Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Metabolic evaluation of dairy cows submitted to three different strategies to decrease the effects of negative energy balance in early postpartum

In early lactation dairy cattle suffer metabolic alterations caused by negative energy balance, which predisposes to fatty liver and ketosis. The aim of this study was to evaluate the metabolic condition of high yielding dairy cows subjected to three treatments for preventing severe lipomobilization and ketosis in early lactation. Fifty four multiparous Holstein cows yielding >30 L/day were divided into four groups: control (CN= no treatment), glucose precursor (PG= propylene-glycol), hepatic protector (Mp= Mercepton®), and energy supplement with salts of linolenic and linoleic faty acids (Mg-E= Megalac-E®). Treatments were administrated randomly at moment of calving until 8 weeks postpartum. Blood samples were collected on days 1, 7, 14, 21, 28, 35, 42 and 49 postpartum. Body condition score (BCS) was evaluated at the same periods and milk yield was recorded at 2nd, 4th, 5th, 6th, 7th, and 8th weeks of lactation. Concentrations of non-esterified fatty acids (NEFA), albumin, AST, ß-hydroxybutyrate (BHBA), cholesterol, glucose, total protein, urea and triglycerides were analyzed in blood samples. Cut-off points for subclinical ketosis were defined when BHBA >1.4 mmol/L and NEFA >0.7 mmol/L. General occurrence of subclinical ketosis was 24% during the period. An ascendant curve of cholesterol and glucose was observed from the 1st to the 8th week of lactation, while any tendency was observed with BHBA and NEFA, although differences among treatments were detected (p<0.05). BCS decreased from a mean of 3.85 at 1st week to 2.53 at 8th week of lactation (p=0.001). Milk yield was higher in the Mg-E group compared with the other treatment groups (p<0.05) Compared with the CN group, the treatments with Mp and PG did not show significant differences in blood biochemistry and milk yield. Cows receiving PG and Mg-E showed higher values of BHBA and NEFA (P<0.05), indicating accentuated lipomobilization. Supplementation with Mg-E also resulted in significant higher concentrations of cholesterol, BHBA, urea, AST and lower values of glycemia. This performance may be explained by the highest milk yield observed with this treatment. Treatments with PG and Mp did not improve milk yield, compared with control cows, but did not show metabolic evidence of ketosis, fat mobilization or fatty liver. These results suggest that treatment with Mg-E improves milk production but induces a higher negative energy balance leading to moderated lipomobilization and ketone bodies production, increasing the risk of fatty liver.

Acid-base balance of dairy cows and its relationship with alcoholic stability and mineral composition of milk

This study aimed to associate the occurrence of acid-base disorders with the alcoholic stability of milk from animals in the field, and to evaluate differences between the mineral composition of milk that was both stable and unstable in alcohol. The sample comprised 96 dairy cows, where the milk and blood of each corresponding animal was collected. The mineral composition of stable and unstable milk in alcohol was different and may be related to acid-base disturbances. The average amount of phosphate was lower in the milk that was unstable in alcohol, while potassium was greater. Frequency of the alcoholically unstable milk cases was higher in the cows with acid-base disturbances. Respiratory alkalosis was the disorder that was most observed.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Inverse convection problem of simultaneous estimation of two boundary heat fluxes in parallel plate channels

This paper deals with the use of the conjugate gradient method of function estimation for the simultaneous identification of two unknown boundary heat fluxes in parallel plate channels. The fluid flow is assumed to be laminar and hydrodynamically developed. Temperature measurements taken inside the channel are used in the inverse analysis. The accuracy of the present solution approach is examined by using simulated measurements containing random errors, for strict cases involving functional forms with discontinuities and sharp-corners for the unknown functions. Three different types of inverse problems are addressed in the paper, involving the estimation of: (i) Spatially dependent heat fluxes; (ii) Time-dependent heat fluxes; and (iii) Time and spatially dependent heat fluxes.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Adaptation of TRIZ Method for Problem Solving in Process Engineering

TRIZ is one of the well-known tools, based on analytical methods for creative problem solving. This thesis suggests adapted version of contradiction matrix, a powerful tool of TRIZ and few principles based on concept of original TRIZ. It is believed that the proposed version would aid in problem solving, especially those encountered in chemical process industries with unit operations. In addition, this thesis would help fresh process engineers to recognize importance of various available methods for creative problem solving and learn TRIZ method of creative problem solving. This thesis work mainly provides idea on how to modify TRIZ based method according to ones requirements to fit in particular niche area and solve problems efficiently in creative way. Here in this case, the contradiction matrix developed is based on review of common problems encountered in chemical process industry, particularly in unit operations and resolutions are based on approaches used in past to handle those issues.

Some reformulations for the quadratic assignment problem

Kombinatorisk optimering handlar om att hitta en bra eller rent av den bästa möjliga lösningen från ett känt antal lösningar eller kombinationer. Ofta är antalet lösningar så enormt att en genomgång av alla olika lösningar inte är möjlig. En av huvudorsakerna till att det forskas inom kombinatorisk optimering är att liknande frågeställningar eller problem uppkommer inom så många olika områden. Påståendet stämmer speciellt bra för kvadratiska tilldelningsproblem(eng. Quadratic Assignment Problem). Sådana problem uppstår då man försöker beskriva en stor mängd tillämpade frågeställningar. Vilken gate skall väljas för flygen på större flygplatser för att minimera den totala väg människorna behöver gå och bagaget förflyttas? Var skall olika avdelningar på en fabrik placeras för att minimera materialförflyttningar mellan avdelningarna? Hur ser ett optimalt tangentbord ut för olika språk? Var skall komponenterna placeras på ett kretskort? De här är alla frågor som kan besvaras genom att lösa kvadratiska tilldelningsproblem. Kvadratiska tilldelningsproblem är dock mycket svåra att lösa. Det beror på att problemet i den standardform det matematiskt formuleras i huvudsak består av produkter av binära variabler. I denna avhandling har problemet omformulerats till en linjär diskret form som innehåller färre variabler. Med omformuleringen har bland annat flera tidigare olösta kvadratiska tilldelningsproblem kunnat lösas till globalt optimum, den bästa möjliga lösningen, för första gången någonsin.

Mannen som objekt och problem : Heikki Waris och betydelsen av kön i vetenskaplig socialpolitik, ca 1930-1970

I avhandlingen analyseras betydelsen av kön i den vetenskapliga socialpolitiken vid 1900-talets mitt, i synnerhet med fokus på Heikki Waris (1901–1989) produktion. Waris var Finlands första professor i socialpolitik, som efter andra världskriget etablerades som ett akademiskt ämne vid de finländska universiteten, och Waris blev känd som en av tidens främsta auktoriteter på den finländska socialpolitiken. Vid en tid då välfärdsstaten etablerades och samhället genomgick en snabb moderniseringsprocess, fokuserade den socialpolitiska forskningen på problem och frågor som främst ansågs beröra den manliga delen av befolkningen, såsom alkoholkonsumtion och relationer inom det industriella arbetet. Detta trots att de nordiska staterna senare skulle bli kända som så kallade kvinnovänliga välfärdsstater, där frågor om kvinnors position och jämställdhet beaktades. I avhandlingen belyses hur de texter Waris skrev, samt den forskning som han initierade, skapade ideal baserade på sundhet, ekonomiskt ansvarstagande, aktivitet och medvetenhet samt hur dessa ideal var kopplade till män och manlighet. Förutom att visa hur ideal konstruerades, studeras även de olika formerna och funktionerna av kön i den socialpolitiska litteraturen. Behandlades kön endast som demografisk kategori eller fanns det ett djupare intresse för mäns och kvinnors positioner och roller? Vilka förhållanden ville Waris och de andra socialpolitikerna belysa med att lyfta fram frågor om kön i sina texter? Waris var även en auktoritet på den snabba moderniseringsprocess som Finland hade genomgått sedan industrialiseringen vid 1800-talets slut. I avhandlingen argumenteras för att män och kvinnor på varierande sätt blev symboler för samhällelig förändring. ------------------------ Väitöskirjassa tutkitaan sukupuolen merkitystä sosiaalipolitiikan tutkimuksessa 1900-luvun puolivälissä. Lähtökohtana on Heikki Wariksen (1901–1989) tieteellinen tuotanto. Waris toimi Suomen ensimmäisenä sosiaalipolitiikan professorina ja kehitti sosiaalipolitiikkaa akateemisena aiheena Suomessa toisen maailmansodan jälkeen. Waris tunnettiin yhtenä aikansa merkittävimpänä suomalaisen sosiaalipolitiikan asiantuntijana. Hyvinvointivaltion rakentumisaikana sosiaalipolitiikan tutkimus keskittyi miehiin liittyviin ongelmiin ja kysymyksiin, kuten alkoholin kulutukseen. Väitöskirjassa osoitetaan miten Wariksen teksteissä, ja Wariksen ohjaamissa väitöskirjoissa rakennettiin terveellisyydelle, elättäjyydelle, aktiivisuudelle sekä tietoisuudelle pohjautuva ihanne, joka oli kytketty miehiin ja miehuuteen. Lisäksi tutkitaan sukupuolen muotoja ja funktioita sosiaalipoliittisessa kirjallisuudessa. Oliko sukupuoli pelkkä väestöllinen kategoria vai osoittivatko sosiaalipolitiikan tutkijat syvällisempää mielenkiintoa miesten ja naisten asemaa sekä rooleja kohtaan? Mitkä asiat huomioitiin sukupuolen avulla? Waris oli myös industrialismin aiheuttaman yhteiskuntamuutoksen asiantuntija. Väitöskirjassa osoitetaan miten miehiä ja naisia käsiteltiin eri tavalla muutoksen symboleina.

Matrix Mind : on managerial reframing in multidimensional problem solving

Det är inte ovanligt att man i organisationer ställs inför problem som inte kan hanteras inom befintlig organisationsstruktur. Skälen kan vara att frågorna har många – ibland konflikterande – dimensioner och perspektiv som samtidigt måste beaktas. I den här avhandlingen studeras vilka tankemönster och föreställningar som fanns när grupper av chefer försökte lösa komplexa problem, som inte hade en naturlig organisatorisk hemvist och hur de omsatte dessa tankemönster i handling. Vad kännetecknade det ledarskap som utövades under problemlösningsprocessen? Avhandlingens empiri hämtas från ledarutvecklingsprogram i två internationellt verksamma företag i Sverige, och omfattar 14 verkliga affärsproblem i dessa företag och den process varigenom de löstes. De 14 seminarierna utgör exempel på hur mångdimensionella frågeställningar framgångsrikt hanteras utanför den befintliga organisationsstrukturen. Studien ger, genom att adressera frågor kring tankesätt och ledningsprocesser, en djupare förståelse för förutsättningarna för detta, och lyfter särskilt fram betydelsen av ett ledarskap som inbegriper begreppen intervention, förmåga och omtolkning. Som ett samlat begrepp introduceras bilden att utöva ledarskapet utifrån ett matrix mind. Att påverka strukturer (i vid mening) och därigenom de förmågor som utvecklas, är del i detta ledarskap. Det sker genom interventioner (ingrepp som påverkar relationer i t ex en grupp) och baserades i den aktuella empirin på uppfattningar om värdet av problematisering, erfarenhetsutbyte och av ett språk, som både beskriver och anger inriktning för aktiviteter. Interventioner i strukturer (och till dem knutna processer) beskriver dock bara delvis detta ledarskap. Att leda med ett matrix mind innefattar också ett nyfiket och kreativt förhållningssätt, och att utifrån detta leda omtolkning av problem. I empirin finns flera exempel på detta. Avhandlingen avser att ge ett bidrag inom såväl organisations- som ledarskapsteori.

Assimilate partitioning in leaves of the raffinose-storing herb Lamium album L.: the effects of altering source-sink balance

In Lamium album, sucrose and raffinose-family oligosaccharides are the major products of photosynthesis that are stored in leaves. Using gas analysis and 14CO2 feeding, we compared photosynthesis and the partitioning of recently-fixed carbon in plants where sink activity was lowered by excision of flowers and chilling of roots with those where sink activity was not modified. Reduction in sink activity led to a reduction in the maximum rate of photosynthesis, to retention of fixed carbon in source leaves and to the progressive accumulation of raffinose-family oligosaccharides. This ultimately affected the extractable activities of invertase and sucrose phosphate synthase. At the end of the light period, invertase activity was significantly higher in treated plants. By contrast sucrose phosphate synthase activity was significantly lower in treated plants. We propose that reducing sink activity in L. album is associated with a shift in metabolism away from starch and sucrose synthesis and towards sucrose catabolism, galactinol utilisation and the synthesis of raffinose-family oligosaccharides.

Chromium mass balance in sodium chlorate process

Kuudenarvoista kromia käytetään natriumkloraatin valmistuksessa prosessin tuotantotehokkuuden ja turvallisuuden parantamiseksi. Kromia kuitenkin poistuu prosessista muutamaa reittiä pitkin. Koska kuuudenarvoisella kromilla on syöpää aiheuttavia, mutageenisiä sekä lisääntymiselle myrkyllisiä ominaisuuksia, olisi tärkeää ymmärtää, miten kromi kulkeutuu prosessin eri osiin, ja kuinka paljon sitä poistuu prosessista. Tämä on tärkeää, jotta osataan hallita kromin käytöstä aiheutuvat riskit, sekä toisaalta myös tehostaa kromin käyttöä prosessissa. Työn tarkoituksena oli tuottaa tietoa kromin käytöstä natriumkloraattiprosessissa. Työssä tutkittiin kromitasetta prosessin keskeisimmissä yksikköoperaatioissa. Myös kromin saostumista katodien pinnalle arvioitiin määrällisesti. Eri prosessinäytteistä tutkittiin lisäksi kromin hapetusasteita. Edellä mainittuja tutkimuskohteita varten määritettiin prosessinäytteiden kromipitoisuus. Eri prosessioperaatioille suoritettiin lisäksi taselaskelmat. Työn tuloksena esitettiin kromitase sekä yksikköoperaatioille että koko prosessille. Erinäisten epätarkkuustekijöiden vuoksi tasetta ei kuitenkaan pystytty määrittämään halutulla tarkkuudella, ja siksi työssä esitettyä tasetta voidaan pitää vain suuntaa antavana laskelmana. Katodien pinnalle saostunutta kromin määrää pidettiin kuitenkin oikean suuruusluokan tuloksena. Prosessinäytteiden hapetusasteita ei voitu arvioida, sillä saadut kokonaiskromitulokset eivät olleet täysin luotettavia. Huolimatta tulosten epätarkkuudesta, työ tuotti tärkeää tietoa prosessin toiminnasta kromin suhteen. Työtä voidaan hyödyntää jatkossa monin tavoin prosessin kromitaseen seurannassa.

Erythrocytes may contain a ouabain-insensitive K+-ATPase which plays a role in internal K+ balance

Erythrocytes are useful in evaluating K+ transport pathways involved in internal K+ balance. Several forms of H+,K+-ATPase have been described in nephron segments active in K+ transport. Furthermore, the activity of a ouabain-insensitive isoform of H+,K+-ATPase expressed in collecting duct cells may be modulated by acid-base status. Various assays were performed to determine if a ouabain-insensitive K+-ATPase is present in rat erythrocytes and, if so, whether it plays a role in internal K+ balance. Kinetic studies demonstrated that maximal stimulation of enzyme activity was achieved with 2.5 mM K+ at pH 7.4. Subsequent experiments were performed on erythrocyte membranes collected from animals submitted to varying degrees of K+ homeostasis: control rats, K+-depleted rats, K+-loaded rats, and rats rendered hyperkalemic due to acute renal failure. As observed in the collecting duct cell studies, there was a significant decrease in the activity of ouabain-insensitive K+-ATPase in the erythrocytes of both K+-loaded and metabolically alkalotic K+-depleted rats. However, this enzyme activity in erythrocyte membranes of rats with metabolic acidosis-related hyperkalemia was similar to that of control animals. This finding may be interpreted as resulting from two potentially modulating factors: the stimulating effect that metabolic acidosis has on K+-ATPase and the counteracting effect that hyperkalemia and uremia have on metabolic acidosis. In summary, we present evidence of a ouabain-insensitive K+-ATPase in erythrocytes, whose activity is modulated by acid-base status and K+ levels.

Situationsfaktorer i sexuellt utnyttjande av barn inverkar på psykosexuella problem : en metaanalys

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