Artefacts teach-math. the meaning construction of trigonometric functions

Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be proficient at all mathematics skill subdomains compared toWhite advanced mathematics students. Interestingly, African American students who take calculus as their highest level of mathematics in high school have similar achievement levels as White advanced mathematics students who have trigonometry/pre-calculus as their highest level of mathematics in high school.

This article applies anthropological theory in exploring how Mathematics teachers imbed indigenous epistemologies in the teaching of pure Mathematics in high schools in South Africa. I spent two months staying in one of the Venda communities sharing at times food and other amenities with the three boys, at the same time collecting data and understanding cultural practices. I observed the participants on a daily basis, playing a mathematical game called “mutoga” in their local language. I also joined them in class where they were taught Mathematics at school. Findings seem to indicate that ethnomathematics epistemologies can successfully be embedded in the teaching of pure Mathematics in South African high schools. I therefore argue that the use of indigenous mediation experiences must assume culturally responsive pedagogy to open up the curriculum and assessment practices to allow for different ways of knowing and being. Initially, a generic argument for the inclusion of indigenous content within the Mathematics curriculum is suggested. Secondly, several exemplar scenarios of teaching praxis including indigenous content are discussed. Finally, evidence on the utility of such exemplar scenarios for students in learning about indigenous peoples and key processes and skills for working with indigenous communities from student feedback are discussed. DOI: 10.5901/mjss.2014.v5n15p327

According to the 2015 national curriculum revision, the high school mathematics 2 textbook introduces the definite integral as the difference of the anti-derivatives at the endpoints. However, because most calculus and elementary analysis textbooks at the university level define definite integral as the limit of Riemann sums, students who learned mathematics according to 2015 curriculum revision in high school are forced to use the word “definite integral” differently in university. Sfard views mathematics as a discourse, and she explains the historical development of mathematics and mathematics learning as the change of discourse in the participationist’s perspective. This article looks at the transition problem of the definite integral from school and university in the commognitive framework of Sfard. The comparative analysis of high school and university mathematics discourse about definite integral demonstrates that the two discourses are incommensurable not only in the different word use of definite integral but also the different meta-rule of using definitions and proving. Furthermore, the historical analysis shows that this meta-level change in the transition can be traced to the mathematical revolution from 18th result-oriented calculus to 19th rigorous calculus based on precise definitions and proof. This analysis helps instructors to understand the nature and meaning of the challenges of students in the transition of definite integral between school and university mathematics, to be aware of the commognitive conflict in the communication with students about definite integral, and to design a lesson that helps student change their discourse. The commognitive perspective can contribute to instructors seeing the didactical possibilities in the transition and improve their teaching approach.

One of the benefits of good education is that it enables individuals to contribute to the development and improvement in the quality of their life, their communities and the nation as a whole. Students’ achievements in mathematics in high school are prerequisites for admission into university and have a significant effect on their academic performance in university. In addition, mathematical and quantitative skills create possibility for better chances for employment, higher wages and higher productivity on job. Thus, mathematics learning and students’ performance in mathematics receive considerable attention from educators, teachers and parents and is important to identify the factors that could influence students’ mathematics achievement to help them improve and make substantial academic progress. This study aims to investigate factors associated with business student’ success in General Mathematics course. The population of the study consists of business students attending first-year at the Faculty of Economy, at University of Tirana for 2012/2013 academic year. Using the simple random sampling, 143 business students were randomly selected and completed a questionnaire during the first week of June 2013. The questionnaire included questions about student characteristics, family characteristics and high school characteristics. The binary logistic regression was used to estimate the impact of lecture attendance, study hours, working status, average grade in mathematics in high school, father education level, mother education level and monthly family income on final examination success. The results indicated that lecture attendance, average grade in mathematics in high school, study hours and working status were statistically significant variables that influenced their final success in General Mathematics course. These findings suggest that, primarily, institution and lecturers must find out ways to increase student performance, and to motivate students for better performance. Enhancing student participation should be a crucial aspect of administration, in order to improve performance. At the same time, the lecturer should also create a good learning environment, to motivate students and engage their interest about the course. DOI: 10.5901/jesr.2014.v4n2p11

(1953). Achievement, Aptitude, and Background of Liberal Arts and Science Students (General Curriculum) Deficient in High School Mathematics. The Journal of Educational Research: Vol. 47, No. 3, pp. 169-180.

In a climate where increasing numbers of students are encouraged to pursue post-secondary education, the level of preparedness students have for college-level coursework is not far from the minds of all educators, especially high school teachers. Specifically within the biological sciences, introductory biology classes often serve as the gatekeeper or a pre-requisite for subsequent coursework in those fields and pre-professional programmes (eg pre-medicine or pre-veterinarian). Thus, how helpful high school science and mathematics experiences are in preparing students for their introductory biology classes is important and relevant for teachers, science educators and policy makers alike. This quantitative study looked at the association between students' high school science and mathematics experiences with introductory college biology performance. Using a nationally representative sample of US students (n = 2667) enrolled in 33 introductory college biology courses, a multi-level statistical model was developed to analyse the association between high school educational experiences and the final course grade in introductory biology courses. Advanced high school science and mathematics coursework, an emphasis on a deep conceptual understanding of biology concepts and a prior knowledge of concepts addressed in well-structured laboratory investigations are all positively associated with students' achievement in introductory college biology.

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community. The findings suggest that high school mathematics education is related to the rural context in two ways. First, the small size produces characteristics unique to rural high schools. Specifically, a small number of mathematics teachers has considerable ability to shape the curriculum, instruction, and students' views of mathematics. The mathematics course offerings reflect a college preparatory curriculum with few mathematics electives offered. Students' experiences are quite similar and their beliefs about the nature and usefulness of mathematics are fairly uniform. Second, mathematics education is related to the socioeconomic aspects of a rural community. Students' knowledge of mathematics that is used in adults' work and daily life comes from experiences with parents and community members. The usefulness of mathematics, and advanced high school mathematics specifically, may not be apparent for students living in communities without mathematics-intensive jobs. Rural high school students studying advanced mathematics are likely exceeding the formal mathematical education level of their parents. The findings also indicated that Wenger's notions of identity and three modes of belonging provided a useful framework for understanding whether or not students participated in advanced mathematics classes. Students' participation in advanced math classes was related to their engagement in the day-to-day practice of mathematics education in the classroom, the place their engagement fit within the broader experiences of life in their imagination, and the alignment of their energies.

While the notion of roots of a quadratic polynomial is rudimentary in high school mathematics, that of its fixed points is uncommon. A real or complex number is a fixed point of a polynomial p ( x ) p ( θ ) = θ. The fact that the notion of fixed point of polynomials is not commonly covered in high school or undergraduate mathematics is surprising because the relevance of the fixed points of a quadratic can be demonstrated easily via iterative methods for the approximation of such numbers as , when the quadratic formula offers no remedy.

Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Euler's formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler's phi function Numerous new exercises, with solutions to the odd-numbered ones Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher-level mathematics, enabling students to study more advanced courses in abstract algebra and analysis.

Introduction and goal. The article dwells upon a topical problem of organizing distant learning, in particular, learning mathematics online. On the basis of literature analysis and analysis of teaching experience the principles of distant teaching of mathematics in middle and high schools were developed. The recommendations on creating effective cooperation of a teacher and learners while teaching online are given. Materials and methods. The identification of approaches to creating principles of teaching mathematics online in middle and high schools was carried out on the basis of analysis of academic literature, experimental teaching and surveying educationalists. Results. The article has practical value for educational institutions: the most popular electronic educational resources and software for teachers of mathematics were analyzed. It is shown how to organize the process of distant learning. The result of the experiment carried out to implement the developed principles of distant learning of mathematics at School No. 1234 (Moscow) are given. Conclusion. The implementation of the developed principles will allow teachers to ensure an effective change from full-time tuition to distant teaching of mathematics in middle and high schools. The rational use of electronic educational resources and software taking into account created recommendations (for example, a principle of basic PC knowledge, principles of completeness, system and interactivity) will allow teachers to optimize their working time without lowering the quality of teaching and interaction with learners.

In the digital age, the integration of information and communication technologies in the teaching of matematics in high school is a necessity. The correct integration of ICT, as a tool to ensure the efficiency of learning, requires a complex approach to the phenomenon from a psychological and pedagogical point of view, in order to identify the optimal conditions for integrating ICT in teaching mathematics in high school. This article is aimed at identifying the specific characteristics of teaching mathematics in high school from a psychological point of view, in order to outline an overview of the benefits of using ICT, but also the risks posed by the incorrect use of ICT in the mathematics instruction process.

This chapter focuses on lessons learned from a four-phase implementation study of the Mathematics-News-Snapshots Project, a research-and-development project designed to bridge the gap between contemporary and high school mathematics by regularly interweaving Math-News-Snapshots in the curriculum. We describe challenges encountered before, during, and after the four phases of the study and how coping with these challenges contributed to its phase-to-phase evolution. Our results show that students gained insight into the nature of contemporary mathematics as a vivid, open-ended, application-rich discipline, and their teachers gained mathematical content for teaching and pedagogical content knowledge. The overarching lesson of the project is threefold: (1) laboratory-style small sample experimentation may obscure the difficulties when implemented in real-life educational systems; (2) curriculum development outcomes and encouraging implementation research results are not sufficient to make change happen because decision making and leadership are also needed; and (3) the gap between school mathematics curricula and contemporary mathematics takes ingenuity, vision, persistence, and courage to overcome.

Problem-solving competency is crucial for social development, especially in complex environments. In mathematics education, problem-solving enhances logic, creativity, and analytical skills, contributing to societal progress. This article identified quantitative information about important publications, authors, resources, and research trends on mathematics problem-solving in high school education using the bibliometric analysis method. The input data is a set of 334 publications from the Scopus database published over four decades from 1983 to 2023. The results show that this field has obtained increasing interest, particularly in the last five years, with the USA and Indonesia being the countries with the most publications and Santos-Trigo and Putri Rii being the most influential authors. Three research trends include problem-solving in teaching mathematics in high schools, especially in teaching geometry and algebra; developing problem-solving and computational thinking skills through STEM education, engineering education, and educational computing for students; and using information technology to solve mathematics problems. These results provide teachers and researchers with helpful information about solving mathematical problems in general education, thereby contributing to shaping and proposing effective research and educational strategies, new teaching methods, training programs, and appropriate educational policies.

For the presentation of the teachers' material more effectively and efficiently; therefore, it needs media learning that can motivate and stimulate students to morale in learning. One of them is by making use of ICT-based learning or media that we often call it TIK. This research aims to describe how the implementation of ICT-based learning media in learning mathematics in high school. This research is a research library. This research's nature is descriptive-i.e. decomposition analysis regularly, then the whole concept of giving comprehension and explanation to taste the result description. The analysis of the data used in this study analyzes the content (content analysis). The results of the research study this library is; (1) the existence of the benefits of ICT-based learning media in education; (2) the presence of the benefits of ICT-based learning media in the process of learning mathematics in high school.

It must be pupils' unpleasant experiences with arithmetic in the grades that cause them to avoid mathematics in high school. Before failure of pupils was ruled out by “progressive” education, arithmetic caused more failures than any other subject in the elementary curriculum. Today a high percentage of pupils show no enthusiasm for arithmetic.