Educators’ perceptions of mathematically gifted students and a socially supportive learning environment – A case study of a Finnish upper secondary school

This article explores five educators’ conceptions of the characteristics of mathematically gifted students and a social learning environment that supports their development in a school for mathematically gifted adolescents in Finland. We conducted this qualitative study through semi-structured interviews and participant observations in a Finnish upper secondary school with a special mathematics program. The research shows that gifted students and their educators form a tight community, the social learning environment of which supports shared motivation, healthy perfectionism, and practicing social skills. The results deepen the understanding of gifted education in the Finnish context and the significance of educators’ shared understanding of social activities as a basis for successful gifted education.Peer reviewe

Teacher-student eye contact during scaffolding collaborative mathematical problem-solving

Teacher’s gaze communicates consciously and unconsciously her pedagogical priorities to the students. By creating and responding to eye contact initiatives, people can communicate both status and affection. This research explores the frequency of teacher-student eye contacts and their connection to teachers’ scaffolding intentions. The data consisted of mobile gaze tracking recordings of two teachers and stationary classroom videos during three collaborative mathematical problem-solving lessons. The quantitative analysis showed that most of the teacher gazes on student faces did not lead to dyadic eye contacts and those gazes that did, occurred often during affective and cognitive scaffolding. These results offer us novel and important insight in the nonverbal part of scaffolding interaction. Eeva Haataja, Miika Toivanen, Anu Laine and Markku S. Hannula University of Helsinki, FinlandTeacher’s gaze communicates consciously and unconsciously her pedagogical priorities to the students. By creating and responding to eye contact initiatives, people can communicate both status and affection. This research explores the frequency of teacher-student eye contacts and their connection to teachers’ scaffolding intentions. The data consisted of mobile gaze tracking recordings of two teachers and stationary classroom videos during three collaborative mathematical problem-solving lessons. The quantitative analysis showed that most of the teacher gazes on student faces did not lead to dyadic eye contacts and those gazes that did, occurred often during affective and cognitive scaffolding. These results offer us novel and important insight in the nonverbal part of scaffolding interaction.Peer reviewe

Crossover Scaling of Wavelength Selection in Directional Solidification of Binary Alloys

We simulate dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with an adaptive-mesh refinement. The spacing of primary branches is examined for a range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a non-trivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers, a result validated using published experimental data.Comment: 4 pages, four figures, submitted to Physical Review Letter

Laaja-alaisen erityisopettajan ja luokanopettajan välinen yhteisopetus inklusiivisessa luokassa

Tiivistelmä. Tässä pro gradu -tutkielmassa on tarkoituksena selvittää laaja-alaisten erityisopettajien ja luokanopettajien kokemuksia heidän välisestä yhteisopetuksesta. Lisäksi tutkielmassa halutaan selvittää, mitkä tekijät opettajien mielestä voivat vaikuttaa toimivan yhteisopetuksen toteutumiseen. Nykyään yhteisopetus on yhä enemmän osana koulujen arkea, joten aihe on hyvin ajankohtainen ja tärkeä. Tutkielman teoreettisen viitekehyksen perustana on yhteisopetuksesta tehdyt tutkimukset sekä aiheesta tehty kirjallisuus. Viitekehyksen teoria pohjautuu tunnettuihin kansainvälisiin ja suomalaisiin teoksiin. Teoriaosassa paneudutaan inkluusioon ja kolmiportaiseen tukeen, jotka ovat osaltaan vaikuttaneet yhteisopetuksen toteutumiseen Suomessa. Lisäksi määritellään yhteisopetus ja sen erilaisia muotoja. Lopuksi tuodaan esille yhteisopetuksen hyötyjä niin opettajien kuin oppilaidenkin näkökulmasta katsoen, sekä haasteita ja edellytyksiä yhteisopetukselle. Tämä tutkielma on laadullinen tutkimus, joka on tehty teemahaastatteluilla. Tutkimuksen kohdejoukkona ovat laaja-alaiset erityisopettajat ja luokanopettajat, joita oli yhteensä kahdeksan. Tutkielmassa käsiteltiin opettajien kokemuksia ja käsityksiä, joten lähestymistapana tutkielmassa on käytetty fenomenologiaa. Tutkielmasta saadut tulokset on analysoitu aineistolähtöisen sisällönanalyysin keinoin. Saaduista tutkimustuloksista nousi esille, että laaja-alaiset erityisopettajat ja luokanopettajat kokivat yhteisopetuksen suurimmaksi osaksi positiivisena. Positiivisena yhteisopetuksesta nähtiin muun muassa opettajien kuormituksen jakaminen ja oppilaan tuen saaminen suoraan hänen omaan luokkaansa. Kuitenkin tuloksista ilmeni myös negatiivisia kokemuksia yhteisopetuksesta. Opettajat kokivat, että yhteisopetus on silloin haastavaa, mikäli opettajat olivat epätasa-arvoisessa roolissa toisiinsa nähden. Tutkimuksen tuloksista nousi esille useita eri tekijöitä, jotka voivat vaikuttaa yhteisopetuksen toteutumiseen. Vaikuttavimmat tekijät olivat resurssit, suunnittelu ja johdon tuki. Tuloksista voidaankin todeta, että yhteisopetuksesta on paljon hyötyjä, mutta tekijöitä sen toimivalle toteutumiselle on monia

”Jokainen lapsi on ainutlaatuinen ja arvokas juuri sellaisena kuin hän on”:yksilöllisyys varhaiskasvatuksessa

Tiivistelmä. Kandidaatintutkielmamme käsittelee narratiivisen kirjallisuuskatsauksen keinoin yksilöllisyyden huomioimista varhaiskasvatuksessa. Tutkielmamme pohjalla toimii Varhaiskasvatussuunnitelman perusteet (2016), jota täydentää aiheesta tehty tutkimus ja kirjallisuus. Varhaiskasvatussuunnitelman perusteissa yksilöllisyys tulee esille useissa kohdissa, mistä voi päätellä, että yksilöllisyyden huomioon ottaminen on tärkeää varhaiskasvatuksen arjessa. Varhaiskasvatussuunnitelman perusteissa (2016, 19) todetaan muun muassa, että ”Jokainen lapsi on ainutlaatuinen ja arvokas juuri sellaisenaan kuin hän on. Jokaisella lapsella on oikeus tulla kuulluksi, nähdyksi, huomioon otetuksi ja ymmärretyksi omana itsenään sekä yhteisönsä jäsenenä.” Tutkielmassa käsittelemme yksilöllisyyden huomioimiseen liittyvien tekijöiden lisäksi hieman myös muutamaa tekijää, joiden alle yksilöllisyys on vaarassa joissain tilanteissa jäädä, eli sukupuolta, monikulttuurisuutta ja ikää. Varhaiskasvatussuunnitelman perusteiden (2016) mukaan yksilöllisyys tulee huomioida toimintakulttuurissa, joka kattaa muun muassa oppimisympäristön ja -käsityksen, työtavat ja vuorovaikutuksen. Nämä samat tekijät nousivat esille myös tutkimusmateriaaleissa, joita tutkimusta varten kävimme läpi. Toimintakulttuuria tulee muokata siten, että se ottaa huomioon erilaiset tarpeet, joita lapsilla on. Varhaiskasvatuksen oppimiskäsityksen tulee huomioida muun muassa lasten kiinnostuksen kohteet ja oppimisympäristön sekä lapsiryhmän moninaisuus ja yksilölliset tarpeet. Työtavoista esille yksilöllisen huomioimisen kannalta nousi havainnointi ja dokumentointi. Tavalla, jolla kasvattaja kohtaa lapsen sekä on hänen kanssaan vuorovaikutuksessa voi tulkita olevan myös vaikutuksensa

Editorial : Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers

This LUMAT special issue is a collection of selected papers from the 24th international conference of mathematical views that was held on August 20–22, 2018 in Helsinki, Finland. The conference was a wonderful opportunity to elaborate issues related to mathematics-related affect among colleagues interested in this area of research. The keynote at the conference was given by Reinhard Pekrun with a title: “Achievement emotions in mathematics”. Out of the 25 conference presentations, 12 were submitted as a manuscript for peer review. We had one reviewer selected among MAVI 24 participants, and another reviewer was invited among mathematics affect researchers who were not at the conference. After the review and revisions, we ended up with eight articles that you can read in this special issue.Non peer reviewe

Dynamics of Spreading of Chainlike Molecules with Asymmetric Surface Interactions

In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short chainlike molecules that cannot form chemical bonds with the surface. We use constant temperature Molecular Dynamics techniques to examine in detail the microscopic structure of the time dependent precursor film. We find that in some cases it can exhibit a high degree of local order that can persist even for flexible chains. Our model also reproduces the experimentally observed early and late-time spreading regimes where the radius of the film grows proportional to the square root of time. The ratios of the associated transport coefficients are in good overall agreement with experiments. Our density profiles are also in good agreement with measurements on the spreading of molecules on hydrophobic surfaces.Comment: 12 pages, LaTeX with APS macros, 21 figures available by contacting [email protected], to appear in Phys. Rev.

Diffusive Spreading of Chainlike Molecules on Surfaces

We study the diffusion and submonolayer spreading of chainlike molecules on surfaces. Using the fluctuating bond model we extract the collective and tracer diffusion coefficients D_c and D_t with a variety of methods. We show that D_c(theta) has unusual behavior as a function of the coverage theta. It first increases but after a maximum goes to zero as theta go to one. We show that the increase is due to entropic repulsion that leads to steep density profiles for spreading droplets seen in experiments. We also develop an analytic model for D_c(theta) which agrees well with the simulations.Comment: 3 pages, RevTeX, 4 postscript figures, to appear in Phys. Rev. Letters (1996

Advancing video research methodology to capture the processes of social interaction and multimodality

In this reflective methodological paper we focus on affordances and challenges of video data. We compare and analyze two research settings that use the latest video technology to capture classroom interactions in mathematics education, namely, The Social Unit of Learning (SUL) project of the University of Melbourne and the MathTrack project of the University of Helsinki. While using these two settings as examples, we have structured our reflections around themes pertinent to video research in general, namely, research methods, data management, and research ethics. SUL and MathTrack share an understanding of mathematics learning as social multimodal practice, and provide possibilities for zooming into the situational micro interactions that construct collaborative problem-solving learning. Both settings provide rich data for in-depth analyses of peer interactions and learning processes. The settings share special needs for technical support and data management, as well as attention to ethical aspects from the perspective of the participants' security and discretion. SUL data are especially suitable for investigating interactions on a broad scope, addressing how multiple interactional processes intertwine. MathTrack, on the other hand, enables exploration of participants' visual attention in detail and its role in learning. Both settings could provide tools for teachers' professional development by showing them aspects of classroom interactions that would otherwise remain hidden.Peer reviewe

Phases of collaborative mathematical problem solving and joint attention : a case study utilizing mobile gaze tracking

Given the recent development of mobile gaze-tracking devices it has become possible to view and interpret what the student sees and unravel the associated problem-solving processes further. It has also become possible to pinpoint joint attention occurrences that are fundamental for learning. In this study, we examined joint attention in collaborative mathematical problem solving. We studied the thought processes of four 15-16-year-old students in their regular classroom, using mobile gaze tracking, video and audio recordings, and smartpens. The four students worked as a group to find the shortest path to connect the vertices of a square. Combining information on the student gaze targets with a qualitative interpretation of the context, we identified the occurrences of joint attention, out of which 49 were joint visual attention occurrences and 28 were attention to different representations of the same mathematical idea. We call this joint representational attention. We discovered that 'verifying' (43%) and 'watching and listening' (35%) were the most common phases during joint attention. The most frequently occurring problem solving phases right after joint attention were also 'verifying' (47%) and 'watching and listening' (34%). We detected phase cycles commonly found in individual problem-solving processes ('planning and exploring', 'implementing', and 'verifying') outside of joint attention. We also detected phase shifts between 'verifying', 'watching and listening', and 'understanding' a problem, often occurring during joint attention. Therefore, these phases can be seen as a signal of successful interaction and the promotion of collaboration.Peer reviewe