From Legos and Logos to Lambda a Hypothetical Learning Trajectory for Computational Thinking
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Pia Niemelä From Legos and Logos to Lambda A Hypothetical Learning Trajectory for Computational Thinking Julkaisu 1565 • Publication 1565 Tampere 2018 Tampereen teknillinen yliopisto. Julkaisu 1565 Tampere University of Technology. Publication 1565 Pia Niemelä From Legos and Logos to Lambda A Hypothetical Learning Trajectory for Computational Thinking Thesis for the degree of Doctor of Science in Technology to be presented with due permission for public examination and criticism in Festia Building, Auditorium Pieni sali 1, at Tampere University of Technology, on the 14th of September 2018, at 12 noon. Tampereen teknillinen yliopisto - Tampere University of Technology Tampere 2018 Doctoral candidate: Pia Niemelä Pervasive Computing Computing and Electrical Engineering Tampere University of Technology Finland Supervisor: Professor Hannu-Matti Järvinen Pervasive Computing Computing and Electrical Engineering Tampere University of Technology Finland Instructors: Professor Petri Ihantola Big Data Learning Analytics Department of Education University of Helsinki Finland Professor Petri Nokelainen Industrial and Information Management Business and Built Environment Tampere University of Technology Finland Pre-examiners: Professor Mike Joy University of Warwick The United Kingdom Professor Arnold Pears KTH Royal Institute of Technology Sweden Opponent: Professor Erkki Sutinen Interaction Design Department of Information Technology University of Turku Finland ISBN 978-952-15-4183-4 (printed) ISBN 978-952-15-4187-2 (PDF) ISSN 1459-2045 Abstract This thesis utilizes design-based research to examine the integration of computational thinking and computer science into the Finnish elementary mathematics syllabus. Al- though its focus is on elementary mathematics, its scope includes the perspectives of students, teachers and curriculum planners at all levels of the Finnish school curriculum. The studied artifacts are the 2014 Finnish National Curriculum and respective learning solutions for computer science education. The design-based research (DBR) mandates educators, developers and researchers to be involved in the cyclic development of these learning solutions. Much of the work is based on an in-service training MOOC for Finnish mathematics teachers, which was developed in close operation with the instructors and researchers. During the study period, the MOOC has been through several iterative design cycles, while the enactment and analysis stages of the 2014 Finnish National Curriculum are still proceeding. The original contributions of this thesis lie in the proposed model for teaching compu- tational thinking (CT), and the clarification of the most crucial concepts in computer science (CS) and their integration into a school mathematics syllabus. The CT model comprises the successive phases of abstraction, automation and analysis interleaved with the threads of algorithmic and logical thinking as well as creativity. Abstraction implies modeling and dividing the problem into smaller sub-problems, and automation making the actual implementation. Preferably, the process iterates in cycles, i.e., the analysis feeds back such data that assists in optimizing and evaluating the efficiency and elegance of the solution. Thus, the process largely resembles the DBR design cycles. Test-driven development is also recommended in order to instill good coding practices. The CS fundamentals are function, variable, and type. In addition, the control flow of execution necessitates control structures, such as selection and iteration. These structures are positioned in the learning trajectories of the corresponding mathematics syllabus areas of algebra, arithmetic, or geometry. During the transition phase to the new syllabus, in-service mathematics teachers can utilize their prior mathematical knowledge to reap the benefits of ‘near transfer’. Successful transfer requires close conceptual analogies, such as those that exist between algebra and the functional programming paradigm. However, the integration with mathematics and the utilization of the functional paradigm are far from being the only approaches to teaching computing, and it might turn out that they are perhaps too exclusive. Instead of the grounded mathematics metaphor, computing may be perceived as basic literacy for the 21st century, and as such it could be taught as a separate subject in its own right. iii Preface My family used to play a lot together, especially games involving strategy. In addition to games, my Mom felt compelled to foster our analytical thinking by providing us with ‘developing toys’, such as puzzles and lego. Mom was also a determined fan of mathematics, and we children almost grew tired of hearing about all of its benefits. Nevertheless, she still managed to sow the seed of interest. Computing grew from another source; my first contact with a computer was due to my uncle and his brand-new computer, a Spectrum. I can well remember sitting in front of a tv display screen with my cousin overwhelmed about opening scenes where computers would change the world, as they inexorably did. After graduating from the Department of Technical Physics (Φ) in Helsinki’s Aalto University, I started working for Nokia as a software engineer, Java being my ‘logo’, the ultimate seedbed of computational thinking. The shift from natural sciences towards software profession had begun, yet the road ahead was going to be bumpy. After Nokia laid off thousands of engineers, including myself, I had once-in-a-lifetime chance to fulfill my other calling: pedagogy. The transition from being a scientific positivist to a relativistic humanist was not easy, but I eventually graduated as a class- and mathematics teacher in 2015 from University of Tampere. I have worked as a progressively inquiring teacher ever since, alternating between teaching and research. This cross-disciplinary thesis synthesizes the accumulated experiences engraved on the palms of my hands, if not quite on my heart. The majority of the research was carried out at Tampere University of Technology under the research project ‘Skills, Education and Future of Work’ funded by the Academy of Finland. I would like to express my sincere gratitude to my professors, Hannu-Matti and the two Petris. Hannu-Matti, you restored my faith in human kind (read: professor kind). It is easy to work for a person that you respect. The thesis was greatly improved by the review comments received from the pre-examiners, Professors Joy and Pears, who pointed out the many vague rambling sections which required more concrete argumentation. During the process, I have shared my troubles with Kati and Martti, my fellow wanderers, and Tiina O., Irina and Katariina. Thank you all for the in-depth discussions and ‘think-tanking’. My thanks also go to Maarit, Maria, Antti J., Antti V., Ville I., Charis, Ekaterina, Chelsea, Adrian, MOT, Google Translator and all the co-authors and reviewers of my publications, but none more so than to Tiina Partanen. In addition, my family, Rikun Ruusut and PEO2017, thanks for providing alternative ideas to ponder when I was simply fed-up with my thesis. Darling Petteri, you are my rock! You gave me the space and time to construct all these models, while keeping the house going in the meantime. Thank You! Last spring, wonder of wonders, we became ‘gamma’ (Γ) and ‘taata’ (Θ). Once the remaining lambdas are finished, there are still plenty of letters for us to explore before the Final Ω. Yours, Pia v Contents Abstract iii Preface v Acronyms ix List of Publications xi 1 Introduction1 1.1 Objectives of the thesis ............................ 2 1.2 Outline and contributions........................... 3 2 Literature review5 2.1 Computational thinking (CT) positioned................... 5 2.2 Didactic research of mathematics in resonance with CT .......... 12 2.3 The anticipated benefits of mathematics-CS integration .......... 16 2.4 The transition of mathematics teachers to CS................ 17 3 Research methods and theoretical frameworks 21 3.1 Socio-constructivism as an underlying epistemology of FNC-2014 . 22 3.2 Design-based research ............................. 26 3.3 Qualitative and quantitative data....................... 28 3.4 Analyses conducted............................... 28 3.5 Method summary................................ 29 4 Overview and relevance of the publications 31 4.1 Publication I: Significance of pedagogy- and context awareness . 32 4.2 Publication II: A holistic view of CS education ............... 33 4.3 Publication III: A problematic switch from visual to textual . 34 4.4 Publication IV: CS curriculum comparison: UK, US, FI.......... 35 4.5 Publication V: Transfer of mathematics teachers’ prior knowledge . 36 4.6 Publication VI: CT/CS integrated in mathematics syllabus . 37 4.7 Publication VII: Necessary but under-taught discrete mathematics . 38 4.8 Publication VIII: Paradigms compared in mathematics-suitability . 39 5 Results and discussion 41 5.1 CT as an embedded commodity of mathematics............... 41 5.2 Mathematics and CS concept overlap..................... 45 5.3 Mathematics teachers’ professional development............... 48 vi Contents vii 6 Conclusions 51 6.1 Implications for FNC-2014........................... 51 6.2 Conclusive CT model ............................. 53 6.3 Further research ................................ 56 Bibliography 57 Publications 69 Acronyms ACM Association for Computing Machinery CAS computer algebra system CAS Computing-At-School teacher coalition (in the UK) CS computer science