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 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.

Achieving the maximum efficiency in teaching a second language (L2) has always been an important issue for educators. Current globalization processes, development of international business relations, political integrations among the various countries throughout the world, and the abilities of latest information and communications technologies (ICT) dictate the more significance of knowledge of foreign languages. All living conditions should be constructed according to the mentioned surrounding changes during the ICT era. Correspondingly, teaching methodologies are also being adapted in order to teach people more efficiently. This paper studies how cellular phones (cell phones) can be used in learning English phrases. In order to examine the impact of cell phones on learning a language an experiment was run among the college and university students in Kazakhstan, supported by GSM Network of KCell (Kazakhstan). This paper discusses the experiment results, in which 126 college and university students participated, and makes some suggestions based on the experimental mobile learning. Study reveals that users could make noticeable improvements learning through their cell phones after the conducted experiment. Positive improvements were noticed on the results of general tests of English language those conducted among all participants of the research.

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 implementation of Lesson Study (LS) varies considerably across countries and institutions and is still in a phase of adaptation and experimentation. This article explains the result and the process of a school-based initiative endeavor to implement LS at a suburban elementary in Padang, Indonesia. The study involved 13 teachers, the principal and 6 classes of students. The data were collected through observation and interview. They were classified on the basis of three noticeable emerging themes- teacher collaboration, scaffolding, and reflection. The data were analyzed qualitatively. The results of data analysis reveal a promising improvement in these aspects. Implementing school- support LS increased by weaving the concept into practice helped teachers develop their professionalism gradually. It was obvious that the teachers felt more at ease to work collaboratively when they designed the lesson. This also affected their design which showed more meaningful learning activities and challenging tasks. Then, the teachers improved the way they scaffolded the pupils. The content of reflection and the way the results of reflection were conveyed became better. The principal’s support and the teachers’ strong willingness to elevate their quality apparently took an important role. In spite of that, there were some challenges in carrying out collaboration, providing appropriate scaffolding, and doing reflection. Changing the teachers’ common practice to LS apparently needs some adjustment and time.

The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we were interested in how sixth-grade primary school students solve non-contextual and contextual problems involving the same mathematical content (in the contextual problems this content still needs to be recognised, whereas in the non-contextual problems it is obvious). The main guideline in the research was to discover the relationship between mathematical knowledge, which is the starting point for solving problems from mathematical literacy (contextual problems), and mathematical literacy. The empirical study was based on the descriptive, causal and non-experimental methods of pedagogical research. We used both quantitative and qualitative research based on the grounded theory method to process the data gathered from how the participants solved the problems. The results were quantitatively analysed in order to compare the success at solving problems from different perspectives. Analysis of the students’ success in solving the contextual and non-contextual tasks, as well as the strategies used, showed that the relationship between mathematical knowledge and mathematical literacy is complex: in most cases, students solve non-contextual tasks more successfully; in solving contextual tasks, students can use completely different strategies from those used in solving non-contextual tasks; and students who recognise the mathematical content in contextual tasks and apply mathematical knowledge and procedures are more successful in solving such tasks. Our research opens up new issues that need to be considered when developing mathematical literacy competencies: which contexts to choose, how to empower students to identify mathematical content in contextual problems, and how to systematically ensure – including through projects such as NA-MA POTI – that changes to the mathematics curriculum are introduced thoughtfully, with regard to which appropriate teacher training is crucial.

This paper explores misconceptions and errors (M/Es) of eighth-grade students in Nepal with a quasi-experimental design with nonequivalent control and experimental groups. The treatment was implemented with teaching episodes based on different remedial strategies of addressing students' M/Es. Students of control groups were taught under conventional teaching-learning method, whereas experimental groups were treated with a guided method to treat with misconceptions and errors. The effectiveness of treatment was tested at the end of the intervention. The results showed that the new guided treatment approach was found to be significant to address students' M/Es. Consequently, the students of experimental groups made significant progress in dealing with M/Es in mathematical problem-solving at conceptual, procedural, and application levels.

This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and understanding the form of row echelon and reduced row echelon forms. In this study, subjects were three prospective mathematics teachers from Swadaya Gunung Jati University Cirebon who were taking matrix algebra courses. This study aims to reveal the conceptual understanding of prospective mathematics teachers in determining the solution to systems of linear equations. The results show that there are still prospective mathematics teachers who only use memory about the properties and procedures in determining whether a matrix is said to be a row echelon form or a reduced row echelon form. Then, there is still weakness in building the algorithms' relationship due to the immature knowledge of the concepts. Researchers found that many prospective mathematics teachers were more comfortable solving problems that were performed procedurally. Further research is needed to determine how the mental construction process and mathematical conceptual knowledge of prospective mathematics teachers are through meaningful learning so that conceptual understanding is maximized.

Science, technology, engineering and mathematics (STEM) education is regarded as one of the formulas to embracing many of our imminent challenges. STEM education benefits the learners by encouraging interest in STEM disciplines. This daunting task needs everyone’s concerted efforts in creating and innovating mathematics teachers’ classroom practices Therefore, a systematic review was conducted to identify best practices for STEM education following the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) by Moher et al. (2015). The reviewed articles were published from 2016 to 2020 and accessed using the Scopus and Web of Science (WoS) databases. Three themes for best practices were identified namely (a) core competencies encompassing 21st-century teaching skills; (b) instructional designs; and (c) requisite STEM execution. Results of PRISMA determined the dominant STEM practices were critical thinking, communication, collaboration, problem-solving, research-based pedagogy, problem-based learning and project-based learning, technological integration, accessibility, professional development and learning support, evidence of effectiveness, access to materials and practitioner support, and scalability. Mathematics teachers should determine the best STEM practices to employ even though there is a lack of studies on integrated STEM domains. When more students are interested in venturing and exploring into the field of STEM, the high demand for STEM related careers could be met by the younger generation.

The initial period of young teachers' careers is always significant in developing their professional capability. This is when teachers start coming into contact with practical teaching, which is more diversified than the theoretical training at the University. In this research, the authors propose a process of combining the Lesson Study model with the micro-lesson teaching method. This process helps young teachers, especially those working in the Northern of Vietnam, improve their planning and implementation of a lesson plan following the Lesson Study model. It has four steps: (1). Plan a Lesson Study; (2). Organize demo teaching and attend lessons; (3): Self-evaluate and discuss lessons; (4): Apply for practical teaching. The methodology research is carried out on 62 young teachers in Vietnam to measure the pre-impact and post-impact results. The results reveal that the researched group has made significant progress on their teaching performances (the average points for their capability of planning lessons have increased from 2.54 to 3.28 and the average points for their capability of implementing lesson plans have increased from 2.48 to 3.18). This development can be considered as an excellent experience to bring the Lesson Study model into Vietnamese schools to improve teaching sustainably.

This study aimed to determine the effect of cognitive and affective factors on the performance of prospective mathematics teachers. Cognitive factors include cognitive independence level and working memory capacity, while affective factor include math anxiety. Mathematical performance was then assessed as basic math skills, advanced math skills and problem-solving ability. This research combined quantitative and qualitative research methods. In order to determine the effects of cognitive independence, working memory capacity, and math anxiety on math performance, multiple regression tests were used. To then see the effects of these three factors on problem-solving ability, a qualitative approach was used. Eighty-seven prospective math teachers participated in this study. Based on the results of the multiple regression, it was found that the level of cognitive independence affects basic math skills but has no effect on advanced math skills. Working memory capacity was seen to positively affect math performance (basic and advanced math skills, problem-solving skills), while mathematics anxiety demonstrated negative effects on advanced math skills and problem-solving skills.

Mathematics anxiety in initial teacher education is a growing issue that reflects on teacher quality and their student’s maths anxiety and abilities. Previous studies have presented a range of different perspectives to mathematics anxiety. We aimed to explore further the reasons of mathematics anxiety in preservice teachers and suggest some intervention strategies in reducing maths anxiety for initial teacher education systems. We used a mixed methodology in this research analysing both qualitative data along with some quantified data derived from qualitative data sources. The findings provide insights to causes of maths and test anxiety along with some intervention strategies that teacher educators can use in their future teaching.

This research aims to determine second-year university students’ understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of 112 student teachers of primary teacher education program at two private universities in Indonesia were involved in this research. A qualitative method with a holistic type case study design was used in this research. The results indicate that a significant percentage of the participants could not correctly interpret and represent fractions. In terms of interpretation, it is found how language could obscure the misunderstanding of fractions. Then, the idea of a fraction as part of a whole is the most widely used in giving meaning to a fraction compared to the other four interpretations, but with limited understanding. Regarding data representation, many participants failed to provide a meaningful illustration showing the improper fraction and mix number compared to the proper fraction. Improvement of fraction teaching at universities - particularly in primary teacher education programs - is needed so that students get the opportunity to develop and improve their knowledge profoundly. We discuss implications for teaching fractions.

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The impact of structured steps that students need to take during the process of solving stoichiometric problems was explicitly analyzed. A total of 108 eighth-grade students participated in the study. Of the overall number of students, half of them were included in the experimental classes, whereas the other half were part of the control classes. Before and after the intervention, contextual problems were administered twice to all the student participants. The study results indicate that the students of the experimental classes exposed to structured steps in solving algebraic problems and the procedural transformations scored better results in solving problems in mathematics for chemistry compared to their peers who did not receive such instruction. Nevertheless, the result shows that although the intervention was carried out in mathematics classes, its effect was more significant on students' achievements in chemistry. The findings and their practical implications are discussed at the end of the study.

This qualitative study is part of a feasibility study conducted by State University of Malang (SUM), Indonesia, to determine stakeholder needs for a study program specializing in managing bilingual education. The study participants included one SUM lecturer who held a managerial position in the division of SUM laboratory schools and twelve teachers/leaders of bilingual schools in some cities in East Java and South Sulawesi. Data were collected using an online questionnaire and in-depth interviews with two selected participants. The results indicate issues related to teachers' English competencies, materials development, and integrating an internationally-oriented curriculum into the national curriculum. Teachers' low English competencies prevented them from conducting teaching and learning bilingually and developing instructional materials in appropriate English. In addition, the combination of national and international curricula was identified as the biggest challenge for bilingual schools. The teachers/leaders were never trained to manage the bilingual program. They learned based on their experiences, and it took years to figure out how to manage bilingual programs successfully. Therefore, the establishment of a new program of study is needed.

This study presented the effect of interactive mathematics (IM) software assisted-teaching on primary three learners' conceptual understanding and performance. The cognitive theory of multimedia learning (CTML) supported the quasi-experimental design of this study drawing on IM software features that fit a multimedia tool for effective learning. This study used a sample of 138 lower primary learners. Learners’ test scores and examples of their work provided data to be analyzed. Learners' conceptual understanding was measured using the percentage of learners who performed a particular item and analyzed using sample learners' work while the overall performance was measured using the mean class scores. From the data analysis, IM-assisted teaching influenced conceptual understanding and performance based on a .05 p-value, the effect size of significance, and learning gains. The analysis of learners’ workings revealed different errors in addition, subtraction, division, and multiplication, which were remarkably reduced in the post-test by IM-supported teaching. This evidenced conceptual understanding development by IM-supported teaching. The study suggested the integration of IM in the Rwandan Competence-Based curriculum and its use as an instructional tool in teaching and learning mathematics at the primary level. Besides, it was recommended that Rwanda Education Board support teachers in developing basic computer skills to effectively create and monitor a multimedia learning environment for effective learning. Furthermore, further similar research would improve the literature about interactive technologies in supporting quality mathematics delivery and outcomes.

Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM.