Lesson starts are transitional events which may cause management problems for teachers This study sought junior secondary school mathematics teachers’ beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior secondary schools in the Tutume Sub-district in Central Educational Region was selected through a purposive random sampling procedure. A questionnaire comprising both closed and open ended questions was designed to collect data then the analysis of results was carried out using descriptive and inferential statistics. As an illustration, a t-test was used to test for differences in teachers’ beliefs by gender while a one-way ANOVA was used to test for difference in their beliefs by experience. The study revealed that most of the teachers expressed their lack of confidence and were incompetent with the use of a calculator in their teaching with female teachers feeling less confident to explain different functions of a calculator than their male counterparts. In addition, the study showed that most of the teachers believed that a calculator was a technological tool that could be useful to the students in the future. On the contrary, most teachers felt that the overuse of calculators by the students could hamper the development of basic computational skills. Therefore, it was recommended that school based training on calculator use should be provided so as to empower teachers with the necessary technological skills for effective classroom instruction. The study findings have implications to research and practice as it provides unique and comprehensive data that will lead to insight for curriculum designers, policy implementers and instructional leaders on effective calculator use in math instruction.

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.

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.

This study aims to design mathematical literacy instruments that have evidence of content and construct validity and are reliable for use as an Assessment for Learning. The research involved eight experts as instrument validators and 273 eighth-grade students of junior high school in Yogyakarta Province. The results showed that the ten mathematical literacy items developed had the V Aiken coefficient index calculated from 0.781 to 0.906 (> 0.75). The results of adequacy testing of samples with KMO and Bartlett show Chi-Square in the Bartlett test of 608,608, the p-value <0.05 and KMO value of 0.781 (> 0.5). The results of testing of the measurement model with Confirmatory Factor Analysis (CFA) produce a Root Mean Square Error of Approach (RMSEA) value of 0.049 (≤ 0.08), chi-s Square of 33.92 (<2df), the p-value of 0.05004 (≥ 0.05). Nine out of the ten items developed had t-value> 1.96, Standardized Loading Factor (SLF) was greater than the critical limit (> 0.3), and Construct Reliability (CR) of 0.78 (> 0.7). It can be concluded that the developed mathematical literacy instrument can measure what must be measured and nine items significantly reflect the construct or latent variable, as well as the level of consistency of a good score.

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.

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.

This study aims to analyze students’ creative thinking skills in answering the problem-solving questions. This study employs qualitative design, involving 110 fifth graders in Malang Municipality and Regency as the subjects. The obtained data were analyzed using the descriptive-explorative approach. The findings reveal that the high-achievers in Mathematics showed good skills in the aspects of fluency and flexibility, but were still struggling in the novelty aspect.  The average-achievers showed good skills in flexibility aspects but were lacking in the fluency and novelty aspects. They showed an understanding of Mathematics problems but found it difficult to decide the solving strategies, and thus their answers were lacking in structure and less systematic. When solving a problem, the calculation made seemed rushing, was less careful, and frequented with trial and error strategy. The low-achievers showed difficulties in understanding the problems. Their answers were not systematic, not well-structured, and not detailed. This indicates that the low-achievers had not shown creative thinking skills in fluency, flexibility, and novelty aspects.

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.

The present study aimed to investigate the relationship between students’ academic motivation, implicit beliefs about intelligence and learning strategies among undergraduate healthcare students. First-year students of healthcare degree courses from a university in Southern Italy were surveyed. The study measured psychological constructs by means of Academic Motivation Scale, Motivated Strategies for Learning Questionnaire, and Dweck’s implicit questions about beliefs of intelligence. Two regression models were computed to assess the association between students’ beliefs about intelligence, motivations for studying, and learning strategies. In the first regression model, predicting students’ use of cognitive strategies from implicit intelligence beliefs and motivations for studying, stronger autonomous motivations were significant predictors of cognitive strategies. The second regression model, predicting students’ use of metacognitive strategies from implicit intelligence beliefs and motivations for studying, was not significant. These findings can be useful to plan tailored educational interventions to promote students’ motivation, incremental beliefs about intelligence and their use of learning strategies positively related with academic performance.

Problem-solving is considered one of the thinking skills that must be possessed in 21^st-century education because problem-solving skills are required to solve all problems that arise. The problem-solving stages that can be used are Polya's four steps, namely, understanding the problem, devising a plan, carrying out the plan, and looking back. Problem-solving skills are essential for solving word problems. Word problems based on arithmetic operations are divided into three types: one-step, two-step, and multistep. This qualitative research aimed to see problem-solving skills viewed from the type of word questions and elementary school students’ third, fourth, and fifth grades. A purposive sampling technique with 22 third-grade students, 28 fourth-grade students, and 21 fifth-grade students was used. The data were collected using documentation, testing, and interview methods. The findings of the study showed that fourth-grade students’ problem-solving skills are better than those of third-grade students, and the problem-solving skills of fifth-grade students are better than those of fourth-grade students. The percentage of Polya's steps always decreases because not all students master problem-solving. Based on the types of questions, the percentage of the one-step word problem is better than that of the two-step while the percentage of the two-step word problems is higher than that of the multistep.

Several concerted movements toward mathematical modeling have been seen in the last decade, reflecting the growing global relationship between the role of mathematics in the context of modern science, technology and real life. The literature has mainly covered the theoretical basis of research questions in mathematical modeling and the use of effective research methods in the studies. Driven by the Realistic Mathematics Education (RME) theory and empirical evidence on metacognition and modeling competency, this research aimed at exploring the interrelationships between metacognition and mathematical modeling and academic year level as a moderator via the SEM approach. This study involved 538 students as participants. From this sample, 133 students (24.7%) were from the first academic year, 223 (41.4%) were from the second and 182 (33.8%) were from the third. A correlational research design was employed to answer the research question. Cluster random sampling was used to gather the sample. We employed structural equation modeling (SEM) to test the hypothesized moderation employing IBM SPSS Amos version 18. Our findings confirmed the direct correlation between metacognition and mathematical modeling was statistically significant. Academic year level as a partial moderator significantly moderates the interrelationships between the metacognitive strategies and mathematical modeling competency. The effect of metacognition on mathematical modeling competency was more pronounced in the year two group compared to the year one and three groups.

Realistic Mathematics Education (RME) has gained popularity worldwide to teach mathematics using real-world problems. This study investigates the effectiveness of elliptic topics taught to 10th graders in a Vietnamese high school and students' attitudes toward learning. The RME model was used to guide 45 students in an experimental class, while the conventional model was applied to instruct 42 students in the control class. Data collection methods included observation, pre-test, post-test, and a student opinion survey. The experimental results confirm the test results, and the experimental class's learning outcomes were significantly higher than that of the control class's students. Besides, student participation in learning activities and attitudes toward learning were significantly higher in the RME model class than in the control class. Students will construct their mathematical knowledge based on real-life situations. The organization of teaching according to RME is not only a new method of teaching but innovation in thinking about teaching mathematics.

Mathematics anxiety has always been an interesting topic to study and discuss in the world of education. This study aimed to (1) investigate the impact of teacher roles, mathematics content, and mathematics anxiety on learning motivation, and (2) explore how students manage mathematics anxiety as a stimulus in learning motivation. This research used mixed methods with embedded concurrent design. The research sample was 100 respondents. The questionnaire instrument was arranged based on a Likert scale with 5 answer choices. This study used a structural equation model and confirmatory factor analysis as data analysis methods. The research findings indicated that: (1) a significant direct impact emerged between mathematics anxiety and students' learning motivation, and there was an indirect impact between the teacher's role and mathematics content on learning motivation; (2) students could manage mathematics anxiety when they were in optimal anxiety or positive anxiety so that they could overcome mathematics anxiety as a stimulus for achievement and deconstruct anxiety into motivation according to experience and personal resources. Results of this study confirmed that the statements about mathematics anxiety which always has a negative impact on motivation and learning achievement is not universal, because mathematics anxiety does not always have a negative impact on motivation and learning achievement if this anxiety is managed effectively.

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.

The main objective of this research was to study the effects of instructional management models and nominal variables on the development of students’ creative thinking. The researchers used the research synthesis of 400 studies on the development of students' creative thinking by a meta-analysis of research according to Cohen. The meta-analysis results revealed that the average effect size of the instructional management model (d = 3.43; [3.10, 3.17]) was positive and had a very high effect size with statistical significance. The most significant influence on the creative thinking development model was creative development theory (d = 4.217; [3.32, 5.11]). In addition, effect sizes varied with the attribute variables of the research, particularly the attribute variable of the research on instruction with the highest effect consisted of research with the focus on language, at the primary level, applied Torrance's creativity theory, designed between one to six lesson plans. Moreover, there was less than one hour per plan, the instructional period including the experiment conducted more than 31 hours and there were four weeks of instruction. In addition, there were six steps for instruction, there had quiz as an assessment tool, number of exams varied between 30 and 39 questions, and knowledge sheets were used as instructional materials. In the context of the meta-analysis, the findings indicated that the teachers should apply creative development theory in developing the students’ creative thinking for more effective instructional management.

This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.

Digital puzzle worksheet (DPW) is innovative teaching material designed using open-source software such as Canva and Liveworksheets. Subsequently, puzzle games in the form of questions can improve problem-solving skills by engaging in metacognitive processes. This research used a case study method to describe the impact of applying the DPW to identify the metacognition levels of students through the assignment of contextual maths problems. The source of informants was third-grade elementary school students in West Java, Indonesia. Test instruments, observation sheets, and interviews were used, while data analysis adopted an iterative model. Furthermore, the method and time triangulation increased confidence in the resulting conclusions. The results showed that male students were at the metacognitive level of ‘strategic use’ and ‘aware use’ for females, based on the characteristics of the observed metacognitive level. The most prominent feature was identifying and determining problem-solving strategies with metacognitive awareness. The reaction of students to the DPW improved problem-solving abilities, expanded conceptual understanding, and enhanced digital technology competence. Therefore, this experience was applied when solving contextual mathematical problem assignments.

The peer tutoring approach is a student-cantered teaching method in which students learn in pairs with teacher supervision. The study discussed in this paper is a systematic literature review related to the effectiveness of peer tutoring approaches which has been published within the last 5 years. A complete text analysis was conducted using 20 research papers stating the impact of the peer mentoring approach for this writing. Among the things obtained from previous studies are the variety of ways to implement peer tutoring approach, the impact on 3 aspects in students which are mathematical achievement, social skills and cognitive skills and the teaching theories used. The findings of the study indicate that most past studies used quantitative research methods with the concept of age peer approach. Then, constructivism theory was the most frequently applied with a sample of high school students. In conclusion, this systematic literature review shows that the peer tutoring approach in mathematics education has many benefits in various aspects and needs to be extended to improve the quality of education.

The problems in education in the countries of the Organization for Economic Cooperation and Development (OECD) vary from country to country. The differences between "upper class" and "lower class" countries in PISA assessment results have led to a research gap. The purpose of this study was to (a) test students' mathematical literacy skills on the Program for International Student Assessment (PISA) test and compare the results using the sum of means across OECD countries; (b) examine the relationship between students' mathematical competence, precision, and self-perception of mathematical literacy skills in the PISA test; and (c) analyze the gaps that exist between the implementation of mathematics instruction in school and the mathematical literacy as measured on the PISA test. This study was designed as a mixed method with an explanatory sequential design. The data collection methods included test procedures, questionnaires, and interviews. The result of this study showed that the overall mean score obtained was below the OECD average. In general, the respondents achieved only level 2 mathematics proficiency. A significant relationship was found between mathematical competence, precision, and self-perception in mathematical skills. On the other hand, there was a gap, namely the difference at the implementation level, where mathematical literacy measured by PISA differed from the measurement of mathematical learning achievement by teachers in school. The results showed that teaching that emphasizes only problem-solving procedures affects low mathematical competence and is not useful enough for students to deal with the PISA mathematics test.

Teachers' learning styles are a crucial part of the learning process as they determine how teachers' brains capture and integrate information linked with the senses. Kurnia, identified as an auditory teacher, was expected to capture written information in a provided numeracy problem. Nevertheless, she prefers to capture visual information, like tables or figures, and utilize them to develop thought-provoking questions. Thus, this study intends to investigate her reasons and the factors affecting Kurnia's decision to utilize visual information as a reference in developing questions. This research adopts a qualitative design covering a case study. Kurnia was selected from 32 teachers from 28 schools; roughly 43% were from public schools, and 57% from private schools. Kurnia placed more emphasis on pictorial information before proposing questions, which was caused by situational factors: the subject matter, the grade level, the student's engagement in the class, the teacher's experience, the teaching experience, and the diversity of students' learning styles. This article recommends that teachers recognize their learning styles to know their strengths and weaknesses in teaching mathematics, and that they convey understandable information utilizing effective instructional methods that represent each learning style of students in the classroom.