This paper reports on part of an ongoing large-scale research on the need to improve science teaching and learning through investigating the Pedagogical Content Knowledge (PCK) of biology teachers for the topic Biodiversity. Six factors have been seen to affect teacher PCK, i.e., content knowledge, knowledge of students, science teaching orientations, knowledge of assessment, knowledge of instructional strategies and knowledge of the curriculum. This research aimed to examine the teacher’s level of content knowledge (CK). A qualitative research paradigm was adopted, and a case study research design used. The case (unit of analysis) was Biology teacher CK, and the subjects were the four teacher participants purposively selected. Lesson observations, teacher interviews and learner questionnaires were used to collect data on teacher CK. A content knowledge analytical framework consisting of five constructs was designed and used to analyse the teacher CK and data triangulated with data collected from interviews and questionnaires. This research revealed that ‘A’ level Biology teachers’ CK vary from teacher to teacher depending on several factors which include teacher identity, planning, workshopping, and motivation among others. Of the four Biology teacher participants, two had adequate CK and the other two exhibited inadequate CK. Inadequate CK was attributed to lack of planning, non-exposure to workshops and lack of teacher motivation. Consequently, this research recommends supervision of teachers from school level to national level, a series of teacher workshops on the demands of the competence-based curriculum and constructive teacher identity as well as introduce factors that enhance teacher motivation. Further research on the content knowledge of Biology teachers in other learning areas is recommended.

Many research studies have been conducted on students’ or pre-service teachers’ geometric thinking, but there is a lack of studies investigating in-service teachers’ geometric thinking. This paper presents a case study of two high school teachers who attended the dynamic geometry (DG) professional development project for three years. The project focused on the effective use of dynamic geometry software to improve students’ geometry learning. The two teachers were interviewed using a task-based interview protocol about the relationship between two triangles. The interviews, including the teachers' work, were videotaped, transcribed, and analyzed based on the three levels of geometric thinking: recognition, analysis, and deduction. We found that the participating teachers manifested their geometric skills and thinking in constructing, exploring, and conjecturing in the DG environment. The study suggests that the DG environment provides an effective platform for examining teachers' geometric skills, and levels of geometric thinking and encourages inductive explorations and deductive skill development.

The purpose of this study was to evaluate synchronous and asynchronous mathematics teaching modalities at Isabela State University. The qualitative research method was used to collect information, opinions, and experiences of Isabela State University mathematics faculty in employing synchronous and asynchronous modes in teaching mathematical courses in terms of strengths, weaknesses, possibilities, and problems. The study's subjects were 15 Mathematics Instructors chosen at random from Isabela State University's nine campuses. A structured interview was created and distributed to participants using Google Form. The limitations on face-to-face encounters prompted the use of such data-gathering technique. The researcher followed up with another video call interview to validate the participants' responses. The data was transcribed and processed using thematic analysis. The findings demonstrated that the synchronous and asynchronous learning modalities both have strengths and disadvantages that influence the quality of the teaching-learning process throughout the epidemic. Given this, distant learning is thought to be more effective when both modalities are used rather to just one of the aforementioned. This is because the strengths of one of the two modalities can solve the flaws highlighted in the other. As a result, mathematics instructors may receive more in-depth training in both asynchronous and synchronous teaching approaches, as well as strategies for becoming more successful teachers during the present school closures.

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.

Research into knowledge which mathematics teachers require to teach abounds. There is also mounting interest among mathematics teacher education researchers to characterize mathematics teacher educator knowledge (MTEK). However, there is a generic dearth of studies focusing on conceptions of mathematics teacher educators (MTE) regarding MTEK. This article is a product of a qualitative case study underscoring teacher educator conceptions in that regard and the investigation involved two MTE who were practicing in a university. The research site was conveniently chosen, and participants were intentionally selected to respond to interview questions which elicited espoused views. Narrative analysis was used through exploration and subsequent interpretation of transcripts which aligned with questions posed. Analyses suggested a complexity to exhaustively categorize the MTEK necessary for MTE to train mathematics teachers. Notwithstanding, MTE believed that MTEK should include understanding of research in mathematics teacher education and teaching, mathematics teacher knowledge, and MTE professional development. Additionally, the findings suggested that MTE acquire mathematics teacher educator knowledge through postgraduate studies, on the job practice, mentorship, and participation in professional development activities. Research in other contexts is recommended to identify mathematics teacher educators’ understandings of MTEK and how that knowledge should be acquired.

Out-of-field teaching in science is a phenomenon in many secondary schools across the world. While the reasons for out-of-field teaching are complex, its incidence is heightened in low socio-economic communities and in regional and remote school locations. Research on out-of-field science teaching in secondary schools has tended to focus on teacher competence, particularly in relation to pedagogical content knowledge. However, while teachers’ beliefs and teaching practices within their specialist subject are shown to be related, it is unclear how teachers’ beliefs and practices alter when teaching across subject boundaries. Using a boundary-crossing lens, where teachers engage in passing back and forth between different contexts, this study explored the relationship between teachers’ beliefs about their in-field and out-of-field discipline (science) and the connections to their teaching practice. Interview data, including a video-stimulated interview of a lesson in a teacher’s specialist field and then a subsequent out-of-field lesson, were analysed using the framework of a belief that investigated the relationships between in-field and out-of-field beliefs and practices. Findings indicate that those who teach science out-of-field revert to traditional ways of teaching, despite being more open and adventurous in their in-field discipline areas. However, there were significant instances of boundary crossing with their pedagogy to support their teaching – both in-field and out-of-field. These findings support the development of structured mechanisms and strategies to assist teachers to cross boundaries to establish new and unique interdisciplinary practices.

During the Covid-19 pandemic, this study investigated the role of metacognitive awareness as a mediator in the correlation between attitude and mathematical reasoning among undergraduates who are first year university students. These studies distribute mathematical reasoning assessments, metacognitive awareness questionnaires, and attitude surveys as research data. One hundred eighty-four undergraduate students from one public institution in Malaysia's Klang Valley area participated in the research. The impact of metacognitive awareness on attitude and mathematical reasoning was studied using Version 25 of the Statistical Packages for the Social Sciences. The findings indicated that undergraduate mathematics and science education students excelled in non-mathematics and science education students in mathematical reasoning capacity. According to the findings, undergraduate mathematics and science education students had good metacognitive understanding and used more approaches in mathematical reasoning assessment. Further study implies that more research should be conducted to assess different demographics, such as institute training teachers' metacognitive awareness and attitude towards mathematical reasoning.

This study aims to describe the implication of the Aptitude Treatment Interaction (ATI) model integrated with character values to increase the students’ skill in solving mathematics story problems. This study applied a quasi-experimental research type using a non-equivalent control group design involving two classes with 30 students each. Data was collected using a test instrument for solving mathematics story problem. Data were analyzed using n-gain descriptive statistical analysis to see the increase in students' skill in solving mathematics story world problems. The results showed that the average score of student's aptitude in solving mathematics story problems is 91.26 which is in the category of very high. There is an increase in the students’ ability with score of an n-gain of 0.77 which is in the category of high. In addition, the results of observations related to the implementation of learning model of the ATI with a percentage of 87.5% in the category of very good. Thus, the character-based ATI learning model can be used to increase the students’ skill in solving mathematics story problem. In addition, it accommodates the character of students who are concerned with learning mathematics so that learning goals can be achieved both from cognitive and attitudinal aspects.

This study examined the impact of the Rwanda African Institute for Mathematical Science, Teacher Training Program (AIMS-TTP) on 228 secondary school students’ interest to learn Mathematics and science taught by 7058-trained teachers over 5-years across 14 districts. Students were exposed to various AIMS-TTP interventions, including industrial visits, science hours, and international day for women and girls in science, mathematics competition, robotics and mathematics challenge, and the Pan African Mathematics Olympiad (PAMO). A survey research design was employed to collect data about students’ interest to learn Mathematics and science, and data on students’ choices of combinations were obtained from the National Examination and School Inspection Authority (NESA) for the academic years 2017 to 2022. Data analysis using bivariate correlation and regression analyses revealed a positive and significant relationship (p<.05) between AIMS-TTP interventions and students’ interest to learn Mathematics and science. Besides, linear regression model indicated that hands-on activities, exposure to mathematics and science role models, science hour and smart classroom were the best predictors of students’ interest to learn mathematics and science (β=.197, p< .05; β=.217, p<.05; β=.234, p< .05; and β=.218, p<.05 respectively). They contributed 66.7 % (Adjusted, R2 = .667, p < .05) of the variance in students’ interest in learning mathematics and science. The AIMS-TTP interventions significantly improved students’ interest to learning mathematics and science. Recommendations include comprehensive training programs with direct student engagement, diverse competitions, and ongoing teacher support through professional development. Future research should focus on students’ STEM interest in Technical, Vocational Education, and Training schools.

Bring your own device (BYOD) policy implementation in schools worldwide has allowed students to learn subjects, including mathematics, using personal mobile devices (PMDs). PMD use has enhanced students’ mathematics enjoyment by bridging the gap between theoretical mathematics concepts and their practical applications, which makes mathematics more meaningful and leads to improved results. Nonetheless, students in Namibian basic education are not authorised to learn with PMDs in school. While students’ PMD use in school remains a topic of debate, there remains a need to investigate its impact on students’ mathematics learning and teachers’ perceptions of BYOD in mathematics classrooms. This study evaluated the perceptions and intentions of 209 Namibian mathematics teachers from the Omusati and Khomas regions regarding students’ mathematics learning using PMDs in schools. Data were collected through an online survey. A structural equation model revealed teachers’ positive intentions towards students’ use of PMDs through BYOD in learning mathematics in school. Perceived usefulness (PU), perceived ease of use (PEoU), and price value (PV) factors directly affected the teachers’ behavioural intentions (BI) towards students learning mathematics through BYOD. PEoU significantly affected teachers’ PU, and PV significantly affected teachers’ PEoU and PU. PU significantly mediated the relationship between PEoU and teachers’ intentions. PV significantly indirectly affected teachers’ intentions through PU. PEoU non-significantly mediated the PV and intention relationship. Practical implications are discussed, and recommendations are offered for the Namibian Ministry of Education, Arts and Culture and teacher training institutions.

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.

This paper derives from a large research project focusing on mathematics and science assessment of student learning in three high-need, rural, and urban secondary schools in Manitoba, Canada. The study employed qualitative methods of semi-structured interviews and classroom video recordings of teaching practice experiences of 12 mathematics and science teachers, with the purpose that explore how authentic assessment forms assist effective teaching to monitor and motivate student learning achievement and growth. The results indicate that about 67% (eight out of the twelve of the participants) of the research participants practice the traditional mode of standard assessment that consists of multiple forms of questioning. The participants' rationale relates to speedy evaluations of student work, preparing feedback reports to parents and students, and objectivity of the assessment process. The other 33% (four out of twelve of the participants) of participants practice authentic assessment that concentrates on: (1) Allowing students to apply what they have learned rather than testing their ability to memorize and regurgitate concepts, (2) Allowing students to personalize their knowledge and values, (3) Encouraging group project-based learning and with the use of rubric for evaluating and monitoring, (4) Promoting deep learning to become life-long learners, (5) Recognizing, acknowledging, and validating diversity in student learning styles, interests, and aspirations, and further, authentic assessment is an excellent opportunity to apply communicative technologies such as podcasts and webinars in learning and undertaking investigations in mathematics and science learning. Furthermore, some participants asserted that authentic assessments are time-consuming, labor-intensive, and resource-demanding, aside from the limited resources and lack of training, which are some of the challenges of implementing authentic assessment. Other participants stated that all teachers must be familiar with using all assessment tools. The paper concludes that the principal plays a critical instructional leadership role in a school-wide implementation of authentic assessment.

Recent studies in mathematics education have focused on students' geometric problem-solving abilities, self-regulation, and the problem-based learning (PBL) model. The goal of this study is to examine how well junior high school students' self-regulation and geometric problem-solving skills are enhanced by the PBL model. In this study, quantitative methods using a quasi-experimental design were used. The sample consisted of 45 students from Amanatul Ummah junior high school in Mojokerto, Indonesia. Five types of instruments were utilized to collect data for this research, namely Syllabus, lesson plans, student worksheets, Self-Regulation Questionnaire (SRQ), and Geometry Problem-solving Test (GPST). The outcomes of the N-Gain test demonstrated how well the PBL model works to help students develop their capacity for self-regulation and geometric problem-solving. Apart from that, there are some notable differences between the traditional technique and the experimental class that is taught using the PBL paradigm. It is advised that similar trials be conducted in the future with a larger population and sample size. In both public and private junior high schools, it is strongly advised that more research be done with a larger population and sample size. Future researchers can also expand the study materials of geometry, not only to flat-sided geometric shapes but even further to curved-sided geometric shapes and also other subject matters.

This study compares experts' and teachers' conceptualization of pedagogical content knowledge (PCK). The study participants included teachers (n=20) enrolled in a graduate mathematics education course on PCK. Participants responded to two open-ended questions: a) describe in your own words what PCK is; b) provide an example of PCK. The responses were collected, qualitatively and quantitatively analyzed, and then compared to those suggested by experts to identify and describe the similarities and differences between teachers’ and experts’ conceptualizations using the Pareto analysis. Experts’ and teachers’ PCK components ranking was analyzed using the nonparametric Mann-Whitney U test. Even though the results of the quantitative analysis were not significant (e.g., the observed U-value is 32 whereas the critical value of U at p < .05 is 13), the qualitative discussion on the differences between expert and teachers’ ranking suggests insightful interpretation of priorities among PCK components across the two groups.

Scaffolding dialogue is a concept in learning that refers to the support or assistance given to individuals during the dialogue process. The main objective of this research is to create a basic structure of dialogue to help and support students during the learning process in improving their algebraic reasoning skills. Algebraic reasoning is a process in which students generalize mathematical ideas from a certain set of examples, establish these generalizations through argumentative discourse, and express them in a formal and age-appropriate way. The study was designed using the grounded theory qualitative model method, which used three sequential steps: open coding, selective coding, and theoretical coding. The research was conducted on students of the mathematics education department at Universitas Islam Sultan Agung. Data collection methods include algebraic reasoning ability tests, questionnaires, and interviews. Data analysis in grounded theory is an iterative and non-linear process that requires researchers to constantly move back and forth between data collection and analysis. This process aims to produce a theory that is valid and can explain phenomena well based on empirical data obtained during research. The dialogue scaffolding strategy framework in improving students' algebraic reasoning abilities includes instructing, locating, identifying, modeling, advocating, exploring, reformulating, challenging, and evaluating.