High School Mathematics Research Articles

The development of a didactic sequence for teaching fundamental trigonometric equations in basic education

The research is related to the teaching and learning of Fundamental Trigonometric Equations. The guiding question of the research was: How will a Didactic Sequence, developed according to the structuring model (UARC), with the aid of concrete material and software, contribute to improvements in the teaching and learning process of Trigonometric Equations? To answer this question, the general objective was defined to propose the development of a Didactic Sequence to enhance the teaching and learning of Fundamental Trigonometric Equations. The didactic sequence is structured according to the construct of Articulated Units of Conceptual Reconstruction (UARC), according to Cabral (2017). Dissertations and textbooks on the subject were analyzed, in addition to a questionnaire via Google Forms being applied to high school mathematics teachers and alumni with questions relevant to the research; the data collected corroborated the methodological objectives outlined. The teaching sequence was applied to an experimental class, while the control class was taught in a traditional way. At the end of the classes, both groups took a test to verify their learning. The analysis of the results is based on the theories of Microgenetic Analysis by Góes (2000) and Discourse Analysis by Mortimer and Scoot (2002). The transcribed learning evidence, together with the average grades on the learning verification test of the experimental class, indicated that the use of the teaching sequence for teaching fundamental trigonometric equations with the help of manipulative materials proved to be an efficient methodological alternative for teaching.

Learning Opportunities for Solving Context-Based Calculus Tasks in Nepal’s High School Mathematics Textbooks

ABSTRACT A vital skill for students to acquire in school mathematics involves solving problems embedded within real-world contexts. The extent to which students achieve intended learning outcomes largely depends on whether textbooks offer opportunity-to-learn (OTL) the assessed concepts and skills. The National Assessment of Students’ Achievements (NASA) reveals a significant deficiency in the performance of Nepali students in solving context-related problems. We conducted a content analysis of the most commonly adopted Nepali mathematics textbooks for grades XI and XII to assess the OTL they afford for tackling context-related problems in calculus. Results show that almost all mathematical concepts were introduced without providing related contexts, and around 95% of worked examples and exercise problems did not have any context and offered little or no opportunities for modeling and mathematization. Although most of the contexts presented in the problems were categorized as real and essential, the cognitive demands of many tasks were lower. The investigated textbooks were not necessarily aligned with Nepal’s updated National Mathematics Curriculum (2018), which underscores the integration of mathematics with real-world applications. Results of this study indicate that the limited access to quality mathematics textbooks might be a significant barrier hindering students’ ability to solve context-related problems.

Research on the Application of Mathematics in Finance

Abstract. Mathematics is a fundamental science and a problem-solving method that plays an important role in revealing the essential laws of the development of certain things. It has rigorous logic, high abstractness, and wide applicability. This brings great difficulties to enterprises, especially high school mathematics because it involves a wide range of knowledge points and complex calculations. Among them, the formation of financial mathematics has greatly promoted the development of China's financial industry. Moreover, in solving financial problems, relevant knowledge and theories of mathematics can be used to analyze and explore financial laws, and the application effect is significant, for example, using deterministic mathematical method and nondeterministic mathematical method to solving question about financial investment and returns; building securities investment portfolio model or asset valuation model to calculating and expressing some economic models. Based on this, this article discusses the application of mathematical knowledge to several financial problems, analyzes the current problems, and looks forward to the future of financial mathematics.

Exploring The Perceptions and Use of Information and Communication Technology Tools Among High School Mathematics Teachers in The Northern Region of Ghana

This study explored the extent to which senior high school mathematics teachers in the Northern Region of Ghana use Information and Communication Technologies (ICTs) in teaching and learning mathematics. A descriptive survey design was employed for the investigation. Using a stratified sampling technique, 20 public high schools in the northern region of Ghana were selected for the study. A simple random sampling was used to select 100 teachers (i.e., 50 teachers from urban and 50 teachers from rural schools) from the 20 schools for the study. Questionnaires were used to collect data for the study. The findings revealed that the mathematics teachers’ perceived knowledge of the benefits of ICT usage for instructional delivery, assessment, and professional learning networks in mathematics were low compared to their actual usage of the ICTs for the same purposes. The findings suggest that the participants utilize ICTs more for social networking than for instructional delivery, assessment, and professional development in mathematics. Further, the findings showed a positive relationship between the teachers’ perceived knowledge of the benefits of ICTs usage for instructional delivery and their actual use of ICTs for instructional delivery. Mathematics teachers from urban schools use ICTs for all instructional purposes more than their peers from rural schools. Implications for ICT policies, teacher training, and professional development are provided.

Quadratic equations with absolute values: an example of developing proof in mathematics students

Proof is the most important and fundamental aspect of mathematics. However, it is generally agreed by mathematics teachers at upper high school and first year university that students lack the ideas of proof. How to develop this in students is a common, difficult and perennial problem. In this paper, we develop some ideas of proof based on the number of solutions of an equation involving a quadratic polynomial and absolute values of linear functions. We begin with the simple idea of making more precise a question that is posed, investigating the problem through exploration, and arriving at some conjectures. We proceed to determine ways to prove the conjectures and thus convert them into theorems. The question discussed in this paper arose in a session for high school students held at the Department of Mathematics and Statistics of the University of Western Australia. The result is an excellent and interesting illustration of problem posing and solving in mathematics that underpins mathematical thinking. The paper is accessible to final year high school and first-year university mathematics students. We expect that it will serve as a resource for and inspire further ideas and examples for mathematics teachers, for teaching proof to students.

APOS Framework Didactize Equivalence Linear Simultaneous Equations in Senior High School Mathematics

Many students followed rote-learned procedural rules without thinking about the meaning of quadratic equations, and the Chief examiners’ reports attributed the trend to poor teaching methods. In certain instances, candidates cannot use even the conventional methods to factorize quadratics equations due to a lack of understanding of the zero-product property in graphing, factorizing, and completing the squares or quadratic formula. In the worst circumstances, the candidates failed to scaffold higher-order quadratic equations using the Conjugale and Equivalence Linear Simultaneous Equation methods. However, the action, process, object, and schema theory which came out of the constructivist learning theory and created by Dubinsky can be applied to teach mathematics. With the aid of the APOS framework, this study sought to digitize the Equivalence Linear Simultaneous Equations in senior high schools. In this mixed-method embedded design, there were 286 first-year students selected from one school. All the students received four phases of the APOS framework. The four phases were collected based on the Actions for Factorization, Processes for Quadratic Formula, Object for Conjugale, and Schema for ELSE method. The data, which was both qualitatively and quantitatively, was analyzed using IBM SPSS Statistics (Version 26) deterministic analytics software. The data collection covered four contact periods of a total duration of four hours. The results showed that students in the Actions and Processes were not statistically significant. However, the results were statistically significant at the Object and Schema phases. It was concluded that students’ learning through the APOS framework improved their academic performance. The positive effect was the triumphant mental constructions involving encapsulation and interiorization in the conjugale and ELSE methods. It was, therefore, recommended that the framework be promoted to find solutions to many other complex mathematics problems.

Interdisciplinary perspectives of applying mathematics in high school, real profile

Analyzing the concerns of human society, we come to the imminent conclusion that mathematics has a particularly important role in all its spheres, leading to the formation of logical - abstract thinking, to the modeling of natural phenomena, to the systematization and ranking of priorities, as well as to the development of algorithms - basis for the other sciences. The continuous need to discover the analysis models of some phenomena led various researchers towards the improvement of classical mathematics (metrics), coming to be dominated by the algebraic side (the science of the discontinuous) combined with the topological one (the science of the continuum) as a response to the combined character of reality. G. Moisil mentioned "...next to (classical) metrical mathematics, logical structural mathematics was elaborated. Modern mathematics is a science dominated by the category of structure" [1]. According to Bellman, the proof of knowledge of phenomena is the precision of their anticipation, a fact based on formulas and mathematical calculations, and Mircea Malița defines the model as "a mental or written, qualitative or mathematical representation of a part of a reality that constitutes a system", which leads to the idea of its practical and experimental applicability. This article aims to exemplify some practical ways of using mathematics in various disciplines as well as to capitalize on the practical side in several other fields.

Conceptual images and learning obstacles in exponentiation and logarithms: A hermeneutic phenomenological analysis

The concept of exponentials and logarithms is one of the essential concepts in mathematics as part of transcendent functions. However, students' understanding of these two concepts has yet to be fully mastered, so there are still errors in solving problems related to these two concepts. This study aims to describe the meaning and meaning process and explore the potential learning obstacles of students based on the meaning and experience of students in obtaining the meaning of exponents and logarithms in senior high school. This qualitative study uses a hermeneutic phenomenological approach with student participants and high school mathematics teachers. Data was collected using tests, documentation, and interviews with students and teachers. Data were analyzed qualitatively to identify learning obstacles and the meaning of exponentials and logarithms. The results showed the meaning of exponents and logarithms according to students, namely exponents as power numbers and logarithms as the opposite of power numbers. In addition, the results also show the existence of learning obstacles in students, both ontogenic, epistemological, and didactic. Based on the findings, these learning obstacles can be considered when developing an appropriate didactic design.

Understanding Barriers to STEM: Teachers' Insights on African American Underrepresentation

This study focuses on the development of a measurement instrument to identify Middle and High School mathematics and science teachers’ beliefs about the main factors of underrepresentation of African American students in STEM (Science, Technology, Engineering, and Mathematics) fields. The research method using the stages of instrument development were (1) test design which involved construction of initial item pool by conducting extensive review of literature and coding of participating teachers personal statements (2) determination of validity which involved expert review process to confirm construct and face validity of items, (3) pilot testing which involved collecting data from a second set of participants, (4) determination of reliability which involves conducting a reliability analysis based on data collected from pilot testing and (5) determination of factorial structure which involved Exploratory Factor Analysis (EFA) to identify underlying factors in participating teachers’ belief structures. First, to obtain trustworthy information, voluntary middle and high school mathematics and science teachers were asked to write personal statements where they explain their main reasons for choosing teaching as a career. Secondly, qualitative data obtained from participating teachers’ personal statements were coded. Coding was applied to identify and to group the phrases or sentences that convey the same or similar reasons. Then results from an extensive literature review on this topic were blended in teachers’ common expressions which were determined because of coding procedure. Then 8 content experts assessed content validity and face validity. Finally, the survey was piloted to African American middle and high school mathematics and science teachers. Fifty-three (53) surveys were completed and received back from teachers. Then, exploratory factor analysis was conducted to identify any underlying factors in the scale. Reliability analyses were also conducted for both the entire survey and for each of the factors. Results of the study suggested four underlying components: (1) Access and Resources, (2) Role Models and Representation, (3) Bias and Discrimination, (4) Curriculum and Pedagogy.

고등학교 수학교사의 디지털·AI 교육과정 실천 사례: 생태학적 교사 행위주체성에 기반한 탐색

With the advent of the era of digital transformation, digital·AI-related policies are being actively promoted in the curriculum. This study aims to explore high school mathematics teachers’ practice of digital·AI curriculum based on ecological approach to teacher agency. For this, interviews were conducted with four high school mathematics teachers, focused on the following research questions: 1) How do high school mathematics teachers practice the digital·AI curriculum? 2) What are the factors that influence high school mathematics teachers’ practice of the digital·AI curriculum? The results of the study showed that high school mathematics teachers practiced the digital·AI curriculum, showing various teacher agency, ranging from neutral·critical acceptance, passive practice, and proactive implementation. In addition, these various practices are influenced by personal factors (prior experience or knowledge, beliefs to mathematics classes, recognition to future competencies) and contextual factors (school environment, attitudes of mathematics teachers at the same school, teacher learning community). This study discusses the usefulness and value of ecological approach to teacher agency in interpreting mathematics teachers’ curriculum practice, and suggests the need for structural, environmental, cultural support to enable teachers' autonomous and independent practice of the digital·AI curriculum.

Making Mathematics Accessible to Visually Impaired High School Learners in South Africa: Teachers’ Instructional Approaches, Assistive Devices and Challenges

ABSTRACT This case study explored the instructional approaches and assistive devices employed by high school mathematics teachers in teaching visually impaired (VI) learners and the challenges encountered by the teachers in facilitating the learners’ construction of mathematical knowledge. The participants were two high school mathematics teachers from a special school for the visually impaired in South Africa. Data was collected via semi-structured interviews and lesson observation. Inadequate skills in using Braille codes, time constraints, lack of learners’ home support structure, and technology failure are some of the challenges encountered by the teachers in teaching the VI learners. The approaches used by the teachers to teach mathematics to the VI learners in this study are direct instruction, contextual linking, scaffolding, peer tutoring, and problem-solving. The technologies the teachers used included text enlargers, text translators, text embossers, structure embossers, and scientific talking calculators. The study recommends in-service training for teachers teaching mathematics to

The Contribution That Utilizing Generative AI for Problem Posing Makes to Pre-Service High School Mathematics Teachers' TPACK

Fifteen pre-service mathematics teachers studying in a teachers college participated in a unique program entitled "From high-tech to teaching" as part of a specialization program for teaching advanced secondary school mathematics. During the course, they solved various mathematical problems and then were asked to pose additional problems and upgrade them to meet precise educational goals by furnishing "prompts" to a generative AI environment (ChatGPT) and refining them as necessary according to predefined steps. To understand how this process contributed to the pre-service teachers' body of technological, pedagogical, and content knowledge (TPACK), they were asked to respond to a questionnaire (ten Likert-type statements; six open-ended questions).The findings indicate that posing problems in an AI environment increased their technological knowledge vis-à-vis the advantages of the environment itself and how to generate effective prompts to obtain relevant responses. They also became aware of some disadvantages. With respect to their technological-pedagogical knowledge, integrating AI at challenging pedagogical junctures (e.g., tailoring problems to students' individual needs) provided diverse pedagogical ideas. Although AI involves some challenges (e.g., all suggestions must be critically examined), overall they expressed satisfaction with the concept and indicated they would use it in the future.

Enhancing High School Mathematics Education Through School-based Research: Development and Mechanisms

In the context of ongoing educational reforms aimed at fostering critical competencies among high school students, this paper explores the implementation and impact of school-based mathematics research (SBR) as a strategic innovation within the high school curriculum. Adopting mixed research methods, in the study questionnaires were distributed to all students and teachers in the early stage to collect and analyze relevant data and than the study combines quantitative analyses of student performance data with qualitative insights from teacher and student feedback to assess the effects of SBR on teaching practices and learning outcomes. This research is based on the fact that the traditional education model cannot meet the needs of cultivating students' thinking ability, and the new curriculum reform has decentralized teaching research to schools. The study is helpful to explore the effect of SBR on the cultivation of teachers' scientific research ability and the improvement of classroom quality. The results show the powerful role of SBR in promoting teaching practice and student participation. Based on school characteristics, it proposes effective teaching improvement measures to improve the quality of mathematics education.

Intrinsic relations among chemistry, physics and mathematics in the brazilian high school: a theoretical-methodological approach

This paper reports an investigation into the dialogical relation among significant learning experiences of Chemistry, Physics and Mathematics contents in an interdisciplinary context. It aimed at answering the following questions that are relevant to the field of Exact Sciences: why do students show little interest in these courses?; where is the problem?; did Chemistry and Physics abandon Mathematics when they started to focus more on qualitative and theoretical concepts than on quantitative ones?; and how can the three courses work together to make both teaching and learning processes easier?. This study presented an actual overview of the Brazilian High School by highlighting strengths and weaknesses from the perspective of Chemistry, Physics and Mathematics teaching. The Brazilian educational scenario showed again that the three courses are the ones that students enjoy the least. The research methodology had a qualitative focus since it had an interpretative and descriptive nature. Answers given to the questions may be found in the text intertwined with some worrisome reflections, which also include the triad teacher-student-educational system. Results showed that further studies are needed to find out the reasons for multiple difficulties found in the intrinsic relations among Chemistry, Physics and Mathematics. It is disappointing to know that no satisfactory practical solution has been proposed so far. Everything has been kept in the educational ideal described by research articles, chapters and motivational quotes.

El constructivismo y las tecnologías para favorecer la enseñanza aprendizaje de la matemática en el Bachillerato

Constructivism focuses on the student as an active participant in his or her training, equipped with the necessary tools to solve various problematic situations. Faced with the challenge of obtaining better results in the learning of students, in this research an analysis is carried out regarding whether the constructivist approach and the use of technological tools favors the teaching-learning process of mathematics in high school. When analyzing the theories on constructivist learning and the conception of constructive alignment, it is considered that the application in this discipline, together with the use of technologies, would produce great benefits to the training process, which is accredited with the evidence of the results obtained by several authors. It is concluded that this methodology could be favorable for achieving meaningful learning in students, which would allow them to better understand, learn, remember and apply mathematical concepts.

Enhancing Measurement and Calculation Education in High School through 3D Printing Technology

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics education remains limited. This research explores the potential and effectiveness of 3D printing technology in enhancing the teaching of measurement and calculation topics in high school mathematics. We designed 3D printed models with a specific focus on shapes, polyhedra, pyramids, and cylinders. These models were created to facilitate hands-on learning experiences for students, enabling them to directly measure, calculate, and experiment with these tangible mathematical objects. The experimental results reveal that students not only learned how to employ measuring tools to gauge the dimensions of tangible mathematical objects but also conducted mathematical experiments related to the 3D printed models. This practical engagement allowed students to gain valuable experiences and foster a deeper understanding of abstract mathematical concepts.

From knowledge acquired at academic mathematics courses to significant changes in instructional practices

This non-interventional study investigates the contribution of university mathematics to teaching high-school mathematics. Data sources included interviews with five teachers who taught high-school mathematics before, during, and after their academic mathematics studies. All teachers provided tangible examples of fundamental changes in instructional practices that they explicitly linked to new knowledge acquired in the academic mathematics courses. The domain of analysis in general, and the topics of integrals and derivatives in particular, were central in the teachers’ illustrations of changes they made in their teaching, although other mathematical topics and domains were also mentioned. The reported changes were mostly associated with emphasis on mathematical explanations, exposition of two key elements of the deductive structure of mathematics: definition and proof, an increased focus on formal mathematics, and portrayal of mathematics as a wide and varied discipline. The study results are discussed in light of the relevant literature.

PHÁT TRIỂN NĂNG LỰC GIAO TIẾP TOÁN HỌC CHO HỌC SINH LỚP 10 TRONG DẠY HỌC CHỦ ĐỀ PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG

Mathematical communication is one of the core competencies that needs to be formed and developed for students in the teaching of Mathematics in high schools. In this research, we have identified the manifestations of mathematical communication competence in 10th-grade students in teaching the topic “Coordinate Methods in the Plane”, based on a survey of opinions from 68 high school mathematics teachers in the provinces of Nghe An and Ha Tinh. Additionally, the research was also conducted with 32 10th-grade students who were assigned several learning tasks related to the topic “Coordinate Methods in the Plane”, with the aim of understanding the manifestations of students’ mathematical communication competence and the mistakes they made related to these manifestations. From there, propose several teaching methods to contribute to the development of mathematical communication competence in students in teaching this topic. Keywords: Mathematical communication competencies; 10th-grade students; coordinate methods in the plane.

Research on the Cognitive Situation of Pre-Service Mathematics Teachers for Teaching Evaluation of High School Mathematics under the New Curriculum Standards in China

Research on the Cognitive Situation of Pre-Service Mathematics Teachers for Teaching Evaluation of High School Mathematics under the New Curriculum Standards in China

Who benefits from high school exit exams? Examining variations in math course-taking by abilities and socioeconomic status

Using the High School Longitudinal Study of 2009, the association between high school exit exams and mathematics course-taking patterns is explored. Exit exams are linked to a decreased likelihood of students taking upward-bound mathematics during their four years of high school. Exit exams are also associated with fewer mathematics credits earned. However, exit exams are linked to increased likelihood of students completing Precalculus or higher, but have no discernible association with completing Algebra II or higher. Importantly, significant disparities exist in these associations, with underprivileged, underperforming students often experiencing limited access to advanced math courses due to exit exams.