Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Visible-light-induced click chemistry

A rapid and catalyst-free cycloaddition system for visible-light-induced click chemistry is reported. A readily accessible photoreactive 2H-azirine moiety was designed to absorb light at wavelengths above 400 nm. Irradiation with low-energy light sources thus enables efficient small-molecule synthesis with a diverse range of multiple-bond-containing compounds. Moreover, in order to demonstrate the efficiency of the current approach, quantitative ligation of the photoactivatable chromophore with functional polymeric substrates was performed and full conversion with irradiation times of only 1 min at ambient conditions was achieved. The current report thus presents a highly efficient method for applications involving selective cycloaddition to electron-deficient multiple-bond-containing materials.

Photochemical design of stimuli-responsive nanoparticles prepared by supramolecular host–guest chemistry

We introduce the design of a thermoresponsive nanoparticle via sacrificial micelle formation based on supramolecular host–guest chemistry. Reversible addition–fragmentation chain transfer (RAFT) polymerization was employed to synthesize well-defined polymer blocks of poly(N,N-dimethylacrylamide) (poly(DMAAm)) (Mn,SEC = 10 700 g mol–1, Đ = 1.3) and poly(N-isopropylacrylamide) (poly(NiPAAm)) (Mn,SEC = 39 700 g mol–1, Đ = 1.2), carrying supramolecular recognition units at the chain termini. Further, 2-methoxy-6-methylbenzaldehyde moieties (photoenols, PE) were statistically incorporated into the backbone of the poly(NiPAAm) block as photoactive cross-linking units. Host–guest interactions of adamantane (Ada) (at the terminus of the poly(NiPAAm/PE) chain) and β-cyclodextrin (CD) (attached to the poly(DMAAm chain end) result in a supramolecular diblock copolymer. In aqueous solution, the diblock copolymer undergoes micellization when heated above the lower critical solution temperature (LCST) of the thermoresponsive poly(NiPAAm/PE) chain, forming the core of the micelle. Via the addition of a 4-arm maleimide cross-linker and irradiation with UV light, the micelle is cross-linked in its core via the photoinduced Diels–Alder reaction of maleimide and PE units. The adamantyl–cyclodextrin linkage is subsequently cleaved by the destruction of the β-CD, affording narrowly distributed thermoresponsive nanoparticles with a trigger temperature close to 30 °C. Polymer chain analysis was performed via size exclusion chromatography (SEC), nuclear magnetic resonance (NMR) spectroscopy, and dynamic light scattering (DLS). The size and thermoresponsive behavior of the micelles and nanoparticles were investigated via DLS as well as atomic force microscopy (AFM).

Unimolecular reaction chemistry of a charge-tagged beta-hydroxyperoxyl radical

β-Hydroxyperoxyl radicals are formed during atmospheric oxidation of unsaturated volatile organic compounds such as isoprene. They are intermediates in the combustion of alcohols. In these environments the unimolecular isomerization and decomposition of β-hydroxyperoxyl radicals may be of importance, either through chemical or thermal activation. We have used ion-trap mass spectrometry to generate the distonic charge-tagged β-hydroxyalkyl radical anion, ˙CH2C(OH)(CH3)CH2C(O)O−, and investigated its subsequent reaction with O2 in the gas phase under conditions that are devoid of complicating radical–radical reactions. Quantum chemical calculations and master equation/RRKM theory modeling are used to rationalize the results and discern a reaction mechanism. Reaction is found to proceed via initial hydrogen abstraction from the γ-methylene group and from the β-hydroxyl group, with both reaction channels eventually forming isobaric product ions due to loss of either ˙OH + HCHO or ˙OH + CO2. Isotope labeling studies confirm that a 1,5-hydrogen shift from the β-hydroxyl functionality results in a hydroperoxyalkoxyl radical intermediate that can undergo further unimolecular dissociations. Furthermore, this study confirms that the facile decomposition of β-hydroxyperoxyl radicals can yield ˙OH in the gas phase.

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

High microwave susceptibility of NaH2PO4 center dot 2H(2)O: Rapid synthesis of crystalline and glassy phosphates with NASICON-type chemistry

High microwave susceptibility of NaH2PO4 . 2H(2)O has been discovered, This hydrated acid phosphate of sodium can be heated upto 1000 K or more when exposed to 2.45 GHz microwaves. Using this, a novel microwave-assisted preparation of a number of important crystalline and glassy materials with NASICON-type chemistry has been accomplished in less than 8 min which is only a fraction of the time required for conventional synthetic procedures, The present single-shot approach to the preparation of phosphates is attractive in terms of its simplicity, rapidity, and general applicability, A ''step-ladder'' heating mechanism has been proposed to account for the high microwave absorbing ability of NaH2PO4 . 2H(2)O.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

A hybrid cellular automata model of multicellular tumour spheroid growth in hypoxic microenvironment

A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Dracocephalum moldavica L. and Melissa officinalis L. : Chemistry and Bioactivities Relevant in Alzheimer’s Disease Therapy

Oksidatiivisen stressin eli liiallisen reaktiivisten happiyhdisteiden määrän soluissa on jo pitkään arveltu olevan tärkeä Alzheimerin taudin kehittymiseen ja etenemiseen vaikuttava tekijä. Tämän vuoksi kiinnostus erilaisten antioksidanttien (yhdisteitä, jotka neutraloivat näitä happiradikaaleja soluissa) mahdollisia terapeuttisia ominaisuuksia Alzheimerin taudin hoidossa on tutkittu laajalti. Tähän mennessä ei kuitenkaan ole vielä onnistuttu löytämään antioksidanttia, joka olisi hyödyksi Alzheimerin taudin hoidossa. Tämän vuoksi on tärkeää pyrkiä löytämään uusia antioksidanttien lähteitä sekä tutkia niistä löytyviä aktiivisia yhdisteitä. Kiinnostus luonnon antioksidantteja kohtaan on kasvanut voimakkaasti viime aikoina. Huomio on kiinnittynyt erityisesti aromaattisista sekä lääkekasveista löytyviin antioksidantteihin. Lamiaceae- perheeseen kuuluvia tuoksuampiaisyrttiä (Dracocephalum moldavica L.) ja sitruunamelissaa (Melissa officinalis L.) on käytetty Iranissa pitkään sekä ruoanlaitossa että lääkinnässä, minkä vuoksi näiden kasvien uutteiden antioksidanttisisältöä päätettiin analysoida käyttäen useaa erilaista in vitro- menetelmää. Näissä kokeissa ilmeni, että uutteilla oli useita antioksidanttisia vaikutuksia. Näistä antioksidanttisista vaikutuksista vastaavia yhdisteitä pyrittiin tunnistamaan käyttäen HPLC-PDA- tekniikkaa, minkä seurauksena niiden havaittiin sisältävän erilaisia polyfenoleita, kuten hydroksyloituneita bentsoeeni- ja cinnamamidihapon johdannaisia sekä flavonoideja. Kummankin kasvin uutteissa runsaimmin esiintynyt yhdiste oli rosmariinihappo. Sitruunamelissaa (M. officinalis) on käytetty antiikin ajoista alkaen kognitiivisten toimintojen häiriöiden hoidossa. Perustuen tietoon kasvin käytöstä perinteisessä lääkinnässä, sen tehoa Alzheimerin taudin hoidossa on tutkittu viime aikoina kliinisin kokein. Sitruunamelissan todettiinkin olevan hyödyksi lievää ja keskivaikeaa Alzheimeimerin tautia sairastavien potilaiden hoidossa. Väitöskirjan osanan olevasta kooste-artikkelista käy ilmi, että tutkimalla lääkekasvien ominaisuuksia voidaan saada arvokkaita suuntaa-antavia vihjeitä Alzheimerin taudin lääkehoidon kehittämiseen. Tämän perusteella päätettiinkin testatata myös sitruunamelissauutteen kykyä estää asetyylikoliiniesteraasin (AChE) toimintaa, koska tämän entsyymin toiminna estämisen tiedetään olevan hyödyksi Alzheimerin taudin hoidossa. Uute kykeni estämään AChE:n toimintaa, minkä vuoksi uutteen sisältämiä komponentteja päätettiin tutkia terkemmin. Uute jaettiin erilaisiin fraktioihin käyttäen HPLC-menetelmää, minkä jälkeen testattiin jokaisen fraktion kykyä inhiboida AchE. Suurin osa fraktioista kykeni inhiboimaan AChE:n toimintaa selkeästi tehokkaammin, kuin raakauute. Kaikista tehokkainta fraktiota analysoitiin tarkemmin sen aktiivisten yhdisteiden tunnistamiseksi, minkä seurauksena sen sisältämät yhdisteet tunnistettiin cis ja trans-rosmariinihapoiksi. Tässä tutkimuksessa tunnistettujen yhdisteiden hyödyllisyyttä Alzheimerin taudin hoidossa tulisi seuraavaksi tutkia erilaisissa in vivo-malleissa. Lisäksi jäljellä olevien fraktioiden kemiallinen koostumus tulisi selvittää sekä antioksidanttiaktiivisuuden ja AChE:n toiminnan inhiboinnin välistä mahdollista yhteyttä tulisi tutkia tarkemmin. Tämä tutkimus osoittaa tuoksuampiasyrtin (D. moldavica) sekä sitruunamelissan (M. officinalis) sisältävän monenlaisia aktiivisia antioksidantteja. Lisäksi sitruunamelissan sisältämät yhdisteet kykenivät estämään asetyylikoliiniesteraasin (AchE) toimintaa. Nämä tulokset tukevat osaltaan väitöskirjan osana olevan kooste-artikkelin johtopäätöksiä, joiden mukaan etnofarmakologinen kasvitutkimus voi osoittautua erittäin hyödylliseksi kehitettäessä uutta lääkehoitoa Alzheimerin tautiin. Lisäksi tässä väitöskirjassa kuvattu tutkimus osoittaakin, että perinteisesti lääkekasvina käytettyä sitruunamelissaa voidaan mahdollisesti hyödyntää uusien Alzheimerin taudin hoitoon käytettävien lääkkeiden kehityksessä.

Click Chemistry Inspired Synthesis of Novel Ferrocenyl-Substituted Amino Acids or Peptides

This work reports on the synthesis of a wide range of ferrocenyl-substituted amino acids and peptides in excellent yield. Conjugation is established via copper-catalyzed 1,3-dipolar cycloaddition. Two complementary strategies were employed for conjugation, one involving cycloaddition of amino acid derived azides with ethynyl ferrocene 1 and the other involves cycloaddition between amino acid derived alkynes with ferrocene-derived azides 2 and 3. Labeling of amino acids at multiple sites with ferrocene is discussed. A new route to 1,1'-unsymmetrically substituted ferrocene conjugates is reported. A novel ferrocenophane 19 is accessed via bimolecular condensation of amino acid derived bis-alkyne 9b with the azide 2. The electrochemical behavior of some selected ferrocene conjugates has been studied by cyclic voltammetry.

An overview of land application of pig effluent-P using soil P chemistry and mass balance calculations.

Attention is directed at land application of piggery effluent (containing urine, faeces, water, and wasted feed) as a potential source of water resource contamination with phosphorus (P). This paper summarises P-related properties of soil from 0-0.05 m depth at 11 piggery effluent application sites, in order to explore the impact that effluent application has had on the potential for run-off transport of P. The sites investigated were situated on Alfisol, Mollisol, Vertisol, and Spodosol soils in areas that received effluent for 1.5-30 years (estimated effluent-P applications of 100-310000 kg P/ha in total). Total (PT), bicarbonate extractable (PB), and soluble P forms were determined for the soil (0-0.05 m) at paired effluent and no-effluent sites, as well as texture, oxalate-extractable Fe and Al, organic carbon, and pH. All forms of soil P at 0-0.05 m depth increased with effluent application (PB at effluent sites was 1.7-15 times that at no-effluent sites) at 10 of the 11 sites. Increases in PB were strongly related to net P applications (regression analysis of log values for 7 sites with complete data sets: 82.6 % of variance accounted for, p <0.01). Effluent irrigation tended to increase the proportion of soil PT in dilute CaCl2-extractable forms (PTC: effluent average 2.0 %; no-effluent average 0.6%). The proportion of PTC in non-molybdate reactive forms (centrifuged supernatant) decreased (no-effluent average, 46.4 %; effluent average, 13.7 %). Anaerobic lagoon effluent did not reliably acidify soil, since no consistent relationship was observed for pH with effluent application. Soil organic carbon was increased in most of the effluent areas relative to the no-effluent areas. The four effluent areas where organic carbon was reduced had undergone intensive cultivation and cropping. Current effluent management at many of the piggeries failed to maximise the potential for waste P recapture. Ten of the case-study effluent application areas have received effluent-P in excess of crop uptake. While this may not represent a significant risk of leaching where sorption retains P, it has increased the risk of transport of P by run-off. Where such sites are close to surface water, run-off P loads should be managed.

Reactivity of Cationic Terminal Borylene Complexes: Novel Mechanisms for Insertion and Metathesis Chemistry Involving Strongly Lewis Acidic Ligand Systems

The reactions of terminal borylene complexes of the type [CpFe(CO)(2)(BNR2)](+) (R = `Pr, Cy) with heteroallenes have been investigated by quantum-chemical methods, in an attempt to explain the experimentally observed product distributions. Reaction with dicyclohexylcarbodiimide (CyNCNCy) gives a bis-insertion product, in which 1 equiv of carbodiimide is assimilated into each of the Fe=B and B=N double bonds to form a spirocyclic boronium system. In contrast, isocyanates (R'NCO, R' = Ph, 2,6-wXy1, CY; XYl = C6H3Me2) react to give isonitrile complexes of the type [CpFe(CO)(2)(CNR')]+, via a net oxygen abstraction (or formal metathesis) process. Both carbodiimide and socyanate substrates are shown to prefer initial attack at the Fe=B bond rather than the B=N bond of the borylene complex. Further mechanistic studies reveal that the carbodiimide reaction ultimately leads to the bis-insertion compounds [CpFe(CO)(2)C(NCy)(2)B(NCY)(2)CNR2](+), rather than to the isonitrile system [CpFe(CO)(2)(CNCy)](+), on the basis of both thermodynamic (product stability) and kinetic considerations (barrier heights). The mechanism of the initial carbodiimide insertion process is unusual in that it involves coordination of the substrate at the (borylene) ligand followed by migration of the metal fragment, rather than a more conventional process: i.e., coordination of the unsaturated substrate at the metal followed by ligand migration. In the case of isocyanate substrates, metathesis products are competitive with those from the insertion pathway. Direct, single-step metathesis reactivity to give products containing a coordinated isonitrile ligand (i.e. [CpFe(CO)(2)(CNR')](+)) is facile if initial coordination of the isocyanate at boron occurs via the oxygen donor (which is kinetically favored); insertion chemistry is feasible when the isocyanate attacks initially via the nitrogen atom. However, even in the latter case, further reaction of the monoinsertion product so formed with excess isocyanate offers a number of facile (low energetic barrier) routes which also generate ['CpFe(CO)(2)(CNR')](+), rather than the bis-insertion product [CpFe(CO)(2)C(NR')(O)B(NR')(O)CNR2](+) (i.e., the direct analogue of the observed products in the carbodiimide reaction).