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.

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.

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.

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 research was conducted to determine the opinions of students (10-11 years) on their engagement to mathematics course. These students are 5th grade students at a secondary school in Turkey. Qualitative research method was used in the research. At the study, designed as case study, a total of seven secondary school students were participated the research. The study group was constituted with “snowball sampling” technique of purposeful sampling methods. The data was collected by a semi-structured interview form. Sixteen-page interviews obtained from the interviews were transferred to the computer. Data analysis was performed in content analysis. Codes were listed as a result of analysis. Common themes were constituted from the codes. As a result of the research, three themes, (cognitive, social and emotional engagement) eleven sub-themes and eighty nine codes were determined. It was seen that the students’ most preferred superficial strategies in terms of cognitive engagement; negative opinions towards group work in terms of social engagement; value given to math course in terms of emotional engagement. Students preferred least getting support sub-theme in terms of cognitive engagement; competitive sub-theme in terms of social engagement; value to the mathematics teacher sub-theme in terms of emotional engagement.

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.

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.

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.

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.

This study aims to determine the impact of the ECIRR(Elicit, Confront, Identify, Resolve, Reinforce) learning model on students' mathematical reasoning abilities in terms of student motivation. The research method used was a quasy-experimental method with a post-test only control design research design. The population of this study was all students in five classes XII Private School. The Samples were taken at class XII AP-2 and XII MM-1 as the experimental class, and class XII AP-1 and XII MM-2 as the control class. The data analysis technique used is hypothesis testing using ANAVA 2 paths. Based on the research results obtained that (a) There is an influence of the ECIRR (Elicit, Confront, Identify, Resolve, Reinforce) learning model on mathematical reasoning abilities. (b) There is an influence of student learning motivation on mathematical reasoning abilities. (c) There is no interaction between the treatment of learning models and categories of students' learning motivation towards mathematical reasoning abilities. So as a whole it can be concluded that the ECIRR (Elicit, Confront, Identify, Resolve, Reinforce) learning model influences the ability of mathematical reasoning and can increase students' learning motivation.

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.

Problem-solving and mathematical communication are essential skills needed by students in learning mathematics. However, empirical evidence reports that students’ skills are less satisfying. Thus, this study aims to improve students’ problem-solving and mathematical communication skills using a Metacognitive-Based Contextual Learning (MBCL) model. A quasi-experimental non-equivalent control group design was used in this study. The participants were 204 fifth-grade students; consisting of experimental (n = 102) and control (n = 102) groups selected using convenience sampling. This study was conducted in four Indonesian elementary schools in the first semester of the academic year 2019/2020. The Problem-Solving Skills Test (PSST) and Mathematical Communication Skills Test (MCST) were used as pre- and post-tests. In order to analyze the data, one-way ANOVA was used at the 0.05 significance level. The results showed that students in the experimental group had higher post-test scores than the control group in terms of problem-solving and mathematical communication skills. It can be concluded that the MBCL effectively promotes fifth-grade students’ problem-solving and mathematical communication skills. Therefore, it is suggested that MBCL should be used more frequently in primary school mathematics to further improve students’ problem-solving and mathematical communication skills.

The purposes of the current study were to develop students' spatial orientation skills using Virtual Mathematics Kits (VMK) and to evaluate VMK as a form of digital media in terms of spatial orientation. This study involved 42 lower-class and 47 higher-class elementary school students as the intervention group and 36 lower-class and 41 higher-class students as the control group. The intervention group was administered spatial orientation activities for 10 weeks. These activities were performed using a VMK to facilitate solving spatial problems. In the end of activities, spatial orientation instruments administered to compare spatial orientation ability on each group. The findings of this study, spatial orientation activities using a VMK improved students' spatial orientation skills. More specific, VMK provides more significant effect on higher-class students. Finally, VMK allows students to explore many ideas and perspectives to solve various spatial problems. VMK can be used as a digital media that helps students to develop spatial reasoning.

The aim of this study was to identify and classify the student’s concept image and its influence on the reasoning of the problem-solving of the derivative. The research used a qualitative description approach and used eight research subjects. From the answers collected upon the given problems, we obtained several variations of students’ concept images, thus it showed how students’ concept image influenced the reasoning. In order to clarify and classify the characteristic of the obtained answers, we summarized there were three categories of the concept image of the derivative, namely symbolically related to a basic formula of the derivative of a function, limit of the ratio of difference value of the functions, and the properties of the derivative of the functions. Furthermore, our study suggested that each student’s concept image affecting the reasoning of the derivative. In addition, we found some misperceptions in answering the problem and misconception in the use of the basic formula of the derivative of the functions among the students’ answers.