Affect in mathematics education: an introduction

The article presents an introduction to the concept of affect in mathematics education research

Polyteam Semantics

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatisation for the associated implication problem. We also characterise the expressive power of poly-dependence logic by properties of polyteams that are downward closed and definable in existential second-order logic (ESO). The analogous result is shown to hold for poly-independence logic and all ESO-definable properties.Peer reviewe

Impact of schizophrenia on anterior and posterior hippocampus during memory for complex scenes.

ObjectivesHippocampal dysfunction has been proposed as a mechanism for memory deficits in schizophrenia. Available evidence suggests that the anterior and posterior hippocampus could be differentially affected. Accordingly, we used fMRI to test the hypothesis that activity in posterior hippocampus is disproportionately reduced in schizophrenia, particularly during spatial memory retrieval.Methods26 healthy participants and 24 patients with schizophrenia from the UC Davis Early Psychosis Program were studied while fMRI was acquired on a 3 Tesla Siemens scanner. During encoding, participants were oriented to critical items through questions about item features (e.g., "Does the lamp have a square shade?") or spatial location (e.g., "Is the lamp on the table next to the couch?"). At test, participants determined whether scenes were changed or unchanged. fMRI analyses contrasted activation in a priori regions of interest (ROI) in anterior and posterior hippocampus during correct recognition of item changes and spatial changes.ResultsAs predicted, patients with schizophrenia exhibited reduced activation in the posterior hippocampus during detection of spatial changes but not during detection of item changes. Unexpectedly, patients exhibited increased activation of anterior hippocampus during detection of item changes. Whole brain analyses revealed reduced fronto-parietal and striatal activation in patients for spatial but not for item change trials.ConclusionsResults suggest a gradient of hippocampal dysfunction in which posterior hippocampus - which is necessary for processing fine-grained spatial relationships - is underactive, and anterior hippocampus - which may process context more globally - is overactive

Facets of Distribution Identities in Probabilistic Team Semantics

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.Peer reviewe

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of fraction knowledge. In the first study, a cross-sectional sample of 84 kindergarteners to third graders completed tasks measuring their spontaneous recognition and use of quantitative relations and then completed the tasks again with explicit guidance to focus on quantitative relations. Findings suggest that SFOR is a measure of the spontaneous focusing of attention on quantitative relations and the use of these relations in reasoning. In the second (longitudinal) study, 25 first graders completed measures of SFOR tendency and a measure of fraction knowledge three years later. SFOR tendency was found to predict fraction knowledge, suggesting that it plays a role in the development of fraction knowledge.</p

Baltic Ecological Recycling Agriculture and Society (BERAS project) - a case of Juva milk system

The aim of the study was to determine the potential, impact and prerequisites of localization and enhanced recycling in a rural food system, illustrated by the case of Juva milk. An interdisciplinary scenario based on the increase of local, organic milk to 50 % of milk comsumption was created and the sustainability was compared, on the basis of the statistics and data collected from the actors, with the present milk system

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions

Affect in mathematics education

There are two different uses for the word “affect” in behavioral sciences. Often it is used as an overarching umbrella concept that covers attitudes, beliefs, motivation, emotions, and all other noncognitive aspects of human mind. In this article, however, the word affect is used in a more narrow sense, referring to emotional states and traits. A more technical definition of emotions, states, and traits will follow later.Peer reviewe

Yleisimpien kipulääkkeiden analysointi jätevesistä UHPLC-MS/MS-menetelmällä

Tiivistelmä. Kipulääkkeitä käytetään runsaasti ympäri maailmaa niiden suotuisten vaikutusten ja helpon saatavuuden vuoksi. Niitä päätyy jätevedenpuhdistuslaitoksille mm. kotitalouksien, sairaaloiden ja teollisuuden jätevesien mukana. Kipulääkkeet poistuvat jätevedestä puutteellisesti, johtuen niiden kemiallisista ominaisuuksista ja puhdistusprosessien heikosta soveltuvuudesta lääkeaineiden poistamiseen. Kipulääkkeet esiintyvät jätevesissä vaihtelevina pitoisuuksina prosessoimattomien ja prosessoitujen jätevesien välillä. Niiden analysointi vaatii menetelmän kannalta riittävän hyvää herkkyyttä ja alhaisia määritysrajoja. Ultrakorkean erotuskyvyn nestekromatografia yhdistettynä tandem-massaspektrometriin (UHPLC-MS/MS) on suosittu menetelmä analysoitaessa lääkeaineiden pitoisuuksia erilaisissa vesi- ja ympäristönäytteissä. Sen tärkeitä etuja ovat lisääntynyt herkkyys, nopea analyysi suurelle määrälle yhdisteitä, alhaiset määritysrajat sekä luotettavuus. Tässä tutkielmassa perehdytään siihen, millaisia pitoisuuksia kipulääkkeille on saatu UHPLCMS/MS-menetelmällä jätevesistä Australiassa, Espanjassa, Pakistanissa, Portugalissa ja Unkarissa. Tarkastelun kohteena olevat kipulääkkeet ovat aspiriini ja salisyylihappo, diklofenaakki, ibuprofeeni, ketoprofeeni, naprokseeni ja parasetamoli. Pitoisuuksia tarkastellaan sekä jätevedenpuhdistamoille virtaavissa että puhdistetuissa jätevesissä, ts. influentti- ja effluenttivesissä. Tutkielmassa tarkasteltujen tutkimusten tulosten perusteella kipulääkkeiden pitoisuudet ovat influenttivesissä tavallisesti tuhansia ng/l ja effluenttivesissä kymmenistä satoihin ng/l. Tulosten perusteella parasetamolin pitoisuudet ovat tyypillisesti korkeimpia influenttivesissä muihin kipulääkkeisiin verrattuna. Effluenttivesien osalta diklofenaakin pitoisuudet ovat olleet poikkeuksellisen suuria ja se poistuu jätevedenpuhdistusprosesseissa huonommin kuin muut kipulääkkeet. Jätevesien sisältämien lääkeaineiden luotettava analysointi on tärkeää, jotta puhdistetun veden käyttö on turvallista. Pitoisuuksista ollaan kiinnostuneita myös mahdollisten ympäristövaikutusten takia