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.

Smooth height/age curves from stem analysis with linear programming

[Abstract]

Revenue Logic inSoftware Business Context

Tutkimuksen tavoitteena oli selvittää ohjelmistotoimialan avaintekijöitä, jotka vaikuttavat yrityksen ansaintalogiikkaan sekä lisätä tietoisuutta ansaintalogiikan muodostumisesta pienissä ja keskisuurissa ohjelmistoyrityksissä. Tutkimuksen teoreettisessa osassa keskityttiin tarkastelemaan ansaintalogiikan, strategian ja liiketoimintamallin käsitteiden suhteita sekä arvioitiin toimialan osatekijöiden, hinnoitteluperiaatteiden ja ansaintamallien vaikutusta ansainnan muodostumiseen ohjelmistotoimialalla. Ohjelmistotuote ja - palveluliiketoimintaa koskien oli merkityksellistä tutkia tuotteistamisasteen ja arvoketjujen vaikutusta ansaintalogiikan muodostumisessa sekä esitellä erilaisia, tyypillisiä ohjelmistotoimialalla käytettäviä hinnoittelumenetelmiä. Työn empiirisessä osassa tarkasteltiin 23 suomalaisen ohjelmistoalan yrityksen ansaintalogiikkaa. Tiedot kerättiin haastatteluin ja analysoitiin laadullisen tutkimuksen keinoin. Tutkimustulokset korostivat ansaintalogiikan 'epämääräisyyttä' terminä mutta osoittivat, että ydinliiketoimintaan keskittyminen, tuote-, palvelu-, tai projektiliiketoiminnan osaaminen, tuotteistusaste ja kanavavalinnat ovat avaintekijöitä ansaintalogiikanmuodostumisessa. Ansaintalogiikan muodostamiseen liittyy paljon yrityksen sisäisiä ja ulkoisia haasteita sekä muutospaineita, eikä ohjelmistotoimialalla ole todennettavissa yhtä yleismaailmallista, menestyksen takaavaa ansaintalogiikkaa.

Python as a programming language for the introductory programming courses

Tämä kandidaatintyö tutkii tietotekniikan perusopetuksessa keskeisen aiheen,ohjelmoinnin, alkeisopetusta ja siihen liittyviä ongelmia. Työssä perehdytään ohjelmoinnin perusopetusmenetelmiin ja opetuksen lähestymistapoihin, sekä ratkaisuihin, joilla opetusta voidaan tehostaa. Näitä ratkaisuja työssä ovat mm. ohjelmointikielen valinta, käytettävän kehitysympäristön löytäminen sekä kurssia tukevien opetusapuvälineiden etsiminen. Lisäksi kurssin läpivientiin liittyvien toimintojen, kuten harjoitusten ja mahdollisten viikkotehtävien valinta kuuluu osaksitätä työtä. Työ itsessään lähestyy aihetta tutkimalla Pythonin soveltuvuutta ohjelmoinnin alkeisopetukseen mm. vertailemalla sitä muihin olemassa oleviin yleisiin opetuskieliin, kuten C, C++ tai Java. Se tarkastelee kielen hyviä ja huonoja puolia, sekä tutkii, voidaanko Pythonia hyödyntää luontevasti pääasiallisena opetuskielenä. Lisäksi työ perehtyy siihen, mitä kaikkea kurssilla tulisi opettaa, sekä siihen, kuinka kurssin läpivienti olisi tehokkainta toteuttaa ja minkälaiset tekniset puitteet kurssin toteuttamista varten olisi järkevää valita.

A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Matkapuhelinverkon MAP-protokollatoteutus älyverkkopalveluiden ohjauspisteeseen

Työssä esitellään yleiseurooppalaisen GSM-matkapuhelinjärjestelmän verkkoelementtejä ja perehdytään niiden väliseen standardoituun merkinantoprotokollaan. Lisäksi tarkastellaan protokollan lyhytsanomien välitykseen liittyviä operaatioita ja niissä tapahtunutta kehitystä standardoinnin eri vaiheissa. Tavoitteena oli toteuttaa GSM-matkapuhelinverkon merkinantoprotokollaan perustuva ohjelma, jonka tehtävänä on välittää lyhytsanomia matkapuhelin- ja lyhytsanomakeskuksen välillä. Matkapuhelimeen päättyvän lyhytsanoman välitykseen liittyy lisäksi reititystiedon hakeminen vastaanottajan kotirekisteristä. Toteutuksessa on ohjelmointirajapinta, joka helpottaa matkapuhelinverkon uusien palvelusovellusten kehittämistä. Toteutus testattiin standardoituja testitapauksia soveltaen. Yhdenmukaisuustestauksessa käytettiin apuna merkinantoanalysaattoria. Testauksessa tarkastettiin, että protokolla toimii loogisesti oikein. Suorituskykyä ei ole voitu testata todellisessa testiympäristössä, mutta ohjelmallisesti toteutettujen simulaattoreiden avulla on saatu hyviä tuloksia.

Simulation Supported Robot Programming using XML

The main objective of this master's thesis is to study robot programming using simulation software, and also how to embed the simulation software into company's own robot controlling software. The further goal is to study a new communication interface to the assembly line's components -more precisely how to connect the robot cell into this new communication system. Conveyor lines are already available where the conveyors use the new communication standard. The robot cell is not yet capable of communicating with to other devices using the new communication protocols. The main problem among robot manufacturers is that they all have their own communication systems and programming languages. There has not been any common programming language to program all the different robot manufacturers robots, until the RRS (Realistic Robot Simulation) standards were developed. The RRS - II makes it possible to create the robot programs in the simulation software and it gives a common user interface for different robot manufacturers robots. This thesis will present the RRS - II standard and the robot manufacturers situation for the RRS - II support. Thesis presents how the simulation software can be embedded into company's own robot controlling software and also how the robot cell can be connected to the CAMX (Computer Aided Manufacturing using XML) communication system.

Tuning Performance of Multi-threaded programs

Diplomityö tarkastelee säikeistettyä ohjelmointia rinnakkaisohjelmoinnin ylemmällä hierarkiatasolla tarkastellen erityisesti hypersäikeistysteknologiaa. Työssä tarkastellaan hypersäikeistyksen hyviä ja huonoja puolia sekä sen vaikutuksia rinnakkaisalgoritmeihin. Työn tavoitteena oli ymmärtää Intel Pentium 4 prosessorin hypersäikeistyksen toteutus ja mahdollistaa sen hyödyntäminen, missä se tuo suorituskyvyllistä etua. Työssä kerättiin ja analysoitiin suorituskykytietoa ajamalla suuri joukko suorituskykytestejä eri olosuhteissa (muistin käsittely, kääntäjän asetukset, ympäristömuuttujat...). Työssä tarkasteltiin kahdentyyppisiä algoritmeja: matriisioperaatioita ja lajittelua. Näissä sovelluksissa on säännöllinen muistinkäyttökuvio, mikä on kaksiteräinen miekka. Se on etu aritmeettis-loogisissa prosessoinnissa, mutta toisaalta huonontaa muistin suorituskykyä. Syynä siihen on nykyaikaisten prosessorien erittäin hyvä raaka suorituskyky säännöllistä dataa käsiteltäessä, mutta muistiarkkitehtuuria rajoittaa välimuistien koko ja useat puskurit. Kun ongelman koko ylittää tietyn rajan, todellinen suorituskyky voi pudota murto-osaan huippusuorituskyvystä.

Lasertyöaseman mekaniikan ohjelmointi

Työssä oli tarkoituksena suunnitella logiikka lasertyöaseman mekaniikan ohjaukseen. Logiikka muodostettiin Alpha Programming –ohjelmalla, mikä ladattiin muodostamisen jälkeen mikrokontrolleriin. Latauksen jälkeen logiikka testattiin ja ilmenevät virheet korjattiin. Korjausten jälkeen logiikkaa saatiin toimimaan oikein.

Promoting Programming Learning. Engagement, Automatic Assessment with Immediate Feedback in Visualizations

The skill of programming is a key asset for every computer science student. Many studies have shown that this is a hard skill to learn and the outcomes of programming courses have often been substandard. Thus, a range of methods and tools have been developed to assist students’ learning processes. One of the biggest fields in computer science education is the use of visualizations as a learning aid and many visualization based tools have been developed to aid the learning process during last few decades. Studies conducted in this thesis focus on two different visualizationbased tools TRAKLA2 and ViLLE. This thesis includes results from multiple empirical studies about what kind of effects the introduction and usage of these tools have on students’ opinions and performance, and what kind of implications there are from a teacher’s point of view. The results from studies in this thesis show that students preferred to do web-based exercises, and felt that those exercises contributed to their learning. The usage of the tool motivated students to work harder during their course, which was shown in overall course performance and drop-out statistics. We have also shown that visualization-based tools can be used to enhance the learning process, and one of the key factors is the higher and active level of engagement (see. Engagement Taxonomy by Naps et al., 2002). The automatic grading accompanied with immediate feedback helps students to overcome obstacles during the learning process, and to grasp the key element in the learning task. These kinds of tools can help us to cope with the fact that many programming courses are overcrowded with limited teaching resources. These tools allows us to tackle this problem by utilizing automatic assessment in exercises that are most suitable to be done in the web (like tracing and simulation) since its supports students’ independent learning regardless of time and place. In summary, we can use our course’s resources more efficiently to increase the quality of the learning experience of the students and the teaching experience of the teacher, and even increase performance of the students. There are also methodological results from this thesis which contribute to developing insight into the conduct of empirical evaluations of new tools or techniques. When we evaluate a new tool, especially one accompanied with visualization, we need to give a proper introduction to it and to the graphical notation used by tool. The standard procedure should also include capturing the screen with audio to confirm that the participants of the experiment are doing what they are supposed to do. By taken such measures in the study of the learning impact of visualization support for learning, we can avoid drawing false conclusion from our experiments. As computer science educators, we face two important challenges. Firstly, we need to start to deliver the message in our own institution and all over the world about the new – scientifically proven – innovations in teaching like TRAKLA2 and ViLLE. Secondly, we have the relevant experience of conducting teaching related experiment, and thus we can support our colleagues to learn essential know-how of the research based improvement of their teaching. This change can transform academic teaching into publications and by utilizing this approach we can significantly increase the adoption of the new tools and techniques, and overall increase the knowledge of best-practices. In future, we need to combine our forces and tackle these universal and common problems together by creating multi-national and multiinstitutional research projects. We need to create a community and a platform in which we can share these best practices and at the same time conduct multi-national research projects easily.

Early nutritional determinants in cardio-metabolic programming – A prospective randomized controlled dietary intervention study

Western societies have been faced with the fact that overweight, impaired glucose regulation and elevated blood pressure are already prevalent in pediatric populations. This will inevitably mean an increase in later manifestations of cardio-metabolic diseases. The dilemma has been suggested to stem from fetal life and it is surmised that the early nutritional environment plays an important role in the process called programming. The aim of the present study was to characterize early nutritional determinants associating with cardio-metabolic risk factors in fetuses, infants and children. Further, the study was designated to establish whether dietary counseling initiated in early pregnancy can modify this cascade. Healthy mother-child pairs (n=256) participating in a dietary intervention study were followed from early pregnancy to childhood. The intervention included detailed dietary counseling by a nutritionist targeting saturated fat intake in excess of recommendations and fiber consumption below recommendations. Cardio-metabolic programming was studied by characterizing the offspring’s cardio-metabolic risk factors such as over-activation of the autonomic nervous system, elevated blood pressure and adverse metabolic status (e.g. serum high split proinsulin concentration). Fetal cardiac sympathovagal activation was measured during labor. Postnatally, children’s blood pressure was measured at six-month and four-year follow-up visits. Further, infants’ metabolic status was assessed by means of growth and serum biomarkers (32-33 split proinsulin, leptin and adiponectin) at the age of six months. This study proved that fetal cardiac sympathovagal activity was positively associated with maternal pre-pregnancy body mass index indicating adverse cardio-metabolic programming in the offspring. Further, a reduced risk of high split proinsulin in infancy and lower blood pressure in childhood were found in those offspring whose mothers’ weight gain and amount and type of fats in the diet during pregnancy were as recommended. Of note, maternal dietary counseling from early pregnancy onwards could ameliorate the offspring’s metabolic status by reducing the risk of high split proinsulin concentration, although it had no effect on the other cardio-metabolic markers in the offspring. At postnatal period breastfeeding proved to entail benefits in cardio-metabolic programming. Finally, the recommended dietary protein and total fat content in the child’s diet were important nutritional determinants reducing blood pressure at the age of four years. The intrauterine and immediate postnatal period comprise a window of opportunity for interventions aiming to reduce the risk of cardio-metabolic disorders and brings the prospect of achieving health benefits over one generation.

Tool-supported invariant-based programming

The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.

Enabling constructive alignment in programming instruction

In this thesis, simple methods have been sought to lower the teacher’s threshold to start to apply constructive alignment in instruction. From the phases of the instructional process, aspects that can be improved with little effort by the teacher have been identified. Teachers have been interviewed in order to find out what students actually learn in computer science courses. A quantitative analysis of the structured interviews showed that in addition to subject specific skills and knowledge, students learn many other skills that should be mentioned in the learning outcomes of the course. The students’ background, such as their prior knowledge, learning style and culture, affects how they learn in a course. A survey was conducted to map the learning styles of computer science students and to see if their cultural background affected their learning style. A statistical analysis of the data indicated that computer science students are different learners than engineering students in general and that there is a connection between the student’s culture and learning style. In this thesis, a simple self-assessment scale that is based on Bloom’s revised taxonomy has been developed. A statistical analysis of the test results indicates that in general the scale is quite reliable, but single students still slightly overestimate or under-estimate their knowledge levels. For students, being able to follow their own progress is motivating, and for a teacher, self-assessment results give information about how the class is proceeding and what the level of the students’ knowledge is.

Web-makrot ja käyttäjäautomaatio web-sovelluksessa: prototyypin suunnittelu ja toteutus

Tämän kandidaatintyön aiheena on web-sovelluksen käyttäjäautomaatio web-makrojen avulla. Työssä esitellään prototyyppitoteutus SaaS-sovellukseen kohdistetusta web-makrojärjestelmästä. Työn teoriaosa esittelee web-automaation ja web-ympäristön keskeisen teknologian. Ratkaisuosa pohjustaa ratkaisuun käytetyn lähestymistavan, esittelee työn prototyyppiratkaisun ja arvioi ratkaisun lopputulosta. Lopputuloksena havaitaan, että prototyyppiratkaisu onnistuu selvittämään makrotoiminnallisuuden toteuttamiseen liittyvät tekniset haasteet. Ratkaisun merkittävimmäksi tekniseksi haasteeksi arvioidaan selainyhteensopivuuden saavutus ja ylläpito. Ratkaisun hyödynnettävyys koko web-sovelluksen mittakaavassa todetaan kuitenkin heikoksi, koska sovelluksen liiketoimintalogiikka rajoittaa makroparadigman käyttöä.