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.

Kollektiivista muistia etsimässä : How Collectivities Remember : Structures and Spaces of Social and Cultural Memory

Ajankohtaista

Hållpunkter för lärande : småbarns möten

Developed from human activities, mathematical knowledge is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans’ everyday life, an environment where people reach agreement regarding certain “laws” and principles in mathematics. Through interaction with worldly phenomena and people, children will always gain experience that they can then in turn use to understand future situations. Consequently, the environment in which a child grows up plays an important role in what that child experiences and what possibilities for learning that child has. Variation theory, a branch of phenomenographical research, defines human learning as changes in understanding and acting towards a specific phenomenon. Variation theory implies a focus on that which it is possible to learn in a specific learning situation, since only a limited number of critical aspects of a phenomenon can be simultaneously discerned and focused on. The aim of this study is to discern how toddlers experience and learn mathematics in a daycare environment. The study focuses on what toddlers experience, how their learning experience is formed, and how toddlers use their understanding to master their environment. Twenty-three children were observed videographically during everyday activities. The videographic methodology aims to describe and interpret human actions in natural settings. The children are aged from 1 year, 1 month to 3 years, 9 months. Descriptions of the toddlers’ actions and communication with other children and adults are analyzed phenomenographically in order to discover how the children come to understand the different aspects of mathematics they encounter. The study’s analysis reveals that toddlers encounter various mathematical concepts, similarities and differences, and the relationship between parts and whole. Children form their understanding of such aspects in interaction with other children and adults in their everyday life. The results also show that for a certain type of learning to occur, some critical conditions must exist. Variation, simultaneity, reasonableness and fixed points are critical conditions of learning that appear to be important for toddlers’ learning. These four critical conditions are integral parts of the learning process. How children understand mathematics influences how they use mathematics as a tool to master their surrounding world. The results of the study’s analysis of how children use their understanding of mathematics shows that children use mathematics to uphold societal rules, to describe their surrounding world, and as a tool for problem solving. Accordingly, mathematics can be considered a very important phenomenon that children should come into contact with in different ways and which needs to be recognized as a necessary part of children’s everyday life. Adults working with young children play an important role in setting perimeters for children’s experiences and possibilities to explore mathematical concepts and phenomena. Therefore, this study is significant as regards understanding how children learn mathematics through everyday activities.

Limits of Meritocracy. How Fields of Study and Gender Segregation Affect Social Stratification in Finland

This dissertation critically reviews the idea of meritocracy from both a theoretical and an empirical perspective. Based on a discussion of classical texts of social philosophy and sociology, it is argued that meritocracy as a concept for social stratification is best compatible with the sociological tradition of status attainment research: both frame social inequality in primarily individualistic terms, centring on the role of ascribed (e.g., gender, social background) and achieved (e.g., educational qualifications) characteristics for determining individuals’ socioeconomic rewards. This theoretical argument introduces the research problem at the core of this dissertation: to what extent can the individualistic conception of social stratification be maintained empirically? Fields of study and their interaction with educational attainment levels play a prominent role in the analysis of this question. Drawing on sociological versions of segmented labour market theory, it is assumed that fields of study may channel individuals into heterogeneous political-economic contexts on the labour market, which potentially modify the socioeconomic benefit individuals derive from their qualification levels. The focus on fields of study may also highlight economic differentials between men and women that derive from the persisting segregation of men’s and women’s occupational and educational specializations rather than direct gender discrimination on the labour market. The quantitative analyses in this dissertation consist of three research articles, which are based primarily on Finnish data, but occasionally extend the view to other European countries. The data sources include register-based macro- and microdata as well as survey data. Article I examines the extent and the patterns of gender segregation within the Finnish educational system between 1981 and 2005. The results show that differences between men’s and women’s field specializations have for the most part remained stable during this period, with particularly high levels of gender segregation observed at lower educational levels. The focus in Article II rests on the effects of gender-segregated fields of study on higher education graduates’ occupational status. It is shown that fields of study matter for accessing professional jobs and avoiding low-skilled positions in Finland: at the early career stage, particularly polytechnic graduates from female-dominated fields are less likely to work in professional positions. Finnish university graduates from male-dominated fields were more likely than their peers with different specializations to work as professionals, yet they also faced a greater risk of being sorted into lowskilled jobs if they failed to make use of this advantage. Article III proceeded to analyse the joint impact of educational qualification levels and fields of study on young adults’ median earnings in Finland between 1985 and 2005. The results show that qualification levels do not confer a consistent benefit in the process of earnings stratification. Advanced qualifications raise median earnings most clearly among individuals specializing in the same field of study. When comparing individuals with different field specializations, on the other hand, higher-level qualifications do not necessarily lead to higher median earnings. Overall, the findings of this dissertation reveal a heterogeneous effect of education for achieving social positions, which challenges individual-centred, meritocratic accounts of social stratification and underlines the problematic lack of structural and institutional dimensions in the dominant account of social status attainment.

Let Go and Remember. How Finnish Communities Experienced and Memorialized School Shootings

This study examines the aftermath of mass violence in local communities. Two rampage school shootings that occurred in Finland are analyzed and compared to examine the ways in which communities experience, make sense of, and recover from sudden acts of mass violence. The studied cases took place at Jokela High School, in southern Finland, and at a polytechnic university in Kauhajoki, in western Finland, in 2007 and 2008 respectively. Including the perpetrators, 20 people lost their lives in these shootings. These incidents are part of the global school shooting phenomenon with increasing numbers of incidents occurring in the last two decades, mostly in North America and Europe. The dynamic of solidarity and conflict is one of the main themes of this study. It builds upon previous research on mass violence and disasters which suggests that solidarity increases after a crisis, and that this increase is often followed by conflict in the affected communities. This dissertation also draws from theoretical discussions on remembering, narrating, and commemorating traumatic incidents, as well as the idea of a cultural trauma process in which the origins and consequences of traumas are negotiated alongside collective identities. Memorialization practices and narratives about what happened are vital parts of the social memory of crises and disasters, and their inclusive and exclusive characteristics are discussed in this study. The data include two types of qualitative interviews; focused interviews with 11 crisis workers, and focused, narrative interviews with 21 residents of Jokela and 22 residents of Kauhajoki. A quantitative mail survey of the Jokela population (N=330) provided data used in one of the research articles. The results indicate that both communities experienced a process of simultaneous solidarity and conflict after the shootings. In Jokela, the community was constructed as a victim, and public expressions of solidarity and memorialization were promoted as part of the recovery process. In Kauhajoki, the community was portrayed as an incidental site of mass violence, and public expressions of solidarity by distant witnesses were labeled as unnecessary and often criticized. However, after the shooting, the community was somewhat united in its desire to avoid victimization and a prolonged liminal period. This can be understood as a more modest and invisible process of “silent solidarity”. The processes of enforced solidarity were partly made possible by exclusion. In some accounts, the family of the perpetrator in Jokela was excluded from the community. In Kauhajoki, the whole incident was externalized. In both communities, this exclusion included associating the shooting events, certain places, and certain individuals with the concept of evil, which helped to understand and explain the inconceivable incidents. Differences concerning appropriate emotional orientations, memorialization practices and the pace of the recovery created conflict in both communities. In Jokela, attitudes towards the perpetrator and his family were also a source of friction. Traditional gender roles regarding the expression of emotions remained fairly stable after the school shootings, but in an exceptional situation, conflicting interpretations arose concerning how men and women should express emotion. The results from the Jokela community also suggest that while increased solidarity was seen as important part of the recovery process, some negative effects such as collective guilt, group divisions, and stigmatization also emerged. Based on the results, two simultaneous strategies that took place after mass violence were identified; one was a process of fast-paced normalization, and the other was that of memorialization. Both strategies are ways to restore the feeling of security shattered by violent incidents. The Jokela community emphasized remembering while the Kauhajoki community turned more to the normalization strategy. Both strategies have positive and negative consequences. It is important to note that the tendency to memorialize is not the only way of expressing solidarity, as fast normalization includes its own kind of solidarity and helps prevent the negative consequences of intense solidarity.

Learning information technology business in a changing industry landscape. Introducing Team Entrepreneurship in Renewing Bachelor Education in Renewing Bachelor Education in Information

Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.

How Lean Six Sigma and Agile principles optimize ITIL-based processes

Imagine the potential implications of an organization whose business and IT processes are well aligned and are capable of reactively and proactively responding to the external and internal changes. The Philips IT Infrastructure and Operations department (I&O) is undergoing a series of transformation activities to help Philips business keeping up with the changes. I&O would serve a critical function in any business sectors; given that the I&O’s strategy switched from “design, build and run” to “specify, acquire and performance manage”, that function is amplified. In 2013, I&O’s biggest transforming programme I&O Futures engaged multiple interdisciplinary departments and programs on decommissioning legacy processes and restructuring new processes with respect to the Information Technology Internet Library (ITIL), helping I&O to achieve a common infrastructure and operating platform (CI&OP). The author joined I&O Futures in the early 2014 and contributed to the CI&OP release 1, during which a designed model Bing Box and its evaluations were conducted through the lens of six sigma’s structured define-measure-analyze-improve-control (DMAIC) improvement approach. This Bing Box model was intended to firstly combine business and IT principles, namely Lean IT, Agile, ITIL best practices, and Aspect-oriented programming (AOP) into a framework. Secondly, the author implemented the modularized optimization cycles according to the defined framework into Philips’ ITIL-based processes and, subsequently, to enhance business process performance as well as to increase efficiency of the optimization cycles. The unique of this thesis is that the Bing Box model not only provided comprehensive optimization approaches and principles for business process performance, but also integrated and standardized optimization modules for the optimization process itself. The research followed a design research guideline that seek to extend the boundaries of human and organizational capabilities by creating new and innovative artifacts. The Chapter 2 firstly reviewed the current research on Lean Six Sigma, Agile, AOP and ITIL, aiming at identifying the broad conceptual bases for this study. In Chapter 3, we included the process of constructing the Bing Box model. The Chapter 4 described the adoption of Bing Box model: two-implementation case validated by stakeholders through observations and interviews. Chapter 5 contained the concluding remarks, the limitation of this research work and the future research areas. Chapter 6 provided the references used in this thesis.