Inverse, composition, and identity: The case of function and linear transformation

Bagley, Spencer; Rasmussen, Chris; Zandieh, Michelle

doi:10.1016/j.jmathb.2014.11.003

Cited by 20 publications

(5 citation statements)

References 11 publications

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“…In this case, there is a restructuring of the old scheme in which students are not familiar with the problem situation at hand, so they need to adjust the information on the structure of the problem with the scheme they have. In this case, the influence of the old scheme was needed to build a new scheme, as revealed by Bagley et al (2015). The findings at the coordinating stage are also in line with the opinions of Hackenberg (2010) and Ramful (2014) who state that mental actions by changing the direction of thinking trigger the accommodation process.…”

Section: Reversible Reasoning Indication For Inverse Function Problemssupporting

confidence: 77%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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Section: Reversible Reasoning Indication For Inverse Function Problemssupporting

confidence: 77%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

View full text Add to dashboard Cite

show abstract

“…Therefore, the existing knowledge of undergraduate students concerning functions is often neglected, and linear transformations, on the one hand, are introduced as ready-made mathematics, and, on the other hand, applications of the topic are introduced in a static way. Research results from the related literature show that students are not fully aware of the mathematical relationship between the notions of function and linear transformation (Bagley, Rasmussen, & Zandieh, 2015). This situation leads to the following question: How may we best facilitate students' connection of the notions of function, matrix and transformation matrix?…”

Section: Literature Reviewmentioning

confidence: 99%

Interactive Tools for Linear Algebra: Geouniud

Lepellere

Zucconi

Asbahi

et al. 2020

SIE

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GeoUniud is a user-friendly platform built-in interactive tutors which allow students to investigate specific tasks by selecting their own input values and working through a problem in a step-by-step fashion together with immediate feedback at each step. Lessons and exercises are stored and organized with a careful use of randomized controlled contents as exercises, geometrical pictures and abstract reasoning. The lessons are augmented by a virtually infinite collection of examples, and by interactive representations of concepts. As example we show the design of two interactive tools about linear transformation and change of basis in order to develop students’ sense-making in a dynamic geometry environment (DGE) within the perspective of semiotic mediation.

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“…The function concept is critical in mathematics and is a core topic in the secondary and undergraduate mathematics curriculum (Bagley et al, 2015 ; Dubinsky & Wilson, 2013 ; Even & Tirosh, 1995 ; Hitt, 1998 ; Oehrtman et al, 2008 ). In abstract algebra, a nationally representative sample of abstract algebra experts recently concluded that topics like homomorphism, isomorphism, and binary operation–all of which are specific types of functions–are some of the most important concepts in the course (Melhuish, 2019 ).…”

Section: Introductionmentioning

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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Inverse, composition, and identity: The case of function and linear transformation

Cited by 20 publications

References 11 publications

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Interactive Tools for Linear Algebra: Geouniud

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

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