This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of student-teacher relationship for a student centered instruction. Analysis over the video made teachers notice points and came to realize the thoughts of students; they had otherwise missed at the classroom. They achieved improvements regarding the awareness of the need to identify the cases presenting the most difficulty to the students in terms of teaching, and the necessity to take precautions regarding such points, to learn about the reason of the difficulty, and to pay attention to the statements by the students. Therefore, it is possible to note that the teachers improved themselves in terms of student’ knowledge with respect to the mathematical knowledge for teaching.

Measuring the quality of the ‘product’ is elemental in education, and most studies depend on observational data about student achievement factors, focusing overwhelmingly on quantitative data namely achievement scores, school data like attendance, facilities, expenditure class size etc. But there is little evidence of learner perceptions. 553 students from two different universities, who graduated from 3 high school types, were asked to respond to two fundamental questions to reflect on school and classroom level achievement factors. 2294 responses produced eight categories in question one, teacher factors being the most preferred (n=424), followed by individual factors (n=404) and then family factors (n=395). As for liking towards a course, 1362 responses were produced, most frequent one being teacher’s attitude (n=205). Results indicate student perspective of causes of achievement is somewhat different from those expressed in quantitative studies. Girls attributed more achievement to study habits, family support whereas boys attributed more to school and technology. More emphasis is needed on perceived achievement factors for a sound evaluation of effectiveness in school.

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.

Schools and teacher induction programs around the world routinely assess teaching best practice to inform accreditation, tenure/promotion, and professional development decisions. Routine assessment is also necessary to ensure that teachers entering the profession get the assistance they need to develop and succeed. We introduce the Item-Level Assessment of Teaching practice (I-LAST) as a flexible framework-based approach for quantitative evaluation of teaching best practice in the induction stages. We based the I-LAST on a novel framework for teaching best practice, and used Fuller’s scale as a framework for understanding the potential of the I-LAST in providing longitudinal measures for growth. Using the context of a year-long teacher induction program in the Midwestern United States, we collected data through an online survey from 46 teaching supervisors who were asked to evaluate their interns. We used the Rasch partial credit model as a criterion for construct validity, and measured dimensionality and reliability from both Rasch and classical frameworks. The I-LAST was found to be a unidimensional, valid, and reliable measure for teaching best practice. It demonstrated the ability to provide reliable scores for specific sub-dimensions of best practice, including those which manifest at various stages along Fuller’s scale. Potential uses of the I-LAST to advance understanding of the role of teacher induction programs in fostering productive growth in new teachers is discussed.

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.

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.

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.

Within the scope of restructuring the secondary education efforts of the Ministry of National Education, it has been decided to abrogate the secondary school level teachers' schools. The purpose of this study is to evaluate Turkey's teacher education practices and the quest for qualified teacher education through the perceptions of the graduates of these high schools. The study is a phenomenological research based on interpretation. Data were obtained through interviews. The data obtained were analyzed in the vetting of candidate teachers, the curriculum to be used in the education process and its accreditation, and whom to be certified as teachers. The main results of this study, conducted with participants from the secondary school level teachers schools’ graduates, show that, in terms of teacher education, teachers' high schools present various opportunities by enrolling successful candidates, educating them as leaders, preparing them for multi-cultural environments. In order to educate qualified teachers, the participants suggest teacher education programs should include individual and group activities, involve training, arts, basic science, and values education courses. In the selection and approval of tenure teacher, besides academic achievement and diploma, advanced communication skills, patience, confidence, and patriotism should be sought in the candidates.

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 researcher investigated the mathematics learning styles of vocational college students during fall 2017 and spring 2018. 94 students enrolled in the vocational college of a public university completed the questionnaire "How Do I Actually Learn?" developed by Forster. Scale has four learning styles: reflective, inquisitive, diligent and user. The results of the research revealed that the most preferred learning model was user learning style in mathematics learning. Most of the students preferred to learn mathematics by writing the solutions, and reading through their notes or work. There were also statistically significant differences in mathematics learning styles among students according to their academic achievement. According to the results, students with high level of success were more inquisitive than students with low levels.

Technology is an indispensable part of the educational curriculum, and large budgets have been allocated to provide technological infrastructure in secondary education institutions in Turkey. It is important that teachers have the technological pedagogical content knowledge (TPCK) to successfully integrate technology into their courses. The aim of this study is to examine the development of the TPCK of a mathematics teacher who participated in in-service training course organized for the use of Geogebra software in geometry teaching. The in-service training is designed in accordance with the Technology Integration Model stages, and Geogebra software is used taking into account the learning outcomes of 9th and 10th grade secondary school geometry. The case study method has been employed, and data was collected through interviews, observation, self-assessment forms, and field notes. The findings show that the in-service training helped the maths teacher integrate technology in the teaching and developed the knowledge of curriculum, students’ understandings and learnings, and instructional strategies and methods. With regard to research recommendations and results, professional development programs that will provide TPCK development can be organized so that teachers can use the ever-evolving technologies in their classes along with the appropriate pedagogical approaches.

In this study, it is aimed to examine the mathematical conceptual skills of 48-72-month-old children attending pre-school education institutions providing a Montessori Approach and Ministry of National Education Pre-school Program (MoNE PSP). The study group consisted of 20 children, who were trained by the Montessori Approach, and 20 children, who continued to attend pre-school education institutions applying the MoNE PSP. The research was carried out in accordance with the state study design of the qualitative research methods, and the data of the study was collected by the structured observation method at the free play/individual work time in the learning centers of the children constituting the study group. A structured observation form was used as the data gathering tool, and mathematical concept skills such as counting, matching, grouping, comparison, positioning, measurement, pattern, part-whole, transactions and creating a graphic were included.  Research data were analyzed with descriptive analysis method, and the frequency and percentage values of the obtained data were calculated. As a result of the study, it was observed that the students trained with the Montessori Approach and MoNE PSP could not create graphics in both groups, while the rhythmic counting and patterning skills were the most observed skills in children. It has been determined that children trained with the Montessori Approach perform more studies, especially on matching, grouping, comparison/ranking, and part-whole skills, compared to the children trained with MoNE PSP. In the light of the results obtained in this research, it is suggested that the play materials that had to be in classes where MoNE PSP was applied should be standardized, and children should be able to get through these materials; also mathematics center should be established in the class level.

A variety of teacher training system was implemented in Turkey until today. One of these systems is pedagogical formation training. The aim of this study was to determine the strengths and weaknesses of the pedagogical formation training according to the opinions of pre-service teachers and the experiences during the pedagogical formation training, to gather information about whether these experiences contributed to their teaching, and to evaluate the place of the pedagogical formation training in teacher employment in the light of this information. The research was carried out using an interview technique of qualitative analysis methods. The study group comprised of 20 pre-service teachers from different undergraduate programs, and they participated in a 14-weekinternship program at a high school in Ankara during the 2017-2018 academic year as a requirement for a training course.  Content analysis method was used for data analysis. As a result of the research, the pre-service teachers stated that they found the internship training in practice schools as useful for future teaching lives, but they did not find the theoretical training given in the classes useful for various reasons. They considered that there are some weak points of the program: the duration of the formation course is short, lessons are late in the evening, classes are crowded, and the teaching staff have negative effects on the students: they are indifferent, and there are almost the same topics in each lesson. This means that they were mostly not satisfied with its overall quality, and so its operability was enough. Like some of the suggestions, it is recommended that duration of the program should be extended to a long period, and the instructors should be selected from those who can give energy to the class, have communication skills, can create discipline in the classroom, and have experience in traditional classroom teaching.

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.

This descriptive and correlational study investigated the effects of using PSPP in learning Statistics on students’ attitudes and performance. The respondents of the study were 200 Grade 11 Senior High School students who were enrolled in Probability and Statistics subject during the Second Semester of School Year 2018-2019. The respondents were randomly selected from those classes across the different academic strands that used PSPP in their Probability and Statistics subject through stratified random sampling. The results revealed that the students have favorable attitudes towards learning Statistics with the use of the PSPP software.  The students became more interested and engaged in their learning of statistics which resulted to an improved academic performance.

This study aimed to describe seven indicators of students’ verbal linguistic intelligence in reading subject. It used a qualitative research method. The subjects of this study were 30 students consisted of 9 male and 21 female students. They took the reading subject in the second semester of the first year. They were given a test of verbal-linguistic intelligence. Seven students were selected to be interviewed because they have verbal-linguistic intelligence and good communication. To find out the validity of the data, the researchers used triangulation of the test results and the results of interviews and triangulation of the second researcher and research assistants. Furthermore, the data were analyzed using the content analysis method which consisted of three steps, they were data reduction, data presentation, and conclusion drawing/verification. The results of the study show that there were seven indicators of verbal-linguistic intelligence of students in reading subject, first, having excellent initial knowledge in mentioning words, second, enjoying wordplay with Scrabble, third, entertaining themselves and other students by playing tongue twisters, fourth, explaining the meaning of the words written and discussed, fifth, having difficulties in mathematics lesson, sixth, their conversation refers to something they have read and heard, and the last, having the ability to write poetry based on personal experience.

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.