This paper represents a revolutionary advancement in our knowledge of postgraduate education which is of increasing significance to national knowledge systems. South African universities produce 26 doctoral graduates for every one million citizens. This means that the low doctoral graduates’ throughput is a huge challenge in South Africa and needs to be addressed. The paper investigated the challenges experienced by postgraduate students (Honors) at an institution of higher education in Limpopo province of South Africa. The group studied consisted of postgraduate students (Honors) from the Department of Mathematics Science and Technology Education, Faculty of Education. Using a qualitative approach, open-ended questionnaire and interview data were collected from eight participants. Data were analyzed thematically and the results revealed that students find it difficult to walk the landmine-infested postgraduate education road without means to shield themselves from the subsequent explosion. The study recommends aspects that improve postgraduate programs’ performance in the Department of Mathematics Science and Technology Education.

Using engineering design to teach science requires teachers to engage in noticing, interpreting, and responding to students’ needs in real-time. While research has begun to focus on how elementary teachers do so, less is known about how teachers instructionally support and optimize students’ ideas through engineering design feedback. In this study we investigate what instructional moves two elementary teachers’ employ to leverage students’ ideas and reasoning and create opportunities for students to exchange design feedback. Data were gathered using classroom observations of teachers’ implementations of a design task focused on sound and energy transformation. Observations were coded for teachers’ use of high-leverage practices, and event maps were created to chronicle teachers’ implementation of the task from start to finish. Event maps were analyzed and compared for discrete instructional activities and modes of classroom organization that supported opportunities for feedback. Findings suggested that while teachers used similar instructional moves, how and when they created opportunities for student design feedback differed, resulting in diverse ways of assessing and supporting students’ understandings. Implications suggest design feedback as both a purposeful and naturally present phenomenon throughout the design process, reflective of the nature of engineering design.

Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.

In this paper, the categories and influence of teachers’ classroom characteristics relative to effective mathematics teaching in secondary schools in Plateau state, Nigeria were examined. The aim was to see how students are assisted to learn mathematics from teachers engaging fully their professional practices fully. Exploratory and descriptive survey research methods were used to examine the trajectories. Sample for the study consisted of 60 trained mathematics teachers from secondary schools in Plateau state that participated in a week-long capacity building workshop on teaching new concepts from secondary school mathematics curriculum in Nigeria organized recently by the state chapter of the Mathematics Association of Nigeria. Purposive sampling technique was used to select the sample based on the fact that the study targeted only mathematics teachers that participated in the capacity building workshop. A 52-item TCCQ on teacher effectiveness, interest, rapport with students, etc. was used for data collection. The findings from the study revealed that mathematics teachers’ ability to teach effectively is significantly associated with many factors including the use of different strategies (χ2=52.75), revision (χ2=47.13), good lesson plans (χ2=53.93) and being friendly with students (χ2=35.66). There was no significant variation regarding how the characteristics influence teacher effectiveness based on qualification (F2, 58=0.689). Among other things, therefore, it was recommended that teachers should be committed to teaching mathematics effectively in the classroom by taking cognizance of the variables especially designing of good lesson plans and previous knowledge irrespective of their qualifications.

In Nigeria, most teachers among other things lack the necessary teaching skills, and mastery of subject matter for effective teaching of mathematics at the secondary school level. These deficiencies have often resulted in high and repeated failure rates in national and standard mathematics examinations. The present study investigated the ability of mathematics teachers to construct practical and realistic word problems in bearing and distance toward mitigating the deficiencies. The research methods adopted were exploratory and descriptive surveys due to the need to explore and analyze the abilities using quantitative techniques. Sample consisted of 292 (35.48%) mathematics teachers who took part in the in-service training workshop organized by the Mathematical Association of Nigeria (MAN) in Plateau state, Nigeria. Purposive sampling technique was used to select the sample that involved the workshop participants only. The instrument ‘construction of practical and realistic word problems in bearing and distance test (CPRWPBDT)’ was used for data collection while the analysis was carried out using simple percentages, mean scores and one-way ANOVA. The findings of the study among other things revealed that the mathematics teacher participants constructed practical and realistic word problems in bearing and distance within 91.67% completion rate, 70.45% of the problems constructed were within the context, at least 75% rate of correctness with little difficulties/errors was observed in sketching (65.90%), and reality (40.90%). The variations observed within the participants in the construction of the problems were statistically not significant. Thus it was recommended among other things that mathematics teachers should undergo regular in-service workshop training to help in developing essential skills themselves for constructing practical/realistic word problems in bearing and distance; and should avoid unnecessary errors for meaningful teaching and learning of bearing and distance.

Research on students’ perceptions of scientists is ongoing, starting with early research by Mead and Metraux in the 1950s and continuing in the present. Continued research interest in this area is likely due to scholarship suggesting adolescents’ impressions of scientists are sourced in-part from media, which influence their interests in science and identity in becoming a scientist. A significant source of images, in which adolescents (or middle school students) view science and scientists, is in their science textbooks. A qualitative content analysis explored images of scientists in three of the major U.S.-based middle grade science textbooks published in the new millennium: sixth grade biology, seventh grade earth science, and eighth grade physical science. The Draw A Scientist Test (DAST) Checklist was employed to assess scientists’ images and the stereotypes therein. From nine textbooks, 435 images of scientists were coded and analyzed by publisher and grade level / area by DAST constructs of appearance, location, careers, and scientific activities. Statistical analyses showed significant variances between grade levels and textbook publishers of scientists. Despite scientists portrayed in active endeavors, traditional tropes of the scowling, older, solitary, white male scientist persist. This study offers insight in leveraging improved images of scientists in textbooks.

This study aims to acquaint high school students with the process of modelling in mathematics teaching. The research lasted 5 weeks with a group of (N=36) high school students of Zenica-Doboj Canton (Bosnia and Herzegovina). Students had an opportunity to learn about functions and their properties, and subsequently about mathematical modelling with linear, quadratic, and logarithmic functions. Examples in the research were related to real-world phenomena and processes. The problems were composed of the following subtasks: creating or testing a model, explaining the results, finding the domain and range, and critical thinking about the model. The research identifies the importance of mathematical modelling in teaching. The results display a positive impact of such an approach on students, their thinking, attitude towards teaching, understanding of the materials, motivation and examination scores. The experiences that both students and teachers may have in a mathematical modelling framework could be extremely important for the academic success. A control group of 36 students took the final exam as well. The students of the experimental group got much better results than the students of the control group. Indeed, learning through mathematical modelling has been shown to contribute to all the aspects of students' expected development.

This study investigated how implementing inquiry-based learning (IBL) can be an effective tool for an instructor to conduct rich formative assessment. Many researchers have documented that IBL promotes active learning from students’ learning perspective. However, little research examines how IBL affects instructors’ teaching practice from teaching perspective. Based on the data collected from a Calculus II class, the author discussed how the structure of IBL class produced rigorous on-going formative assessment during classroom teaching from the three aspects: helping the instructor “see” student thinking; helping the instructor “see” the level of student understanding; helping the instructor catch teachable moments. The rigorous on-going formative assessment, in turn, helped change student classroom behaviors in terms of asking more questions, showing deep thinking, and gaining confidence.

The ability to think critically is a basic competency that must be possessed by students. This study aims to determine the level of critical thinking skills of junior high school students in Bima Regency, West Nusa Tenggara, Indonesia. Various studies have been carried out that explain how important students' critical thinking skills are, but there have not been too many studies on efforts to develop and empower students' critical thinking skills in a practical way. In this thesis, we introduce the technique of empowering students' critical thinking skills by developing a virtual laboratory media based on problem based learning on the material of the human excretory system. In this development, use software construct2 to develop a device which is then integrated with a problem based learning model. It is proven that a virtual laboratory based on problem based learning can improve the critical thinking skills of junior high school students in Belo Kaputen Bima District. We hope that the development of PBL-based virtual laboratory media can improve dramatically, such as the use of 3-dimensional and 4-dimensional software to improve students' understanding of critical and constructive thinking without losing quality.

The students' low science process skills are caused by learning that is still dominated by the teacher, so it is necessary to develop a learning approach that focuses students in the learning process. One approach that can be used is learning that integrates science, technology, engineering, and mathematics (STEM). This study aims to measure the improvement of students' science process skills that are integrated with the STEM approach on the reaction rate material. This research is a quantitative research with a pre-experimental design type, one group pretest-posttest with a sample of 30 students from class XI SMA Negeri 9 Pontianak, taken by random sampling technique. The data collection tool used is a subjective test of science process skills. The results showed that there was an effect of the STEM approach on the students' science process skills on the reaction rate material, with a score of 76.11, good criteria. Among the aspects of science process skills measured, including observation, classifying, calculating, predicting, inferring, and communication, the communication aspect of students experienced a significant increase from a score of 3.33 to 91.1. This study shows that the STEM approach to reaction rate learning effectively improves students' science process skills.

This paper reports an exploratory study on the pre-service teachers’ content knowledge on school calculus. A calculus instrument assessing the pre-service teachers’ iconic thinking, algorithmic thinking and formal thinking related to various concepts in school calculus was administered to a group of pre-service mathematics teachers. Their performance on five of the items is reported in this paper. Other than their good performance in the iconic recognition of stationary points, their recognition on points of inflexion, differentiability and notion of minimum points was relatively poor. In addition, they appeared to lack the algorithmic flexibility in testing the nature of stationary points and the formal thinking about definition of an extremum point. The implications of the findings are discussed.  

The study on mathematical performance was significant enough to be studied further to measure students' self-efficacy. Although studies on student self-efficacy in math performance from a gender perspective were abundant, studies on this relationship from the perspectives of ethnic culture and gender were scarce. Therefore, the objective of this study was to examine the self-efficacy of Bugis Junior High School students in solving math problems based on gender. The researchers used an algebra problem in the context of the Bugis ethnic culture. For this data set, two of 25 students at a public junior high school in Bone, South Sulawesi, Indonesia, were interviewed based on ethnicity and gender. Qualitatively, the triangulation technique was employed for data analysis. The study results revealed that male students outperformed girls in terms of self-efficacy, namely magnitude, strength, and generality, in math performance. Furthermore, female students had lower self-efficacy in terms of confidence, supportive experience in completing math tasks, and confidence in their ability to complete math tasks in similar or different contexts, compared to male students, who had higher self-efficacy. This result provided new knowledge by exploring the characteristics of students' self-efficacy by integrating ethnicity and gender.

This study aims 1) to determine the effectiveness of the Mind-Mapping based Aptitude Treatment Interaction model towards creative thinking and 2) to explain the mathematical creative thinking process based on the creative level. The number of participants was 26 students who took the Multivariable Calculus course in the odd semester of 2020/2021. This research used the mixed-concurrent embedded method. The data collection techniques were validation, observation, creative thinking tests, and interviews. The results showed that 1) the Mind-Mapping based Aptitude Treatment Interaction model was effective in developing creative thinking, as indicated by the average creative thinking score of the experimental class, which was higher than the control class and 2) the characteristics of students mathematical creative thinking process varied following the creative thinking levels. The students mathematical creative thinking level consists of not creative (CTL 0), less creative (CTL 1), quite creative (CTL 2), creative (CTL 3), and very creative (CTL 4). Students at the CTL 2, CTL 3, and CTL 4 can meet the aspects of fluency, flexibility, and originality.

Learning in STEM subjects is to a high degree based upon understanding logic, especially in subjects like mathematics. It has always been challenging to preserve the benefits of on-campus teaching and learning while digitalizing the teaching of mathematics. In this article an approach to design for a suitable online pre-calculus course is discussed, that aims to address the challenges. The main focus will be on student active learning in synchronous online environments, technical teaching methods in lectures, and pre-planning of the course. The final exam in the course was held as a closed-book proctored exam on-campus with pen and paper, providing data on comparisons of the final exam scores with the exam from the previous year, in which the entire course was held on-campus. The results indicate a positive effect from the presented design. Also, student surveys indicated high student satisfaction.

The current study investigated whether: (1) using an interactive presentation (IP) platform could affect the amount of usage of the practices of making orchestrating mathematical discourse- sequencing and connecting students' responses. (2) using an interactive presentation (IP) platform could affect the amount of narratives constructed by students. Fifty seventh-grade students participated in the study; those students were divided into control and experimental groups. Qualitative and quantitative analyses were performed based on voice recordings and field notes. The results revealed that the teacher using (IP) asked nearly three times more questions that connected students’ responses (i.e., questions that involved valuing students' ideas, exploring students' answers, incorporating students’ background knowledge, and encouraging student-to-student communication). We also saw that the students participated in the learning processes. The students in the experimental group presented three times as many narratives as those in the control group. We present several excerpts from the transcripts of the classroom discussions to illustrate our findings. Discussion of the implications and limitations of these results and make recommendations based on those results.

The diversity of definitions of science literacy has resulted in a diversity of measurement tools. However, adult science literacy is mainly assessed on short standardized and non-contextualized questions, thus making the study of adult science literacy more qualitative than quantitative. Here we describe the rationale, development, and validation of a questionnaire that associates the use of science in the specific science-related setting of parents of hard of hearing children with general and topic-specific science knowledge. The questionnaire went through four developmental steps: (1) gathering input from hearing rehabilitation experts and parents, (2) testing the close-ended questionnaire (n=10), (3) open-ended questionnaire (n=24), (4) online close-ended questionnaire (n=91). These all assessed general science knowledge, contextual science knowledge in the field of hearing and parents' advocacy knowledge and attitudes. These steps and the resulting assessment tool can thus inform the further development of measures of adult science literacy in context. The findings suggest that although general science knowledge enables the application of science to everyday science-related problems it only explained a small proportion of the variance in contextual science knowledge. Thus, the results strongly point to the importance of measuring adults' science literacy in a context that is relevant to the responders. The findings also underscored the disappointing outcomes of secondary science education, in that formal scientific background predicted general science knowledge but did not account for contextual science knowledge at all. This should elicit concern as to the ability of students to use science knowledge in future personally important science related contexts.

The ability of students to build problem-solving models using procedural knowledge can be viewed from several aspects, including Mastery of Mathematical Problem Solving (MPS), understanding concepts and application of concepts, the relationship between learning outcomes of mathematics and interest in learning, and examine the contribution of the ability to understand concept problems, the application of concepts to the ability of MPS, as well as student difficulties and some of the advantages of students in solving problems. This experimental study aims to explain the effect of the MPS model using procedural knowledge on solving mathematical problems for Junior High School Students (JHSS). The findings showed that 1) The MPS method using procedural knowledge significantly improved learning outcomes, but the mastery of MPS for JHSS was still unsatisfactory. 2) MPS teaching could still not improve meaningful learning outcomes. However, when JHSS applied the concepts, calculations, and problem-solving aspects, MPS teaching improved meaningful learning outcomes. 3) Students' interest in learning mathematics in the two sample classes was classified as positive. Shortly, MPS teaching accustoms students to think systematically and creatively and not just give up on the problems they face.

3D printer technology and 3D design are used in many fields and are gaining various uses day by day. It is seen that the quality of education and training has increased with the effective use of 3D technology in the education and training environment. This study aims to investigate the attitudes of Pre-Service Teachers about the use of 3D printer activities made with Tinkercad in science education. 43 science pre-service teachers participated in the study, which lasted 8 weeks. A mixed research method was used in this study. The problem-solving scale and the attitude scale towards the use of 3D printers in science education were applied to the pre-service teachers. To collect the research data, the attitude scale was applied as a pre-test and post-test. For Paired samples, a t-test was applied and analyses were performed. In qualitative studies, semi-structured student interview questions were applied. According to the findings of the study, there was a significant increase in students' positive attitudes towards the use of 3D printers in science education. Tinkercad and 3D printer trainings have been given and applications have been made within the scope of these trainings. There have been 6 activities related to 3D printers. Thanks to 3D printers, students have the opportunity to present creative ideas and things they imagine to life by making designs in their minds. It seems that abstract concepts related to the sciences are embodied with a 3D printer and turned into tangible objects. Examining a physical object makes it easier for students to identify mistakes they have made in designs. It is seen that they do creative and solution-oriented work against the problems they encounter. Thus, it is predicted that learning will be more permanent and effective.

Reflection requires someone to think in deep and express the impression of a phenomenon or an event. Reflection can be defined as a mirror to look at and see the personal insights, feelings, motivation, or purposes of individuals within a particular context and practice in a realistic way. This study examined the nature of pre-service science teachers’ reflections during the last semester of the teacher education program. There were four cases as student-teachers attending science teacher education program in northwest region of Turkey. The qualitative data, written reflections and researcher field notes were utilized and analyzed through inductive methods. The results indicated that even though pre-service science teachers learned scientific practices and inquiry, they were not able to implement due to some constraints: mentor teachers forced them to teach on a traditional basis. They could only complete the required four-hour teaching practice. Student teachers reflected on their learning as becoming a science teacher, but their actions were restricted, and they could not find supportive community in school and classroom context.

The overall aim of this study is to examine the association between Swedish students’ attitudes towards mathematics, mathematics achievement as measured by the Trends in Mathematics and Science Study (TIMSS), socioeconomic status (SES), and educational background variables. A further aim is to investigate whether students’ attitudes towards mathematics have a mediating role between their mathematics achievement and their background. Several indicators of students’ SES and background, taken from both the TIMSS 2015 database and from Swedish official registers, were used. The overall results show that there were differences in attitudes towards mathematics in relation to the different SES and educational background measures. There are also associations between students’ SES and both TIMSS mathematics achievement and their attitudes towards mathematics. The students’ attitudes towards mathematics only had a small mediation role between the students’ backgrounds and TIMSS mathematics achievement. Finally, although the mediation models had a better fit when including other information, the mediation effect was lower. Practical implications of the obtained results are discussed.