No description available.

This dissertation focuses on the development and testing of a conceptual framework for student motivation in mathematical discussion. Specifically, this document integrates Yackel and Cobb's (1996) framework with aspects of Self-Determination Theory (SDT), as described by Ryan and Deci (2000). Yackel and Cobb articulated the development of students' mathematical dispositions through discussion by facilitating student autonomy, incorporating appropriate social norms and co-constructing sociomathematical norms. SDT mirrors these factors and describes a similar process of self-regulation through fulfillment of the individual needs of autonomy, social relatedness, and competence. Given the conceptual overlap, this dissertation examines the connection of SDT with mathematical discussion with two studies. The first study examined the effect of student frequency of explaining mathematics on their perceived autonomy, competence and relatedness. Results of HLM analyses found that more frequent explanation of mathematics had a positive effect on students' perceived mathematics autonomy, mathematics competence, and relatedness. The second study used a triangulation mixed methods approach to examine high school geometry students' classroom discourse actions in combination with their perceived autonomy, competence, and relatedness. Results of the second study suggest a higher perceived sense of autonomy is indicative of more engagement in mathematical talk, but a measure of competence and relatedness are needed for such engagement to be fully indicative of mathematical discourse. Rather, students who lacked a measure of perceived competence or relatedness would cease participation in mathematical discussion when challenged by peers. While these results need further investigation, the results of the second study provide evidence that indicates the necessity of fulfilling all three SDT needs for engagement in mathematical discussion. Evidence from both the first and second studies presented in this dissertation provides support for the conceptual framework presented. / Ph. D.

Denna fallstudie belyser gymnasieelevers arbete i små grupper med ett problem kopplat till derivata och syftar till att belysa faktorer som gynnar eller hindrar individernas deltagande i och utveckling av den matematiska kommunikationen i klassrummet. Studien har sin teoretiska förankring i Anna Sfards kommognitiva ramverk, där lärande i matematik ses som deltagande i en matematisk diskurs. Under mer än ett årtionde har larmrapporter om svenska elevers bristande kunskaper i matematik avlöst varandra. Forskningsrapporter pekar på olika faktorer bakom denna sjunkande kunskapsutveckling. Den rådande undervisningskulturen, där eleverna i hög grad arbetar individuellt med uppgifter ur läroboken, ses som en förklaring till de försämrade resultaten, och att undervisningen inte ger eleverna möjlighet att utveckla samtliga föreskrivna förmågor i ämnet. För att uppnå detta betonar både forskningsfältet och den nya läroplanen från 2011 vikten av att eleverna kommunicerar i matematik. I detta perspektiv finns ett behov av att belysa skillnader i elevernas deltagande i kommunikationen om matematik, inte minst i samband med lärande i smågrupper, och hur detta antas påverka elevernas förutsättningar till lärande. Studiens fokus är riktat mot deltagarnas olika bidrag till gruppens matematiska diskurs, det vill säga då eleverna kommunicerar om matematiska objekt eller processer, och hur dessa påverkar elevernas förutsättningar och deltagande i kommunikationen. Fokus är också riktat mot den kommunikation som handlar om deltagarna i gruppen, vad eleverna gör och hur de värderar varandras sätt att delta i den matematiska diskursen i klassrummet. Denna kommunikation, benämns i ramverket för subjektifiering och antas vara sammankopplad med individens lärande i matematik. Datainsamlingsmetoder som använts är intervjuer, audio- och videoinspelningar och användning av audiovisuella pennor för att sammanföra verbal och skriftlig kommunikation. Diskursen ses som den naturliga analysenheten. I analysens första steg studerades den matematiska diskursen avseende skillnader i innehållet i deltagarnas yttranden. I ett andra analyssteg fokuserades på interaktionsflödet i gruppen för att förstå mer av skillnader i varje elevs deltagande och bidrag till kommunikation. Studiens resultat visar på stora skillnader avseende deltagande och innehåll i elevernas kommunikation, både på grupp- och individnivå. Elevernas utveckling av den matematiska diskursen gynnas av användningen av flera olika mediatorer för att representera de matematiska objekten. När eleverna erbjuds kopplingar till en tidigare erövrad diskurs, leder det till diskursiva framflyttningar. Eleverna visar sig vidare ha stora svårigheter att tolka och använda det formella matematiska symbolspråket som stöd för matematiserandet. Elevernas tolkning av likhetstecknet, olikhetstecknet och symbolen f´(x) på en processnivå skapar hinder för att utveckla den matematiska diskursen i önskvärd riktning. Den diskurs som handlar om deltagarna och deras egenskaper (identifiering) utgör ca 10 % av samtliga yttranden och är i stort sett samtliga negativa omdömen, ofta använda i syfte att utesluta eller införliva sig själva eller andra från deltagande i matematiserandet. Forskningsstudien visar på ett behov av ytterligare kunskap om hur matematiklärare på bästa sätt kan organisera arbete i smågrupper för att öka elevernas engagemang och kvaliteten på elevernas matematiserande. Studien pekar vidare på vikten av att matematiklärare belyser och varierar användningen av olika mediatorer för att representera de matematiska objekt som är föremål för lärandet. Fallstudien belyser även vikten av att bygga upp det tillåtande arbetsklimat där eleverna inte bedömer sig själva och andra, utan istället vågar ställa de frågor som innebär att de blir alltmer delaktiga i den matematiska diskursen. Ett behov framträder av ytterligare forskning riktad mot inte bara mot den bedömning som sker mellan lärare och elev, utan också mot den bedömning som pågår i klassrummet mellan eleverna, vilket kan påverka vilka roller de väljer eller tilldelas i klassrummet. Detta kan antas vara av stor vikt för hur eleverna kommunicerar om matematik med andra deltagare i klassrummet, vilket också kan antas påverka lärandet. / This case study takes its focus on upper secondary school students’ work in small groups with a problem related to the derivative. The analysis aims to identify factors that promote or hinder an individual’s participation in and development of the mathematical communication in the classroom. The theoretical basis of the study is Anna Sfard’s commognitive framework, where learning mathematics is seen as participating in a mathematical discourse. For more than a decade, reports about Swedish students’ decreasing levels of school mathematical knowledge have been put forward. Research points to various factors behind this development. The prevailing educational culture, where students largely work individually from the textbook, is seen as one explanation for the deterioration in the results, and that teaching does not give students the opportunity to develop all the required competencies in the curriculum. To achieve this, both research and the new Swedish curriculum from 2011 emphasize the importance of student communication in mathematics. In this perspective, there is a need to highlight the differences in student participation in the communication of mathematics in the classroom, particularly in the context of small group learning, and how this is assumed to influence students’ opportunities for learning. The focus of the research is directed towards the participants’ contributions to the group’s mathematical discourse, i.e. when they communicate about mathematical objects or processes, and how these affect students’ opportunities and participation in the communication. Focus is also directed to the communication that involves participants in the group, what the students are doing and how they evaluate each other’s way to participate in the mathematical discourse in the classroom. This type of communication is in the framework referred to as subjectifying, and is assumed to affect the individual’s mathematical learning. Data collection methods used are interviews, audio and video recordings, as well as “smart pens” to combine verbal and written communication. In the first step of the analysis, the mathematical discourse was studied regarding differences in the content of the participants’ utterances. The second step of analysis focused on the interaction flow of the group to understand more of the differences in each student’s participation and contribution to the communication. The results point to big differences regarding participation and content in student communication, both at group level and individual level. The development of students’ mathematical discourse benefits from the use of multiple mediators to represent the mathematical objects. When connections to a previously acquired discourse are offered, this leads to discursive advancements. Students were observed to have difficulties to interpret and use the formal mathematical symbolic language that would support their mathematizing. Students’ interpretation of the equality sign, the sign for inequality, and the symbol f´(x) on a process level, create obstacles to developing the mathematical discourse in the desired direction. The discourse about the participants and their own traits  (identification) constitutes about 10% of all utterances and are almost all negative reviews, frequently used in order to exclude or incorporate themselves or others from participating in the mathematizing activity. This research study points to a need for more knowledge about how mathematics teachers can best organize work in small groups to increase student engagement and the quality of their mathematizing. The study also indicates the importance of mathematics teachers highlighting and varying the use of different mediators to represent the mathematical objects to learn. The case study also highlights the importance of building up a permissive environment in which students do not evaluate themselves and others, but instead dare to ask questions that will make them increasingly involved in the mathematical discourse. A need emerges for further research not only on the assessment between teacher and student, but also on the assessment that goes on in the classroom between the students, which can affect what roles they take or are assigned to in the classroom. This can be assumed to be of great importance to the way students communicate about mathematics with other students in the classroom, which is also likely to influence learning.

This study examined the features of the classroom discourse in eight Algebra I classes from two urban high schools with diverse student populations. In particular, by using the discursive analysis perspective, the type of communication between teachers and students was examined. The study investigated to what extent teachers' patterns of discourse change as a result of the number of ELLs present or their particular teaching experiences and ESOL endorsement. Furthermore, the impact of teachers' cultural and linguistic backgrounds upon ELLs' mathematics experiences was explored, particularly the teachers' patterns of discourse and adjustments to their teacher talk, or modifications of instructions that contributed to ELLs' engagement in the mathematics classroom. Data analysis from various sources (observations, video-recordings, frequency counts, interviews, the teachers' self-evaluations, and the researcher's and the ELLs' evaluations) indicated that to some extent all teachers changed their patterns of discourse simply due to the presence of ELLs, regardless of the total number in the class. Teachers with more teaching experience and with ESOL training had a smaller number of ELLs in their classes, whereas in both schools the novice teachers were assigned to teach classes with the highest number of ELLs. The novice teachers frequently used almost the same strategies as their more experienced colleagues did. Yet the qualitative analysis of the type of modifications to their speech they made, the type of questions they asked, and the provision of information of higher cognitive demand according to Bloom's Taxonomy indicated that even though all teachers needed improvement in using these strategies, the more experienced teachers with ESOL training applied those strategies to a fuller extent. They more often used slower and simpler speech and different questioning techniques sensitive to the ELLs' level of English language acquisition (i.e., pre-production, early-production, and speech emergence) and provided the students with content specific, enriched information. However, they still did not ask enough questions that could provide the ELLs with opportunities to justify and explain their opinions, and rarely led the discussions to a point which could move the ELLs to the highest level of the subject-specific literacy - intermediate speech and fluency in mathematics in English.

No description available.