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.

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 purpose of this study was to investigate the effect of creative drama as a teaching method on academic achievement and retention in social studies, students’ attitude towards social studies of 4th grade. The research is designed according to quasi-experimental model. The research was conducted with 4th year students in a public school in Adana in Turkey. There are 42 students in experimental group and 39 in control group. Creative drama activities were used to develop social studies achievement and attitude of students as a treatment for the experimental group. The treatment consisted of 15 hours, 40 minutes sessions that equal a class hour in school and 3 hours a week. Control groups had been taught by classroom teachers as the way they do traditionally. Data collection tools are “Attitude Towards Social Studies Scale” developed  by Gencel “Achievement Test” developed by the researchers.  Data were processed by using covariance analysis. Findings indicated that creative drama method has a significant effect on social studies achievement and students’ attitude towards social studies but not a significant effect on retention of social studies knowledge.

Mathematics educators have reported on many issues regarding students’ mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts. This study aimed to investigate the opinions of primary-school teacher education students in terms of their perceptions of difficulty level of the mathematics courses, change in their achievement, if there is any, and interest in mathematics after completing these courses, and factors affecting their achievement and interest level in these courses. Being qualitative in nature, this study was a case study. The data were analyzed using the content analysis and descriptive methods. According to the results, most students stated that they faced mathematics course content with unexpected level of difficulty. After taking basic mathematics courses, the percentage of students with decreased level of interest and achievement in mathematics was found higher than the students who experienced an increase in their interest and achievement. Students underlined such significant factors for the change of their interest and achievement in mathematics as prior knowledge, lecturer(s), and content coverage. Finally, most of the students viewed mathematics courses as a beneficiary tool for their professional development.

This study investigated prospective mathematics teachers’ reflections on the experience of designing and conducting one-to-one clinical interviews with middle school students in the context of an elective course on use of video in teacher learning. Prospective teachers were asked to write about weaknesses and strengths in student understanding as well as their own performance as an interviewer in terms of asking questions and responding to student thinking in their reflections on conducting clinical interviews. Furthermore, prospective teachers were also asked to reflect on what they would do differently in order to conduct better clinical interviews.  Nature of prospective teachers’ reflections were analyzed by using existing frameworks (through constructs of reflection-on-action and reflection-for-action) and by using thematic analysis. Results of data analyses revealed that prospective teachers had more difficulties in providing meaningful reflection-for-action which was related to alternative decisions and planning for future similar interviews. Thematic analysis results revealed prospective teachers’ learning were grouped under three categories: conducting clinical interviews as part of being a teacher, complexity of conducting clinical interviews, and personal theories about middle school students. There are implications for both teacher learning and research.

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 qualitative case study is to investigate prospective mathematics teachers’ subject matter knowledge of the underlying concepts of standard and nonstandard algorithms used to solve the problems with whole numbers. Twenty three prospective mathematics teachers enrolled in the Elementary Mathematics Education Program of one of the most successful universities in Turkey were the participants of the study. The data was collected through four tasks containing basic algorithms. More specifically, the Ones Task assessed participants’ understanding of the underlying place value concepts of standard algorithms. The Andrew Task and the Doubling Task required participants to conceptualize and interpret nonstandard strategies. In the Division Task, participants were expected to provide in-depth explanation for the difference between multiplication and division and between partitive division and measurement division. The content analysis method was used to analyze the data. The results of the study revealed that more than half of the prospective mathematics teachers had knowledge about the place value of 1 in addition and subtraction, and also multiplication. However, most of the prospective teachers could not explain the underlying principle and the meaning of the nonstandard algorithm in subtraction. Similar to their knowledge on subtraction, prospective teachers’ knowledge on division was limited.

This study aims to evaluate elementary school math teachers' self-efficacy beliefs about classroom management. With the aim of investigating elementary school math teachers' self-efficacy beliefs about classroom management, a classroom management self-efficacy scale was developed.  The 5 point likert scale is composed of 46 items. The scale was applied to 142 math teachers working at elementary schools in Diyarbakir central district. Data were analyzed in terms of gender, seniority, classroom population and weekly course load. To analyze the data, t-test, one way variance analysis (ANOVA), Scheffe and LSD tests were used. The results showed that the math teachers have a positive self-efficacy belief of classroom management and that male teachers are better at maintaining discipline in class. In addition, the research shows that teachers with more experience are better at course design and classroom management and that classroom population has an effect on math teachers' self-efficacy beliefs about classroom management.

Recent science education standards emphasize the importance of the instruction of nature of science (NOS) concepts at all levels of schooling from pre-K to K-12. Delivering a proper NOS education to students is excessively dependent on their teachers with an adequate understanding of NOS concepts. The present study investigated the science conceptions of preschool and elementary teacher candidates. The data collected from a total of 506 prospective teachers were analyzed with respect to the following demographic variables: majors, genders, grade levels, high schools and GPAs of teacher candidates. “Student Understanding of Science and Scientific Inquiry (SUSSI)” developed originally by Liang et al. (2008) was the instrument used to collect data in this study. The data analyses were conducted using MANOVA and Pearson Correlation Coefficient. The corresponding mean scores of the teacher candidates in specific aspects of NOS ranged from “poor” to “informed” conceptions of science. All but one of the demographic variables yielded statistically insignificant results on the NOS conceptions of teacher candidates. The majors of the teacher candidates were detected as a significant variable influencing the conceptions of the teacher candidates. The results of the study were discussed in reference with the relevant literature.

The purpose of this study was to evaluate pre-service science teachers’ argumentation skills, attitudes and knowledge levels regarding organ transplantation and donation (OTD). Teachers play a fundamental role in providing information to children/adolescents and could influence their attitudes. Organ transplantation is a life-saving hope for many people, but shortage of organs for transplantation is a universal problem. Having a positive attitude and true knowledge are essential for teachers that affect students’ future attitude toward this topic. The research method was descriptive and cross-sectional. The sample of research was 472 pre-service science teachers, who were sampled by using convenient sampling method and are students of Science Education Department at four different public universities. Data collection instruments were developed by researchers as valid and reliable questionnaire in order to determine the attitudes, knowledge levels and argumentation skills of pre-service teachers regarding OTD. Results observed that the pre-service science teachers' argumentation skills in a socio-scientific subject such as OTD were at a very low level, their attitudes were at a moderate level, and their knowledge level was above the average. Results of the study have shown that graduated high school type and grade level have played important roles in the positive attitudes, high argumentation skills and high knowledge level about organ donation. No significant difference was found in the attitudes and knowledge level of pre-service science teachers toward OTD in terms of gender. The gender only affected the ability of argumentation.

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.

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of abstract algebra course from two individual assignments given to the students. The students who could provide the best answers from the first and second individual assignments were chosen to be the respondents. The data from the second assignment, then, was analyzed through presentation, interpretation, coding, making a pattern, leveling and continued with clarification through an interview. The results of the study show that there were six patterns of structure sense answers and five levels of structure senses made by the students as the profile of structure sense. The conclusion is the inability to recognize the structure of the set elements, operation notations, and binary operation properties is one of the causes of the constraints in structuring the proof construction of the group. Thus, a thinking of mathematics connection is needed in structure understanding as a connection between symbol in learning and the symbol of abstract.

A sample of 327 engineering bachelor students from a public university in Mexico took part in an information integration study to explore systematic thinking underlying propensity for cheating during a course exam. All study participants were provided with written descriptions of 12 scenarios pertaining to the academic evaluation criteria and were asked to rate the likelihood that they would cheat under such circumstances. The 12 scenarios reflected the experimental manipulation of three orthogonal factors: teacher’s teaching style, type of exam, and modality of assessment. Analysis results revealed four distinct attitudes toward cheating among students, two of which were independent of context (low and high desire to cheat) while the remaining two were context-dependent (low and moderate desire to cheat). All groups showed systematic thinking underlying their possible desire to cheat that was typified by the use of a summative cognitive rule for integrating information related to academic cheating. However, evaluation of factor relevance varied across the groups.

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 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.

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.