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)...

Fifield faces a hard road to bring Australia’s media regulations into the 21st century

With his feet barely under the desk, Communications Minister Mitch Fifield has flagged a renewed attempt to change Australia’s media laws. Given his predecessor Malcolm Turnbull’s long-standing interest in the field – dating all the way back to his work with Kerry Packer in the 1980s – Fifield can expect the new prime minister’s backing. Fifield is set to meet with media bosses as early as next week.

The purposes of history? Curriculum studies, invisible objects and twenty-first century societies

A new intellectual epoch has generated new enterprises to suit changed beliefs and circumstances. A widespread sentiment in both formal historiography and curriculum studies reduces the “new” to the question of how knowledge is recognized as such, how it is gained, and how it is represented in narrative form. Whether the nature of history and conceptions of knowledge are, or ought to be, central considerations in curriculum studies and reducible to purposes or elevated as present orientated requires rethinking. This paper operates as an incitement to discourse that disrupts the protection and isolation of primary categories in the field whose troubling is overdue. In particular, the paper moves through several layers that highlight the lack of settlement regarding the endowment of objects for study with the status of the scientific. It traces how some “invisible” things have been included within the purview of curriculum history as objects of study and not others. The focus is the making of things deemed invisible into scientific objects (or not) and the specific site of analysis is the work of William James (1842-1910). James studied intensely both child mind and the ghost, the former of which becomes scientized and legitimated for further study, the latter abjected. This contrast opens key points for reconsideration regarding conditions of proof, validation criteria, and subject matters and points to opportunities to challenge some well-rehearsed foreclosures within progressive politics and education.

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation coefficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle either from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.

The Roman Republican Navy : from the sixth century to 167 BC

Työ käsittelee Rooman laivaston kehitystä, toimintaa ja osallistumista laajenemispolitiikkaan, jossa Rooma kasvoi kaupunkivaltiosta Välimeren hallitsijaksi. Rooma on aikaisemmissa tutkimuksissa nähty maavaltiona vailla kiinnostusta merenkulkuun. On katsottu, että ainoa merkittävä merisota Rooman historiassa on ensimmäinen puunilaissota (264-241 eKr.) ja että siinäkin roomalaiset (jotka historioitsija Polybius kuvaa vasta-alkajiksi) menestyivät Karthagoa vastaan turvautumalla laskusiltoihin, joiden avulla he saattoivat muuttaa meritaistelun maataisteluksi. Polybiuksen kuvaukseen on aina tähän asti luotettu. On katsottu että Roomalla ei ollut laivastoa ennen ensimmäistä puunilaissotaa ja että Rooma kaikissa sodissaan panosti merisodankäyntiin mahdollisimman vähän. Tämä työ pyrkii kumoamaan nämä käsitykset. Laivasto oli osallisena ja ehdottoman välttämätön kaikissa Rooman laajenemispolitiikan käänteissä. Arkeologian tiedot osoittavat, että ennen ensimmäistä puunilaissotaa Rooma kehittyi ja siitä tuli merkittävä kaupunki nimenomaan kaupankäynnin ja ulkomaisten kontaktien seurauksena. Se ei siis ollut puhdas agraarivaltio. Roomalaisilla oli laivasto jo viimeistään 500-luvulta lähtien eKr. ja sitä käytettiin Rooman laajentaessa valtaansa Italiassa. Näin ollen ensimmäisessä puunilaissodassa läntisen Välimeren herruudesta kilpaili kaksi merivaltiota, Rooma ja Karthago. Toinen puunilaissota (218-201) tunnetaan yleensä Hannibalin tulosta Alppien yli Italiaan, mutta se oli myöskin merkittävä merisota ja karthagolaiset hävisivät sen nimenomaan merellä. Rooma osallistui kilpailuun itäisen Välimeren hallinnasta ja kukisti Makedonian ja Syyrian laivastot, jotka eivät olleet mitenkään Rooman laivaston veroisia. Kaikista Rooman vastustajista Karthagolla olisi ollut suurin mahdollisuus pysäyttää Rooman laivaston voittokulu toisessa puunilaissodassa. Laivastoa käytettiin moniin eri tarkoituksiin. Suuret meritaistelut eivät ole ainoa osoitus laivastojen mukanaolosta ja merkityksestä, vaan on myös otettava huomion sotalaivojen rakenne ja toimintaedellytykset. Sotalaivat oli rakennettu taisteluita varten ja niissä oli hyvin niukasti säilytystilaa. Niiden oli päästävä laskemaan maihin aina kun miehistö tarvitsi vettä, ruokaa ja lepoa. Laivastot saattoivat toimia vain niiden rannikoiden tuntumassa, joiden satamiin ja laskupaikkoihin niillä oli turvallinen pääsy. Roomalaiset olivat hyvin tietoisia tästä. Suuret merentakaiset sotaretket Afrikkaan, Espanjaan, Kreikkaan ja Vähän-Aasian rannikolle perustuivat kaikki siihen, että Rooman laivasto hallitsi purjehdusreittejä ja sopivia laskupaikkoja ja saattoi huolehtia joukkojen ja varusteiden kuljettamisesta kaukana taisteleville armeijoille. Samalla Rooman laivasto kävi itsenäistä sotaa merellä ja haastoi ja kukisti kaikki Välimeren merivaltiot. 130-luvulle eKr. tultaessa se oli lyönyt vihollisensa ja riisunut aseista liittolaisensa; Rooman laivasto hallitsi Välimerta yksin.

Language and Letters of the Bluestocking Network : Sociolinguistic Issues in Eighteenth Century Epistolary English

This study deals with language change and variation in the correspondence of the eighteenth-century Bluestocking circle, a social network which provided learned men and women with an informal environment for the pursuit of scholarly entertainment. Elizabeth Montagu (1718 1800), a notable social hostess and a Shakespearean scholar, was one of their key figures. The study presents the reconstruction of Elizabeth Montagu s social networks from her youth to her later years with a special focus on the Bluestocking circle, and linguistic research on private correspondence between Montagu and her Bluestocking friends and family members between the years 1738 1778. The epistolary language use is investigated using the methods and frameworks of corpus linguistics, historical sociolinguistics, and social network analysis. The approach is diachronic and concerns real-time language change. The research is based on a selection of manuscript letters which I have edited and compiled into an electronic corpus (Bluestocking Corpus). I have also devised a network strength scale in order to quantify the strength of network ties and to compare the results of the linguistic research with the network analysis. The studies range from the reconstruction and analysis of Elizabeth Montagu s most prominent social networks to the analysis of changing morphosyntactic features and spelling variation in Montagu s and her network members correspondence. The linguistic studies look at the use of the progressive construction, preposition stranding and pied piping, and spelling variation in terms of preterite and past participle endings in the regular paradigm (-ed, - d, -d, - t, -t) and full / contracted spellings of auxiliary verbs. The results are analysed in terms of social network membership, sociolinguistic variables of the correspondents, and, when relevant, aspects of eighteenth-century linguistic prescriptivism. The studies showed a slight diachronic increase in the use of the progressive, a significant decrease of the stigmatised preposition stranding and increase of pied piping, and relatively informal but socially controlled epistolary spelling. Certain significant changes in Elizabeth Montagu s language use over the years could be attributed to her increasingly prominent social standing and the changes in her social networks, and the strength of ties correlated strongly with the use of the progressive in the Bluestocking Corpus. Gender, social rank, and register in terms of kinship/friendship had a significant influence in language use, and an effect of prescriptivism could also be detected. Elizabeth Montagu s network ties resulted in language variation in terms of network membership, her own position in a given network, and the social factors that controlled eighteenth-century interaction. When all the network ties are strong, linguistic variation seems to be essentially linked to the social variables of the informants.

Productivity of the suffixes -ness and -ity in 17th-century English letters : A sociolinguistic approach

Tässä työssä tutkitaan englannin kielen substantiivijohtimien -ness ja -ity produktiivisuutta 1600-luvulla kirjoitetuissa kirjeissä. Näitä lähes synonyymisiä johtimia käytetään yleensä merkitykseltään abstraktien substantiivien muodostamiseen adjektiiveista (esim. productive 'produktiivinen' > productiveness tai productivity 'produktiivisuus'). Johtimista -ity on lainautunut englantiin ranskasta ja myöhemmin myös latinasta; se on sekä fonologialtaan että semantiikaltaan läpinäkymättömämpi kuin kotoperäinen -ness. Lisäksi -ity-johdinta on käytetty enimmäkseen formaaleissa tilanteissa ja tieteellisissä teksteissä, kun taas -ness on ollut yleiskäyttöisempi. Tutkielman lähestymistapa on sosiolingvistinen: oletetaan, että johtimien produktiivisuus (eli valmius muodostaa uusia johdoksia) voi vaihdella eri sosiaaliryhmissä. Sosiolingvistiikkaa ei ole aiemmin juurikaan sovellettu produktiivisuuden tutkimiseen. Tutkimusaineistona on Helsingin yliopiston VARIENG-tutkimusyksikön laatima Corpus of Early English Correspondence, varhaisista englanninkielisistä kirjeistä koostuva korpus eli elektroninen tekstikokoelma, joka on suunniteltu historiallisen sosiolingvistiikan tarpeisiin. Korpuksen 1600-luvun kirjeitten yhteenlaskettu pituus on noin 1,4 miljoonaa sanaa, ja ne on kirjoitettu vuosina 1600-1681. Tutkielman tärkeimpänä produktiivisuusmittarina käytetään johtimien avulla muodostettujen eri sanojen eli tyyppien lukumäärää. Hypoteesina on, että -ity-tyyppien määrä on keskimääräistä pienempi huonosti koulutettujen sosiaaliryhmien kirjeissä. Näitä olivat 1600-luvulla naiset sekä alhaisimmat yhteiskuntaryhmät, kuten talonpojat ja käsityöläiset. Johtimen -ness tyyppimäärissä ei odoteta esiintyvän sosiolingvististä variaatiota. Tutkielmassa käsitellään myös tyyppimäärien vertailuun liittyviä metodologisia ongelmia. Koska vaikkapa naisilta ja miehiltä on eri määrä dataa, ei heidän tyyppimääriään voida suoraan verrata keskenään. Esimerkiksi tyyppimäärien normalisointi tuhatta sanaa kohti ei myöskään ole mahdollista, koska tyyppien lukumäärä ei kasva lineaarisesti korpuksen kasvaessa. Tutkielmassa esitetään kielitieteessä harvoin käytetty tilastotieteellinen menetelmä, jonka avulla korpuksen eri osista saatuja tyyppimääriä voidaan verrata koko korpukseen ja testata, ovatko ne tilastollisesti merkittävän pieniä tai suuria. Toisin kuin monet yleisemmät menetelmät, tämä tyyppikertymiin ja permutaatiotesteihin perustuva metodi ei vaadi yksinkertaistavien oletuksien tekemistä. Tutkimustulokset vahvistavat hypoteesin oikeaksi: naisten -ity-tyyppien lukumäärä on tilastollisesti merkittävän alhainen, kun taas -ness-tyyppien määrissä ei ole tilastollisesti merkittäviä eroja. Alhaisimpien yhteiskuntaryhmien osalta tuloksia ei saada, koska niiltä on korpuksessa liian vähän dataa. Analyysissä paljastuu myös yllättävä eroavaisuus: korpuksen ajallisesti ensimmäisessä puoliskossa (1600-1639) on merkittävän vähän -ity-tyyppejä. Tämä voidaan tulkita kielelliseksi muutokseksi: -ity-johtimen produktiivisuus kasvaa kirjeissä 1600-luvun aikana. Saattaa olla, että johtimen produktiivisuus on ensin kasvanut formaalimmissa tekstilajeissa, joista lisääntynyt käyttö on sitten levinnyt myös kirjeisiin, ehkäpä 1640-luvun sisällissodan synnyttämien kontaktiverkostojen siivittämänä. Tuloksien perusteella voidaan sanoa, että sosiolingvistinen vaihtelu on merkittävä tekijä ainakin joittenkin johtimien produktiivisuudessa, joten vaihtelua on syytä tutkia enemmänkin. Tutkimuksessa käytetty metodi mahdollistaa osakorpuksien tyyppimäärien luotettavan vertailun melko pienissäkin korpuksissa, joten se soveltuu hyvin niin historialliseen kielitieteeseen kuin sosiolingvistiikkaankin.

Focus on Form : J. J. Tikkanen, Giotto and Art Research in the 19th Century

My doctoral dissertation is on Johan Jakob Tikkanen (1857 1930), the first professor of art history in Finland, and his significance and methods in the context of late 19th and early 20th-century European art history. Tikkanen was one of the pioneering scholars in the field of medieval art research, and, along with Anton Springer, Heinrich Wölfflin, Aloïs Riegl, Adolfo Venturi, Franz Wickhoff, Julius von Schlosser, Aby Warburg, Emile Mâle and others, one of the scholars who defined art history as an independent academic discipline. Tikkanen s scholarly interests and his methods resemble those of many formalistically oriented German and Austrian art historians of his time. He became well known throughout Europe, mainly for his studies on illustrated medieval manuscripts. Tikkanen s dissertation, Der Malerische Styl Giotto s Versuch zu einer Characteristik Desselben, from 1884 was regarded in its day as the best form-analytical study on the painter. It has a central position in the present thesis, as it already included nearly all the methods that Tikkanen used and elaborated upon throughout his career. Giotto also gives a good perspective for comparing Tikkanen s ideas with a long art-historical tradition. Tikkanen was profoundly interested in artistic creativity. In his own words, he wanted to study das künstlerische Können , artistic ability, instead of das künstlerische Wollen or artistic will, which was an important theoretical issue in art history in the late 19th century. This starting point led him to the history of style and iconographical research. Along with the Danish art historian, Julius Lange, he was one of the first scholars who began to study the meaning of gestures and postures in art. In my dissertation I have emphasized the importance of Tikkanen s personal art education. I regard it as having influenced both his scholarly argumentation and his working methods. I have also written a short overview of the situation of art history in Finland and in Northern Countries before Tikkanen s time in order to give an idea of his scientific background. My thesis is a critical and historiographical study on J. J. Tikkanen s role in the development of art history and its methodology.

Approaching Sacred Pregnancy : The Cult of the Visitation and Narrative Altarpieces in Late Fifteenth-Century Florence

The study focuses on the Visitation as a narrative subject of altarpieces in late fifteenth-century Florence. Although the Visitation was a well-known story in both verbal and visual representations since the early medieval period, it became a popular subject of altarpieces only towards the end of the fifteenth century. In this study, the first part provides an overview of the complex religious and historical background to an emerging cult of the Visitation. Devotional practices focusing on the Visitation belong in a context of late medieval Marian devotion and in 1389 a new feast of the Visitation was introduced into the liturgical calendar of the Catholic Church. Because of the ongoing schism within the Catholic Church, the feast was not unanimously accepted across Western Europe until the later part of the fifteenth century. Contrary to a widely disseminated view, the feast of the Visitation cannot be associated with Franciscan spirituality, but was rather a clearly defined Dominican project that primarily emphasised the importance of peace and unity within the Christian Church. Simultaneously with the gradual acceptance of the new feast, visual representations of the Visitation began to appear at the centre of altarpieces. The Visitation exemplifies an increasing preference for narrative subjects within the genre of the altarpiece. The second part of the study presents an analysis of the concept of the narrative altarpiece and highlights the complexities involved in combining a narrative content with the traditional devotional function of the altarpiece. In detailed case studies some prominent art works produced in Florence between 1490 and 1503 are discussed within a framework of contextual analysis, narrative theory and iconography. Altarpieces by Domenico Ghirlandaio, Piero di Cosimo and Mariotto Albertinelli represent visual manifestations of a cult of the Visitation with roots in late medieval devotional practices. At the same time, the altarpieces highlight the multiple functions of altarpieces in a culture where art works responded to a variety of social and religious needs. Building on earlier studies, each case study presents new insights and evidence not considered in previous art historical research.

Tree-ring based hydroclimate reconstruction over northern Vietnam from Fokienia hodginsii: eighteenth century mega-drought and tropical Pacific influence

We present here the first statistically calibrated and verified tree-ring reconstruction of climate from continental Southeast Asia.The reconstructed variable is March-May (MAM) Palmer Drought Severity Index (PDSI) based on ring widths from 22 trees (42 radial cores) of rare and long-lived conifer, Fokienia hodginsii (Po Mu as locally called) from northern Vietnam. This is the first published tree ring chronology from Vietnam as well as the first for this species. Spanning 535 years, this is the longest cross-dated tree-ring series yet produced from continental Southeast Asia. Response analysis revealed that the annual growth of Fokienia at this site was mostly governed by soil moisture in the pre-monsoon season. The reconstruction passed the calibration-verification tests commonly used in dendroclimatology, and revealed two prominent periods of drought in the mid-eighteenth and late-nineteenth enturies. The former lasted nearly 30 years and was concurrent with a similar drought over northwestern Thailand inferred from teak rings, suggesting a ``mega-drought'' extending across Indochina in the eighteenth century. Both of our reconstructed droughts are consistent with the periods of warm sea surface temperature (SST)anomalies in the tropical Pacific. Spatial correlation analyses with global SST indicated that ENSO-like anomalies might play a role in modulating droughts over the region, with El Nio (warm) phases resulting in reduced rainfall. However, significant correlation was also seen with SST over the Indian Ocean and the north Pacific,suggesting that ENSO is not the only factor affecting the climate of the area. Spectral analyses revealed significant peaks in the range of 53.9-78.8 years as well as in the ENSO-variability range of 2.0 to 3.2 years.

Long-term trends in fertility of soils under continuous cultivation and cereal cropping in southern Queensland. IX. Simulation of soil carbon and nitrogen pools using CENTURY model

Cultivation and cropping of soils results in a decline in soil organic carbon and soil nitrogen, and can lead to reduced crop yields. The CENTURY model was used to simulate the effects of continuous cultivation and cereal cropping on total soil organic matter (C and N), carbon pools, nitrogen mineralisation, and crop yield from 6 locations in southern Queensland. The model was calibrated for each replicate from the original datasets, allowing comparisons for each replicate rather than site averages. The CENTURY model was able to satisfactorily predict the impact of long-term cultivation and cereal cropping on total organic carbon, but was less successful in simulating the different fractions and nitrogen mineralisation. The model firstly over-predicted the initial (pre-cropping) soil carbon and nitrogen concentration of the sites. To account for the unique shrinking and swelling characteristics of the Vertosol soils, the default annual decomposition rates of the slow and passive carbon pools were doubled, and then the model accurately predicted initial conditions. The ability of the model to predict carbon pool fractions varied, demonstrating the difficulty inherent in predicting the size of these conceptual pools. The strength of the model lies in the ability to closely predict the starting soil organic matter conditions, and the ability to predict the impact of clearing, cultivation, fertiliser application, and continuous cropping on total soil carbon and nitrogen.

Eradication of invasive species: progress and emerging issues in the 21st century

At an international conference on the eradication of invasive species, held in 2001, Simberloff (2002) noted some past successes in eradication—from the global eradication of smallpox (Fenner et al. 1988) to the many successful eradications of populations (mostly mammals) from small islands (e.g. Veitch and Bell 1990; Burbidge and Morris 2002). However, he cautioned that we needed to be more ambitious and aim higher if we are to prevent and reverse the growing threat of the homogenization of global biodiversity. In this chapter we review how the management strategy of eradication—the permanent removal of entire discrete populations—has contributed to the stretch in goals advocated by Simberloff. We also discuss impediments to eradication success, and summarize how some of the lessons learnt during this process have contributed to the other strategies (prevention and sustained control) that are required to manage the wider threat posed by invasive alien species. We concentrate on terrestrial vertebrates and weeds (our areas of expertise), but touch on terrestrial invertebrates and marine and freshwater species in the discussion on emerging issues, to illustrate some of the different constraints these taxa and habitats impose on the feasibility of eradication.

Eighteenth century style dining area; Steinharter residence; Munich Architecture; Residences; Interior

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