Learning Of Algebra Research Articles

Investigating transgressive actions undertaken by students while studying mathematics via primary sources

We describe an exploration informed by transgressionism and supported by data collected from students’ report of learning abstract algebra via curriculum materials where primary historical sources are central to their design, namely Primary Source Projects (PSPs). PSPs require students to actively engage with primary source texts written by historical mathematicians and counter students’ more traditional mathematical learning experiences. We explore the components forming transgressive triads consisting of <i>outcomes</i> of <i>transgressive actions</i> taken to overcome <i>boundaries </i>encountered in students’ study of mathematics. Particularly, we focus on transgressive actions undertaken by students and provide exemplars identified from data to empirically support our theoretical conceptualisations. We end with a discussion by proposing research that draws upon transgressions in both learning mathematics via PHS in particular and with regard to other approaches in undergraduate mathematics education which may place students in contexts in which their familiar is made unfamiliar.

Design and Evaluation of the Digital Algebra Game for Children

Children may find learning algebra challenging as the algebraic concepts are abstract for them. To address this challenge, contextualizing algebraic concepts through storytelling and gamification can foster a more enjoyable and comprehensive learning experience. In this study, we introduced the Digital Algebra Game (DAG), a low-fidelity prototype designed to leverage digital game-based learning and storytelling frameworks. Our evaluation involved 96 children aged 9 to 11, along with four teachers, in a primary school setting. Thematic analysis of interview data revealed a positive reception of DAG among both children and teachers. The most unique feature of this game lies in students' ability to transform equations into stories. This approach is believed to not only enhance students' creative thinking but also contribute to their success in mathematics Furthermore, the narratives constructed by students around equations within their daily lives with familiar objects are particularly noteworthy. These insights underscore the potential of incorporating personal experiences into educational game design to enhance engagement and understanding. By bridging the gap between abstract concepts and tangible experiences, educational games like DAG have the potential to enhance learning processes and make mathematics more accessible and enjoyable for children.

The Development of Powerpoint-Assisted Algebra Learning Media to Increase Students’ Mathematical Communication Ability on Junior High School

The matter of algebraic form is crucial to study because the matter of the algebraical form is not only related to other mathematical matters but also related to everyday life, but there are still many students who have difficulty in communicating the explanation of the origin of the algebraic form. This is because the learning media used by the teacher is not interactive, so it affects the student's understanding and communication skills. For this reason, the study aims to cultivate the interest in learning and cultivate students' mathematical communication skills by developing algebraic learning media supported by a PowerPoint application. The method used in this research is research and development, with the development of a modified 4-D model in three stages namely determining, designing, and developing. The tool used to measure the quality of the learning media is a validation questionnaire for measuring the validity and student response to strengthen practicality. The results of this study show that the quality of the learning media meets the valid criteria with an overall average score of 79% and From the test carried out against students obtained an average scoring of 76%. Thus, the development of algebra learning media supported by the PowerPoint application has good quality and can be used in mathematical learning.

The Impact of GeoGebra in Analytic Algebra: A Bibliometric Review

GeoGebra is a software that is often used in mathematics learning. GeoGebra is an electronic program that contains a set of tools that equip students with mathematical skills. This research aims to look at research trends related to algebra learning that integrates GeoGebra. This research is literature review research, there are 95 publications collected from the Scopus database which are then analyzed using the bibliometric analysis method assisted by the Vos viewer application. Data taken from the Scopus database was refined in 4 stages, namely identification, filtering, eligibility, and inclusion, resulting in 95 publications. The research results show that Spain and Austria are the most influential countries and have high cooperation with other countries in this field. The focus of research related to GeoGebra on algebra material is, 1) geometry and students; 2) GeoGebra and algebra; 3) elementary geometry and computational theory; 4) dynamic geometry and computer algebra. The new themes in this research are symbolic computation, quantifier elimination and real quantifier elimination. This research not only enriches the scientific literature in the fields of GeoGebra and algebra but also provides practical guidance for educators and researchers to improve mathematics teaching and learning methods in the future.

The algebraic learning of middle school students’ evolution during a school year: a statistical large-scale study based on results in mathematics didactics

AbstractThis large-scale study characterizes the algebraic learning of a cohort of nearly 800 French students during the last year of middle school (9th grade, 14–15 years old) and examines their evolution in relation to the composition of the classes to which the students belong. Based on the Anthropological Theory of the Didactic (ATD), the study is founded both on a reference model of elementary algebra and on technological-theoretical levels characterizing the students’ reasoning and their knowledge regarding institutional expectations. These are used to code the data and define the statistical variables on which multivariate descriptive analyses are carried out. Students’ learning is analyzed through Pépite, an algebra test given at the beginning and at the end of the year. A cluster analysis resulted in three distinct clusters of similar classes and of similar students both at the beginning and end of the grade 9 school year. They are interpreted didactically and could be useful for a teacher who has to manage the heterogeneity of learning in a class. Some classes and students move from one cluster to another between the beginning and the end of the year, showing a wide variety of ways in which students’ algebra learning progresses or regresses over a school year.

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.

The Development of 7th Grade Students’ Algebraic Thinking Through Task-assisted Instruction

This study aims to investigate how the algebraic thinking skills of seventh-grade students develop with the task-assisted teaching approach. The study was conducted in a seventh-grade class at a public school in Istanbul. The tasks were designed to support the basic components of students’ algebraic thinking processes - pattern recognition, writing algebraic expressions, constructing and solving equations. During the implementation, the students in the class were divided into groups of three and four, and a teacher candidate in each group was responsible for implementing the tasks. Teacher candidates were informed about the instructions provided by the researcher, the implementation principles, and possible student errors before each task. The entire implementation process was recorded with the consent of the students. This paper focused on the pattern recognition component of algebraic thinking. Video analysis and students' responses showed that their algebraic thinking processes improved in the pattern recognition component, and furthermore, the pattern recognition component evaluation through qualitative analysis showed that there was an improvement in the students' algebraic thinking skills compared to their previous performance. The results indicate that task-assisted instruction could be an effective method for improving students' algebraic thinking skills and supporting their algebra learning.

English learners learn from worked example comparison in algebra

Comparison is an important mechanism for learning in general, and comparing two worked examples has garnered support over the last 15 years as an effective tool for learning algebra in mainstream classrooms. This study was aimed at improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to effective mathematics learning in an ESOL (English to Speakers of Other Languages) context. It investigated a novel instructional approach to help English Learners (ELs) develop better understanding in mathematical reasoning, problem solving, and literacy skills (listening, reading, writing, and speaking). Findings suggest that MLS-WEPs not only enhanced ELs’ ability to solve algebra problems, but it also improved their written explanation skills and enabled them to transfer such skills to different mathematical concepts. Moreover, when controlling for ELs’ prior knowledge, the effectiveness of the MLS-WEPs intervention for performing and explaining calculations did not vary by their English proficiency.

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.

Mengeksplore aljabar awal di sekolah menengah: kombinasi analisis bibliometric dan meta analisis

The aims of this study is to analyze publications on early algebra in middle schools to contribute to the development of related literature. A total of 234 articles on early algebra published in various Scopus databases between 2013 and 2024 were retrieved and analyzed through a bibliometric analysis approach and 19 articles through a Comprehensive Meta Analysis (CMA). The results showed fluctuating trends in research related to early algebra in middle schools. The surge in publications using VOSviewer and RStudio from 2013 to 2024 did not align with a corresponding increase in average citations, contributing to a stagnation in the average citation per year. The noticeable upward trend in the volume of publications on early algebra since the beginning of 2013 indicates a dynamic and evolving research landscape in this field. This consistency suggests a widespread and sustained interest in early algebra research beyond the confines of a single country, further emphasizing its global relevance and significance. Integrating multimedia technology into early algebra instruction significantly enhances student learning outcomes. Moreover, access to technology and enhanced learning resources through technology integration can play a more crucial role in improving the effectiveness of early algebra learning in countries with lower income levels.

The Ethnomathematical Approach Through The Methodology: Contextualization, Decontextualization and Recontextualization (CDR) and Its Contribution to The Learning of: Arithmetic, Geometry and Algebra

Objective: The objective of this article is to investigate the applicability of the CDR Method within the Ethnomathematics approach, in order to make possible the optimization and improvement of the teaching of the main branches of mathematics in Ecuador. This topic has been the product of several investigations carried out at the Institute for Research in Ethnosciences of the Central University of Ecuador, IIEC-UCE, particularly in the area of Ethnomathematics. Theoretical Framework: under a theoretical and practical frame of reference, with the purpose of showing the possibility of achieving a meaningful, coherent, environmentally sensitive and contextualized learning in the geopolitical reality. It is considered that the main contribution will be to support the construction of an own episteme and identity with the Andean ancestral roots. As for the methodology, we worked with focus groups formed by students of the cycle called General Basic Education. Method: It is proposed to investigate the applicability of the Ethnomathematical approach through the methodology: Contextualization, Decontextualization and Recontextualization, CDR and its contribution to the learning of arithmetic, geometry and algebra. The stages are described and the cyclical relationship that exists in a dialectical, systematic and propositive process that aims to make a disruption with the traditional algorithmic, decontextualized and memorized methodology that is usually used in the educational system is shown. The use of this method is proposed. Results and Discussion: The results obtained are considered satisfactory and it was observed that the CDR can be adopted by teachers interested in changing their teaching methods in the classroom, in addition, it is easily adaptable to different educational levels and areas of knowledge such as: History, Chemistry, Arts, Medicine, among others. Implications of the research: The research aims to provoke a cause-effect situation, where the causality is based on the deficiency of mathematics education in the country and the effect that would produce the approach of contextualization in the different facets: historical, social, political, etc., to produce meaningful learning. Originality/Value: It is considered original because it presents a new approach to mathematics education; CDR is both a disruptive strategy for learning mathematics in connection with the environment, the Andean episteme and its unique ontology. It IS also an axiological alternative insofar as it incorporates the Andean ethos as a referential philosophical framework.

Simplifying algebraic expressions with brackets: Insights into Grade 10 learners’ structure sense through a study of their errors

Developing structure sense is an important part of learning algebra. We investigated learners’ structure sense of algebraic expressions involving brackets. This led us to propose the constructs surface structure sense and systemic structure sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we coded incorrect responses for surface and systemic structure errors. The initial analysis revealed that the presence of more brackets supports surface structure sense. However, learners overgeneralised the presence of brackets to represent multiplication in situations involving subtraction. The arrangement of brackets also led to errors in the order of operations. Further analysis suggested that regular application of procedures on familiar algebraic structures may give the illusion of systemic structure sense. We recommend that the teaching of algebraic expressions must emphasise what the arrangement of an expression means before focusing on how to operate on the expression.Contribution: The research contributes to mathematics teaching by suggesting teaching strategies to improve on learners’ understanding of the role of brackets in algebraic expressions, by considering the arrangement of the components in structures.

Creative thinking for learning algebra: Year 10 students’ problem solving and problem posing with quadratic figural patterns

There is increasing focus on giving all students opportunities to develop their creative thinking in mathematics. In a fine-grained qualitative case study, Australian Year 10 (15–16-year-old) students experienced problem-solving and problem-posing tasks in a learning sequence designed to elicit creative thinking through visualization and with algebraic (functional) concepts. This article shares findings on two pairs’ creative processes and work products for generalizing and creating quadratic figural growing patterns, related to the cognitive, affective, and aesthetic dimensions of learning. Post-sequence data on the class's preferences for types of creative thinking tasks are also shared. Students were found to exhibit different creativity aspects in their problem solving and varying levels of meta-representational competency in their problem posing. The students evidenced diverse affective responses to the different types of tasks, with proportionally more students preferring problem solving to problem posing. Some implications for engaging secondary mathematics students in creative thinking tasks are shared along with recommendations for future research.

PENGARUH MODEL PEMBELAJARAN AIR BERBANTU MEDIA LAGU MATERI ALJABAR TERHADAP KEMAMPUAN PEMAHAMAN KONSEP

The purpose of this study was to analyze and improve the concept understanding abilities of class VII students using the AIR learning model assisted by algebra song. This research uses a type of experimental research with a one group pretest-posttest design. This type of experimental research is included in quantitative research methods. The sampling technique uses cluster random sampling technique. The instrument for collecting data in this research is a test instrument in the form of pretest and posttest questions. All students in class VII F were given pretest questions on real numbers and their operations. At the next 2 meetings, treatment was given in the form of learning algebra material using the AIR learning model assisted by algebra song. After the treatment was carried out, posttest questions on algebra material were given to students. Next, analysis of all data is carried out using the following steps: analysis of initial and final data, data presentation stage, and conclusions. The results of the research show that there is an increase in students' ability to understand concepts by using the AIR learning model assisted by algebra song media. The use of the AIR learning model assisted by algebra song is said to be significant in improving the ability to understand concepts because the proportion of students after being given the AIR learning model assisted by algebra song who completed it exceeded the KKM score (>70) of more than 75% of the total number of students

Pembelajaran Berbasis Proyek Menggunakan Software Matematika Geogebra Terhadap Kemampuan Komputasi Siswa

The use of digital technology in mathematics education material makes it a very interesting and urgent matter regarding the level of students' abilities regarding the material they are studying, whether students understand mathematics material more easily or have more difficulty understanding it. Geogebra is a free math learning software program that supports a variety of math topics. for use at school. Initially, GeoGebra was only used for learning algebra and geometry, but as it developed, many new features were added and increasingly enriched the existing features. The research method used in this research uses a literature study research method where researchers study the results of previous research. The results of this research conclude that the use of Geogebra mathematics software in learning has a positive influence on students' computing knowledge, learning through Geogebra software makes mathematics learning easier for students to understand and understand, students are more enthusiastic about studying mathematics because teachers balance conventional and mathematics. integrated mathematics learning. Project-based learning using Geogebra mathematics software is more popular with students, thereby increasing students' abilities and enthusiasm for learning mathematics.

Symbol Sense Ability of Students to Solve Linear, Quadratic, and Rational Equations

In learning algebra, one of the skills needed to be acquired by students is solving equations, such as linear equations in one variable and quadratic equations. This study aims to analyze the symbol sense ability of students by investigating strategies used to solve algebraic equations that consist of linear, quadratic, and rational equations. A qualitative descriptive method was conducted. The instrument included a test with one linear equation, one quadratic equation, and three rational equations (involving linear or quadratic factors). The test was administered to 12 students from 12th-grade high school in Bandung. Each student was asked to solve it in two different ways of answers if possible. The results showed that students were able to use symbol sense strategies for solving problems. However, there were still mistakes in solving algebraic squared value concepts, affecting their final results of the answers. We conclude that even if students can use their symbol sense abilities properly, they need to pay attention to their mathematics concepts. Keywords: Symbol Sense Ability, Solve Linear, Quadratic, Rational Equations

An Innovative Model to Promote Secondary Students' Critical Thinking Skills in Algebra Learning

This research aims to explore a learning model based on 21st-century skills and the Australian curriculum to cultivate students’ critical thinking skills in junior secondary mathematics algebra learning. This study used a mixed method. Quantitative data was collected through a questionnaire that provided information about perceptions of the challenges in learning algebra. Qualitative data was collected through semi-interviews with secondary mathematics teachers, which provided an opportunity for teachers to evaluate their understanding of critical thinking skills for algebra, it further clarified teachers’ expectations of mastering the key algebraic contents. Based on the data from the questionnaire and semi-interview, a practical model for embedding critical thinking skills and strategies in learning algebra was designed. The mathematical curriculum in Victoria and Australia were explored as they provided the basis of the model.

Difficulties in Studying Abstract Algebra at the Undergraduate Level

This study has attempted to explain the major challenges that undergraduate students face when learning abstract algebra. Students at the undergraduate level totaling one hundred twenty (120) were chosen as the sample size. In this study, the survey design is based on the positivist paradigm. Probability sampling was used to select the students of undergraduate level. For the validation of this study, self-administrated Likert type questionnaires were employed, along with extensive discussion with mathematics teachers who have taught and are presently teaching algebra at the undergraduate level. According to survey results, there were four main reasons—Formalism and Rigor, Lack of Prior Knowledge, Teaching and Learning Technique, Assignment and Assessment, -that hindered the students’ ability to learn abstract algebra. The research outcomes in terms of motivation, self- esteem and challenges of the respondents will be helpful to understand the nuances of teaching and learning abstract algebra at higher education in Nepal.

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.

잠재프로파일 분석을 통한 초등학생들의 산술-대수 구조 감각 탐색

Developing arithmetic structure sense at the primary school level is imperative for grasping the structure of algebraic expressions and progressing successfully into algebraic learning. In this study, we aimed to investigate elementary school students’ arithmetic-algebraic structure sense from an early algebraic thinking perspective. A total of 239 students in grades 3~6 completed a written test, comprising items related to the five factors of arithmetic-algebraic structure sense: structure of equivalence and modeling, arithmetic, numerical situations, patterns, and function. The collected data was analyzed by applying latent profile analysis to examine whether it was possible to identify subgroups of students with different structure-sense profile. The analysis revealed four latent profiles, allowing for the identification of different performance abilities related to five factors of arithmetic-algebraic structure sense. Building upon these findings, this study discussed implications for pedagogical support to develop elementary school students' arithmetic-algebraic structure sense.