<p>I detta arbete har vi undersökt hur elever beskriver att ett laborativt arbetssätt i matematik påverkar deras lärande. Studien har utförts på ett studieförberedande och ett yrkesförberedande program på gymnasiet i klasser som läser kursen matematik A. Vi har använt oss av en enkätundersökning i båda klasserna och intervjuer med tre elever från respektive klass. Vårt resultat pekar på att det finns ett antal positiva faktorer som eleverna anser påverkar deras lärande vid ett laborativt arbetssätt i matematik. Dessa faktorer är att undervisningen blir rolig och intressant, varierad, verklighetsanknuten och leder till kommunikation mellan elever. Vi har även hittat ett fåtal negativa faktorer med ett laborativt arbetssätt i matematik. Det studieförberedande programmet påpekade tidsaspekten och det yrkesförberedande programmet framhöll att klassrumsmiljön blir stökigare. De flesta elever tyckte att en varierad undervisning är viktig och att ett laborativt arbetssätt är roligt. En slutsats av det är att ett laborativt arbetssätt kan leda till att elever känner sig mer motiverade att lära sig matematik. Våra slutsatser av undersökningen är att de positiva faktorer eleverna betonat inte endast beror på att arbetssättet var laborativt, utan det faktum att det inte var ett traditionellt arbetssätt.</p>

<p>The purpose of this study is to compare different ways to teach mathematics in the school's lower age groups, and to examine whether certain practices increase students' desire and motivation to learn the subject. The questions used to determine the purpose is the following:<strong> </strong></p><ul><li>What vision has the students in the class at maths? </li><li>How does the teaching of mathematics in the class look like?</li><li>What vision has the students in the class at working with different approaches in education?</li><li>Does the traditional approach  and the options that I am examining meet the steering documents requirements?<strong> </strong></li></ul><p><strong> </strong>The essay is organized as a qualitative study. The study was conducted in an elementary school in Sweden, third grade. The methods used included interviews with students and observations in the classroom. I have also completed three lessons in which I introduced students to three different approaches. Mathematics lessons that this third grade has, begins and ends with the students work individually with the math book. Is it possible to increase students' desire to mathematics by introducing different approaches? For example if the mathematic lesson is based on a mathematics contest, in which students work in groups to discuss and argue for solving various problems. When using different methods in mathematics does the students have the chance to find their way of learning, where the different approaches gives students the chance to examine the mathematics with different senses. All are individuals, and therefore have different ways to learn.<strong></strong></p>

During recent years, the trend of Swedish students’ negative performance and results in mathematics has been discussed. It is agreed that a change in teaching methods is necessary in order to solve this issue. Thus we found it interesting to take a closer look at an alternative way of teaching. The purpose of this study was to find out what teachers and students associate concrete mathematics with and make a comparison between them. A qualitative method based on interviews was used to reach the purpose. The data was analyzed and the result was that two groups took form: Knowledge and Game. Both teachers and students agree on the fact that concrete mathematics brings a positive variation into the classroom and motivates the students. Concrete mathematics also contributes with practicing, collaboration and discussions. The most distinctive difference between teachers and students’ associations is their view on knowledge. On one hand the teachers claimed that concrete mathematics contributes with better learning, but on the other hand the students claimed that they learn better or just as well by using workbooks in mathematics. The study also showed that students tended to see concrete mathematics as if it were a game. Based on this result we think that it is important that the teachers have a clear purpose with their teaching methods and make the students aware of their purpose. We claim that this is decisive in order to make the students feel that their activities are meaningful. / Svenska elevers försämrade resultat i matematik har under de senaste åren diskuterats. Ett förändrat arbetssätt i matematik anses ibland vara det som behövs för att vända denna negativa trend. Detta fick oss att vilja titta närmare på ett alternativt arbetssätt. Syftet med studien var att ta reda på vad lärare och elever på högstadiet associerar ett laborativt arbetssätt i matematik med, samt göra jämförelser mellan dessa associationer. För att kunna uppnå syftet genomfördes en kvalitativ undersökning i form av intervjuer. Intervjumaterialet analyserades sedan och de associationer som framkom delades in i två grupper, Lärande och lek. Både elever och lärare förknippar ett laborativt arbetssätt i matematik med att det leder till variation och ökad motivation. Arbetssättet bidrar, enligt lärarna även till att eleverna kan hjälpa varandra samt att de får träning i att samarbeta och diskutera. Den tydligaste skillnaden är att lärarna associerar ett laborativt arbetssätt som gynnsamt för lärandet, medan eleverna här menar att de lär sig lika bra eller bättre med läroboken. Studien visade även att ett laborativt arbetssätt ofta likställs med lek från elevernas sida. Utifrån detta finner vi det viktigt att lärarna har ett tydligt syfte med laborationerna, klargör syftet för eleverna, samt även följer upp genomförda laborationer. Detta för att undervisningen ska vara meningsfull och utvecklande för eleverna. Risken tror vi annars är att görandet hamnar i fokus på bekostnad av lärandet.

Syftet med detta arbete har varit att ta reda på elevers kunskaper om de geometriska begreppen dm3 och m2 samt hur lärarna undervisar i dessa avsnitt. Detta har vi tagit fram genom att först göra en litteraturstudie följt av intervjuer. Av litteraturen fick vi fram att laborativt arbete och materiel är essentiella delar i geometriundervisningen och har så varit under hela skolans historia. Det gäller att använda materielen på rätt sätt för att få ett bra resultat. Resultatdelen, med intervjuer, visade att elevernas kunskaper gällande begreppen är vaga och ofullständiga. Deras resultat var sämre än vad vi trodde med undantag för de starka eleverna. Lärarna ger underbetyg till sin egen undervisning när de misstänker att eleverna har en dålig uppfattning om begreppen. Lärarna uppvisar varierande grad av laborativt arbete som till största delen är tillfredsställande och de ställer sig till största delen positivt till att arbeta laborativt.

Det talas om den svenska skolan och matematik i olika sammanhang. Under senare år har det gjorts flera utvärderingar och studier som visar att elevers kunskaper inom matematikämnet har försämrats. Skolverket rapporterar också att lusten att läramatematik försämrats och att problematiken kanske ligger i undervisningens utformning. Syftet med denna studie är att belysa lärares intentioner kring arbete med laborativ matematik och lyfta fram deras tankar kring vad arbetssättet/angreppssättet kan innebära för elevers lärande. Jag kommer också att lyfta fram möjligheter och hinder som lärare upplever kring arbetssättet. För att besvara frågeställningarna har jag genomfört en kvalitativ, semi-strukturerad intervjustudie med fem lärare som undervisar i år 4-6 alternativt år 7-9. Resultatet från studien visar att laborativ matematik har positiv inverkan på elevers lärande. Det skapar engagemang, nyfikenhet och lust att lära matematik. Det framkommer också att lärare upplever att ett laborativt arbetssätt ger elever varaktiga kunskaper och värdefulla referenspunkter. Vidare beskrivs att lärare ser stora möjligheter med att arbeta laborativt. Resultaten visar exempelvis att lärarna upplever att de kan erbjuda elever en undervisning som utvecklar, utmanar och stimulerar. Att arbeta laborativt ger också möjligheter att visualisera och konkretisera matematiken, och det kan fungera som ett verktyg för att bygga broar mellan konkret och abstrakt. I resultatet beskrivs också faktorer som lärare upplever kan utgöra hinder eller begräsningar då man vill arbeta laborativt, såsom tid, ekonomi och svårigheter att hitta bra uppgifter. Sammantaget visar studien att lärare upplever laborativ matematik som en viktig del i undervisningen och som ett värdefullt verktyg för att skapa variation och ge alla elever en lustfylld och givande matematikundervisning.

Mathematics is a central topic in today's education debate, including discussion of its educational quality and various teaching methods. Today basically two different teaching methods are used; one is the textbook based method, with the book in focus and the other one the laboratory method by which teaching is performed through practical applications. The purpose of this study was to examine four primary school teachers' view of these two teaching methods by means of four relevant inquiries. By interviewing the four teachers, advantages and disadvantages were highlighted and the purpose was achieved. In order to support the analysis, two theories applied; the socio-cultural perspective and the cognitive perspective. The results of this study together with previous research disclosed advantages and disadvantages of both methods and none turned out to be better than the other. However, two aspects were prominent in the study;   time saving and   individual adaptation.   Time saving was considered a major advantage of textbook based instruction because it facilitates the work of teachers in planning lessons. In contrast, the laboratory approach was considered time consuming.  However, individual adaptation was considered to be more beneficial by the laboratory teaching method. Thus, it is important to be aware of that implementing individualized education also is time consuming, and teachers must ask themselves whether they have time to do or not to do this. Finally, it is central that teachers are aware of the two teaching methods, with their opportunities and constraints, and that the teachers consider this when choosing teaching method. Of course it is not necessary to select either method; it is also possible to mix both of them.

The purpose of this study is to compare different ways to teach mathematics in the school's lower age groups, and to examine whether certain practices increase students' desire and motivation to learn the subject. The questions used to determine the purpose is the following: What vision has the students in the class at maths? How does the teaching of mathematics in the class look like? What vision has the students in the class at working with different approaches in education? Does the traditional approach  and the options that I am examining meet the steering documents requirements?  The essay is organized as a qualitative study. The study was conducted in an elementary school in Sweden, third grade. The methods used included interviews with students and observations in the classroom. I have also completed three lessons in which I introduced students to three different approaches. Mathematics lessons that this third grade has, begins and ends with the students work individually with the math book. Is it possible to increase students' desire to mathematics by introducing different approaches? For example if the mathematic lesson is based on a mathematics contest, in which students work in groups to discuss and argue for solving various problems. When using different methods in mathematics does the students have the chance to find their way of learning, where the different approaches gives students the chance to examine the mathematics with different senses. All are individuals, and therefore have different ways to learn.

<p>During recent years, the trend of Swedish students’ negative performance and results in mathematics has been discussed. It is agreed that a change in teaching methods is necessary in order to solve this issue. Thus we found it interesting to take a closer look at an alternative way of teaching. The purpose of this study was to find out what teachers and students associate concrete mathematics with and make a comparison between them. A qualitative method based on interviews was used to reach the purpose. The data was analyzed and the result was that two groups took form: Knowledge and Game.</p><p>Both teachers and students agree on the fact that concrete mathematics brings a positive variation into the classroom and motivates the students. Concrete mathematics also contributes with practicing, collaboration and discussions. The most distinctive difference between teachers and students’ associations is their view on knowledge. On one hand the teachers claimed that concrete mathematics contributes with better learning, but on the other hand the students claimed that they learn better or just as well by using workbooks in mathematics. The study also showed that students tended to see concrete mathematics as if it were a game. Based on this result we think that it is important that the teachers have a clear purpose with their teaching methods and make the students aware of their purpose. We claim that this is decisive in order to make the students feel that their activities are meaningful.</p> / <p>Svenska elevers försämrade resultat i matematik har under de senaste åren diskuterats. Ett förändrat arbetssätt i matematik anses ibland vara det som behövs för att vända denna negativa trend. Detta fick oss att vilja titta närmare på ett alternativt arbetssätt. Syftet med studien var att ta reda på vad lärare och elever på högstadiet associerar ett laborativt arbetssätt i matematik med, samt göra jämförelser mellan dessa associationer. För att kunna uppnå syftet genomfördes en kvalitativ undersökning i form av intervjuer. Intervjumaterialet analyserades sedan och de associationer som framkom delades in i två grupper, Lärande och lek.</p><p>Både elever och lärare förknippar ett laborativt arbetssätt i matematik med att det leder till variation och ökad motivation. Arbetssättet bidrar, enligt lärarna även till att eleverna kan hjälpa varandra samt att de får träning i att samarbeta och diskutera. Den tydligaste skillnaden är att lärarna associerar ett laborativt arbetssätt som gynnsamt för lärandet, medan eleverna här menar att de lär sig lika bra eller bättre med läroboken. Studien visade även att ett laborativt arbetssätt ofta likställs med lek från elevernas sida. Utifrån detta finner vi det viktigt att lärarna har ett tydligt syfte med laborationerna, klargör syftet för eleverna, samt även följer upp genomförda laborationer. Detta för att undervisningen ska vara meningsfull och utvecklande för eleverna. Risken tror vi annars är att görandet hamnar i fokus på bekostnad av lärandet.</p>

For many years, I have tried to understand why students end up in difficulties in mathematics. As a future teacher, it is extremely important to have knowledge of the various factors that leads to difficulties in mathematics. As a teacher it is obvious to meet the students who find mathematics a difficult subject, and, therefore it is necessary to have a broader knowledge of how to respond and support these students. According to Ahlberg, number of students with mathematics difficulties is increasing every year, therefore, it is important to help students and organize a supporting school environment that promotes and encourages learning (Ahlberg 2001, p. 104-105). The aim of this degree project is find out, with the help of selected teachers, various factors that may lead to the basis for the students’ mathematics difficulties. The aim is also to find out how teachers work in order to support students with mathematics difficulties. I interviewed four trained mathematics teachers. All pedagogues have years of experience of teaching students with mathematics difficulties and all have had mathematics in their undergraduate studies. In my interviews, I used a tape recorder so that I could focus on questions, answers, and also be involved in as well as reflect over what was said. The results showed that there are various reasons for difficulties in mathematics and different ways of working to address student´s difficulties in mathematics. Mathematics difficulties can depend on emotional obstructions, a poor self-confidence, planning difficulties, a poor working memory, language difficulties, reading and writing difficulties and deficiencies in the didactical field. The result also showed that students’ difficulties can be reduced through dialogue, group works and a laboratory work.

There has been a lot of debate in media about mathematics teaching in grade school in Sweden. Many students experience that mathematics in grade school is abstract, which leads to decreased interest of mathematics in early years. An international study indicates that Swedish students in class 4 do not fulfill the mean for mathematics according to EU/OECD countries. The study also shows that Sweden practice a textbook driven education, compared to other countries. The aim for this study was to find out how a few pedagogues for class F-6 teach mathematics, and why they have chosen to educate the way they do. It was relevant to investigate if these pedagogues use a laboratory education method in their teaching, and if so, which profits and disadvantages they experience by using this method. I decided to use qualitative interviews, according to an interview guide, which agreed to the aim and the question form of the study. The empiric material that was collected from these interviews were analyzed and discussed with support from theories and earlier research, which I found relevant to this study. In the theoretical reference frame, I decided to use the most relevant of Piagets, Vygotskijs and Deweys views and thoughts of children’s knowledge, development and learning. The conclusion for this study is that all pedagogues used variation in their operation mode and in their mathematic education, where the textbook and a laboratory education are included.  Their choice of using a certain method is founded on the experience where many students think that mathematics is an abstract subject where all are different and learn mathematics in different ways. The pedagogues say that variation in operation mode where the students can participate in their learning at the same time as the mathematics makes visible, increases the condition for the students to understand mathematics. In the investigation, it was found that some of the pedagogues discovered a big student group alongside with few education hours that are reserved for mathematics, as a difficulty to use a laboratory working method in the spread they would like to.