meet the cut-off statistic value, and therefore, the model is considered fit, with the Construct Reliability Estimation (CR) of .93, Composite Reliability of  = .95, and maximum reliability of Ω = .96. The results obtained reveal that the PMI scale has good, valid and reliable psychometric properties. Therefore, PMI can be used to measure the level of metacognition of students when solving physics problems. Future studies using PMI are also discussed.

This research study presents the PGBE model for teaching and learning percentages with students of Grade 7 when their cognitive development enables the conceptual understanding of percentages as proportional statements, and offers the possibility for more effective matching of them with fractions and decimal numbers. The abbreviation PGBE presents the interrelation of the poster method and three instructional models through which different types of students’ mathematical knowledge about percentages can be built. Hence, P stands for the poster method through which the recognition of students’ previous knowledge about percentages can be done, G represents different grids that can be used for building concrete type of knowledge about them; B signifies the bar model for developing students’ proportional understanding of percentages, and E represents the extended bar model for fostering students’ principled-conceptual understanding of percentages. The effectiveness of the implementation of the PGBE model is assessed by organizing two cycles of piloting and conducting the experimental method with 263 students of ten Grade 7 classes. The results of the study show that the implementation of the PGBE model has had an impact on the learning of students, stimulating an in-depth learning and a long lasting knowledge about percentages for this cohort of students.

The development of the revolution era 4.0 which increasingly rapidly demands the wider community to have the ability to think creatively mathematically. One effort to improve the ability to think creatively is through quality education. Quality education can be improved through to train thinking using the right learning model. This study aims to see which results are more effective in improving students' thinking skills between the two learning models applied. The two models are Problem Based Learning (PBL) and Aptitude Treatment Interaction (ATI) models. This research method uses quasi experimental method with a posttest only control test design not control group. This study uses two group subjects with two experimental classes. The analysis of the data used the hypothesis testing of the non-correlated 2-sample t-test. Based on the research results obtained Aptitude Treatment Interaction (ATI) models have a better effect on students' creative thinking abilities compared to Problem Based Learning (PBL) models.

This research aims to develop open ended-based worksheet in improving students' high-level thinking skills on static fluid materials. The method used in this research is Research and Development (R&D) with 3 steps namely, the initial stage, then the design and development of the product, and finally the product testing. The data analysis technique for product effectiveness is with the main field trials, namely (1) N-gain analysis, (2) paired t-test, (3) ANCOVA, and finally (4) effect size test. From the test results obtained information that conducted 10 students showed the results of the development worksheets obtained the average worth of development products by 90% this value is included in the very high category, while the student response of the average of 88% and also the readability response of 89% in the very high category. In the results of the n-gain analysis also show the value is0.70, that mean medium category. From the results of this study, it can be concluded that worksheets based on open ended can improve students' higher-order thinking skills. So, in further development we suggest that open ended-based on worksheet is not only applied to static fluid material, but also in other materials.

Mathematics is one of the most challenging subjects for many students. A similar problem is faced by special needs students, such as students with Autism Spectrum Disorder (ASD). Various instructional strategies are implemented by specialists to help ASD students understand mathematics in schools. To explore the impacts of an instructional strategy of mathematics on ASD students, the authors conducted a review of literature from 2011 to 2017 using various databases including ProQuest Digital Dissertations and Theses Full Text, Google Scholar, and Science Direct. A total of 39 articles were found. Most of the instructional strategy aimed to assist ASD students in solving mathematics problems. The implications of the study are also discussed in this literature review, which indicates that teachers need to use the appropriate instructional strategy to meet the needs of students with ASD and maximize their mathematics learning outcomes in schools.

This study aims to determine the effect of the application of the Search, Solve, Create, and Share (SSCS) learning model to the mathematical reflective thinking skills and the students' mathematical problem-solving abilities. This research is a type of Quasi-Experimental Design research with a 2x2 factorial research design. Data collection techniques in this study in the form of documentation and tests at Private school in Bandar Lampung with 28 students of experiment classes and 28 students of control classes. Data analysis techniques used are the normality test and homogeneity test. Testing the hypothesis in this study using the Multivariate Analysis of Variance (MANOVA) test. Based on the results of the study, The calculation of the MANOVA test, it was concluded that there was an influence on the application of the SSCS learning model to students' mathematical reflective thinking skills. The application of the SSCS learning model to the mathematical reflective thinking ability has an influence percentage of 91.9%. The application of the SSCS learning model to mathematical reflective thinking skills and mathematical problem solving abilities has a relatively high level of effectiveness.