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.

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.

This study attempts to reveal pre-service teachers’ conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers’ definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers’ figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals.

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.

The aim of this research is to determine the thoughts of the teachers about the concepts of "Smart Board", "Computer", "Internet" and "Social Media" from the Instructional technologies of the secondary school teachers with different branches through metaphors. In the research, a qualitative research model was used to identify teachers' thoughts in metaphor analysis from various branches about the use of instructional technologies in the national field. Within the scope of the qualitative research model, the phenomenology design was used. In order to find out what kind of thoughts teachers have about teaching materials from the participants "Smart Board / Computer / Internet / Social Media is like / similar to…..; Because ..." they were asked to complete their covenants. As a result of the research, 25 valid metaphors belonging to the concepts of smart board, computer, social media and 27 of internet concept were obtained from secondary school teachers. The most book (f = 4) metaphor for smart board concept, brain and memory (f = 2) metaphors for computer concept, most air (f = 3) and medicine, ocean, water (f = 2) metaphors for internet concept and the drug and virus (f = 2) metaphors related to the concept of social media. The metaphors of the concept of smart board are classified into 5 conceptual categories with common characteristics related to each other, 6 categories with common features related to computer and internet concepts, and 7 conceptual categories with social media concept related to each other. In the research, it was reached that the secondary school teachers expressed positive opinions about the concept of smart board and computer, partially negative about the concept of the internet but more negative opinions about the concept of social media.

The purpose of this study is to examine the opinions of middle school mathematics teachers on the integration of mathematics course and social issues. For this purpose, qualitative research method was used in this study. As for determining the participants of the research, criterion sampling among purposeful sampling methods was used. Being a middle school mathematics teacher as an occupation was considered as a criterion for determining the participants. The participants of the research consist of 13 middle school mathematics teachers in Turkey. So as to collect the research data, the semi-structured interview form created by the researchers was used. The data analysis was performed according to the content analysis, and Nvivo 10 program was used for the analysis. As a result of this study, the themes of the situation and methods of the integration of mathematics course and social issues, the attainment of democratic values in mathematics course and the ways of its attainment, gaining awareness of social justice and equality in mathematics course and the ways of its gaining, the activities performed by teachers for social issues in mathematics course and the teachers’ suggestions for the integration of mathematics course and social issues were reached and the results were discussed within this frame.

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 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 aim of this study is to explain and predict prospective preschool teachers’ academic achievements depending on goal orientations they adopt, their critical thinking dispositions and self-regulation skills. Research sample constitutes of 265 prospective preschool teachers attending the Faculty of Educational Sciences in Cukurova University. Research data were collected with the 2x2Achievement Goal Orientations Scale, Self-Regulation Questionnaire and Critical Thinking Disposition Scale. Demographical information about prospective teachers’ gender, age, grade level and academic grade point averages were obtained with the personal information form. For the analysis of research data, One-Way Analysis of Variance (ANOVA) and discriminant analysis were used. In this study; it was concluded that prospective teachers with high level of learning approach orientation, critical thinking disposition and self-regulation skills had higher levels of academic achievement. However, it was determined that distinguishing variables among prospective preschool teachers with low, medium and high level of academic achievement included learning approach, performance approach goal orientation and critical thinking disposition and self-regulation skills. Correct classification percentage of distinguishing variables according to prospective preschool teachers’ levels of academic achievement was determined as 48.8%. Considering the fact that prospective teachers’ achievement-goal orientations, critical thinking dispositions and self-regulation skills may increase their academic achievement and shape their future teaching performances, it is suggested to implement programs that will contribute to the development of such skills and orientations among prospective preschool teachers.

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.

Gender differences in mathematics learning outcomes are still evident in many countries participating in large scale international testing, as well as in national testing in Israel, the context in which the study reported here was conducted. The participants were 281 students from three Israeli elementary schools and were in grades 4 and 6. The students completed a questionnaire with items based on a selection of variables included in explanatory models for gender differences in mathematics. It was found that many students held gendered beliefs related to mathematics learning, particularly when the questions asked related to themselves or to significant others in their lives (parents and teachers); the views of the majority of students were gender neutral. When presented with two photographs -a man, and a woman- and asked who was the one more likely to work with mathematics, it was clear that the students’ choices and explanations echoed perceptions of mathematics as a male domain.

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.

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.

Preschool education is fundamental to shape children’s aptitudes and skills in early life. Ecuador is following a global education trend for starting-up mathematical thinking at earlier development ages, but this is only reflected in vehement curricular changes that are not supported properly. As a result, the safeguarding of a good children’s education appears to be lessened. This work aimed to evaluate the mathematics thinking practices in preschools of Pasaje city, Ecuador. The investigation employed a descriptive approach, hence data were collected from 65 teachers and 810 parents from public and private preschools by means of interviews and questionnaire in an attempt define some causes (teacher’s education, children’s socio-economical and family circumstances) that impair the initiation of the numerical, spatial and metric and geometric aptitudes in children. The results showed that not only preschool practices but also the home environment linked to socio-economic status appear to have positive or unfavorable influences on their children’s education.

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.