Prospective teachers’ conceptions of what characterize a gifted student in mathematics

This paper explores Swedish prospective teachers’ conceptions of what characterise a gifted student in mathematics. This was studied through a qualitative questionnaire focusing on attributions. The results show that a majority of the students attribute intrinsic motivation to gifted students, more often than extrinsic motivation. Other themes were other affective factors (e.g. being industrious), cognitive factors (e.g. easy to learn), and social factors such as good behaviour and background.

Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

NAVET's Boxes - an Evaluation of the Post-Visit Loan Service at a Science Centre in Borås

Many pedagogues believe science centres to be a good complement to the more formal school teaching. For a visit to a science centre to be as educational as possible, there is a need for pre-visit information of some sort, a guided visit, and post-visit work. Many science centres offer loan services of different kinds. At Navet, a science centre in Borås, teachers can borrow boxes with experiments connected to the different themes they provide. The experiments are supposed to be a continuation of the visit and help settle the knowledge gained during the visit. This thesis is an evaluation of how the boxes function in the schools, and what the teachers think of them. The study was conducted through questionnaires and interviews with both teachers and the staff at Navet. The results of the study are very positive. Many teachers have been involved with Navet from the very beginning and they see a visit to Navet as an integrated part of their teaching. Some boxes work better than others and some might need clearer information, but overall the teachers see the boxes as timesavers, as a way to vary their teaching more easily, and as a help for teachers not specialized in mathematics and science.

Communication in Smoking Cessation and Self-management : a study at Nurse-led COPD-clinics in Primary Health Care

ABSTRACTThe general aim of this thesis was to investigate behavioral change communication at nurse-led chronic obstructive pulmonary disease (COPD) clinics in primary health care, focusing on communication in self-management and smoking cessation for patients with COPD.Designs: Observational, prospective observational and experimental designs were used.Methods: To explore and describe the structure and content of self-management education and smoking cessation communication, consultations between patients (n=30) and nurses (n=7) were videotaped and analyzed with three instruments: Consulting Map (CM), the Motivational Interviewing Treatment Integrity (MITI) scale and the Client Language Assessment in Motivational Interviewing (CLAMI). To examine the effects of structured self-management education, patients with COPD (n=52) were randomized in an intervention and a control group. Patients’ quality of life (QoL), knowledge about COPD and smoking cessation were examined with a questionnaire on knowledge about COPD and smoking habits and with St. George’s Respiratory Questionnaire, addressing QoL. Results: The findings from the videotaped consultations showed that communication about the reasons for consultation mainly concerned medical and physical problems and (to a certain extent) patients´ perceptions. Two consultations ended with shared understanding, but none of the patients received an individual treatment-plan. In the smoking cessation communication the nurses did only to a small extent evoke patients’ reasons for change, fostered collaboration and supported patients’ autonomy. The nurses provided a lot of information (42%), asked closed (21%) rather than open questions (3%), made simpler (14%) rather than complex (2%) reflections and used MI non-adherent (16%) rather than MI-adherent (5%) behavior. Most of the patients’ utterances in the communication were neutral either toward or away from smoking cessation (59%), utterances about reason (desire, ability and need) were 40%, taking steps 1% and commitment to stop smoking 0%. The number of patients who stopped smoking, and patients’ knowledge about the disease and their QoL, was increased by structured self-management education and smoking cessation in collaboration between the patient, nurse and physician and, when necessary, a physiotherapist, a dietician, an occupational therapist and/or a medical social worker.Conclusion The communication at nurse-led COPD clinics rarely involved the patients in shared understanding and responsibility and concerned patients’ fears, worries and problems only to a limited extent. The results also showed that nurses had difficulties in attaining proficiency in behavioral change communication. Structured self-management education showed positive effects on patients’ perceived QoL, on the number of patients who quit smoking and on patients’ knowledge about COPD.

Upper secondary school students' gendered conceptions about mathematics

This study explores Swedish Natural Science students' conceptions about gender and mathematics. I conducted and compared the results from two questionnaires. The first questionnaire revealed a view of rather traditional feminities and masulinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between the traits the students ascribed as gender different and the traits they ascribed to themselves.

Elevers möjlighet till reflektion i matematikundervisningen : En studie i grunskolans årskurs 9

Studiens huvudsakliga syfte är att få kunskap kring om och hur elever i skolår 9 stimuleras till reflektion i matematikundervisningen. Den tidigare forskning som presenteras i litteraturgenomgången visar på reflektionens betydelse i lärprocessen och ger riktlinjer för vilka aktiviteter som uppmanar till respektive hämmar elevers reflektion. Genom en kvalitativ fallstudie, med i huvudsak lektionsobservationer som utgångspunkt och med efterföljande lärarintervjuer som stöd, har syftet uppnåtts genom att kartlägga den aktivitet som förekommer i praktiken. Undervisningsaktiviteter som kan uppvisa en positiv respektive negativ effekt på elevers möjlighet till reflektion har vid bearbetning och analys av materialet kunnat urskiljas. Resultatet visar att trots att lärare är positivt inställda till metakognition och ett reflekterande arbetssätt förekommer endast i vissa fall tillfällen då eleven stimuleras till reflektion och denna får ske. Vanligt förekommande i lärares undervisning är situationer som skulle kunna fungera som reflektionsstimulerande om de ges utrymme och reflektionen följs upp. Studiens resultat kan bidra till att påminna och göra lärare medvetna om vilka aktiviteter som stödjer reflektion samt förmedla vikten av att eleverna redan i grundskolans tidigare år undervisas om och utsättas för en undervisningspraktik som kontinuerligt kräver förekomsten av reflektion.

Muntlig framställning : att tolka och förstå kunskapskraven i nationellt prov SVA 1

Den här studien har haft som syfte att studera om kvalitetskraven i betygsskalan stämmer överens mellan nationellt prov i SVA1 och motsvarande kursplan svenska som andraspråk 1 (SVA1) samt på vilket sätt det nationella provet underlättar tolkningen av kunskapskraven i kursplanen för SVA1. Undersökningen begränsar sig till att omfatta enbart den muntliga delen, delprov A muntlig framställning. För att beskriva och analysera vilka kunskaper som anses vara eftersträvansvärda i muntlig framställning har en kvalitativ innehållsanalys genomförts som ger en grundmodell till den efterföljande kunskapsanalysen. Resultaten från studiens innehållsanalys visar fram en hur processen kring den muntliga framställningen utgår från den retoriska arbetsmodellen med ett gediget förberedande arbete som följs upp med anförande och avslutas med elevresponser. Resultatet från kunskapsanalysen visar hur eleverna behöver behärska en kombination av kunskapsformerna episteme, techné och fronesis för att uppfylla betygskraven på de högre nivåerna. Studiens slutsatser är att kvalitetskraven stämmer överens mellan det nationella provets bedömningsmatris och kursplanen i svenska som andraspråk 1 (SVA 1) vad gäller bedömningen av elevens språkliga kvaliteter. Dessutom går det att dra slutsatsen att de krav på anpassning till det retoriska sammanhanget också är krav som återfinns i kursplanen men beskrivs mer allmänt i ett språkutvecklande perspektiv vilket underlättar tolkningen av kunskapskraven i kursplanen. Studien visar hur eleven för att få det lägsta betyget (E) behöver kunskaper om en retorisk framställning och att eleven kan presentera ett förberett innehåll inför en publik.

Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Teachers' conceptions about students' mathematical reasoning : Gendered or not?

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking. 

A reason to believe : beliefs as an influence on students task solving

Upper secondary students’ task solving reasoning was analysed, with a focus on what grounds they had for different strategy choices and conclusions. Beliefs were identified and connected with the reasoning that took place. The results indicate that beliefs have an impact on the central decisions made during task solving. Three themes stand out: safety, expectation and motivation.

Layout och typografi i vetenskapliga artiklar : En kartläggning av konventioner gällande grafisk formgivning inom matematik, medicin och utbildningsvetenskap

En deskriptiv visuell innehållsanalys genomfördes med en korpus bestående av vetenskapliga artiklar från 30 topprankade tidskrifter jämnt fördelade på de tre disciplinerna matematik, medicin och utbildningsvetenskap, med syfte att undersöka om det fanns ett samband mellan tidskrifternas disciplintillhörighet och den grafiska formgivningen. Kartläggningen omfattade layout (bl.a. sidformat, spalter, marginalstorlek, användning av grafiska element, placering av tabeller, figurer och pagina) och typografiskt utseende hos titel, rubriker, brödtext och abstrakt (t.ex. teckenstorlek, textjustering, teckengrovlek, typsnitt, färg och radavstånd). Resultaten visar att disciplinerna använde olika men även gemensamma konventioner i sitt grafiska utseende. Matematik uppvisade enkelspaltig layout med liten typografisk variation, genomgående användning av typsnitt från familjen Transitional eller Transitional/Didone för hela dokumentet, avsaknad av kulört färg och sällan användning av grafiska element. Medicin uppvisade större variation med användning av kulört färg, icke-centrerad typografi med både sansseriff- och seriff-typsnitt, grafiska element och ramar som förstärker det ofta använda dubbelspaltiga gridsystemet. Utbildningsvetenskap uppvisade en grafisk design som återfanns i båda disciplinerna, men påminde mest om matematik till utseendet. Kodbok ingår i sin helhet som bilaga. Uppsatsen i sig är delvis formgiven med utgångspunkt i de erhållna resultaten.

Rapport från projektet Multimodala uppgifter och bedömning i matematik : Video och kollaborativa samtal som metod vid lärares bedömning av elevers matematiska kunskaper

This research will discuss some experiences from a four year school research study. It was conducted in cooperation with teachers from four municipalities in Dalarna. The aim of the research was to examine teachers´ professional development when they participated in collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. The study had two foci one was to investigate methods and tools that teachers can use to develop their ability to assess their students while working on multimodal tasks. The other was to examine how video can be used by teachers wanting to obtain knowledge about assessing students. The study is based on several theories about when teachers collaborate to create new knowledge. The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. A basic assumption of the framework here is that meanings are made and communicated in mathematics through a wide range of semiotic modes. By using video as an essential tool in the research the framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners were also needed. The findings can be divided into the following themes: the use of tasks for assessment, collaborative discussion, equipment, ethical dilemmas. Collaborative discussions were evaluated as a meaningful way of sharing knowledge. The use of video recordings in association with these discussions raised important ethical issues. Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work. In this way the project highlighted more general aspects of school development. The research also concerns teachers´ use of collaborative discussions in assessment work, multimodal tasks in mathematics and video as a research tool in general.

Konkret material i matematikundervisningen – bekymmer och motsättningar : En systematisk litteraturstudie om laborativ matematik

Laborativt arbete med konkret material är en arbetsform inom matematiken som på en del håll åter fått uppsving i ett försök att råda bot på svenska elevers försämrade prestationer i och intresse för matematik. Denna litteraturstudies syfte är att undersöka vilka faktorer som kan påverka negativt vid laborativt arbete med konkret material i matematikundervisningen. I resultatet av litteraturstudien synliggörs huvudsakligen två faktorer som är av större betydelse för undervisningens utfall samt en faktor av mindre betydelse, elevernas ålder. Den första faktorn behandlar valet av material och materialets utformning, vilket kan inverka på elevernas förståelse. Om det konkreta materialet är mycket likt de föremål elever möter i sin vardag, såsom pizzaslices eller pengar, kan denna likhet störa elevernas matematiska förståelse genom att för stor uppmärksamhet riktas mot igenkännandet och att se föremålen som potentiella leksaker, istället för att se dem som konkreta symboler för abstrakt matematik. Detta tycks inte åldersbetingat, utan förekommer i olika årskurser. Den andra faktorn som uppmärksammats är lärarens vägledande roll. Läraren behöver adekvat kompetensutveckling och professionellt stöd i arbetet med konkret material för att öka chanserna att arbetssättet får ett så gynnsamt utfall som möjligt. Läraren spelar en stor roll i både valet av konkret material och i hur instruktioner samt vägledning ges. Det är också viktigt att läraren i undervisningen bjuder in till interaktion och kommunikation om elevernas funna resultat och lösningsförslag för att stärka elevernas förståelse. Sökandet efter relevant litteratur genomfördes i AABRI, ERIC, Google Scholar, Libris, och Summon.