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.

This exploratory study is concerned about the extent to which a sample of 163 pre-school, primary and secondary Brazilian school teachers, expressed their opinion on how neuroscience might help their teaching and pupils´ learning. Evaluation instruments for Brazilian pupils were analysed. Two questionnaires were completed by the teachers. Results of a quantitative analysis indicated that in general teachers believe that neuroscience may contribute to the teaching and learning of their subject matter. An outline for an elective neuroscience and education course is presented. Educational implications are discussed.

Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was explored along with a survey of areas of difficulty and student attitudes. This involved looking at student perceptions of their experiences, the nature of the difficulties they have with mathematics and possible reasons for these difficulties. The overall aim is to explore the extent of the effect of working memory and to gain insights so that practical ways forward to enhance mathematics education can be identified. It was found that limited working memory capacity has a very strong influence on performance, confirming other studies. Indeed, if the cognitive load exceeds the capacity of working memory, understanding becomes a casualty, with consequent attitude deterioration. Students need to be able to see that mathematics has a purpose in being able to be applied to real-life situations. However, attempts to develop applications may often generate further working memory overload. Curricula devised by those outside the classroom can sometimes be inappropriate while topics causing the greatest problems at these ages and include areas of geometry, statistics and the applications of mathematics.

Technological Pedagogical Content Knowledge (TPACK) is a model that explains how teachers use technology more effectively in the context of technological, pedagogical, and content knowledge. Teachers' TPACK competencies play great importance in this regard. Lesson study has also been playing significant roles in the development of teachers' professional trainings. When the researches on TPACK and lesson study have been analyzed, the research is expected to provide significant contributions to the literature. This study aims to present reflections from a lesson study practice that carried out to urge techno-pedagogical competencies of the secondary school mathematics teachers and to reveal the development of teachers’ progress. The study used case study method, and it was conducted with three in-service teachers. The research data were collected through semi-structured interviews, voice recorder, and observation notes. To analyze the collected data, descriptive analysis method was used. The results have revealed that teachers have made much more progress in designing, implementing, and problem solving in terms of TPACK competencies. It has also been determined that teachers’ development of openness to the innovations was limited. This limitation appeared to emerge as a result of teachers’ time anxiety and insufficient knowledge regarding the use of technology.

In order to reflect the integration of the teachers’ content knowledge, pedagogical knowledge, and technology usage skills to the class context and to provide the expected outputs for the program's purposes, it is needed to be revealed the different dimensions of Technological Pedagogical Content Knowledge (TPACK). In this study, it was aimed to investigate the teacher training programmes related to pre-service science teachers’ TPACK. This study was designed as a cross-sectional study. In the 2015-2016 academic year, a total of 269 pre-service teachers (73 of them from 1st grade, 73 of them from 2nd grade, 87 of them from 3rd and 36 of them from 4th grade students) attending Science Education Department participated in this study. As a data collection tool, 7 subscales of “Technological Pedagogical Content Knowledge Scale of Pre-Service Teachers”; namely, technology knowledge, pedagogical knowledge, content knowledge, technological pedagogical knowledge, technological content knowledge, pedagogical content knowledge, and technological pedagogical content knowledge were used. According to the results, as the class level of pre-service teacher increases, their level of technological pedagogical content knowledge increases as well. Moreover, there is a significant difference on behalf of pre-service teachers at the 1st grade in all dimensions of technological pedagogical content knowledge scale.

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.

The state of mathematical thinking is considered to have an effect on the formation of anxiety regarding teaching mathematics. It is hypothesized that with the formation of mathematical thinking, the anxiety in teachers regarding teaching mathematics will be reduced. Since mathematical thinking is a skill acquired starting from the early years of education, the anxiety in form teachers in primary school regarding teaching mathematics is important. Within this context, the objective of this study is to investigate the effect of mathematical thinking states of form teachers on their anxieties regarding mathematics teaching. The sample group comprises 194 form teachers working in state schools of Bagcilar district, Istanbul province in the spring term of 2015-2016 academic year. As data collection tools, mathematical thinking scale and anxiety scale for the mathematics teaching anxiety of form teachers were used. To test the predictive power of mathematical thinking regarding the mathematics teaching anxiety, Multiple Linear Regression Analysis was used. It was found that the form teachers had high mathematical thinking scores and had low anxiety scores. A low degree, negative and significant correlation was found between the mathematical thinking and anxiety of form teachers regarding mathematics teaching. Moreover, it was found that mathematical thinking had an effect on the anxiety in form teachers regarding mathematics teaching.

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 aim of this study is to determine the problem solving skills and science process skills of six year-old children who attended kindergarten and whether or not there is a difference in problem solving skills and science process skills of children receiving and not receiving the education with GEMS program. In the study using the experimental model with pre-test, post-test and control group, the sample group consisted of a total of 25 children including 11 children in experimental group and 14 children in control group who attended the preschool education. The “GEMS Program” was applied throughout a school year after applying pre-test to the children in the experimental group. In the scope of the study, “General Information Form” to obtain the data about the children and their families, “Parental Evaluation Form” including the evaluation of the parents about their children, “Problem Solving Scale in Science Education (PSSSE)” to determine the problem solving skills of the children and “Science Processes Observation Form (SPOF)” to measure the science process skills of the children were used. According to the results of the study, while a statistically significant difference was observed between the Problem Solving Scale in Science Education mean scores of the children in the experimental group who participated in the GEMS Education Program and of the children in control group, no statistically significant difference was observed between the mean scores obtained by the children in the experimental group from Science Processes Observation Form and the mean scores of the children in the control group.

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.

A modern teaching method influences both direct and indirect learning achievement through the student's nonacademic factors. The researcher has an intention to examine the influences of new teaching methodology on mathematics achievement towards mathematics attitude, achievement motivation, and self-efficacy of students as mediating variables (n teacher = 117, n student = 2,205). The Multilevel Structural Equation Modeling revealed that attitude towards mathematics is the most important factor in explaining the academic achievement of individual students. It could be explained the variance with achievement motivation and perceived self-efficacy of students by 60.50%. As for the modern teaching method, there was a positive effect on achievement both directly and indirectly through all three factors with statistical significance and explained conjointly about the variance of student achievement in each classroom by 99.00%. This finding suggests the importance and direction of teaching design that covers the development of relevant factors as proposed in discussions and implementations.

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.

This study was aimed at investigating whether or not there is an interaction between learning approach and social intelligence towards response fluency. A number of 126 eighth grade students (M = 13.9; SD = 0.5 years) in Bojonegoro, Indonesia were randomly selected to participate in this study. This research used 2x3 factorial quasi-experiment with the matching static comparison design. The statistical Analysis Of Covariance (ANCOVA) ware implemented for analysis of data in the study. The results show that: there is a significant difference in response to fluency between students who learn with a scientific approach and direct learning approach; there are significant differences in response to fluency between students who have high, medium, and low social intelligence, both in scientific and direct learning approaches, the students with high social intelligence levels have better response to fluency than those with moderate social intelligence or low, and the students with moderate social intelligence have better response to fluency than those with low social intelligence, in all levels of social intelligence, the students who were taught by using scientific approach have better response to fluency than those who were taught by using direct learning approach.

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.

Methods of education in schools should promote students' activeness, self-awareness, initiative and creativity; be suitable with the characteristics of each class and subject; foster self-study methods, ability to work in groups, practice skills to apply knowledge into practice, and impact emotions to bring joy as well as excitement to students. Experiential education is a method of teaching and meets the above requirements. In fact, experiential activities are closely related to teaching and educational activities in schools, in order to create an environment for learners, associate theory with practice, and unify awareness with action and learners, and have the opportunity to experience their own behavior. The main purpose of this study was to evaluate the performance of activities through experience in solving problems about the equation of a circle and investigate students' attitudes as well as beliefs in such activities. The experimental class included 30 10th grade students and was taught by experiential learning model, while the control class also had 30 students and was taught in a conventional way of teacher’s guidance. Both quantitative and qualitative methods were used to analyze and evaluate the collected data. The results showed that the experimental class achieved better mathematical results than the control class as well as had a positive learning attitude, showing interest in the learning topic.

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 empowerment of metacognitive skills has an important role in increasing the capacity of critical thinking and active control of students' cognitive processes in learning. Metacognitive skills can be enhanced through the implementation of learning strategies involving higher-order thinking. The RQA, ADI, RQA integrated with ADI are constructivistic learning strategies that can accommodate these skills. The researches specifically examining the correlation between metacognitive skills and critical thinking skills at the implementation of RQA, ADI, and RQA integrated with ADI learning strategies are still rarely found. This research is a correlational research, aiming at revealing the correlation between metacognitive skills and critical thinking skills. The data of metacognitive skills and critical thinking skills are collected by using a valid and reliable essay test. The samples of this research are the fourth semester (IV) biology education students programming Animal Physiology course in the 2016/2017 academic year consisting of 109 students. The results of this research show that (1) there was a significant correlation between metacognitive skills and critical thinking skills at the implementation of the four learning strategies, (2) the regression equations analyzed using Anova obtain regression lines (not coincide), and non parallel regression lines (intersected); meaning that there is a difference in the increase rate and magnitude of the critical thinking skills influenced by the four learning strategies. It is expected that the teachers and the lecturers always strive to improve the quality of the learning process through the implementation of active and constructive learning 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.