This is a preliminary paper about a large research project on social mathematics. It proposes points mathematics, a variant of social mathematics, as a viable context for teaching mathematics to adults. Points mathematics, focuses on observing, representing and investigating patterns, regularities and quantitative relationships stemming from convertible points, that businesses offer to their customers/clients for the purpose of encouraging loyalty and for boosting up sales in competitive markets. Using ten illustrative examples, the paper asserts that points mathematics provides practical, realistic context for teaching fundamental mathematics concepts and skills to adult students. These include, but not limited to, the four operations of mathematics (addition, division, subtraction and multiplication), variable, linear equation, graph, rates, percent, ratio, patterns and proportion. The paper is grounded in the theory of realistic mathematics education (RME), that posits that the teaching and learning of mathematics should be contextually-based; entails explaining and solving contextual problems; and establishing high-level interactive relationship between learning and teaching. The paper concludes with three recommendations to guide mathematics teachers of adults who want to implement points mathematics as part of their mathematics curriculum. However, the paper is the first phase of a large research project that explores social mathematics and how it could be integrated in mathematics curricular contents for adult students.

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.

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.

The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding  . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.

The study examines the effectiveness of employing semiosis in the teaching and learning of the Quadratic Equation. The first goal is to compare results of De Saussure and Peirce models within the semiotic theory. The second goal is to determine the commonest effective semiotic objects student teachers mostly employ to solve for the roots in quadratic equations. This research method was mixed methods concurrent and adopted both quantitative and qualitative approach. The instruments for the study were teacher-made tests and interview guide structured on the likert scale. In the teacher-made tests, two sets of twenty questions were set and distributed to the respondents. The sets of questions were similar and each twenty questions were based on De Saussure and Peirce Semiotic Models. The analyses employed both quantitative and qualitative. In the quantitative analysis, three categorical independent variables were fixed on and Pierre and De Saussaure models, objects of Pierre and De Saussaure models, and diachronicity, trichronicity, categorization and quadratic equations, after satisfying normality and independent assumptions of t-test and ANOVA techniques. The qualitative analysis with ensured anonymity, confidentiality and privacy of respondents and transcribed responses from semi-structured interview guide. The results of the commonest semiotic objects improved significantly classroom interactions with Peirce model than with De Saussure model. They perceived the Peirce model as being broader, comprehensive, universal and ICT-compliant. We therefore recommended further quasi-experimental studies on semiotic objects to improve upon the use of cultural objects.

As international concerns about the prevalence of out-of-field teaching have grown, so have discussions about how to support out-of-field teachers. In Ireland, the Professional Diploma in Mathematics for Teaching, a two-year professional development program, was created for out-of-field mathematics teachers. A pre-test, post-test, and final survey examined the program’s impact on participating teachers’ mathematical knowledge, confidence in teaching curricular content, and classroom practice. Findings offer evidence of development in participating teachers’ mathematical knowledge and self-efficacy after completing the program. They also raise important concerns about persistent weaknesses in participating teachers’ mathematical knowledge, particularly related to key areas of the curriculum.

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 aimed to examine the alignment of the Philippine mathematics teacher education curriculum with the 2021 mathematics literacy framework of the Programme for International Student Assessment (PISA). Such study could inform the Philippine Commission on Higher Education (CHED) if its mandated bachelor’s degree in secondary education major in mathematics could produce teachers at the secondary level prepared to deliver the expectations of PISA to mathematically literate 15-year-old learners. Through document analysis, the researcher reviewed the alignment of two official documents accessible online: the 2017 Philippine mathematics teacher education curriculum and the 2021 PISA mathematics literacy framework. Three mathematics education experts validated the researcher’s analysis. The results revealed alignment of the content and competencies covered by the teacher education curriculum and PISA mathematics literacy framework. However, the researcher found gaps in the curriculum in terms of its responsiveness in capturing some contexts and 21st century skills emphasized in PISA 2021 mathematics literacy framework. The study provided recommendations in addressing the gaps to inform needed updating in the teacher education curriculum to meet the expectations of PISA as a step to meeting the international standards of quality educational program.

Mathematics teaching efficacy is an important construct as confidence in one’s ability to teach influences teaching practices. This paper explores pre-service primary teachers’ mathematics teaching efficacy on entry to initial teacher education and the extent that pre-tertiary mathematics experiences and resultant beliefs affected their mathematics teaching efficacy. A mixed-methods approach combined the Mathematics Teaching Efficacy Beliefs Instrument (N=420) and qualitative interviews (N=30). The findings suggest medium personal mathematics teaching efficacy among participants with limited conceptions of what mathematics teaching involves. While uncertain regarding their immediate teaching ability, participants reported confidence regarding their potential. Mathematics teaching outcome expectancy was high; however, an undercurrent of conviction exists that external factors, most notably learners’ natural mathematical ability, are critical to student learning.

The focus of this action research was to adapt Bruner’s 3-tier theory to enhance conceptual knowledge of teacher trainees on integer operations. It looks into how learners' conceptual knowledge of integer operations changes over time, as well as their attitudes toward using the 3-tier model. Eighty-two (82) teacher trainees, who were in their first year semester one of the 2020/2021 academic year were purposely selected for the study. Data was collected using test and semi-structured interviews. The study found that using Bruner’s 3-tier theory contributed to substantial gains in conceptual knowledge on integers operations among learners.  It was also found that learners proffered positive compliments about the Concrete-Iconic-Symbolic (C-I-S) construct of lesson presentation and how it built their understanding to apply knowledge on integers operations. Learners also largely proffered positive image about C-I-S construct as it aroused interest and activated unmotivated learners. On these bases, the study concludes that lessons presentations should mirror C-I-S construct in order to alleviate learning difficulties encountered on integer operations. To do this, the study suggests that workshops on lesson presentation using C-I-S construct be organized for both subject tutors, mentors and lead mentors to re-equip their knowledge and to buy-in the idea among others.

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 Program for International Student Assessment (PISA) was developed by the Organization for Economic Cooperation and Development to measure students’ knowledge and skills needed for today’s society. PISA is a large-scale assessment of 15-year-old students in reading, mathematics, and science. In this analysis of PISA data from Bosnia and Herzegovina (BIH), we examined the relationship between gender, mathematics achievement, and perceived meaning in life in BIH students. The sample for this analysis comprised 6480 students (3148 females and 3332 males). The results of the analysis revealed a small but statistically significant, negative relationship between mathematics and the student’s perception of the meaning in life. Boys achieved higher scores in mathematics than girls, but the difference was relatively small. In addition, boys’ rating of meaning in life was higher than that of girls. Knowing what factors influence mathematical achievement might help educators create better intervention programs. In conclusion, we provided some possible explanations for these data.

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.

Numerical literacy refers to the knowledge and ability to use various numbers and basic mathematical symbols to solve problems, while math self-concept means the assessment of students’ skills, abilities, enjoyment, and interest in the subject. However, children with special needs and normal students in inclusive Elementary Schools are yet to sufficiently acquire learning that accommodates literacy and maths self-concept. This causes a need for the implementation of a children-friendly learning process. Therefore, this study aimed to identify the factors influencing the numeracy level and math self-concept, and also explore the obstacles in implementing children-friendly learning in order to facilitate students’ abilities. A qualitative method was applied because of in-depth data exploration regarding children with special needs, while the utilized instruments include tests, questionnaires, and interviews. Both the data collected and the analysis are qualitative, which are obtained through excavation, identification, and description. Consequently, this paper was able to (a) describe the factors influencing the numeracy level and math self-concept in inclusive elementary schools; (b) explore the barriers to implementing children-friendly learning; and (c) identify the relationship between students’ numeracy and math self-concept.

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.

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.

The study investigated the attitudes of Biology teachers towards the Biology Competence-Based Curriculum (BCBC) and their instructional practices at the lower secondary school level in Nyamagabe district, Rwanda. A descriptive survey design was adopted. Also, a purposive sampling technique was used to select 26 (16 male and 10 female) teachers of Biology. Data were collected using a questionnaire addressed to Biology teachers in selected schools and analyzed and presented in terms of frequencies, percentages, mean, and standard deviation. A one-way ANOVA was employed in the hypothesis testing. The findings indicated that these teachers had positive attitudes towards the implementation of BCBC. As for female ones, they had more positive attitudes towards BCBC implementation than the male ones. Considering those from boarding schools, they had a more positive attitude than the ones from day schools. Additionally, teachers with less teaching experience had more favorable attitudes than those with long experience. Teachers' age did not have any effect on their attitudes. The study also revealed that teachers of Biology rarely applied competence-based approaches in their teaching and assessment processes of students’ learning. It was inferred that the usage of CBC approaches differed significantly among teachers from boarding and day schools. The usage of CBC assessment methods did not differ significantly among teachers. From the findings, it was concluded that CBC seems not to be effectively implemented in the lower secondary schools under the study. Consequently, a recommendation was made to facilitate Biology teachers in schools with in-service training for professional development.