Social norms are patterns of behavior expected within a particular society in a given situation. Social norms can be shared belief of what is normal and acceptable shapes and enforces the actions of people in a society. In the educational classroom, they are characteristics that constitute the classroom participation structure. Sociomathematical norms are fine-grained aspects of general social norms specifically related to mathematical practices. These can include, but are not limited to, a student-centered classroom that includes the expectation that the students should present their solution methods by describing actions on mathematical objects rather than simply accounting for calculational manipulations. For this action research study, my goal was to determine if the role of the teacher would influence the social and sociomathematical norms in a mathematics classroom and in what ways are sociomathematical norms reflected in students' written work. I focused specifically on students' mathematics journal writing and taped conversations. I discovered that students tended to not justify their work. Also, I discovered that my idea of justification was not really justification. I learned from this and was able to change my idea of justification. By encouraging the students to socialize in mathematics class, I found that the quality of their dialogue improved. Students readily discussed mathematical concepts within small groups and whole class discussions.

I varje klassrum och elevgrupp förekommer normer och förväntningar (Skott, Jess, Hansen & Lundin, 2010). Normer skapas i interaktion mellan lärare och elever, vilket leder till att normer byggs upp i klassrummet (Cobb & Yackel, 1996). Om det saknas förståelse och samsyn om normer finns det risk för att elevernas matematiklärande hämmas. Studiens syfte är att beskriva vilka sociomatematiska normer som visar sig i ett klassrum, i årskurs 5. Den teoretiska utgångspunkten för studien är socialkonstruktivism. 40 elever från en skola i Sverige observerades och åtta av dem samt en lärare intervjuades för att synliggöra vilka sociomatematiska normer som förekom under de observerande lektionerna. Därefter fick läraren och åtta elever beskriva normerna. Resultatet visade att det inte råder en samsyn mellan läraren och eleverna kring de tre normerna: 1) diskussion som arbetssätt för att förstå det matematiska innehållet 2) ett godtagbart matematiskt svar och slutligen 3) det matematiska språket och dess betydelse i undervisningen.  Det fanns en viss samsyn kring de sociomatematiska normerna dock beskrevs skillnader, vilket påverkar lärarens och elevernas syn på vad matematikundervisningen innebär. Slutsatsen av studien är att det i vissa fall finns ett glapp mellan lärarens och elevernas förståelse kring normer. Normen kan därmed ha skapats omedvetet, vilket i sin tur påverkar lärarens och elevernas agerande och var de lägger fokus på i matematikundervisningen. / In every classroom and group of students it occurs norms and expectations (Skott, Jess, Hansen & Lundin, 2010). Norms creates in interaction between the teacher and students, which conduce to that norms establish in the classroom (Cobb & Yackel, 1996). If the knowledge and consensus about norms is missing there is a risk that the students mathematical learning will be inhibit. The aim of the study is to describe which sociomathematical norms that shows in one classroom, in 5th grade. The theoretical basis of the study is social constructionism. 40 students from a school in Sweden was observed and eight of them and one of the teacher was interviewed in order to emphasize which sociomathematical norms that occurs during the observed lesson. Subsequently the teacher and eight students got to express the norms. The result showed that it’s not prevail a consensus between the teacher and students about the three norms: 1) discussion as a way to work 2) an acceptable mathematic answer and at last 3) the mathematic language and its meaning in the education. There was a consensus between some of the sociomathematical norms differences were founded though, which influences the teacher and the student view of what the mathematical education implicates. The conclusion of the study is that in some cases there is a gap between the teacher and the students’ knowledge about norms. The norm has accordingly been created unknowingly, which in turn can influence the teacher and the students acting and where they put their focus in their mathematical education.

This exploratory study investigated the influence of High Performance Team (HPT) training on sociomathematical norms and differing levels of the Math-Talk Learning Community framework (Math-Talk) when sixth-grade student teams solved challenging mathematics problems while working in teams. HPT training involved (1) training students on distinct roles in the team problem-solving process, (2) challenging students with complicated mathematical problems, and (3) holding students accountable for contributions to the team. This research project explored the initial stages of the relationship between HPT and student-to-student mathematics conversations though the lens of the Math-Talk Learning Community framework. The researcher studied four teams (i.e., four cases) with four middle school students in each team/case during a 7-week timeframe. The research study had three phases. The first phase involved gathering baseline data regarding the students’ sociomathematical norms. During the second phase, the students were trained to work in HPT and then solved challenging mathematics problems in teams. During the last phase, the researcher collected data to explore shifts in sociomathematical norms and student autonomy after the students had the opportunity to be trained and work in HPT. The researcher used descriptive statistics to analyze the quantitative data and open and axial coding to analyze the qualitative data. The analysis included both within- and cross-case analysis. The descriptive statistics used to analyze the changes in sociomathematical norms and Math-Talk levels indicated that the levels of sociomathematical norms increased when teachers gave students opportunities to participate in mathematics discussion. Specifically, students were most adept in the area of explaining and justifying reasoning and least skilled in the area of indicate when solutions are valid. The role of the teacher was key to maintaining high levels of Math-Talk. The teachers needed to give appropriate support to maintain these levels in three different areas: (1) select problems that were the appropriate level of complexity and provide scaffolding when needed, (2) ensure students understood the context for the mathematics problems, and (3) teach students how to find their own errors or be ready to give feedback regarding whether students’ answers were correct.

Students do not always evaluate explanations based on the mathematics despite their teacher's effort to be the guide-on-the-side and delegate evaluation to the students. This case study examined how the use of three features of the Discourse—authority, sociomathematical norms, and classroom mathematical practices—impacted students' evaluation and contributed to students' failure to evaluate. By studying three pre-service elementary school students' evaluation methods, it was found that the students applied different types of each of the features of the Discourse and employed them at different times. The way that the features of the Discourse were used contributed to some of the difficulties that the participants experienced in their evaluation of explanations. The results suggest that researchers in the field must come to believe that resistance to teaching methods is not the only reason for student failure to evaluate mathematical explanations and that authority is operating in the classroom even when the teacher is acting as the guide on the side. The framework developed for the study will be valuable for researchers who continue to use for their investigation of individual student's participation in mathematical activity.

Denna studie beskriver hur en kommunal grundskola i sydvästra Indien undervisar matematik.Vår frågeställning var: Hur fungerar en indisk statlig grundskola arbetar med matematik? Vilka är lärarnas uppfattningar om skolans sätt att undervisa? För att ha möjlighet att fördjupa oss i frågorna undersökte vi även Hur lärarnas föreställningar om matematik påverkar normerna i klassrummet utifrån ramen av Yack och Cobbs normteori. Det är en kvalitativ studie där vi utförde observationer av undervisningen och intervjuer med lärare och rektorn på skolan om deras syn på matematikundervisningen, under tre veckor. Vi samlade också information om och dokumenterade deras matematikverkstad.Utifrån våra intervjuer och observationer kunde vi dra slutsatsen att samtliga på skolan arbetade med en aktivitetsbaserad undervisning där matematik lärs med hjälp av manipulativt, laborativt material. De arbetade tillsammans i ett arbetslag med en strävan att uppfylla läroplanens mål och med en gemensam arbetsmetod. Vi fann också att lärarnas värderingar och föreställningar om hur matematik ska läras ut, påverkar de normer som verkar i klassrummet.Denna studie kan inte generaliserbar eftersom detta är en fallstudie på denna skola. Dock förespråkar den indiska läroplanen att undervisningen ska ske utifrån elevnära aktiviteter, men matematikverkstaden på denna skola var speciell och utvecklad på denna skola. / For our study, we visited a Government Lower Primary School in India to inquiry about how a school in another schooling context teaches mathematics. Our research questions were: How does an Indian Government Lower Primary School work with mathematics? What are the teachers' perceptions of the school’s teaching approach? In addition to these questions and to inquire deeper into this subject, we also investigated How do the teachers’ perceptions and method of teaching connect to Yackel and Cobb’s framework of the different kinds of norms operating in the classroom?We did a qualitative study, staying at the school for three weeks to interview teachers about their method of teaching mathematics as well as observing how they were teaching mathematics and the norms that operated in the classroom. We also gathered information about their mathematics laboratory. During our interviews and observations we came to the conclusion that the school worked with activity-based learning by using manipulative materials. All teachers as well as the principal cooperatively strived to meet the curricula objectives, with the same teaching approach. We also found that the teachers’ values and beliefs about how mathematics should be taught, affect the norms operating in the classroom.This study cannot be generalised for all schools in India or even in this area. This study is a minor study which only considered one particular school which used an interesting teaching method, activity-based learning with manipulatives.

This qualitative study documents the establishment of new social and sociomathematical norms in a second grade classroom. The teacher allowed students to speak directly to one another without having to raise their hands first during whole group mathematics instruction. Reform efforts in mathematics and the standards for mathematical practice contained in the Common Core State Standards call for students to discuss their reasoning with each other. Data were collected through interviews with the teacher and students, field notes, and video-recorded lessons over the course of 23 days. An online survey tool was utilized to share selected video of the teacher's instruction. Initial professional development topics were chosen from research in mathematics education related to the social construction of understanding. Ongoing professional development was responsive to what occurred during instruction. The literature suggests that teachers often utilize traditional teaching methods and struggle to deviate from established patterns regardless of their desire to implement change. The teacher in this study learned that allowing students to talk openly provided him with insight into their mathematical conceptions and misconceptions. The students initially viewed mathematics as a set of rules to follow and exhibited the role of passive recipients of information. This changed as students were provided opportunities to participate in discussions and in doing so developed a new understanding of their role during mathematics lessons. Mathematical errors became a catalyst for communication and were viewed by students as opportunities for assisting their peers.

In an attempt to examine classroom dialogue within a second grade classroom, I encouraged students to participate in mathematics discussions without needing to raise their hands before speaking. I challenged this traditional social norm and established sociomathematical norms as the study progressed. My study showed the effects of this change on the dialogue of students in my classroom. Focus was placed on the participation in classroom discussions when traditional social and sociomathematical norms were in place as well as when new norms were established. The study helped determine the effects of student-centered dialogue on conceptual understanding as demonstrated in the students' discussions, participation, and written expression.

There are two purposes to this study. The first was for me, as a teacher, to try something new in my instruction and grow from it. The second purpose of this study focused on the students. I wanted to see what level of performance in problem solving my students are at currently, and how the use of journaling and discourse affected the students' problem solving abilities. A problem-solving unit was taught heuristically in order to introduce students to the various strategies that could be used in problem solving. Math journals were also used for problem solving and reflection. Classroom discourse in discussion of problem solving situations was used as a means of identifying strategies used to solve the problem. Explanations and justifications were then used in writing and discourse to support students' solution and methods. An analytic problem-solving rubric was used to score the problems solved by the students. These scores, along with explanations and justifications, and discourse were used as data and analyzed for common themes. The results of this study demonstrate overall improvement in student performance in problem solving. Heuristic instruction the students received on strategies in problem solving helped to improve their ability to not only select an appropriate strategy, but also implement it. This unit, along with the problem solving prompts solved in the journals, helped to improve the students' performance in explanations. It was discourse combined with all the previous instruction that finally improved student performance in justification.

Syftet med studien är att göra en empirisk undersökning om hur elever i årskurs 6 upplever kooperativt lärande i matematikundervisningen inom problemlösning. Baserad på en intervju undersöker studien också hur kooperativt lärande kan ha betydelse för elevers resonemangs.- och kommunikationsförmågor. En intervju utförs i studien som ger anledning till att eleverna innan intervjun genomför ett lektionsmoment med kooperativt lärande. Efteråt analyseras samt diskuteras intervjun genom att förena data med teorin sociomatematiska normer. Detta för att ta reda på hur elevers upplevelse och normer kan beskrivas. Resultatet pekar på att kooperativt lärande inom problemlösning kan upplevas mer positivt. Det är normer i klassrummet som kan ha en betydelse för att elever ska kunna utveckla sina resonemangs- och kommunikationsförmågor. Med utgångspunkt i analysen kan kooperativt lärande i matematikundervisningen vara ett komplement för ett mer välstrukturerat grupparbete med engagemang, gemensamhet, samarbete och möjlighet till lärande.

<p>Syftet med detta examensarbete är att undersöka undervisning och lärande under en matematiklektion som präglas av traditionell skolmatematik. Metoden för undersökningen var en deltagande observation av en matematiklektion i åk 3 på gymnasiet. Med hjälp av begreppen matematikens lärandeobjekt, matematiska resurser, eleven som lärande aktör och sociomatematiska normer har jag tolkat de resultat som genererats från observationen. Två slutsatser som kan dras av undersökningen är att eleverna stimuleras till att bli oberoende lärande aktörer i undervisningen av traditionell skolmatematik samt att det i första hand är läraren som synliggör potentiella matematiska resurser för eleverna. Medvetenheten om elevernas användande av matematiska resurser skulle kunna påverka elevernas lärande genom att läraren synliggör matematiska resurser på ett mer medvetet sätt.</p> / <p>The aim with this degree project is to examine teaching and learning during a mathlesson characterized by traditional school mathematics. The method of the study was aparticipant observation of a mathematics lesson in year 3 in upper secondary school. Using the concepts of mathematical learning objects, mathematical resources, and pupil as an active learner in combination with socio-mathematical norms, I have interpreted the results generated from the observation. Two main conclusions can be drawn from the study. Firstly, pupils are encouraged to become independent as active learners in the teaching of traditional school mathematics. Secondly, it is primarily the teacher who makes potential mathematical resources visible and available for the pupils. With an increasing awareness of pupils’ use of mathematical resources, teachers can affect pupils’ learning by making potential mathematical resources explicit in a more conscious way.</p>