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.

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.

Algebraic reasoning involves representation, generalization, formalization of patterns and order in all aspects of mathematics. Hence, the focus of algebraic reasoning is on patterns, functions, and the ability to analyze situations with the help of symbols. The purpose of this study was to develop a test instrument to measure students' algebraic reasoning abilities based on cognitive systems in Marzano's taxonomy. The cognitive system in Marzano's taxonomy consists of four levels, including retrieval, comprehension, analysis, and knowledge utilization. According to the stage of cognitive development, students are at the level of knowledge utilization. At this level, students can make decisions, solve problems, generates and test hypotheses, as well as carry out investigations that are in line with indicators of algebraic reasoning abilities. The stages in developing the test instrument were based on three phases: preliminary investigation phase, prototyping phase, and assessment phase. The study obtains a set of valid and reliable algebraic reasoning test instruments for students based on the cognitive system in Marzano's taxonomy. Through the development of an algebraic reasoning test instrument based on Marzano's taxonomy, students can build' thinking habits so that active learning exercises occurs.

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.  

A mathematics instructor with limited knowledge of content and pedagogy has little room for improvement or novelty in the classroom or the ability to arouse students' interest in learning mathematics. This case study was conducted in a foundation center of one of the public universities in Malaysia. The target of current research was to investigate the influence of lesson study (LS) on lecturers’ pedagogical content and content knowledge. The LS group comprises of seven lecturers of the mathematics group and the researcher. The group collaboratively prepared a research lesson on the subject of even and odd functions. Data gathered through interviews and observations on the lecturers’ activities in discussion meetings. Data from observations and interviews were analyzed descriptively and through thematic analysis method respectively. The results of this study show lecturers improved their knowledge in content and pedagogy considerably about even and odd functions. They enhanced their teaching knowledge through collaborative work and sharing of experiences. It seems the findings of this research not only help lecturers to have better performance in teaching the even and odd functions but also encourage them to experience the LS approach in teaching other mathematical concepts.

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.

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.

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.

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.

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.

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.

Learning to teach mathematics has become crucial since its application in real life cannot go unmentioned. The desire of mathematics education researchers to make mathematics concepts easier for pre-service teachers to easily understand has attracted attention. This has become indispensable since after college, pre-service teachers are deployed from K-12 to assist learners in understanding mathematics concepts. The study aimed to ascertain how improvement in the learning of mathematics concepts using the Problem-based learning (PBL) approach could be understood and/or explained among pre-service teachers. This was viewed in two folds: how improvement in learning outcomes using the PBL approach could be explained; and how pre-service teachers’ disposition about the PBL could be explained/understood. Exploratory case study design involving qualitative and quantitative data was concurrently gathered and used. This involved the use of data collection instruments such as focus group discussion, pre-post-test scores, PBL observation protocol, and PBL disposition questionnaire. The study showed that the PBL method improved the learning of mathematics concepts among pre-service teachers. Pre-service teachers also showed a positive disposition (interest, belief, and attitude) toward the PBL intervention. The authors advocated for the conduct of a longitudinal study to understand the direction of change over time.

In the domain of engineering education, the crucial role of mathematics, especially Calculus, cannot be overstated, as it lays the foundational groundwork for numerous sciences, technology, engineering and mathematics (STEM) courses. The integration of mathematics into STEM disciplines is achieved through the practical application of mathematical concepts in real-world scenarios or in conjunction with other STEM subjects, thereby enhancing the coherence of engineering studies and acting as a significant motivational catalyst for students. This paper presents an analytical narrative of a practical mathematics assignment, woven into the Calculus curriculum and other STEM courses from 2013 to 2018. It delves into the potential impacts of these practical assignments on student performance and attitudes by evaluating data sourced from final exam scores and anonymous course surveys, both before and after the intervention period. Through the analysis of an extensive dataset comprising 1526 final exam scores, this study endeavors to make a substantive contribution to Future Technology Studies (FTS), focusing on the strategic harmonization of mathematics and STEM courses to enrich the educational experience and foster a more cohesive and applied learning framework in these disciplines.

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.