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.

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 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 aim of this study was to explore the degree to which a professional development (PD) program designed using GeoGebra influences a group of Turkish middle school teachers’ beliefs in relation to mathematics and role of GeoGebra in mathematics education. In order to collect the required data, the PD course was established to provide six teachers with an opportunity to obtain practical experiences with and necessary knowledge about the use of GeoGebra in mathematics education. In this context, a multiple case study approach was utilized, in which mathematics teachers were observed and interviewed using a variety of procedures to expose qualitative data about their beliefs and the dynamics of their beliefs changes during the course. The main findings illustrated that teachers’ beliefs were transformed to some extent in favour of the use of GeoGebra, as well as using constructivist ideas in their mathematics teaching and learning can be attained through the GeoGebra based PD course. In fact, the relationship amongst stated beliefs and intended teaching practice is complex and the social issues were very influential on teachers’ pedagogical decisions. This research also introduces some suggestions for researchers who focus on professional development of mathematics teachers relative to their beliefs..

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.

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 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.

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.

Achieving educational goals is based on the skills and competence of teachers; therefore, professional development of teachers is important to policy and decision-makers. Worldwide, the percentage of teachers who leave the profession within their first years of teaching is high therefore, professional support is essential to ease on their integration. Previous research indicates a positive and significant correlation between teachers' self-efficacy and their attitudes toward the teaching profession. Our study included three hypotheses: 1) teachers' pedagogical applications serve as mediators for the relationship between teachers' self-efficacy and their attitudes toward the profession; 2) participating in a professional development school (PDS) training program interacts with teachers' self-efficacy in predicting their attitudes toward the profession; and, 3) participation in a PDS training program will positively affect the two variables. A close and open-ended questionnaire was replied by 300 novice teachers, some of whom participated in the PDS program and others who did not. Findings indicate that the relationship between teachers' sense of self-efficacy and their attitudes towards the teaching profession was partially mediated by: applying constructivist pedagogical practices; matching to differences between learners; collaboration between fellow teachers; accountability; planning and teaching management; and academy-community relationships. Participation in a PDS program was not found as a moderator variable for this relationship, but novice teachers who participated in this program had a significant higher sense of self-efficacy and more positive attitudes towards the teaching profession. Findings are important for designing novice teacher training programs with an emphasis on the implementation of specific pedagogical practices.

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.

The identification of students’ mental models is crucial in understanding their knowledge of scientific concepts. This research aimed to develop a Mental Models Representation Instrument on Newton's Laws (MeMoRI-NL). The ADDIE (Analyzing, Designing, Developing, Implementing and Evaluating) model was used as a research method. The sample consisted of 30 students of 15-16 years-old at one of senior high school in Tatar Pasundan. The data was examined using Rasch analysis on validity, reliability, level of difficulty, and distributions of students’ mental models. Students’ mental models were classified as Scientific (SC), Synthetic (SY), Synthetic almost Misconception (SYM), and Initial (IN) model. Based on the evaluating stage, students’ mental models are mostly in the SYM and IN model. Consequently, it can be concluded that the Mental Models Representation Instrument on Newton's Laws (MeMoRI-NL) can be developed using the ADDIE model and most of the students' mental model has not been following scientific knowledge. Based on this research, teachers or educators should enhance students' mental models, especially for female students.

This research aims to test (1) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on written mathematical communication skills, (2) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills, (3) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on the written mathematical communication skills from each cognitive style, and (4) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills from each learning model. This quantitative research employed a quasi-experimental method. The research sample consisted of 240 fifth-grade elementary school students in Jebres District, Surakarta, Indonesia. Data collection techniques included tests of written mathematical communication skills and cognitive styles. The data were analyzed using prerequisite (normality, homogeneity, and balance), hypothesis, and multiple-comparison tests. The findings prove that (1) PP model with Indonesian realistic mathematical education approach is more effective than the PP and direct instruction models, (2) field-independent cognitive style is better than field dependent, (3) PP with Indonesian realistic mathematical education is as effective as the PP model, but more effective than the direct instruction model, and the PP model is more effective than the direct instruction model in each cognitive style, and (4) in the PP learning model with Indonesian realistic mathematical education approach, field-independent cognitive style is same skill as with field-dependent, but field-independent is better than field-dependent cognitive style in the PP and direct instruction learning models.

Covid-19 has accelerated the speed of technocratic transformation in teaching and learning. Previous researches on whether technology enhances students’ motivation towards learning or burdens them with additional layer of anxiety in learning the nitty gritty of technology itself have mixed results. The purpose of this study was to explore early undergraduate students’ beliefs about learning mathematics with technology. These research participants were first-year female undergraduate students in a public university in the United Arab Emirates (UAE). The study comprised of phase one with qualitative task-based interviews with four female first-year undergraduate students. Phase two included a quantitative belief survey with a sample of 62 students from the same institution. I constructed four major belief categories from the iterative process of interview data analysis– technology for computing and graphing, technology for speed and accuracy, technology for a short-cut but not for meaning, and affective aspects of beliefs. The quantitative survey result demonstrated that a majority of participants (about 75.8%) were found to be using some kinds of technological tools while learning mathematics. About 90% of them reported using a calculator while learning mathematics. A majority of participants (54.9%) believed that technology helps them in learning mathematics, and about 50% of them also believed that the use of technology improves their learning of mathematics.

Descriptive correlational research was conducted to discover misconceptions on Rate of Reaction (RR) that impact on Chemical Equilibrium (CE) misconceptions. This research was conducted to 245 eleventh-grade students of High School in Gowa, South Sulawesi, Indonesia, that have been studied the RR and CE topics. Misconceptions data were collected using three-tier tests and semi-structured interviews. The data were analyzed using descriptive and correlational analysis. Description of RR misconceptions that impact on CE misconceptions are determined with the percentage of students who consistently experience misconceptions about RR and CE. There were six misconceptions in RR that have an impact on CE, which are: Misconceptions related to changes in the reaction rate with time; The effect of temperature on the rate of reaction; The effect of adding catalysts to the activation energy; and the mathematical affect relating to the rate of reaction and number of moles. Misconceptions in RR and CE have 0.39 correlation coefficient, based on Spearman's formula. These results indicate that the impact of misconception in RR on CE is moderate. This study suggests that education practitioners should eliminate the misconception of prerequisite concepts before teaching the next related concepts.

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.

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.