Forskning har visat att användandet av konkret material i matematikundervisningen ökar elevers motivation till inlärning samt attlärare får lättare att differentiera sin undervisning. Denna studies syfte är att få ökad kunskap om lärares syn på användning av konkret material i undervisning om addition med tiokamraterna. Till undersökningen valdes en kvantitativ metod med kvalitativa inslag. Genom en webbaserad enkät med nio flervalsfrågor samt en fritextfråga samlades data in från 19 lärare i Jämtlands län. Enkäten skickades via e-post till lärare och rektorer i Jämtlands län. Resultatet visade att 63 procent av respondenterna anser atteleverna har lättare att befästa 10-kamraterna vid arbete med konkret material, medan 26 procent anser att det stämmer till viss del. För att ta till sig den generella matematiken som är abstrakt behöver eleverna kunna koppla samman den konkreta matematiken med de abstrakta matematiska symbolerna. Samtliga respondenter anser att användandet av konkret material i undervisningen om tiokamraterna bidrar till att eleverna klarar övergången mellan konkret och abstrakt representation bättre. Vidare visade resultatet även att användningen av konkret material i undervisningen gör den mer lustfylld, samt att många av de konkreta material som lärarna använder bidrar till att undervisningen blir mer vardagsnära

Projektets mål är att aktivisera området kring Høvik kirke i Norge. Utgångspunkten är att förbättra och vidareutveckla existerande kvaliteter på kyrkotomten, samt att utgå ifrån dessa i skapandet av nya element. Projektet syftar till att omskapa kyrkohöjden till en trevlig plats att vara på, för kyrkans besökare såväl som för andra. Viktiga fokusområden är kyrkohöjdens roll som lokalt kulturcentrum, kyrkobyggnaden som lokal identitetsmarkör och landmärke, och historiska sammanhang i närområdet. Projektet har tre huvudkomponenter: park, församlingshem, och en ny tillbyggnad. Kyrkohöjden är i dag något av en icke-plats. Den nya parken blir övergångszon mellan kyrkan, församlingshemmet och omgivningarna i övrig. Som ett av mycket få publika gröntstråk blir den en naturlig plats att vistas på för ortens invånare. Nya gångvägar vill också bringa många förbi den vackra kyrkobyggnaden. Omformningen av församlingshemmet tar hänsyn till församlingens behov och önskningar. Bottenvåningen fylls av publika funktioner som bibliotek och café, och fasaden får en mer tillgänglig och inviterande karaktär. Tillbyggnaden er projektets syntes, och bidrar till att knyta ihop parken och den existerande byggnaden. Platsens roll som kulturcentrum förstärks också genom att tillbyggnaden genom sin funktion möjliggör ökade kulturella aktiviteter. / The project focuses on developing the site around Høvik church, near Oslo in Norway, into a hub of local culture. The main strategy has been to improve and develop the existing qualities and connections of the site, and to use these as points of departure for the creation of new elements. The project has three main components. Firstly, the development of a park on the hill, creating a public green space to be enjoyed both by church goers and others. Secondly, renovating and improving the existing parish building (built 1971), based on the needs and wishes of the congregation. Finally, a small addition, which connects both to the park and the existing building, taking inspiration from and adding qualities to both. Themes addressed in the research and development are the church as a landmark and focal point for local identity, the connections to the history and development of the area, and the role of the church in the local society.

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Denna studie har tagit avstamp från den fenomenografiska forskningsansatsen och fyra lärare har blivit intervjuade i syfte att vinna kunskap om deras uppfattningar gällande introduktion till räknesätten addition och subtraktion samt hur inversa operationer integreras i undervisningen. Kunskapsluckor mellan teori och praktik upplevs, detta då resultatet visade att alla fyra lärare, på ett eller annat sätt, använt sig av samtidig introduktion av räknesätten trots att bara två av lärarna uttryckte att de gjorde det. Likaså för att ingen av de intervjuade lärarna använder begreppet inversa operationer trots att de allihop visar på användning av det i undervisningen. De intervjuade lärarna ser fördelar med att använda sig av konkreta material i undervisningen och uttrycker att de oftast går från konkret till abstrakt. Men både de intervjuade lärarna och tidigare forskning lyfter att det konkreta materialet i vissa fall är distraherande för eleverna.

Research efforts have focused on synthesis of linear, long-chain branched, and novel crosslinked polyesters for applications spanning from pressure sensitive adhesives to biomedical applications. Altering polymer topology and functionality using different synthetic strategies was enabled tailoring the thermomechanical, rheological, and adhesive properties of polyesters. The synthesis and characterization of linear, long-chain branched, and crosslinked networks are described focusing on the structure-property relationships. Aliphatic low-Tg polyesters with linear and long-chain branched topology were synthesized using melt polycondensation for pressure sensitive adhesive applications. Relationships between molecular weight, polymer composition, and adhesive performance were investigated. Melt rheological studies and the characterization of adhesive properties indicated that adhesive performance was enhanced with increasing molecular weight. Moreover, a series of long-chain branched low-Tg polyester were investigated to determine the influence of branching and molecular weight. Tailoring the degree of branching enabled the control of rheological and adhesive properties. Characterization of adhesive properties revealed that long-chain branched polymers displayed an enhanced cohesive strength. In addition, utilization of different comonomer compositions allowed tailoring thermal and adhesive properties of low-Tg polyesters over a wide range. Biodegradable networks were synthesized for the first time using base-catalyzed Michael addition of acetoacetate functionalized polyesters with acrylates. Linear and star-shaped poly(caprolactone) (PCL) oligomers with different molecular weights were functionalized and crosslinked. Thermomechanical properties were evaluated as a function of precursor molecular weight and crosslink density. The glass transition temperature and the extent of crystallinity of the networks were dependent on the molecular weight of the PCL segment. Moreover, dynamic mechanical analysis (DMA) indicated that molecular weight of the oligomeric precursors influenced the plateau modulus of the networks as a result of the differences in crosslink density of the networks. In addition, covalently crosslinked networks were synthesized from Michael addition reaction of acetoacetate-functional oligomeric poly(trimethylene succinate)s and poly(trimethylene adipate)s with neopentylglycol diacrylate. The oligomeric polyesters with telechelic hydroxyl functionality were synthesized from renewable monomers, adipic acid, succinic acid, and 1,3-propanediol using melt polycondensation. The molecular weights of the precursors were varied systematically to probe the influence of molecular weight on thermomechanical properties of the networks. The extent of crystallinity and mechanical properties were dependent on the molecular weight of the oligomeric polyester precursors which also controlled crosslink density. Moreover, Michael addition chemistry was utilized to crosslink low-Tg polyesters to improve cohesive strength for PSA applications. In order to determine the influence of temperature and catalyst levels, crosslinking reactions were monitoring using measurement of loss and storage moduli during the reaction. Networks having different levels of gel fractions were investigated to elucidate the influence of degree of crosslinking on thermomechanical and adhesive properties of low-Tg polyesters. / Ph. D.

The first successful synthesis and isolation of a boronic acid was reported in 1860 by Frankland in the pursuit of novel organometallic compounds. For more than a century, further studies of boronic acids were sparsely published. Suzuki and Miyaura jumpstarted the field in 1979 with an innovative carbon-carbon bond forming reaction employing an organoboronic acid and a carbon halide under palladium catalysis. Indeed, the Nobel Prize in Chemistry was awarded to Professor Akira Suzuki, along with Professors Richard Heck and Ei-ichi Negishi, in 2010 for their important contributions in palladium-catalyzed cross-coupling chemistry. Over the last 30 years, reports on organoboron compounds have increased exponentially. This dissertation describes the author's contributions to the development of preparative methods for organoboronic acid derivatives using transition metal-catalyzed reactions of diboron reagents. A unique "mixed" diboron reagent was developed (PDIPA diboron) that contains sp2- and sp3-hybridized boron atoms, unambiguously confirmed by X-ray crystallography. PDIPA diboron is sufficiently activated internally through a dative-bonding amine to selectively transfer the sp2-hybridized boron regioselectively, in the presence of copper, to electron deficient alkenes including α,β-unsaturated ketones, esters, amides, aldehydes, and nitriles to provide the corresponding boratohomoenolates. A unique β,β-diboration of an α,β-acetylenic ketone was also discovered. The scope of PDIPA diboron reactions was then expanded to a set of substrates with a more complex structural backbone. Allenoates are α,β,γ-unsaturated esters with orthogonal pi systems, which pose several possible difficulties with the regioselectivity of addition, not to mention known isomerizations catalyzed by copper. However, we successfully installed the boron moiety regioselectively on the β-carbon of a variety of allenoates, providing a vinyl boronic ester, and also observed exclusive formation of the (Z)-isomer from racemic starting materials. The resulting vinyl boronic ester was then shown to be an excellent Suzuki-Miyaura cross-coupling partner, affording a diastereopure, trisubstituted alkene in quantitative yield. Commercially available bis(pinacolato)diboron has shown remarkable stability towards hydrolysis and autoxidation. Using this reagent, we developed a copper- and amine-catalyzed boration protocol performed entirely in water and open to air. Using only 1 mol% copper, extraordinary activity was observed. UV-Vis, 11B NMR, and solvent kinetic isotope experiments were employed to gain insight into the mechanism, which showed the possibility of autocatalysis. Attempts to control stereoselectivity were not successful, although these results were rationalized by a dynamic catalyst structure. / Ph. D.

Current research efforts have focused on the synthesis of novel, segmented, cross-linked networks and thermoplastics for emerging technologies. Tailoring macromolecular structures for improved mechanical performance can be accomplished through a variety of synthetic strategies using step-growth polymerization. The synthesis and characterization of novel Michael addition networks, ionene families, and ion-containing polyurethanes are described, with the underlying theme of fundamentally investigating the structure-property relationships of novel, segmented macromolecular architectures. In addition, it was discovered that both covalent and electrostatic crosslinking play an important role in the mechanical properties of all types of polymers described herein. Novel cross-linked networks were synthesized using quantitative base-catalyzed Michael chemistry with acetoacetate and acrylate functionalities. These novel synthetic strategies offer unique thermo-mechanical performance due to the formation of a multiphase morphology. In order to fundamentally elucidate the factors that influence the kinetics of the Michael addition reaction a detailed analyses of model compounds were conducted in the presence of an in-situ IR spectrometer to optimize reaction conditions using statistical design of experiments. Networks were then prepared based on these optimized conditions. The mechanical performance was evaluated as a function of molecular weight between crosslink points. Furthermore, the incorporation of hydrogen bonding within the monomer structure enhanced mechanical performance. The changes in morphological, thermal, and mechanical properties evaluated using dynamic mechanical analysis (DMA) and tensile behavior are described. In addition, the use of preformed urethane segments provides a safer method for incorporating hydrogen bonding functional groups into macromolecules. In order to compare the thermomechanical and morphological properties of ion-containing polyurethanes to non-charged polyurethanes, poly(tetramethylene oxide)-based polyurethanes containing either a novel phosphonium diol or 1,4-butanediol chain extenders were prepared using a prepolymer method. The novel phosphonium polyurethane was more crystalline, and it was presumed that hydrogen bonding in the non-charged polyurethane restricted polymer mobility, and reduced PTMO crystallinity, and hydrogen bonding interactions were significantly reduced due to the presence of phosphonium cations. These results correlated well with mechanical property analysis. The phase separation and ionic aggregation were demonstrated via wide-angle X-ray scattering, small-angle X-ray scattering, scanning transmission electron microscopy, and energy-dispersive X-ray spectroscopy during STEM imaging, as described herein. In addition, a novel polyurethane containing imidazolium cations in the hard segment was synthesized and behaved very similarly to the phosphonium cation-containing polyurethane. Ammonium ionenes, which contain quaternary nitrogen in the macromolecular repeating unit, have many potential uses in biomedical applications. They offer interesting coulombic properties, and the charge density is easily controlled through synthetic design. This property makes ionenes ideal polyelectrolyte models to investigate the influence of ionic aggregation on many physical properties. Ammonium ionenes were prepared via the Menshutkin reaction from 1,12-dibromododecane and 1,12-bis(N,N-dimethylamino)dodecane. The absolute molecular weights were determined for the first time using an on-line multi-angle laser light scattering (MALLS) in aqueous size exclusion chromatography (SEC). Tensile testing and DMA were used to establish structure-property relationships between molecular weight and mechanical properties for a series of 12,12-ammonium ionenes. Furthermore, degradation studies in the presence of base support the possibility for water-soluble coatings with excellent mechanical durability that are amenable to triggered depolymerization. A novel synthetic strategy was utilized to prepare chain extended 12,12-ammonium ionenes containing cinnamate functional groups. In the presence of UV light, the polymers chain extended, and the resulting ionenes possessed enhanced thermomechanical properties and increased molecular weight. In addition, the novel synthesis of imidazolium ionenes was demonstrated, and the charge density was tuned for appropriate applications using either low molecular weight segments or oligomeric precursors. The change in charge density had a profound role in imidazolium ionene thermal and mechanical behavior. / Ph. D.

The versatility of organoboron compounds has been demonstrated by their use as synthetic intermediates and more recently in therapeutic applications since the FDA approval of Velcade©. As a result, transition metal-catalyzed protocols to incorporate boron reagents into unsaturated compounds have been extensively researched. While an abundance of literature protocols have been reported, the majority utilize harsh reaction conditions in combination with expensive reagents. This dissertation discloses the author’s contributions to the development of efficient, cost-effective, and operationally simple transition metal-catalyzed borylation protocols with alkynes and diboron reagents. An open-to-air copper(II)-catalyzed aqueous borylation protocol of alkynoates and a symmetrical diboron reagent is reported. Conjugate addition of the boryl-copper species to the electrophilic β-carbon provided β-boryl-α,β-unsaturated esters in moderate to excellent yields. Exclusive (Z)-stereochemistry was confirmed by nOe experiments. The resulting vinyl boronate esters are useful cross-coupling partners. The scope of the aqueous β-borylation protocol was extended to the unsymmetrical diboron reagent, pinB-Bdan. This alternative protecting group has emerged as an orthogonal protecting group and alters the reactivity of the boron moiety. Activation of the pinacol moiety to form the Lewis acid-base adduct allowed for the chemoselective transfer of the 1,8- diaminonapthalene moiety to the β-carbon. An alternative novel synthesis of vinyl, allyl diboronate esters from propargylic alcohols has also been described. Formation of a leaving group in-situ with a palladium- and coppercatalyzed protocol can lead to several competing reaction pathways and the formation of multiple products. Fortunately, the resulting vinyl, allyl diboronate esters were stereoselectively synthesized in moderate GC yields despite significate decomposition during purification, as confirmed by stability studies. The terminal diboration of allenes was previously the only reported method for the synthesis of vinyl, allyl diboronate esters. / Ph. D.

Ion-containing macromolecules continue to stimulate new opportunities for emerging electro-active applications ranging from high performance energy devices to water purification membranes. Progress in polymer synthesis and engineering now permit well-defined, ion-containing macromolecules with tunable morphologies, mechanical performance, ion conductivity, and 3D structure in order to address these globally challenged technologies. Achieving tailored chemical compositions with high degrees of phase separation for optimizing conductivity and water adsorption remains a constant synthetic challenge and presents an exciting opportunity for engineering sophisticated macromolecular architectures. This dissertation will introduce unprecedented charged polymers using conventional free radical and anionic polymerization to incorporate ionic functionalities based on phosphonium cations. This new class of copolymers offers unique properties with ionic functionality for tailorable electro-active performance. / Ph. D.