Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level

Melhuish, Kathleen; Fagan, Joshua B.

doi:10.1007/978-3-319-99214-3_2

Cited by 14 publications

(16 citation statements)

References 28 publications

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“…The core concept in abstract algebra has a productive potential to connect to the middle school level. Binary functions and operations as initial concepts play essential roles in many abstract algebra topics [21].…”

Section: Introductionmentioning

confidence: 99%

The Influence of Independent Learning and Structure Sense Ability on Mathematics Connection in Abstract Algebra

Junarti¹,

Sukestiyarno²,

Mulyono³

et al. 2020

Proceedings of the International Conference on Science and Education and Technology (ISET 2019)

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This study aimed to reveal the influence of independent learning and structure sense ability on mathematics connection in abstract algebra through mentoring modules as an initial step to overcome the students' difficulties in learning and to habituate students to recognize the structure sense and mathematics connections through weekly tasks. This research was conducted at the fifth-semester students of the Mathematics Education Study Program for 7 weeks. A quantitative research design with two independent variables (independent learning and structure sense ability) and one dependent variable (mathematics connection ability) was employed in this study. This study took 26 students for the sample. The data to measure independent learning was gathered through a questionnaire; the data to recognize the structure sense ability was gathered through weekly tasks, and the students' mathematics connections were measured through a test. The results of simple regression and multiple regression analyses, simultaneously with independent learning and structure sense variables, affect students' mathematics connection ability in abstract algebra course. The results indicate that independent learning is more dominant than structure sense ability in influencing students' mathematics connection ability. Thus, in order to achieve high mathematics connection abilities, students should, first, have high independent learning, and then develop the ability to recognize structure sense.

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Section: Introductionmentioning

confidence: 99%

The Influence of Independent Learning and Structure Sense Ability on Mathematics Connection in Abstract Algebra

Junarti¹,

Sukestiyarno²,

Mulyono³

et al. 2020

Proceedings of the International Conference on Science and Education and Technology (ISET 2019)

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show abstract

“…Changing this certainly poses many educational problems for learners (cf. [39,44,60,61]), but, as we will see, they can be overcome. An acceptance survey [62] of the Hildesheim Teaching Concept for Abstract Algebra is currently being conducted with individual learners in the laboratory setting-the results of which we will report in a follow-up paper.…”

Section: Discussionmentioning

confidence: 91%

“…So when trying to generalize such concepts, one has to evoke a sense of caution in the student. A study by Melhuish [44] has shown that students overgeneralize and conflate properties such as associativity and commutativity. In addition, they found that conceptual understanding of groups is tied to the understanding of binary operations.…”

Section: Properties Of Binary Operationsmentioning

confidence: 99%

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What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics

Veith

Bitzenbauer

2022

Mathematics

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In this paper, we present a novel concept for an abstract algebra course at the secondary school level. Against the backdrop of findings from mathematics education research, we discuss benefits that arise from teaching abstract algebra to secondary school students. We derive suitable content items as well as educational ideas on how to implement them into mathematics classrooms. We build on frameworks from mathematics education research to design a teaching-learning sequence that enables a beneficial learning trajectory across three units—the result is a coherent teaching concept that encompasses Magmas in a hands-on way. It can be used for either extra-curricular activities or advanced courses in mathematics classes, and can be of benefit for mathematics learners.

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“…Much of the functions literature focuses on a covariational (e.g., Carlson, 1998 ; Carlson et al, 2002 ; Oehrtman et al, 2008 ) approach to functions, in which a function is viewed primarily as a relationship between two quantities that are changing in tandem. Although a covariational perspective is a very useful way to conceive of functions in courses like algebra and calculus, it is not useful in an abstract algebra setting because it “superimposes an ordinal system on function, which does not underlie many of the discrete structures in abstract algebra” (Melhuish & Fagan, 2018 , p. 22). Thus, a significant portion of the research on functions in the mathematics education literature is not able to account for the ways in which students must reason about functions in abstract algebra.…”

Section: Literature Reviewmentioning

confidence: 99%

Analyzing the Structure of the Non-examples in the Instructional Example Space for Function in Abstract Algebra

Uscanga

Cook

2022

Int. J. Res. Undergrad. Math. Ed.

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The concept of function is critical in mathematics in general and abstract algebra in particular. We observe, however, that much of the research on functions in abstract algebra (1) reports widespread student difficulties, and (2) focuses on specific types of functions, including binary operation, homomorphism, and isomorphism. Direct, detailed examinations of the function concept itself–and such fundamental properties as well-definedness and everywhere-definedness–are scarce. To this end, in this paper we examine non-examples of function in abstract algebra by conducting a textbook analysis and semi-structured interviews with abstract algebra instructors. In doing so, we propose four key categories based upon the definitive function properties of well-definedness and everywhere-definedness. These categories identify specific characteristics of the kinds of non-examples of function that abstract algebra instruction should emphasize, enabling us to hypothesize how students might be able to develop a robust view of function and explain in greater detail the nature of the reported difficulties that students experience.

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Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level

Cited by 14 publications

References 28 publications

The Influence of Independent Learning and Structure Sense Ability on Mathematics Connection in Abstract Algebra

The Influence of Independent Learning and Structure Sense Ability on Mathematics Connection in Abstract Algebra

What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics

Analyzing the Structure of the Non-examples in the Instructional Example Space for Function in Abstract Algebra

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