Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Sustainable Computer Science Education

As the world becomes more technologically advanced and economies become globalized, computer science evolution has become faster than ever before. With this evolution and globalization come the need for sustainable university curricula that adequately prepare graduates for life in the industry. Additionally, behavioural skills or “soft” skills have become just as important as technical abilities and knowledge or “hard” skills. The objective of this study was to investigate the current skill gap that exists between computer science university graduates and actual industry needs as well as the sustainability of current computer science university curricula by conducting a systematic literature review of existing publications on the subject as well as a survey of recently graduated computer science students and their work supervisors. A quantitative study was carried out with respondents from six countries, mainly Finland, 31 of the responses came from recently graduated computer science professionals and 18 from their employers. The observed trends suggest that a skill gap really does exist particularly with “soft” skills and that many companies are forced to provide additional training to newly graduated employees if they are to be successful at their jobs.

University students’ regulation of learning and text processing – examples from medical and teacher education

The general aim of the thesis was to study university students’ learning from the perspective of regulation of learning and text processing. The data were collected from the two academic disciplines of medical and teacher education, which share the features of highly scheduled study, a multidisciplinary character, a complex relationship between theory and practice and a professional nature. Contemporary information society poses new challenges for learning, as it is not possible to learn all the information needed in a profession during a study programme. Therefore, it is increasingly important to learn how to think and learn independently, how to recognise gaps in and update one’s knowledge and how to deal with the huge amount of constantly changing information. In other words, it is critical to regulate one’s learning and to process text effectively. The thesis comprises five sub-studies that employed cross-sectional, longitudinal and experimental designs and multiple methods, from surveys to eye tracking. Study I examined the connections between students’ study orientations and the ways they regulate their learning. In total, 410 second-, fourth- and sixth-year medical students from two Finnish medical schools participated in the study by completing a questionnaire measuring both general study orientations and regulation strategies. The students were generally deeply oriented towards their studies. However, they regulated their studying externally. Several interesting and theoretically reasonable connections between the variables were found. For instance, self-regulation was positively correlated with deep orientation and achievement orientation and was negatively correlated with non-commitment. However, external regulation was likewise positively correlated with deep orientation and achievement orientation but also with surface orientation and systematic orientation. It is argued that external regulation might function as an effective coping strategy in the cognitively loaded medical curriculum. Study II focused on medical students’ regulation of learning and their conceptions of the learning environment in an innovative medical course where traditional lectures were combined wth problem-based learning (PBL) group work. First-year medical and dental students (N = 153) completed a questionnaire assessing their regulation strategies of learning and views about the PBL group work. The results indicated that external regulation and self-regulation of the learning content were the most typical regulation strategies among the participants. In line with previous studies, self-regulation wasconnected with study success. Strictly organised PBL sessions were not considered as useful as lectures, although the students’ views of the teacher/tutor and the group were mainly positive. Therefore, developers of teaching methods are challenged to think of new solutions that facilitate reflection of one’s learning and that improve the development of self-regulation. In Study III, a person-centred approach to studying regulation strategies was employed, in contrast to the traditional variable-centred approach used in Study I and Study II. The aim of Study III was to identify different regulation strategy profiles among medical students (N = 162) across time and to examine to what extent these profiles predict study success in preclinical studies. Four regulation strategy profiles were identified, and connections with study success were found. Students with the lowest self-regulation and with an increasing lack of regulation performed worse than the other groups. As the person-centred approach enables us to individualise students with diverse regulation patterns, it could be used in supporting student learning and in facilitating the early diagnosis of learning difficulties. In Study IV, 91 student teachers participated in a pre-test/post-test design where they answered open-ended questions about a complex science concept both before and after reading either a traditional, expository science text or a refutational text that prompted the reader to change his/her beliefs according to scientific beliefs about the phenomenon. The student teachers completed a questionnaire concerning their regulation and processing strategies. The results showed that the students’ understanding improved after text reading intervention and that refutational text promoted understanding better than the traditional text. Additionally, regulation and processing strategies were found to be connected with understanding the science phenomenon. A weak trend showed that weaker learners would benefit more from the refutational text. It seems that learners with effective learning strategies are able to pick out the relevant content regardless of the text type, whereas weaker learners might benefit from refutational parts that contrast the most typical misconceptions with scientific views. The purpose of Study V was to use eye tracking to determine how third-year medical studets (n = 39) and internal medicine residents (n = 13) read and solve patient case texts. The results revealed differences between medical students and residents in processing patient case texts; compared to the students, the residents were more accurate in their diagnoses and processed the texts significantly faster and with a lower number of fixations. Different reading patterns were also found. The observed differences between medical students and residents in processing patient case texts could be used in medical education to model expert reasoning and to teach how a good medical text should be constructed. The main findings of the thesis indicate that even among very selected student populations, such as high-achieving medical students or student teachers, there seems to be a lot of variation in regulation strategies of learning and text processing. As these learning strategies are related to successful studying, students enter educational programmes with rather different chances of managing and achieving success. Further, the ways of engaging in learning seldom centre on a single strategy or approach; rather, students seem to combine several strategies to a certain degree. Sometimes, it can be a matter of perspective of which way of learning can be considered best; therefore, the reality of studying in higher education is often more complicated than the simplistic view of self-regulation as a good quality and external regulation as a harmful quality. The beginning of university studies may be stressful for many, as the gap between high school and university studies is huge and those strategies that were adequate during high school might not work as well in higher education. Therefore, it is important to map students’ learning strategies and to encourage them to engage in using high-quality learning strategies from the beginning. Instead of separate courses on learning skills, the integration of these skills into course contents should be considered. Furthermore, learning complex scientific phenomena could be facilitated by paying attention to high-quality learning materials and texts and other support from the learning environment also in the university. Eye tracking seems to have great potential in evaluating performance and growing diagnostic expertise in text processing, although more research using texts as stimulus is needed. Both medical and teacher education programmes and the professions themselves are challenging in terms of their multidisciplinary nature and increasing amounts of information and therefore require good lifelong learning skills during the study period and later in work life.

Two Cultures of Arts Education, Finland and Canada? An integrated View

Taidekasvatuksen kaksi kulttuuria, Suomi ja Kanada? Integroitu näkemys Tutkimuksessa kuvataan kanadalaisen Learning Through The Arts –pedagogiikan mukainen suomalainen kokeiluhanke, jonka aikana taiteilija–opettaja-parit opettivat yhdessä eri oppiaineita koululuokille: esim. matematiikkaa tanssien, biologiaa maalaten tai yhdistäen eri taiteenlajeja projektimuotoiseen oppimiseen. Hanketta arvioitaessa nousee esille, ei niinkään yksittäisten taiteilijoiden ja opettajien toiminta, vaan pikemminkin Kanadan ja Suomen rakenteelliset sekä kulttuuriset eroavuudet. Tutkimus sivuaa myös Suomessa käytävää keskustelua taiteen hyödyllisyydestä ja pohtii samalla taito- ja taideaineiden asemaa koulussa. Työn teoreettisessa osassa integroidaan opetussuunnitelmateoriaa, kasvatuksen historiaa ja filosofiaa, tähdentäen taidekasvatuksen merkitystä osana koko ihmisen kasvatusta. Opetussuunnitelmateorian osalta tarkastellaan romanttista ja klassista opetussuunnitelmaa, jotka eroavat toisistaan menetelmiensä, sisältöjensä, tavoitteidensa sekä arvioinnin osalta. Ns. kovat ja pehmeät aineet tai matemaattis-luonnontieteelliset aineet vastakohtanaan humanismi, voidaan ymmärtää sekä historiallisia että epistemologisia taustojaan vasten. Pepperin maailmanhypoteesien mukaisesti on kasvatuksen ongelmien ratkaisemiseksi hahmotettavissa neljä selvästi toisistaan eroavaa lähestymistapaa: formismi; organisismi; mekanisismi; sekä kontekstualismi. Kantin filosofiaan viitaten tutkimus puolustaa käsitystä taiteesta rationaalisena ja propositionaalisena kokonaisuutena, joka ei ole vain kommunikaation väline, vaan yksi todellisuuden kohtaamisen lajeista, tiedon ja etiikan rinnalla. Näin ajateltuna taito- ja taidekasvatuksen tulisi olla luonteeltaan aina myös kulttuurikasvatusta. Tutkimuksen tulosten perusteella voidaan väittää, että moniammatillinen yhteistyö monipuolistaa koulun opetusta. Mikäli huolehditaan siitä, että taiteilijat saavat riittävästi koulutusta opettamiseen liittyvissä asioissa, on mahdollista käyttää taiteilijoita opettajien rinnalla koulutyössä.

Thinking Outside the Box: Enhancing Science Teaching by Combining (Instead of Contrasting) Laboratory and Simulation Activities

The focus of the present work was on 10- to 12-year-old elementary school students’ conceptual learning outcomes in science in two specific inquiry-learning environments, laboratory and simulation. The main aim was to examine if it would be more beneficial to combine than contrast simulation and laboratory activities in science teaching. It was argued that the status quo where laboratories and simulations are seen as alternative or competing methods in science teaching is hardly an optimal solution to promote students’ learning and understanding in various science domains. It was hypothesized that it would make more sense and be more productive to combine laboratories and simulations. Several explanations and examples were provided to back up the hypothesis. In order to test whether learning with the combination of laboratory and simulation activities can result in better conceptual understanding in science than learning with laboratory or simulation activities alone, two experiments were conducted in the domain of electricity. In these experiments students constructed and studied electrical circuits in three different learning environments: laboratory (real circuits), simulation (virtual circuits), and simulation-laboratory combination (real and virtual circuits were used simultaneously). In order to measure and compare how these environments affected students’ conceptual understanding of circuits, a subject knowledge assessment questionnaire was administered before and after the experimentation. The results of the experiments were presented in four empirical studies. Three of the studies focused on learning outcomes between the conditions and one on learning processes. Study I analyzed learning outcomes from experiment I. The aim of the study was to investigate if it would be more beneficial to combine simulation and laboratory activities than to use them separately in teaching the concepts of simple electricity. Matched-trios were created based on the pre-test results of 66 elementary school students and divided randomly into a laboratory (real circuits), simulation (virtual circuits) and simulation-laboratory combination (real and virtual circuits simultaneously) conditions. In each condition students had 90 minutes to construct and study various circuits. The results showed that studying electrical circuits in the simulation–laboratory combination environment improved students’ conceptual understanding more than studying circuits in simulation and laboratory environments alone. Although there were no statistical differences between simulation and laboratory environments, the learning effect was more pronounced in the simulation condition where the students made clear progress during the intervention, whereas in the laboratory condition students’ conceptual understanding remained at an elementary level after the intervention. Study II analyzed learning outcomes from experiment II. The aim of the study was to investigate if and how learning outcomes in simulation and simulation-laboratory combination environments are mediated by implicit (only procedural guidance) and explicit (more structure and guidance for the discovery process) instruction in the context of simple DC circuits. Matched-quartets were created based on the pre-test results of 50 elementary school students and divided randomly into a simulation implicit (SI), simulation explicit (SE), combination implicit (CI) and combination explicit (CE) conditions. The results showed that when the students were working with the simulation alone, they were able to gain significantly greater amount of subject knowledge when they received metacognitive support (explicit instruction; SE) for the discovery process than when they received only procedural guidance (implicit instruction: SI). However, this additional scaffolding was not enough to reach the level of the students in the combination environment (CI and CE). A surprising finding in Study II was that instructional support had a different effect in the combination environment than in the simulation environment. In the combination environment explicit instruction (CE) did not seem to elicit much additional gain for students’ understanding of electric circuits compared to implicit instruction (CI). Instead, explicit instruction slowed down the inquiry process substantially in the combination environment. Study III analyzed from video data learning processes of those 50 students that participated in experiment II (cf. Study II above). The focus was on three specific learning processes: cognitive conflicts, self-explanations, and analogical encodings. The aim of the study was to find out possible explanations for the success of the combination condition in Experiments I and II. The video data provided clear evidence about the benefits of studying with the real and virtual circuits simultaneously (the combination conditions). Mostly the representations complemented each other, that is, one representation helped students to interpret and understand the outcomes they received from the other representation. However, there were also instances in which analogical encoding took place, that is, situations in which the slightly discrepant results between the representations ‘forced’ students to focus on those features that could be generalised across the two representations. No statistical differences were found in the amount of experienced cognitive conflicts and self-explanations between simulation and combination conditions, though in self-explanations there was a nascent trend in favour of the combination. There was also a clear tendency suggesting that explicit guidance increased the amount of self-explanations. Overall, the amount of cognitive conflicts and self-explanations was very low. The aim of the Study IV was twofold: the main aim was to provide an aggregated overview of the learning outcomes of experiments I and II; the secondary aim was to explore the relationship between the learning environments and students’ prior domain knowledge (low and high) in the experiments. Aggregated results of experiments I & II showed that on average, 91% of the students in the combination environment scored above the average of the laboratory environment, and 76% of them scored also above the average of the simulation environment. Seventy percent of the students in the simulation environment scored above the average of the laboratory environment. The results further showed that overall students seemed to benefit from combining simulations and laboratories regardless of their level of prior knowledge, that is, students with either low or high prior knowledge who studied circuits in the combination environment outperformed their counterparts who studied in the laboratory or simulation environment alone. The effect seemed to be slightly bigger among the students with low prior knowledge. However, more detailed inspection of the results showed that there were considerable differences between the experiments regarding how students with low and high prior knowledge benefitted from the combination: in Experiment I, especially students with low prior knowledge benefitted from the combination as compared to those students that used only the simulation, whereas in Experiment II, only students with high prior knowledge seemed to benefit from the combination relative to the simulation group. Regarding the differences between simulation and laboratory groups, the benefits of using a simulation seemed to be slightly higher among students with high prior knowledge. The results of the four empirical studies support the hypothesis concerning the benefits of using simulation along with laboratory activities to promote students’ conceptual understanding of electricity. It can be concluded that when teaching students about electricity, the students can gain better understanding when they have an opportunity to use the simulation and the real circuits in parallel than if they have only the real circuits or only a computer simulation available, even when the use of the simulation is supported with the explicit instruction. The outcomes of the empirical studies can be considered as the first unambiguous evidence on the (additional) benefits of combining laboratory and simulation activities in science education as compared to learning with laboratories and simulations alone.