MODERN MATHEMATICS IN SECONDARY SCHOOLS

School Science and MathematicsVolume 18, Issue 2 p. 112-123 VALID AIMS AND PURPOSES FOR THE STUDY OF MATHEMATICS IN SECONDARY SCHOOLS Alfred Davis, Alfred Davis Francis W. Parker School, SSO Webster Ave., ChicagoSearch for more papers by this author Alfred Davis, Alfred Davis Francis W. Parker School, SSO Webster Ave., ChicagoSearch for more papers by this author First published: February 1918 https://doi.org/10.1111/j.1949-8594.1918.tb02098.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume18, Issue2February 1918Pages 112-123 RelatedInformation

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

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.

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.

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.

BackgroundSTEM (Science, Technology, Engineering, and Mathematics) fields are in high demand for qualified personnel worldwide, yet drop-out rates of a career path in STEM occur at various points in lifespan. Based on a big-data analysis of 534,590 records retrieved from the Israeli Central Bureau of Statistics for several points in time over one and a half decades, the study aims to examine the various pathways of which secondary school students take toward STEM-related careers, and to characterize each pathway based on various demographic and educational factors.ResultsThe study presents a three-tier tree, which highlights eight pathways leading to STEM or non-STEM bachelor's degrees. An important finding is the recognition of a non-linear pathway, demonstrating the biggest ‘leak’ from STEM in secondary school to non-STEM in higher education. Further, findings indicate that choosing advanced mathematics, majoring in physics and computer science in secondary school, and excelling in mathematics or science major at secondary school, have a lasting effect on STEM persistence in higher education. Additionally, males and non-minorities populations have the highest likelihood of choosing STEM for future studies.ConclusionsThe study contributes theoretically to broadening the conceptualization of various pathways toward pursuing a STEM career across important choice stages in people’s lifespan. Moreover, the study provides insight into the long-term effect of education choices made in secondary school, as well as demographic and educational factors, on future choice for study.

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 functions that are performed by modern mathematics as a science exert a decisive influence on the formation of the content and methods of instruction and on the formation of the poly-technical principles of mathematics in secondary schools. Mathematics occupies an important place in the general system of human knowledge in our time. As one of the foundations of natural science and technology, it has changed its status appreciably among other sciences, has expanded the sphere of its direct application to an extraordinary degree, and has become more and more penetrating in the majority of areas of human knowledge and activity. The methods of mathematics are widely used in the management of enterprises and branches of the economy, and in the economy are used for the automation of industrial production and the introduction of automated (assembly] lines and plants, machines, machine tools, and mills with programmed controls. Today mathematics is also beginning to penetrate traditionally nonmathematical areas: biology, medicine, linguistics, and so forth.

A secondary school in Melbourne, Australia piloted an innovative programme in Year 10 Advanced Mathematics, in which the students recorded screencasts as a method of student-led peer learning. The four mathematics teachers who piloted the programme were interviewed to gain their perspectives on their experience and the outcomes of the initiative. Thematic analysis revealed the teachers did not recognize a need to adapt their pedagogy to integrate the technology effectively into their teaching. Three of the teachers were also focused on the quality of the screencast product rather than scaffolding the lessons to enable impactful student-led learning. One teacher who did scaffold his lessons felt unable to lead the other teachers in a consistent approach to the project. The study underscores the need for teacher professional development in pedagogical methods for student-centred, technology-enabled learning if the integration of digital technologies in twenty-first century secondary school classrooms is to be successful.

This study investigates the use of the history of mathematics in secondary school mathematics coursebooks designed according to the new curriculum prepared in 2018 and to make alternative suggestions in which mathematics history can be used. For this purpose, four mathematics coursebooks, which were decided to be taught in schools affiliated to the Turkish Ministry of National Education for four years as of 2018, were analyzed by document analysis method, and this research attempted to determine to what extent the history of mathematics was used in these coursebooks. While making this analysis and analyzing the data, the categories proposed by Erdoğan et al. (2015) were used, including “historical notes,” “notes on usage areas of mathematics,” “applications with historical notes,” and “historical elements in students‟ extracurricular activities.” As a result of the study, it was found out that the 27 elements of the history of mathematics used in the coursebooks were mostly included at the fifth grade, in thelead-in stage, in the area of learning numbers and operations, in the form of small historical snippets about the historical development of situations other than mathematics. In light of these findings, it can be suggested that the history of mathematics is not used sufficiently in secondary school mathematics coursebooks.

This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape Province. Elements of Gumperz and Mercer’s work on lesson categories and Dowling’s Domains of Mathematical Practice were used to analyse data. Results showed that code switching frequency in general was inconsistent across different lessons for the same teacher. Code switching frequency by all teachers was, however, consistently highest during questioning and explaining when teaching. All participating teachers used code switching strategies most consistently in the public domain and least consistently in the esoteric domain. Some formal isiXhosa translations of mathematical terms were consistently and precisely used and some were not. Two major forms of code switching emerged, namely borrowing code switching and transparent code switching. Very little transparent code switching, which is critical for supporting students’ understanding and thinking in mathematics, was evident in teacher language. Teachers were consistent in the use of borrowed terms. We conclude that consensual understanding of best practices for code switching is required to promote code switching that is precise, consistent, transparent and thus supportive of teaching for conceptual understanding of mathematics in secondary schools.

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.

ABSTRACTThis study aimed to develop and validate a student self‐report questionnaire to assess the extent of higher‐order thinking skills (HOTS) in secondary school mathematics instruction. The study employed random sampling techniques to select study participants. The validation study comprised 496 students, while the pilot study involved 111 secondary school students. The development process involved expert review, exploratory factor analysis (EFA), and confirmatory factor analysis (CFA) to ensure content validity, structural clarity, and psychometric soundness. With 27 items that explained 54.5% of the total variance, EFA supported a four‐factor structure: Teachers' Instructional Practice (TIP), Critical Thinking (CT), Problem Solving (PS), and Creative Thinking (CRT). CFA confirmed a 26‐item model with excellent fit indices (CFI = 0.980, RMSEA = 0.029), strong construct reliability (CR > 0.84), and acceptable average variance extracted (AVE > 0.5). A second‐order factor model was tested and validated, revealing HOTS as a higher‐order construct that subsumes CT, CRT, and PS. However, TIP continued to be a separate but connected factor. The final instrument meets the relevant criteria set by the Standards for Educational and Psychological Testing. It offers a reliable, valid, and context‐sensitive tool for evaluating cognitive engagement in mathematics education. The developed student self‐report questionnaire holds significant potential for research, diagnostic assessment, and instructional improvement in both local and international settings. Finally, the authors discussed limitations and directions for future research.

The purpose of this study was to investigate the effect of digital concept cartoons and maps in eliminating misconceptions of secondary school students. The research was conducted with 67 students who were studying at three different branches of 7th grade of secondary school. The research was conducted according to semi-experimental design with pre-test, post-test control group, and quantitative and qualitative research methods (mixed pattern) were used together. Accordingly, the mathematics classes in the Study Group I were conducted by the DCC method and the mathematics courses in the Study Group II were conducted by the DCM, and the mathematics courses in the control group were processed by traditional teaching method. In order to determine the students’ misconceptions before and after the experiment, Misconception Test was used which was applied as Pre-test and Post-test. In addition, students’ opinions and observation processes related to the use of DCC and DCM in mathematics class were included in the experimental process. As a result of the data analysis, there was no statistically significant difference between Study Group I, Study Group II and control group when the results of the Misconception test of the control and study groups were compared. In addition, students stated that the use of DCC and DCM in mathematics course have advantages such as making the courses enjoyable, drawing attention, increasing interest in the course, and visualizing the course topics. In the direction of the findings obtained from the research, various suggestions were made to the teachers and researchers about the use of DCC and DCM in secondary school mathematics courses.