The main purpose of this study is to determine the amount of time-dependent learning of "solving problems that require establishing of single variable equations of the first order" of the seventh grade students. The study, adopting the screening model, consisted of a total of 84 students, including 42 female and 42 male students at the seventh grade. Data was collected using an assessment tool consisting of 10 open-ended questions. The findings show that the learning group of 84 students were behind the value closest to the full learning level by a score of 0.013. While the female students reached the lower limit of 0.987 specified for the full learning level in a period of 3.2 course hours, the male students reached this limit in 4.0 course hours. The learning amount of 0.999, which is the closest value to the full learning level, was reached by the learning group in a period of 9.7 course hours, the female students in 8.5 course hours, and the male students in 11.3 course hours. In addition to this, the data obtained showed that learning difficulties among to the learning groups decreased as the space below the curve of time and learning amount decreased. As a result of the study, it was recommended that it is possible to determine the closest course periods for the full learning level for each of the gains found in all levels of education and all teaching programmes, which define certain learning outcomes within a certain time.

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.

Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was explored along with a survey of areas of difficulty and student attitudes. This involved looking at student perceptions of their experiences, the nature of the difficulties they have with mathematics and possible reasons for these difficulties. The overall aim is to explore the extent of the effect of working memory and to gain insights so that practical ways forward to enhance mathematics education can be identified. It was found that limited working memory capacity has a very strong influence on performance, confirming other studies. Indeed, if the cognitive load exceeds the capacity of working memory, understanding becomes a casualty, with consequent attitude deterioration. Students need to be able to see that mathematics has a purpose in being able to be applied to real-life situations. However, attempts to develop applications may often generate further working memory overload. Curricula devised by those outside the classroom can sometimes be inappropriate while topics causing the greatest problems at these ages and include areas of geometry, statistics and the applications of mathematics.

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 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.

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.

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 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.

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these problems and the groups’ reflective diaries regarding their problem posing and solution processes. The data were analyzed by using content analysis and the codes were constructed according to the problems’ contents. The participants' diaries were examined in terms of generated codes and the expressions supporting/relating the codes were determined. While designing the problems, the participants considered the factors such as being interesting, understandable, appropriateness to real life and modelling process, model construction, and usability of different mathematical concepts. Their solutions were generally handled in terms of usage of the mathematical statements, appropriateness to the modelling process and being meaningful for real life. Modelling training should be provided to enable the student teachers to develop modelling problems and their designs should be examined and the feedbacks should be given.

Currently, it is taken for granted that teachers have to take into account the conceptions in order to achieve some efficient learning, the latter are generally resistant and may hinder the learning. Studies have shown that learning amounts to make conceptions evolve which play a determining role in the appropriation of scientific concepts such as neurotransmission, which is the subject of our study. This concept is present in the Life Science syllabus as early as high school. The aim of this study is to assess the impact of an interactive approach on the evolution of students' conceptions of neurotransmission. For this purpose, a questionnaire was administered to the first two years’ students (second year) in the Life Sciences stream at Dhar El Mahraz Faculty of Science in Fez during the academic year 2016-2017. This questionnaire was in the form of a pre-test and a post-test on learning/teaching of neurotransmission. The results of the study showed that the approach which was adopted had a positive effect on the evolution of the students' conceptions of neurotransmission in that it apparently contributed to a conceptual change for them.

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.

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.

Environmental learning in the 21st century must be contextual and require the ability of Higher Order Thinking Skills (HOTS) to solve environmental problems such as green consumerism. The purpose of this study was to implement an Android-based Supplementary Book of Green Consumerism (SBGC) to improve students' HOTS abilities in environmental learning. The method used experiment with a sample of 144 students in 8th grade of Junior High School. Students divided into 72 students in control classes and 72 students in experimental classes. The treatment given was in the form of using SBGC in the experimental classes. The results showed that the students HOTS score increased significantly in the pre-post test in the experimental class or when compared to the control class. Increased in the experimental classes from a score 15.7 (very low) to 32.73 (low). Meanwhile, when compared between the experimental classes with a score 32.73 (low) and control classes with a score 25.25 (very low). This showed that SBGC is easy to understand. SBGC is also interesting so that makes students become active in learning. The conclusion of this study was that SBGC can increased students' HOTS in environmental learning.

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.

Mathematics is one of the most challenging subjects for many students. A similar problem is faced by special needs students, such as students with Autism Spectrum Disorder (ASD). Various instructional strategies are implemented by specialists to help ASD students understand mathematics in schools. To explore the impacts of an instructional strategy of mathematics on ASD students, the authors conducted a review of literature from 2011 to 2017 using various databases including ProQuest Digital Dissertations and Theses Full Text, Google Scholar, and Science Direct. A total of 39 articles were found. Most of the instructional strategy aimed to assist ASD students in solving mathematics problems. The implications of the study are also discussed in this literature review, which indicates that teachers need to use the appropriate instructional strategy to meet the needs of students with ASD and maximize their mathematics learning outcomes in schools.

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.

Learning models that can improve critical thinking, skills collaborate, communicate, and creative thinking are needed in the 21st-century education era. Critical and creative thinking are the two essential competencies of the four skills required in the 21st century. However, both are still difficult to achieve well by students due to a lack of thinking skills during mathematics learning. This study was conducted to determine the model of learning that is appropriate to develop students' critical and creative thinking skills. The study used three-class samples from eighth grade. The first class is given the problem-posing lesson; the second class is given contextual learning and third class as a control class. The results of the study indicate that improving students' critical and creative thinking skills are included in the moderate category for types using contextual learning and problem-posing. Also, it is found that contextual learning is more effective for improving critical thinking skills when compared with learning problem posing and expository learning. Meanwhile, learning problem posing is more useful to enhance creative thinking skills compared with contextual and expository learning.