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On Difficult Topics in Theoretical Computer Science Education Science Topics Computer in Theoretical Difficult On EMMA ENSTRÖM EMMA DOCTORAL THESIS IN COMPUTER SCIENCE STOCKHOLM, SWEDEN 2014 On Difficult Theoretical in Computer Topics Science Education KTH Aeronautical and Vehicle Engineering On Difficult Topics in Theoretical Computer Science Education EMMA ENSTRÖM TRITA-CSC-A 2014:15 ISSN 1653-5723 ISRN-KTH/CSC/A–14/15-SE ISBN 978-91-7595-267-3 KTH ROYAL INSTITUTE OF TECHNOLOGY KTH www.kth.se COMPUTER SCIENCE AND COMMUNICATION 2014 On Difficult Topics in Theoretical Computer Science On Difficult Topics in Theoretical Computer Science Education Education EMMA ENSTRÖM EMMA ENSTRÖM Doctoral Thesis Doctoral Thesis Stockholm, Sweden 2014 Stockholm, Sweden 2014 TRITA-CSC-A 2014:15 TRITA-CSC-A 2014:15 ISSN 1653-5723 KTH School of Computer Science and Communication ISSN 1653-5723 KTH School of Computer Science and Communication ISRN-KTH/CSC/A–14/15-SE SE-100 44 Stockholm ISRN-KTH/CSC/A–14/15-SE SE-100 44 Stockholm ISBN 978-91-7595-267-3 SWEDEN ISBN 978-91-7595-267-3 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framläg- Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framläg- ges till offentlig granskning för avläggande av teknologie doktorsexamen i datalogi ges till offentlig granskning för avläggande av teknologie doktorsexamen i datalogi fredagen den 17 oktober 2014 klockan 14.00 i Sal F3, Kungl Tekniska högskolan, fredagen den 17 oktober 2014 klockan 14.00 i Sal F3, Kungl Tekniska högskolan, Valhallavägen 79, Stockholm. Valhallavägen 79, Stockholm. © Emma Enström, 2014 © Emma Enström, 2014 Tryck: E-print AB Tryck: E-print AB iii iii Abstract Abstract This thesis primarily reports on an action research project that has been This thesis primarily reports on an action research project that has been conducted on a course in theoretical computer science (TCS). The course is conducted on a course in theoretical computer science (TCS). The course is called Algorithms, data structures, and complexity (ADC) and is given at called Algorithms, data structures, and complexity (ADC) and is given at KTH Royal Institute of Technology in Stockholm, Sweden. KTH Royal Institute of Technology in Stockholm, Sweden. The ADC course is an introduction to TCS, but resembles and succeeds The ADC course is an introduction to TCS, but resembles and succeeds courses introducing programming, system development best practices, prob- courses introducing programming, system development best practices, prob- lem solving, proving, and logic. Requiring the completion of four program- lem solving, proving, and logic. Requiring the completion of four program- ming projects, the course can easily be perceived as a programming course by ming projects, the course can easily be perceived as a programming course by the students. Most previous research in computer science education has been the students. Most previous research in computer science education has been on programming and introductory courses. on programming and introductory courses. The focus of the thesis work has been to understand what subject matter 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 is particularly difficult to students. In three action research cycles, the course has been studied and improved to alleviate the discovered difficulties. We has been studied and improved to alleviate the discovered difficulties. We also discuss how the course design may color students’ perceptions of what also discuss how the course design may color students’ perceptions of what TCS is. Most of the results are descriptive. TCS is. Most of the results are descriptive. Additionally, automated assessment has been introduced in the ADC Additionally, automated assessment has been introduced in the ADC course as well as in introductory courses for non-CS majors. Automated course as well as in introductory courses for non-CS majors. Automated assessment is appreciated by the students and is directing their attention to assessment is appreciated by the students and is directing their attention to the importance of program correctness. A drawback is that the exercises in the importance of program correctness. A drawback is that the exercises in their current form are not likely to encourage students to take responsibility their current form are not likely to encourage students to take responsibility for program correctness. for program correctness. The most difficult tasks of the course are related to proving correctness, The most difficult tasks of the course are related to proving correctness, solving complex dynamic programming problems, and to reductions. A cer- solving complex dynamic programming problems, and to reductions. A cer- tain confusion regarding the epistemology, tools and discourse of the ADC tain confusion regarding the epistemology, tools and discourse of the ADC course and of TCS in general can be glimpsed in the way difficulties man- course and of TCS in general can be glimpsed in the way difficulties man- ifest themselves. Possible consequences of viewing the highly mathematical ifest themselves. Possible consequences of viewing the highly mathematical problems and tools of ADC in more practical, programming, perspective, are problems and tools of ADC in more practical, programming, perspective, are discussed. It is likely that teachers could explicitly address more of the nature 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 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 instance regarding the use of such words and constructs as “problem”, “verify a solution”, and “proof sketch”. a solution”, and “proof sketch”. One of the tools used to study difficulties was self-efficacy surveys. No One of the tools used to study difficulties was self-efficacy surveys. No correlation was found between the self-efficacy beliefs and the graded perfor- correlation was found between the self-efficacy beliefs and the graded perfor- mance on the course. Further investigation of this is beyond the scope of this mance 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 thesis, but may be done with tasks corresponding more closely and exclusively to each self-efficacy item. to each self-efficacy item. Didactics is an additional way for a professional to understand his or her Didactics is an additional way for a professional to understand his or her subject. Didactics is concerned with the teaching and learning of something, subject. Didactics is concerned with the teaching and learning of something, and hence sheds light on that “something” from an angle that sometimes is 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 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 can enrichen the understanding of the subject itself, which is one goal with this work. this work. iv iv Sammanfattning Sammanfattning I den här avhandlingen diskuteras ett aktionsforskningsprojekt som har I den här avhandlingen diskuteras ett aktionsforskningsprojekt som har utförts på kursen ADK (Algoritmer, datastrukturer och komplexitet) vid utförts på kursen ADK (Algoritmer, datastrukturer och komplexitet) vid KTH i Stockholm. Kursen är en introduktion till teoretisk datalogi (TCS) KTH i Stockholm. Kursen är en introduktion till teoretisk datalogi (TCS) och ges för civilingenjörsstudenterna i datateknik. och ges för civilingenjörsstudenterna i datateknik. ADK-kursen är en fortsättningskurs till tidigare kurser i programmering, ADK-kursen är en fortsättningskurs till tidigare kurser i programmering, systemutveckling och logik. Då den bland annat omfattar fyra stora program- systemutveckling och logik. Då den bland annat omfattar fyra stora program- meringsuppgifter, kan studenterna lätt uppfatta den som ytterligare en pro- meringsuppgifter, kan studenterna lätt uppfatta den som ytterligare en pro- grammeringskurs. Tidigare forskning om undervisning och lärande i datatek- grammeringskurs. Tidigare forskning om undervisning och lärande i datatek- nik/datavetenskap handlar vanligtvis om introduktionskurser i programme- nik/datavetenskap handlar vanligtvis om introduktionskurser i programme- ring. ring. Fokus för den här avhandlingen har varit att förstå vilka begrepp och idéer Fokus för den här avhandlingen har varit att förstå vilka begrepp och idéer som studenterna uppfattar som extra svåra. Under tre aktionsforskningscyk- som studenterna uppfattar som extra svåra. Under tre aktionsforskningscyk- ler har kursen studerats och förändrats för att förbättra den och avhjälpa ler har kursen studerats och förändrats för att förbättra den och avhjälpa svårigheterna. En diskussion förs också kring hur kursens diskurs och dess svårigheterna. En diskussion förs också kring hur kursens diskurs och dess aktiviteter kan påverka studenternas uppfattning om vad TCS är. Resultaten aktiviteter kan påverka studenternas uppfattning om vad TCS är. Resultaten är till övervägande del beskrivande. är till övervägande del beskrivande. Utöver detta har automaträttning införts, både i ADK-kursen och på and- Utöver detta har automaträttning införts, både i ADK-kursen
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