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From theory to practice: NP-completeness for every CS student
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0003-3199-8953
2013 (English)In: ITiCSE '13 Proceedings of the 18th ACM conference on Innovation and technology in computer science education, Association for Computing Machinery (ACM), 2013, 16-21 p.Conference paper (Refereed)
Abstract [en]

NP-completeness is one of the most central concepts in computer science, and has been extensively applied in many diverse application areas. Despite this, students have problems grasping the concept and, more specifically, applying it to new problems. Independently, we have identified these problems at our universities in different countries and cultures. In an action research approach we have modified our courses and studied the effects. We here present some promising results. Our approach is mainly based on the idea of making more evident the fact that proving a new NP-completeness result is not at all different from designing a new algorithm. Based on this idea, we used tools typically used to teach algorithms (such as automatic program assessment and algorithm visualization systems), accompanied by other activities mainly devoted to augmenting the motivation to study computational complexity and forcing students to think and adopt a standpoint.

Place, publisher, year, edition, pages
Association for Computing Machinery (ACM), 2013. 16-21 p.
, Annual Conference on Innovation and Technology in Computer Science Education, ITiCSE, ISSN 1942-647X
Keyword [en]
Algorithm visualization, Assessment, NP-completeness, Self-efficacy, Action research, Automatic programs, Diverse applications, Self efficacy, Algorithms, Engineering research, Students, Teaching, Formal logic
National Category
Computer Science Learning
URN: urn:nbn:se:kth:diva-133890DOI: 10.1145/2462476.2465582ScopusID: 2-s2.0-84881120385ISBN: 978-145032078-8OAI: diva2:663426
18th ACM Conference on Innovation and Technology in Computer Science Education, ITiCSE 2013, 1 July 2013 through 3 July 2013, Canterbury

QC 20131111

Available from: 2013-11-11 Created: 2013-11-11 Last updated: 2014-09-29Bibliographically approved
In thesis
1. On difficult topics in theoretical computer science education
Open this publication in new window or tab >>On difficult topics in theoretical computer science education
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis primarily reports on an action research project that has been conducted on a course in theoretical computer science (TCS). The course is called Algorithms, data structures, and complexity (ADC) and is given at KTH Royal Institute of Technology in Stockholm, Sweden.

The ADC course is an introduction to TCS, but resembles and succeeds courses introducing programming, system development best practices, problem solving, proving, and logic. Requiring the completion of four programming projects, the course can easily be perceived as a programming course by the students. Most previous research in computer science education has been on programming and introductory courses.

The focus of the thesis work has been to understand what subject matter is particularly difficult to students. In three action research cycles, the course has been studied and improved to alleviate the discovered difficulties. We also discuss how the course design may color students’ perceptions of what TCS is. Most of the results are descriptive.

Additionally, automated assessment has been introduced in the ADC course as well as in introductory courses for non-CS majors. Automated assessment is appreciated by the students and is directing their attention to the importance of program correctness. A drawback is that the exercises in their current form are not likely to encourage students to take responsibility for program correctness.

The most difficult tasks of the course are related to proving correctness, solving complex dynamic programming problems, and to reductions. A certain confusion regarding the epistemology, tools and discourse of the ADC course and of TCS in general can be glimpsed in the way difficulties manifest themselves. Possible consequences of viewing the highly mathematical problems and tools of ADC in more practical, programming, perspective, are discussed. It is likely that teachers could explicitly address more of the nature and discourse of TCS in order to reduce confusion among the students, for instance regarding the use of such words and constructs as “problem”, “verify a solution”, and “proof sketch”.

One of the tools used to study difficulties was self-efficacy surveys. No correlation was found between the self-efficacy beliefs and the graded performance on the course. Further investigation of this is beyond the scope of this thesis, but may be done with tasks corresponding more closely and exclusively to each self-efficacy item.

Didactics is an additional way for a professional to understand his or her subject. Didactics is concerned with the teaching and learning of something, and hence sheds light on that “something” from an angle that sometimes is not reflected on by its professionals. Reflecting on didactical aspects of TCS can enrichen the understanding of the subject itself, which is one goal with this work.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. vi, 94 p.
TRITA-CSC-A, ISSN 1653-5723 ; 2014:15
National Category
urn:nbn:se:kth:diva-152357 (URN)978-91-7595-267-3 (ISBN)
Public defence
2014-10-17, F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)

QC 20140929

Available from: 2014-09-29 Created: 2014-09-25 Last updated: 2014-09-29Bibliographically approved

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