Teaching Of Algebra Research Articles

Metacognitive training for algebra teaching to high school students: An action research study

Metacognition is an essential concept in mathematics education research. Studies indicate that high school students in Turkey must demonstrate expected success in learning mathematics in general and algebra in particular. To this end, the Ministry of National Education has initiated a mathematical mobilization in Turkey. Mathematics mobilization is a project that will adapt the learning of mathematics to daily life skills, making learning more accessible and ensuring that students love this course from an early age. In the initial interviews with teachers as part of this mobilization, teachers stated that high school students needed to exhibit sufficient metacognitive planning and monitoring strategies. Therefore, they required assistance in planning and monitoring their learning processes and motivating them to learn. The literature shows that metacognitive planning and monitoring are effective in teaching algebra. In this context, the research “How can metacognitive strategies be developed in high school students’ algebra learning?” seeks an answer to this problem. Based on preliminary teacher interviews, the researchers created action plans in collaboration with teachers. In the circular model, researchers tested these action plans and revised them. As a result of the cycle being repeated three times, researchers developed a teaching technique based on metacognitive planning and monitoring for high school students. The study’s findings demonstrate that metacognitive training taught students metacognitive planning, monitoring, prediction, awareness, and motivation strategies.

Didactic strategy of linear algebra with collaborative learning in mathematics pedagogical training

This article details the design and implementation of a didactic intervention strategy aimed at enhancing the pedagogical skills of mathematics education students in the teaching of linear algebra. Given the challenges students often face in grasping abstract mathematical concepts, the intervention leverages the Anthropological Theory of Didactics and Collaborative Learning as its theoretical framework. The phases of the intervention's execution in the classroom, along with the key elements for successful implementation, are thoroughly outlined. The results indicate significant improvements in academic performance in the units’ covering determinants, matrices, and systems of linear equations, while challenges persist in the unit on vector spaces. In terms of task genres, students showed proficiency in defining and calculating, although there was a lower level of mastery in demonstrating. The study concludes that, despite a general unfamiliarity with autonomous learning, the future educators were able to become active and effective contributors to their own mathematical knowledge construction through collaborative group work.

Research on the Use Power Point (PPT) in Junior High School Mathematics Classroom Teaching

Since PowerPoint (hereinafter referred to as PPT) is of great significance to mathematics teaching, more and more attention has been paid to how to use PPT effectively in junior high school mathematics classroom teaching. This paper uses the method of theoretical analysis, through the analysis of the characteristics of PPT, the current teaching situation and the problems existing in students' mathematics learning, combined with the various requirements of the Mathematics Curriculum Standards for Compulsory Education (2022 Edition) (hereinafter referred to as The Standards) for junior high school mathematics teaching, puts forward four strategies for using PPT in junior high school mathematics classroom teaching. Through analysis, we can know that PPT is characterized by its powerful presentation function, dynamic presentation effect, lacks of procedural presentation, multiple ways of emphasis, and strong inclusiveness. The current problem of students in mathematics learning is students do not have a firm grasp of basic knowledge and have an inaccurate understanding of many concepts, students' ability to analyze and solve mathematical problems is weak, and they cannot accurately understand the conditions and requirements of the problems, students lack enthusiasm for learning mathematics, and students have improper learning methods and lack the habit of writing on time. The current situation of mathematics classroom teaching is teachers pay too much attention to the teaching of problem-solving methods and calculations and neglect the inspiration and training of problem-solving ideas, teachers' teaching resources are obsolete, and the use of information technology in teaching is inadequate, teachers' teaching methods are rigid and lack diversity and innovation, and the interaction between teachers and students is mostly ineffective and the overall participation of students is low. The standard puts forward specific requirements for the teaching of number and algebra, graphics and geometry, statistics and probability in junior high school. Therefore, through the above analysis, we give the following suggestions: 1. Making full use of the multiple emphasis effect of PPT to highlight different mathematical symbols; 2. Skillfully using the dynamic presentation function of PPT to make the process of mathematical knowledge formation dynamic; 3. Expanding the scope of use of PPT and give full play to the value of PPT in all aspects of teaching; 4. Integrating and collocating a variety of technologies reasonably, and use PPT in a variety of ways to teach mathematics. These strategies can be used for reference by junior high school mathematics teachers in practical teaching.

Exploration of Integrating Mathematical Culture into the Teaching of Linear Algebra

Exploration of Integrating Mathematical Culture into the Teaching of Linear Algebra

Epistemological justification

AbstractEpistemological justification is a way of thinking that manifests itself through perturbation-resolution cycles revolving around the question why and how was a piece of mathematical knowledge conceived? The paper offers a conceptual framework for constituent elements of epistemological justification. The framework provides: (a) a theoretical basis for epistemological justification, (b) criteria for its occurrence, and (c) analysis of its relation to mathematical explanation. The criteria are illustrated by a series of learning-teaching events taken from teaching experiments aimed at investigating the learning and teaching in linear algebra. The contribution of the proposed framework is three-fold: (a) it addresses a critical aspect of proof understanding not explicitly addressed in the literature; (b) it goes beyond the traditional treatment of mathematical understanding and production into questions about learners’ conceptualization of the origins of mathematical knowledge; and (c) it theorizes instructional approaches that can advance this conceptualization among students.

Preparing elementary pre-service teachers to teach early algebra: A conceptual replication study

Early algebra can prepare elementary students for the transition they will need to make from arithmetic and algebra. Although teacher preparation programs emphasize the teaching of early algebra, research on how to prepare elementary pre-service teachers (PSTs) to teach early algebra is still scarce. The replication study reported in this article was a conceptual replication study designed to examine Iranian PSTs’ reasoning about pre-symbolic early algebra by looking at what was more, somewhat, and less challenging. The aims of the replication study aligned with the original study (Hohensee, 2017). Results from the replication study show that participating PSTs (N = 15) found the early algebra approach to variables and functions more challenging, indeterminable unknowns somewhat challenging, and equivalence and equations less challenging. We make comparisons with the original study, as well as offer implications and suggestions for preparing PSTs to teach early algebra.

Teachers’ mathematical work based on examples presented in the teaching of algebra in secondary education

Both international examination results and scientific evidence related to the teaching and learning of school algebra point to the necessity for analyzing mathematical practice in the classroom. In this context, we have formulated the research objective of characterizing the mathematical work that teachers favor based on the examples that they implement in the teaching of topics within the domain of secondary school algebra. To this end, this study is situated within the interpretive paradigm utilizing an instrumental collective case study approach. The study design entails the selection of two representative cases of mathematics teachers in Chilean schools, with the objective of understanding and describing their mathematical work in the secondary school classroom based on the examples they present. The results show that the first teacher utilizes varied examples that activate distinct forms of mathematical thinking, promoting the activation of both instrumental and discursive genesis. In contrast, the second teacher follows a more traditional approach, with the use of examples to illustrate and motivate, and a direct presentation of knowledge, activating primarily semiotic genesis, in which a transition between the numerical and the algebraic is lacking. Ultimately, the results highlight the importance of deeper consideration of the choice of examples in the teaching of algebra and how these examples can influence students’ learning. Furthermore, additional ideas are put forward for future work in this line of research associated with the use of examples in the classroom.

Semiotic mediation of gestures in the teaching of early algebra: the case of the equal sign

Semiotic mediation of gestures in the teaching of early algebra: the case of the equal sign

Application of Offline and Online Hybrid Mode in Linear Algebra Teaching

Application of Offline and Online Hybrid Mode in Linear Algebra Teaching

Integrating the Case Studies Pedagogy and the Anthropological Theory of Didactics to Enhance the Teaching and Learning of Algebra in Undergraduate STEM Education

Methodology case studies plays a pivotal role in STEM education, especially in teaching undergraduate algebra. This article emphasizes the power of real-world scenarios and active pedagogy, a student-centered approach that makes abstract algebraic ideas tangible. The Anthropological Theory of Didactics (ATD) is spotlighted as a perspective that treats mathematical knowledge as a cultural artifact, embedding mathematics concepts deeply within cultural and historical contexts. By comparing active pedagogy with ATD, the article unveils a compelling overlap that values the significance of context in learning. Students don't just engage actively but also delve into the cultural essence of mathematical problems, gaining a profound understanding. Addressing the hurdles undergraduates face in transitioning from high school algebra to university level, the article suggests activities that merge active pedagogy and ATD. This holistic approach has the potential to transform algebra education into a more engaging, relevant, and culturally resonant experience.

Exploration on Hybrid Teaching Mode of College Public Mathematics: Taking Linear Algebra Course as an Example

The rapid development of science and network technology has changed the way people study. Constructing a mixed teaching model by integrating online and offline teaching, and organic integration of knowledge, abilities, and comprehensive qualities, cultivate the mathematical literacy and comprehensive abilities of the students, and it can also efficiently improve teaching efficiency and quality. This work mainly expounds the following two aspects. The first aspect is analyzing the advantages and current problems of the hybrid teaching model in mathematics in college; the second aspect is introducing the application of hybrid teaching mode in linear algebra teaching through case studies.

The challenge of structuralist thinking in abstract algebra: a transition problem

This paper deals with the issue of transitions in the teaching and learning of abstract algebra throughout the Bachelor in France, focusing on the notion of ideal in ring theory which is seen as a gateway to structuralist thinking. In the framework of the Anthropological Theory of the Didactic, the notion of structuralist praxeologies, endowed with structuralist levels, is used to analyse a corpus of course documents from three upper-secondary teachers which cover the teaching of ideals through the Bachelor. Hausberger's three-phase model for structuralist transitions, which generalises Winsløw's model of the concrete to abstract transition in analysis, is applied to discuss the issue of transitions. Our research results cover a description of structuralist praxeologies developed throughout the Bachelor around the notion of ideal, a discussion of discontinuities and ruptures that are observed, and the identification of strategies developed by teachers to handle these transitions as they carry out the internal didactic transposition.

Trends, insights, and developments in research on the teaching and learning of algebra

Trends, insights, and developments in research on the teaching and learning of algebra

Methodology for specialized teaching of the subject �Algebra and Beginnings of Analysis� for high school students

Relevance. The educational system of the Republic of Kazakhstan is gradually being updated based on international requirements. Changes have also affected the methodology of profile teaching of the subject �Algebra and Beginnings of Analysis� as an important element of training of high school students.Purpose. The purpose of this study is to reveal the features of profile teaching of the subject �Algebra and Beginnings of Analysis� in the conditions of updating the content of education.Methodology. To achieve the goal, the methods of analysis and synthesis, comparison, generalization, as well as the author�s questionnaires were used.Results. The study revealed the features of the new educational paradigm of the Republic of Kazakhstan, described the essence of updating the content of education and identified changes in the methodology of teaching mathematical disciplines. The role of profile teaching of the subject �Algebra and Beginnings of Analysis� for high school students was determined. To determine the actual problems in the methodology of teaching the subject �Algebra and Beginnings of Analysis�, a study was conducted among 129 students of profile senior classes of secondary general education schools of the Republic of Kazakhstan. The results of the study demonstrated that students receive the necessary knowledge in the process of studying the subject �Algebra and Beginnings of Analysis� according to the updated methodology, but there is a lack of innovative technologies in the learning process and feedback from teachers. The methods of improving the methodology of profile education in the subject �Algebra and Beginnings of Analysis� were suggested, including additional work with teachers and improvement of their innovative competences, gamification of the educational process and providing students with opportunities to apply their knowledge in practice.Conclusions. The results of this study can be used by the management of secondary general education schools of the Republic of Kazakhstan, as well as by teachers of mathematical disciplines to improve the educational process and better training of students of profile high schools.

The Practice of Linear Algebra Teaching Reform under the Curriculum Ideological and Political Perspective

The Practice of Linear Algebra Teaching Reform under the Curriculum Ideological and Political Perspective

GeoGebra in the teaching of Abstract Algebra: An approach to dihedral groups through Didactic Engineering

Resumo Este estudo aborda o ensino de grupos diedrais finitos, sua importância em diversas áreas, dificuldades dos estudantes de licenciatura no tema e a escassez de trabalhos sobre a temática. O objetivo é apresentar uma proposta para explorar as propriedades algébricas de rotações e reflexões em grupos diedrais com o aporte do GeoGebra. A abordagem fornece suporte teórico ao professor na compreensão e no ensino de sua estrutura algébrica e propriedades por uma perspectiva visual, a partir de uma situação didática apoiada em uma construção no software. A metodologia adotada foi a Engenharia Didática e a sessão de ensino foi estruturada seguindo as dialéticas da Teoria das Situações Didáticas. Almeja-se que a proposta apresentada contribua para a possível integração do GeoGebra ao ensino de Álgebra Abstrata, considerando a potencial contribuição de uma abordagem visual do tema na prática docente.

Good in theory, difficult in practice: An examination of secondary algebra teachers’ views about RtI

Research about response to intervention (RtI) programs has primarily focused on the elementary level, and there is a noticeable lack of research specific to secondary mathematics RtI programs. As such, the focus of this qualitative study was secondary algebra teachers’ perceptions and self-efficacy for the implementation of RtI. Research participants consisted of eight secondary algebra teachers that had implemented RtI programs and had at least five years of teaching experience. A semi-structured interview protocol was utilized to discuss the types of interventions they utilized, perceptions of the implementation, beliefs in their ability to effectively implement RtI, along with their view of the training they received. The researcher found student behavior, time, and training had negative impacts on teachers’ perceptions and self-efficacy towards implementing RtI programs. While participants in the study exhibited an understanding of the various tiers of intervention along with the processes involved in RtI, we conclude that there was an overall lack of preparation to work within an RtI system. The findings of this research study are of particular importance for school administrators and secondary mathematics teachers to better understand the latent barriers for successful RtI implementation. The findings of this study help these key individuals better understand the perceptions and barriers for implementing secondary mathematics RtI.

Current Situation and Breakthrough of Linear Algebra Teaching

Current Situation and Breakthrough of Linear Algebra Teaching

Reflection and Innovation of Linear Algebra Teaching

Reflection and Innovation of Linear Algebra Teaching

Research on Improving the Quality of Linear Algebra Teaching Based on Teaching Evaluation

Research on Improving the Quality of Linear Algebra Teaching Based on Teaching Evaluation