Why math?

Bruce, Kim B.; Drysdale, Robert L. Scot; Kelemen, Charles; Tucker, Allen B.

doi:10.1145/903893.903918

Cited by 43 publications

(16 citation statements)

References 4 publications

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“…The Computer Science education literature points towards decision mathematics as being the most useful preparation for undergraduate Computer Science [8,24,25,26].…”

Section: Impact Of Mathematical Backgrounds On Performancementioning

confidence: 99%

Decision Mathematics as Preparation for Undergraduate Computer Science

Darlington¹,

Bowyer²

2017

IJMECS

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“…The Computer Science education literature points towards decision mathematics as being the most useful preparation for undergraduate Computer Science [8,24,25,26].…”

Section: Impact Of Mathematical Backgrounds On Performancementioning

confidence: 99%

Decision Mathematics as Preparation for Undergraduate Computer Science

Darlington¹,

Bowyer²

2017

IJMECS

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“…For example, a number of data structures, such as the String and the Tree data structures, as well as regular expressions, context-free grammars, and programming languages are usually defined recursively [17,24], and to prove their properties, proof by induction is needed. Regular expressions, context-free grammars, and the Tree data structure have a wide variety of applications in computer science, two of which are compiler construction and text-search applications [2,6,17]. Furthermore, recursive/inductive definitions and proofs by induction are also central to many other areas of computer science, such as program verification [8,16], program efficiencytime complexity [10], and correctness of algorithms-be they recursive or non-recursive [4,10,19,24].…”

Section: Significance Of This Researchmentioning

confidence: 99%

Computer science students' difficulties with proofs by induction

Polycarpou

2006

Proceedings of the 44th Annual Southeast Regional Conference

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Induction is an important concept for computer science and yet students have difficulties understanding it. The current literature on students' difficulties with induction is concerned with difficulties students have while proving a statement by induction. My research focuses on identifying difficulties that students may have prior to proving a statement. In particular, the present paper is concerned with students' understanding of the recursive/inductive definition of the elements the statement is about. My study is contextualized within the undergraduate computer science curriculum, and its results show that students' performance with proofs by induction improves after class instruction, but not as it would be desirable. Moreover, they suggest that students who understand recursive/inductive definitions can successfully perform a proof by induction, while students who do not are either not able to perform proofs by induction, or if they are, they do so mechanically. In addition, students' performance is affected by their past knowledge and experience, as well as the context in which a problem is presented.

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“…Moreover, induction can improve students' understanding of and performance with CS concepts such as programming languages, recursion [14,37], and algorithm design [25], as well as serve as a medium for teaching them. According to Bruce, Drysdale, and Kelemen [5], "Programmers with a good understanding of mathematical induction find it much easier to write and, even more importantly, provide convincing arguments for the correctness of recursive algorithms" (p.5). In addition, the results of a study conducted by Page [28] show that proofs by induction play a major role in software design and implementation.…”

Section: Introductionmentioning

confidence: 99%

A conceptual approach to teaching induction for computer science

2008

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In this paper, we present an approach to teaching induction that we call the "conceptual route" of teaching induction. Proofs by induction are central to the study of computer science and students come across them in many courses of their curricula. It is documented in the literature that in general students have difficulties with proofs by induction. Even though through the years some solutions were proposed to improve the situation, recent studies show that students are still having difficulties. Currently, proofs by induction take up too little of the computer science curriculum, and they are taught as a step-by-step procedure to be followed, which is not sufficient for students to gain conceptual understanding. In contrast, our approach aims at students' conceptual understanding by shifting their focus from the syntactic form of proofs by induction to their substance. The theoretical underpinning of our approach is an operationalization of the Induction Principle.

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Why math?

Abstract: The mathematical thinking, as well as the mathematics, in a computer science education prepares students for all stages of system development, from design to the correctness of the final implementation.

Cited by 43 publications

References 4 publications

Decision Mathematics as Preparation for Undergraduate Computer Science

Decision Mathematics as Preparation for Undergraduate Computer Science

Computer science students' difficulties with proofs by induction

A conceptual approach to teaching induction for computer science

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