Defining Basic Concepts of Mathematics

The work of the School Mathematics Study Group (SMSG) is well known. Reports of its objectives, its organization, and its scope of activity have appeared in various sources.1 This present account relates to one of the Study Group's more recently organized activities, the SMSG Project on Elementary-School Mathematics.

This study aimed to explore the effect of teachers’ motivation on students’ academic performance in mathematics in public lower day secondary schools in Rwanda, specifically the case of Kirehe district. The study had three specific objectives which were to determine the influence of recognition and rewards of teachers on students’ academic performance in mathematics in public lower day secondary schools in Kirehe District, to determine the influence of in-service training of teachers in improving academic performance of students in mathematics in public lower day secondary schools in Kirehe District, to investigate the influence of teachers’ remuneration and incentives on students’ academic performance in mathematics in public lower day secondary schools in Kirehe District. The results of this study will support the Ministry of Education (MINEDUC), along with its bodies NESA and REB, which are responsible for monitoring and evaluating the academic performance of secondary schools, in making informed decisions on initiatives to address challenges faced by teachers and school management. Findings of this study will also enrich the existing knowledge and literature on teacher motivation, primarily benefiting academicians. One theoretical frame work, Self-Determination Theory underpinned and supported this research. In this research, descriptive survey design for quantitative and qualitative data collection and analysis were implied. The study gathered data through questionnaires and interview guides. Specifically, the questionnaires were made for Mathematics teachers while interview guides were designed for deputy head teachers and school head teachers. The study’s target population was 348 respondents made of 232 Mathematics teachers from Public lower day secondary schools, 58 deputy head teachers and 58 school head teachers from all public lower day secondary schools in Kirehe district, Rwanda. The selection of the participants for this study employed various methods, including both simple random and purposive sampling techniques. A sample size of 186 was chosen by using Yamane formula. The quantitative and qualitative data analysis in terms of frequency, percentage, mean, standard deviation, correlational analysis, Regression analysis, Analysis of Variance (ANOVA), and Regression Coefficient involved the use of Statistical Package for the Social Sciences (IBM SPSS 22.0) where each item from the questionnaires and interview guides was systematically categorized. Subsequently, the analysis revealed a strong positive correlation between students' academic performance in mathematics and teacher’s recognition and rewards (r = .901, p = .000). This suggests that when teachers are recognized and rewarded for their efforts, it positively impacts student achievement in mathematics. Additionally, a moderately strong positive correlation was found between students ‘academic performance in mathematics and in-service training of teachers (r = .701, p = .000). This implies that providing teachers with ongoing training and professional development opportunities contributes to improved student outcomes in mathematics. Finally, a moderately strong positive correlation was observed between students ‘academic performance in mathematics and teacher remuneration and incentives (r = .757, p = .000). This suggests that compensating teachers fairly and providing them with incentives can positively influence their effectiveness and, consequently, student achievement. The analysis demonstrates that all three teacher related factors: recognition and rewards, in-service training, and remuneration and incentives are significantly correlated with students' academic performance in mathematics in public lower day secondary schools in Kirehe district. To measure the results reliability, test and retest all methods were used in measurement of the reliability. The supervisor reviewed all data collection instruments items before the administration of data collection to ensure it validity. The research concluded by providing recommendations based on the findings of the study.

Learning mathematics in the secondary school – that is, learning the content of the secondary school mathematics curriculum – has, until recently, been rarely offered to learners with Down syndrome. This chapter aims to change that, showing how mathematics might be made accessible to learners with Down syndrome, and why this is important to do. Teachers who have done this have described this as some of the best teaching they have done! In this chapter Is it possible? Even if it is, should we do this? Examples of adjustments to secondary mathematics topics Using the tools of mathematics (e.g. calculators, spreadsheets, graphing software) to access the curriculum Problem-solving, reasoning and justifying – the processes of mathematics Assessing learning

2020 Timoshenko Medal Acceptance Lecture: Mechanics: Evergreen and Forever New

Chinese–English bilingual programs in China advocate using both English and Chinese in instruction. Mathematics teachers in these schools need to use English as the medium of instruction to achieve the learning objectives of the school mathematics curriculum and also meet the English proficiency goals. Mathematics textbooks play a crucial role in teaching and learning within such a learning environment. This study presents a comparative study aiming to examine how linear equation unit is arranged in secondary school mathematics textbooks (i.e., IB, IGCSE, and Chinese textbooks) in Chinese-English bilingual schools. It explores the similarities and differences in these three series of textbooks. Four aspects of linear equations in different textbooks are compared: the number of examples, the distribution of contents, the learning activities, chapter review exercises. The results show that the three textbooks have different approaches and priorities that emphasize the positions and weights of the linear equation unit. The textbooks in China contain the highest percentage of linear equation contents and pay the most attention to explaining and analyzing how to set the unknown variable and using the concept of the linear equation to solve real-life problems. The findings can enrich teachers’ and researchers’ knowledge of mathematics textbooks in international schools in China and put forward some suggestions to improve the effectiveness of using textbooks in such schools.

This JiM project set out to research the current state of understanding of mathematical justification by both Singapore secondary school students and Mathematics teachers across the different content strands in the Singapore secondary Mathematics curriculum. This timely and relevant project was started to complement the current goal of the Ministry of Education (MOE) on fostering reasoning in the learning of Mathematics in schools. While MOE focuses on the reasoning process, our study examined the outcomes of this reasoning process. For many years, mathematical reasoning and communication have been two key process skills in the Singapore Mathematics Framework under the Processes component. Thus, mathematical reasoning and justification are essential components of any mathematical activity that students should be familiar with. Yet from our personal communications with secondary school mathematics teachers between 2013 and 2016 and evidence from GCE O and N Level examiners' reports, we obtained the impression that many students, as well as mathematics teachers, struggled to navigate mathematical justification successfully. Mathematics teachers seemed to point students' difficulties in justification to several student-related factors. Other than those factors, we, however, speculated that there might be other potential obstacles, which contribute to students' poor performance in justification tasks. Therefore, this JiM project was undertaken to explore the quality of written justifications constructed by secondary school students and their mathematics teachers, with the aim of proposing a professional development (PD) programme that would allow the teachers to better engage their students in mathematical reasoning and justification more effectively, thereby improving the quality of written justifications provided by their students.

A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools is a programmatic research project at the National Institute of Education (NIE) funded by the Ministry of Education (MOE) in Singapore through the Office of Education Research (OER) at NIE. The main goal of the project is to collect a set of data that would be used by two studies to research the enacted secondary school mathematics curriculum. The project aims to examine how competent experienced secondary school teachers implement the designated curriculum prescribed by the MOE in the 2013 revision of curriculum. It does this firstly by examining the video recordings of the classroom instruction and interactions between secondary school mathematics teachers and their students, as it is these interactions that fundamentally determine the nature of the actual mathematics learning and teaching that take place in the classroom. It also examines content through the instructional materials used—their preparation, use in classroom and as homework. The project comprises a video segment and a survey segment. Approximately 630 secondary mathematics teachers and 600 students are participating in the project. The data collection for the video segment of the project is guided by the renowned complementary accounts methodology while the survey segment adopts a self-report questionnaire approach. The findings of the project will serve several purposes. They will provide timely feedback to mathematics specialists in the MOE, inform pre-service and professional development programmes for mathematics teachers at the NIE and contribute towards articulation of “Mathematics pedagogy in Singapore secondary schools” that is evidence based.

<p style="text-align:justify">Research on instructional quality has been of great interest for several decades, leading to an immense and diverse body of literature. However, due to different definitions and operationalisations, the picture of what characteristics are important for instructional quality is not entirely clear. Therefore, in this paper, a scoping review was performed to provide an overview of existing evidence of both generic and subject-didactic characteristics with regard to student performance. More precisely, this paper aims to (a) identify both generic and subject-didactic characteristics affecting student performance in mathematics in secondary school, (b) cluster these characteristics into categories to show areas for quality teaching, and (c) analyse and assess the effects of these characteristics on student performance to rate the scientific evidence in the context of the articles considered. The results reveal that teaching characteristics, and not just the instruments for recording the quality of teaching as described in previous research, can be placed on a continuum ranging from generic to subject-didactic. Moreover, on account of the inconsistent definition of subject-didactic characteristics, the category of ‘subject-didactic specifics’ needs further development to establish it as a separate category in empirical research. Finally, this study represents a further step toward understanding the effects of teaching characteristics on student performance by providing an overview of teaching characteristics and their effects and evidence.</p>

This study reviewed conceptual, theoretical and empirical literatu re on problem affecting the effective use of information and communication technology in teaching and learning of mathematics in secondary schools. Secondary source of information based on prior studies on the subject are examined in terms of methodology, research findings and recommendations. Descriptive research methodology was used to analyze the content of the theoretical, conceptual and empirical literature for this study. The study was anchored on Radical Constructivism Theory and Social Constructivism Theory. According to the study, technology is developed to solve problems associated with human need in more productive ways. If there is no problem to solve, the technology may not be developed and/or not adopted. Applying this principle to educational technology would mean that educational institution should create and adopt technologies that address educational problems, of which there are many. Majority of the findings from most of the empirical review indicates a positive relationship between teaching and learning of Mathematics and the use of information and communication technology in secondary schools. Those that indicates a negative relationship states that lack of knowledge of the teachers, low level of training and retraining of resource person, lack of relevant equipment, poor infrastructures, such as computers, network and power especially in the rural areas are some of the factors that makes the use of information and communication technology inhibit the teaching and learning of mathematics in secondary schools. It was concluded that the use of ICT in teaching and learning mathematics can make the teaching process more efficient as well as enhance the students’ capabilities in understanding basic concepts. It was recommended among others that the government, academic institutions and different stakeholders such as curriculum planners, policy makers, experts, teachers, students and parents to be serious and aware of these issues and their consequence.

The study explored the influence of teachers’ mathematical knowledge for teaching on students’ achievement, retention and attitude towards mathematics in secondary schools in Nigeria. The study was guided by three research questions and hypotheses. The study employed correlational survey research design. The population of the study comprised 3.5 million secondary school students and 100,000 mathematics teachers from the six geopolitical zones of Nigeria.The sample size for the study consisted of 500 secondary school students and 100 mathematics teachers, selected proportionally from each geopolitical zone.The primary research instrument for this study was a structured questionnaire designed to collect data on teachers’ MKT and students’ achievement, retention, and attitude towards mathematics. The content and construct validity of the instrument was established. The instrument had a reliability value of 0.76 determined using Cronbach alpha. Data obtained with the aid of the instrument were analysed using coefficient of determination and Pearson correlation. The results revealed significant positive relationship between the components of mathematical knowledge for teaching (MKT) and students’ achievement, retention and attitude towards mathematics. The study concluded that teachers’ mathematical knowledge for teaching (MKT)—which encompasses subject matter content knowledge (SMCK), pedagogical content knowledge (PCK), knowledge of learners’ learning difficulties (KLD), and understanding of learners’ misconceptions (ULM)—plays a significant role in shaping students’ achievement, retention, and attitude towards mathematics. It was recommended among others that school administrators should provide regular, targeted training programs to improve teachers’ subject matter content knowledge, pedagogical content knowledge, and ability to address students’ misconceptions, thereby enhancing student achievement, retention, and attitudes towards mathematics.

Much of the current debate among researchers revolves around the differences on the view of mathematics in secondary schools. The present research is concerned with the issue of whether or not students’ view of mathematics in secondary schools in terms of the type of schools’ factors are different between general high schools (Sekolah Menengah Atas referred to as SMA) and vocational high schools (Sekolah Menengah Kejuruan referred to as SMK) or not in the Riau province - Indonesia. This research involved a total of 276 secondary school students, 131 students from SMA and 145 students from SMK. A survey design was employed to investigate the students’ view of mathematics among secondary school students using the questionnaire. The quantitative data was statistically analyzed using MANOVA. Findings of this study indicated that a one-way MANOVA analysis revealed a significant multivariate main effect for SMK and SMA. It was concluded that SMK had a more positive view than SMA. SMK had a higher effort, mastery of goal orientation and self-confidence. These findings imply that teacher should consider students’ view of mathematics to present the most suitable learning strategy which can be imposed for students in order to boost their mathematics achievement

As part of a PhD researching teacher’s positive emotions in secondary mathematics education, I am exploring the role of play as both instigator and product of emotions. Play has recognised social, creative, cognitive and especially emotional benefits for young children. However, as students mature, do they still respond to play? Teaching mathematics in secondary school is not normally associated with play, but as illustrated below, can appear in many forms. I will argue that, in the hands of a skilled practitioner, playfulness can benefit teacher, students, and their mathematics learning. This paper explores the unique nature of play in everyday classrooms using a sample of observations and interviews with experienced UK teachers. I conclude that play appears in many subtle forms, playing various roles in a mathematics classroom.

Teachers' knowledge for teaching mathematics in secondary school is incomplete without the inclusion of knowledge of technology integration in teaching. Developing technology pedagogical content knowledge (TPACK) of pre-service teachers is essential in teacher preparation programs because PSTs gain knowledge of how to use technology in mathematics teaching before beginning their practice. This study investigates how preservice mathematics teachers' TPACK emerges during the secondary mathematics methods and field-based courses. The instructors supported the growth of PSTs' knowledge for teaching secondary mathematics and integrating technology in the method courses. The evidence of TPACK knowledge included data from lesson plans and lesson reflections, technology presentations, and semi-structured exit interviews through content analysis. Recommendations for policy and practice are elaborated.

The renewed interest in secondary school mathematics that resulted during preparedness and war periods did not instigate this investigation, as the problem here presented seemed important at any time in a plane geometry course. However, the criticisms from various sources of the content and methods of secondary school mathematics provided some motivation for this attempt to study one phase of the entire problem.

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the concepts (O. Hazzan and R. Zazkis, Reducing abstraction: the case of school mathematics, Educ. Stud. Math. 58 (2005), pp. 101–119). Reducing abstraction as a theoretical framework has been used for explaining students’ thought process in areas of advance mathematical topics in collegiate mathematics. By analysing two tenth-grade algebra honour students’ ways of thinking on quadratic functions, this article shows how the notion of reducing abstraction can be used for analysing students’ mental processes in secondary school mathematics and provides insights into students learning about graphs as well as reports two different strategies on translation tasks as an act of reducing the level of abstraction: one provides an effective method, while the other becomes misleading.