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.

Group mentoring for junior medical students: perceptions of mentees and mentors

Entering medical school can be associated with a number of difficulties that can hinder students' performance. Mentoring programs are designed to help students circumvent difficulties and improve their learning and personal development. The current study aimed to evaluate the perceptions of both students and mentors regarding a recently introduced, group-based mentoring program designed to support first-year students. After one year of regular meetings, students and mentors' perceptions of the program were assessed by means of structured questionnaires. Response content categories were identified through multiple readings. Both regular attendees and non-participating students had positive opinions about the program. Mentors were highly satisfied at having participated and acknowledged that the program has been useful not only for assisting students, but also for fostering their own personal and professional development. In conclusion, the group-based mentoring program is feasible and can elicit positive views from both mentors and students. In addition, faculty members' participation as mentors can also be beneficial, since the program appears to contribute to their own personal and professional development

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

Secondary seed dispersal of Ricinus communis Linnaeus (Euphorbiaceae) by ants in secondary growth vegetation in Minas Gerais

In this study, I tested the efficacy of ants as secondary seed dispersers of Ricinus communis in southeastern Brazil. In a natural population of 143 individuals, I determined the ballistic dispersal distance for 62 seeds and 100 additional seeds were experimentally offered to ants in groups of ten seeds along a transect of 50 m. Fifty-three seeds were removed by ants, mainly by the leafcutter Atta sexdens (90.4%). The dispersal distance by ants was high, compared to the global average (4.38 m ± 0.74 m vs. 0.96 m), but was lower than the ballistic distance (7.27 m ± 0.13 m). Ants increased the total dispersal distance (8.66 m ± 0.60 m), but the main benefit for the plant was the directed dispersal, with seed deposition on the enriched soil of ant nests.

Effect of light intensity and growth substratum on plant development and production of secondary metabolites in Cordia curassavica (Jacq.) Roem. & Schult

Cordia curassavica (Jacq.) Roem. & Schult. (Boraginaceae), also referred to as Cordia verbenacea DC, has been traditionally used for medicinal purposes. This study was driven to verify the behavior of the species in similar conditions to its natural environment, such as high light intensity and sandbank soil, and in conditions of low light intensity and fertilized substratum (dystroferric red nitosoil plus earthworm humus). The growth of the plant, the income of leaf crude extracts and, in the alcoholic extract, the number of substances found in thin layer cromatography and the toxicity of the substratum was observed. The results indicated that the growth of the root biomass, stem and leaves in discharge or lower light intensity was similar, but smaller in sandbank soil than in fertilized soil. The relative income of extracts in ether of petroleum and alcohol was larger in high light intensity and fertilized substratum. The light intensity and the substratum type didn't affect the number of substances detected in the alcoholic extract or the toxicity of this extract. Stains corresponding to the rosmarinic acid were only evidenced in some samples of the alcoholic extract, not allowing the verification of the effect of the treatments about its production.

Middle school mediocrity : quality and inequality in secondary education

Centrala teman i min avhandling är parallellskolesystem, linjedelning och segregering i högstadier och gymnasier. Det finns stora skillnader mellan länder gällande den årskurs då eleverna sorteras in i olika nivåer genom skilda klasser eller skolor. I Tyskland och Nederländerna till exempel delas eleverna upp före högstadiet medan Sverige och Finland har enhetsskolor på högstadienivå. Jag argumenterar att parallellskolesystem har en positiv effekt på elevernas testresultat i årskurserna före linjedelningen. Eleverna har incitament att jobba hårdare för att komma på i den akademiska linjen. Jag undersöker incitamentseffekter empiriskt, och hittar mönster konsistenta med incitamentseffekter både i brittisk och i internationell data. Det andra bidraget i avhandlingen är metodologiskt. Nationalekonomer brukar behandla testresultat från t.ex. IQ-tester eller internationella PISA-undersökningar som om absoluta nivån på poängantalen har betydelse i sig. I verkligheten antyder de endast en rangordning. Jag visar att normalfördelade testresultat i många fall ligger tillräckligt nära dess pengavärde på arbetsmarknaden för att ändå kunna tolkas som absoluta.

Litter fall production and decomposition in a fragment of secondary Atlantic Forest of São Paulo, sp, southeastern Brazil

Litter fall consists of all organic material deposited on the forest floor, being of extremely important for the structure and maintenance of the ecosystem through nutrient cycling. This study aimed to evaluate the production and decomposition of litter fall in a secondary Atlantic forest fragment of secondary Atlantic Forest, at the Guarapiranga Ecological Park, in São Paulo, SP. The litter samples were taken monthly from May 2012 to May 2013. To assess the contribution of litter fall forty collectors were installed randomly within an area of 0.5 ha. The collected material was sent to the laboratory to be dried at 65 °C for 72 hours, being subsequently separated into fractions of leaves, twigs, reproductive parts and miscellaneous, and weighed to obtain the dry biomass. Litterbags were placed and tied close to the collectors to estimate the decomposition rate in order to evaluate the loss of dry biomass at 30, 60, 90, 120 and 150 days. After collection, the material was sent to the laboratory to be dried and weighed again. Total litter fall throughout the year reached 5.7 Mg.ha-1.yr-1 and the major amount of the material was collected from September till March. Leaves had the major contribution for total litter fall (72%), followed by twigs (14%), reproductive parts (11%) and miscellaneous (3%). Reproductive parts had a peak during the wet season. Positive correlation was observed between total litter and precipitation, temperature and radiation (r = 0.66, p<0.05; r = 0.76, p<0.05; r = 0.58, p<0.05, respectively). The multiple regression showed that precipitation and radiation contributed significantly to litter fall production. Decomposition rate was in the interval expected for secondary tropical forest and was correlated to rainfall. It was concluded that this fragment of secondary forest showed a seasonality effect driven mainly by precipitation and radiation, both important components of foliage renewal for the plant community and that decomposition was in an intermediate rate.

LITTERFALL ASSESSEMENT IN A FRAGMENT OF SECONDARY TROPICAL FOREST, IBIÚNA, SP, SOUTHEASTERN BRAZIL1

ABSTRACT The present study aimed to analyze the production and decomposition of litterfall in a fragment of secondary Atlantic forest in the region of Ibiúna, SP, from April 2012 to March 2013. The litterfall production was estimated by 30 collectors distributed randomly in an area of 1000 m2, where the deposited material was collected every 15 days. The decomposition of litterfall was estimated through the mass loss in the period of study. After collecting, the material was dried in an oven at 65 °C for seven days to achieve a constant weight. The decomposition constant k was obteined according to Shanks and Oslon (1961) and the time for 50% and 95% of decomposition was estimated. It was found a higher litterfall production in October (454.3 kg ha-1) and lower production in July (164.9 kg ha-1), with a total amount produced of 3.5 Mg ha-1 year-1. A delay of one month in the precipitation and relative humidity showed great influence in the litter production during the study. The decomposition rate (k) was 3.1 and the time to decompose 50% of the material was estimated in 2 and ½ months and for 95% of the litterfall the time was estimated in 11 and ½ months. The production and decomposition values of this work are within the range found in other sites of secondary tropical forests.

Technical-economic analysis of different lighting systems for broiler poultry

ABSTRACT Broiler poultry is highly dependent on artificial lightening. Power consumption costs of artificial lighting systems is the second largest expense related to broiler industry, second only to feed expenses. Therefore, the current study focused to analyze technical and economic feasibility of replacing incandescent lamps already used in aviaries with other lamp types. Costs related to power consumption, implementation and maintenance of the lighting systems were evaluated with the aid of financial mathematics using net present value, return over investment and payback. Systems composed of six lamp types were analyzed in two different configurations to meet the minimum illuminance of 5 and 20 lux and for use in conventional sheds and dark house. The lamps tested were incandescent (LI) of 100 W, compact fluorescent (CFL) of 34 W, mixed (ML) 160 W sodium vapor (SVL) of 70 W, tubular fluorescent T8 (TFL T8) of 40 W and tubular fluorescent T5 (TFL T5) of 28 W. For the systems tested, it was found that the tubular fluorescent lamps T8 and T5 showed the best results of technical and economic feasibility.

Pragmatic competence of Finnish learners of English: Meaning in interaction in secondary and upper secondary schools

Tutkin pro gradu -tutkielmassani englannin kielen oppijoiden pragmaattista kompetenssia. Tarkoitukseni oli selvittää, miten suomalaiset yläkoululaiset ja lukiolaiset osaavat käyttää englannin kieltä erilaisissa kommunikaatiotilanteissa. Tutkielmani voidaan sijoittaa välikielen pragmatiikan tutkimukseen. Halusin selvittää, millä tasolla suomalaisten oppijoiden pragmaattinen kompetenssi on ja kehittyykö se yläkoulun ja lukion välillä. Lisäksi tutkin, vaikuttavatko oppimisympäristö ja oppimismahdollisuudet oppijoiden kykyyn käyttää englannin kieltä. Toisin sanoen vertasin englantipainotteisilla luokilla olevia oppilaita formaalin opetuksen oppijoihin sekä tutkin, vaikuttavatko englanninkieliset vapaa-ajan aktiviteetit ja oppijoiden mahdolliset oleskelut englanninkielisissä maissa heidän pragmaattiseen kompetenssiinsa. Tutkimukseni kohderyhmä koostui yläkoulun kahdeksasluokkalaisista ja lukion toisen vuosikurssin opiskelijoista. Testasin neljä eri ryhmää, joissa oli sekä formaalissa opetuksessa olevia oppijoita (yksi ryhmä kahdeksasluokkalaisia ja yksi ryhmä toisen vuosikurssin opiskelijoita) että kielipainotteisten luokkien oppijoita (yksi ryhmä kahdeksasluokkalaisia ja yksi ryhmä toisen vuosikurssin opiskelijoita). Arvioin kohderyhmäni pragmaattista kompetenssia monivalintatestillä, jossa testattiin oppijoiden kykyä käyttää ja ymmärtää implikaatioita, tilannekohtaisia rutiineja sekä puheakteja. Taustakysymysten avulla selvitin, kuinka usein oppijat käyttivät englantia vapaa-aikanaan ja olivatko he vierailleet englanninkielisissä maissa. Tutkimustulokseni osoittavat, että suomalaisten yläkoululaisten ja lukiolaisten pragmaattinen kompetenssi oli korkea. Pragmaattinen kompetenssi kehittyi kahdeksasluokkalaisten ja lukion toisen vuosikurssin välillä. Kehitys oli suurempaa formaalissa opetuksessa kuin kielipainotteisilla luokilla. Englantipainotteisilla luokilla olevat oppilaat suoriutuivat testistä paremmin kuin formaalin opetuksen oppilaat. Tosin erot olivat tilastollisesti merkitseviä vain yläkoulussa. Tutkimuksessani siis päättelin, että vieraskielinen opetus vaikutti enemmän nuorempiin oppijoihin. Eri oppimismahdollisuudet osoittautuivat haastaviksi analysoida. Tulokset osoittivat, että vain englanninkielisessä maassa oleskelulla oli vaikutusta oppijoiden pragmaattiseen kompetenssiin. Kysyttäessä vapaa-ajan aktiviteettien merkitystä oppijat kuitenkin kertoivat, että ne auttoivat heitä testiin vastaamisessa enemmän kuin englanninopetuksessa käydyt asiat. Kouluissa tulisikin jatkossa painottaa yhä enemmän vuorovaikutteista kieltenopetusta.

Abscesso intrabdominal tardio pós colecistectomia laparoscópica

Perforation of the gallbladder during laparoscopic cholecystectomy may be associated with intraperitoneal gallstone spillage. Several complications secondary to lost gallstones in the abdominal cavity have been described. We report a rare complication of abdominal abscess secondary to two gallstones left in the abdominal cavity. A 75-year-old female presented with spontaneous drainage of pus through the umbilicus five years after laparoscopic cholecystectomy. An ultrasonographic evaluation of the abdomen revealed a solid mass of 56x26 mm of diameter, with acoustic shadow, localized distal to the umbilicus. At laparotomy, an abscess with two biliary calculi was drained. The patient had good recovery, with no complication.

Closure of large wounds using rubber bands in rabbits

OBJECTIVE: to verify the effectiveness of the rubber elastic band in the treatment of large wounds of the body wall of rabbits by means of traction of its edges. METHODS: we studied 30 New Zealand rabbits, divided into three groups (n=10): Group 1- healing by secondary intention; Group 2- removal and eutopic repositioning of skin as full thickness skin graft; Group 3- Approximation of wound edges with elastic rubber band. In all animals, we removed a segment of the back skin and subcutaneous tissue down to the fascia, in accordance with an acrylic mold of 8cm long by 12cm wide. All animals were observed for 21 days. RESULTS: two animals of groups 1 and 2 had wound abscess. In Group 2, there was partial or total graft loss in 90% of animals. The complete closure of the wounds was observed in four animals of Group 1, six of Group 2 and eight of Group 3. There was no difference between the scar resistance values of groups 2 and 3, which were higher than those in Group 1. The scars of the three groups were characterized by the presence of mature connective tissue mixed with blood vessels and inflammatory infiltration, predominantly polymorphonuclear. CONCLUSION: the tensile strength of the wound edges with rubber elastic band is as efficient as the skin graft to treat rabbits' large body wounds.

Ultrasonografic changes in the axillary vein of patients with lymphedema after mastectomy

OBJECTIVE: To determine the prevalence of sonographic abnormalities (SA) in the axillary vein of patients with and without post-mastectomy lymphedema. METHODS: We studied a sample of 80 women, divided into two equal groups, with and without lymphedema, with B mode ultrasound, color and pulsed Doppler. The primary variable, SA, is defined as change in the venous diameter, parietal thickening, intraluminal images, compressibility, parietal collapse at inspiration and feature of the axillary venous flow on the operated side. Secondary variables were: stage of lymphedema, surgical technique, number of radio and chemotherapy sessions, limb volume, weight and age. The differences between the proportions in the groups were determined using the Chi-square test and / or Fisher's test. For continuous variables, we used the Mann-Whitney Test. To estimate the magnitude of the associations, we used the prevalence rate of SA in both groups as a measure of frequency, and as a measure of association, the prevalence ratio (PR) obtained as a function of relative risk (RR) and estimated by the test Mantel-Haenszel homogeneity test. We adopted the statistical significance level of 5% (p < 0.05). RESULTS: only the criterion "parietal thickening" was strongly associated with the lymphedema group (p = 0.001). The prevalence of SA was 55% in patients with lymphedema and 17.5% in the group without it, with difference in prevalence of 37.5%. CONCLUSION: the prevalence of SA was higher in patients undergoing mastectomy with lymphedema than in those without lymphedema.