Advanced Mathematics for Secondary School Teachers: Mathematicians’ Perspective

Yan, Xiaoheng; Marmur, Ofer; Zazkis, Rina

doi:10.1007/s10763-020-10146-x

Cited by 9 publications

(9 citation statements)

References 35 publications

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“…This is because a teacher needs to know where all the topics that he teaches "go", what one does with them later on and what mathematical theorems are implied from them" (Even, 2011, p. 945). This ascertainment is congruent with the assessed view of mathematicians in a study by Yan and Marmour (2022) according to which "the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their potential to offer connections across mathematical domains, mathematical experience for the development of problem-solving abilities and increased epistemological awareness of the subject" (Yan & Marmour, 2022, p. 553). These aspects further manifested in a follow-up study by Shamash et al (2018), where pre-service teachers were prompted to design a teaching unit dedicated to solving polynomial equations: The participating teachers chose a historical narrative for their unit in which they introduced the evolution of solving polynomial equations through radicals via Galois theory.…”

Section: (538%)supporting

confidence: 72%

How do pre-service teachers view Galois theory? A questionnaire study

Veith,

Girnat,

Winkler

et al. 2024

EURASIA J Math Sci Tech Ed

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algebra is an important part of mathematics teacher education as it provides the rigorous mathematical foundations for many mathematics topics covered in school classrooms. Throughout their academic career, many secondary mathematics teachers even enroll in more advanced algebra courses, which often culminate in Galois theory. However, very little is known about educational aspects of Galois theory and respective mathematics education research is scarce. We contribute to closing this gap by reporting on the results of an exploratory questionnaire study with a sample of n=39 pre-service mathematics teachers, inquiring about the raison d’être of incorporating Galois theory into teacher education: Is Galois theory viewed as useful for their later profession and which connections are drawn to the secondary mathematics classroom? On the one hand, the results of our study indicate that a vast majority of pre-service teachers do not perceive studying Galois theory as meaningful and struggle to exemplify connections between Galois theory and secondary school mathematics. On the other hand, a small share of the participants experienced Galois theory as an important part of mathematics that elegantly connects a variety of algebraic and geometric notions.

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Section: (538%)supporting

confidence: 72%

How do pre-service teachers view Galois theory? A questionnaire study

Veith,

Girnat,

Winkler

et al. 2024

EURASIA J Math Sci Tech Ed

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“…Through mathematics, students are taught how to communicate effectively, concisely, and clearly while being given the skills to present information in various forms. Furthermore, mastery of mathematics can enhance students' logical and accurate thinking abilities, shape their understanding of spatial dimensions, and give them satisfaction when tackling complex problem-solving challenges [3,4]. Additionally, problem-solving and mathematical communication techniques are viewed as instructional tools that may enhance the standard of mathematics instruction in educational settings, including primary schools.…”

Section: Introductionmentioning

confidence: 99%

Impact of the team-assisted individualization learning model on mathematical problem-solving, communication, and self-regulated learning

Najoan,

Kumolontang,

Ester

et al. 2024

ijirss

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The importance of mathematics in various aspects of life cannot be ignored. Every discipline, from the natural sciences to the social sciences, has a connection with mathematics. Therefore, understanding mathematics that is relevant to its context is very important. One step in understanding mathematics’ implications is through effective learning models in elementary schools. This study aims to analyze the impact of the Cooperative Learning type and Team type-assisted individualization (TAI) learning model on three main aspects of mathematics learning at the elementary school level: mathematical problem-solving, mathematical communication, and self-regulated learning skills (SRLS). Quantitative methods were used in this study, with a quasi-experimental design involving two groups: an experimental group and a control group. A total of 64 students were involved in this study, with each group consisting of 32 evenly distributed students. The data collection instruments comprised mathematical problem-solving, communication tests, and Self-Regulated Learning Skills (SRLS) scale instrument sheets. The results of the data analysis revealed significant differences between the experimental and control groups regarding mathematical problem-solving ability, mathematical communication, and SRLS. This study shows that the Cooperative Learning type Team Assisted Individualization (TAI) learning model has positive implications for improving students' abilities in three key aspects of mathematics learning: students' ability to solve mathematical problems, their ability to communicate in a mathematical context, and their ability to learn independently.

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“…At the heart of mathematics lies problem-solving, and advanced mathematics elevates this skill to a higher plane (Zazkis and Leikin, 2010). By instilling systematic and methodical approaches in students, it fosters qualities such as perseverance, adaptability, and an appreciation for incremental progress (Yan et al 2022). These problem-solving capabilities transcend the realm of mathematics and find utility in diverse disciplines such as science, engineering, economics, and computer science, offering a significant competitive edge in future careers (Asian-Chaves et al 2021).…”

Section: Introductionmentioning

confidence: 99%

The Significance of Advanced Mathematics in Secondary and Higher Education

2023

European Economic Letters

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Learning advanced mathematics in high school or college offers a myriad of benefits to students in academic, personal, and professional pursuits as it presents them with the opportunity to engage in critical, abstract, and logical thinking. By tackling complex problems, students enhance their cognitive abilities, learning to dissect intricate issues into manageable components and devise coherent strategies to resolve them. This process of reasoning and problem-solving fosters brain development and elevates overall cognitive skills. The present study delves into the advantages of learning advanced mathematics in high school or college.

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Advanced Mathematics for Secondary School Teachers: Mathematicians’ Perspective

Cited by 9 publications

References 35 publications

How do pre-service teachers view Galois theory? A questionnaire study

How do pre-service teachers view Galois theory? A questionnaire study

Impact of the team-assisted individualization learning model on mathematical problem-solving, communication, and self-regulated learning

The Significance of Advanced Mathematics in Secondary and Higher Education

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