This diploma thesis deals with the comparison of historical solutions of word problems with student solutions. Its aim was to describe how students solve historical word problems, while looking for analogies between student and historical solutions. This intention led me to a better understanding of student solutions. The theoretical part of the thesis describes important concepts for algebraic word problems, such as a variable, algebraic expression or algebraic word problem. In the historical part I describe chronologically the development of algebra from antiquity through the Middle Ages and the Renaissance to the Baroque. In each period, I mention important mathematicians of the time and present several solved word problems. In most cases, I analyze these solutions from the perspective of today's mathematics. The theoretical part describes the research that took place at the eight-year grammar school. As part of the research, I gave students 6 historical tasks across historical periods and then analyzed the ways in which students solved problems. I found that for most of the tasks, there were solutions similar to the historical solutions among the student's solutions. Some historical methods appeared very often. An example is the use of addition instead of multiplication, or division, as used by the...

Much research has been done showing the difficulty people have with word problems. This has been shown to be true for many types of word problems and for different demographics. Questions have remained unanswered regarding the reasons for this difficulty. It has been unclear if the word problems were hard because the people had forgotten or had not yet learned how to do the math calculations involved or for some other reason. This study deals with high school students who are currently in a high school level math class. They were given an assessment involving word problems and number-only problems. The results demonstrate that these students can do the math calculations needed for the problems but that the difficulty lies in their ability to formulate the word problems into correct mathematical expressions. Among the students in math classes higher than Secondary 2, it cannot be shown that those who have passed Financial Literacy demonstrate a significantly higher ability to do word problems with p > 0.05.

Arts-Across-the-Curriculum is gaining popularity in the field of education as arts programs are being cut from schools and teachers looks for ways to incorporate art in their classroom. Most of these teachers have minimal formal arts training, but recognize the importance of introducing their students to various fine arts disciplines. These educators seek opportunities to learn new ways to bring arts to their students and may bring teaching artists into their classrooms to teach students or teachers. The clear connection between drama and the core subjects of history and literature allow teaching artists to easily create units utilizing both curriculum areas. Mathematics does not present clear connections to drama and the prevalence of mathematics anxiety, especially in the arts, prevents connections from being made. As an educator, theatre artist and lover of mathematics, Arts-Across-the-Curriculum provides me a opportunity to meld these together as a way to help young people find excitement in their education. Partnering with a fourth grade teacher, I developed a unit of lesson plans using playwriting as a way to understand word problems that was user-friendly for a teacher with no arts training. The Dramath Unit was integrated into the class as part of regular curriculum taught by the participating classroom teacher. Based on feedback from the participating teacher, I revised the unit for future use.

Vi har genomfört en studie med en kvantitativ ansats, i syfte att undersöka hur elevers läsförståelse kan påverka deras resultat i de nationella proven i matematik. Detta görs för att bidra med kunskap till lärare om var det är mest nödvändigt att lägga ner tid för elevers kunskapsutveckling i matematik. Metoden som används i denna studie innefattar en analys av dokument som innehåller data som samlats in från drygt 200 elevers resultat i de nationella proven i svenska och matematik för året 2021/2022. Den data som samlades in bearbetades genom regressionsanalyser. Det statistiskt signifikanta resultatet i studien visar på en stark korrelation mellan elevers läsförståelse och deras prestation i de nationella matematikproven. Slutsatsen framhäver att det kan finnas olika förklaringar till varför resultatet ser ut som det gör, en av orsakerna skulle kunna vara att de nationella proven i matematik innehåller för många textuppgifter som gör att elevernas läsförståelse kan spela en alltför betydande roll. / We have conducted a study with a quantitative approach, aiming to investigate how students' reading comprehension might influence their performance in the national mathematics exams. This is done to contribute knowledge to teachers about where it is most crucial to allocate resources for student success in mathematics. The method employed in this study involves an analysis of documents containing data gathered from over 200 students' results in the national exams in Swedish and mathematics for the year 2021/2022. The collected data was processed through regression analyses. The statistically significant result in the study reveals a strong correlation between students' reading comprehension and their performance in the national mathematics exams. The conclusion highlights that there are different explanations for why the result appears as it does, one of which is that there may be too many word problems in the national mathematics exams, and students' reading comprehension might play an overly significant role.

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Syftet med studien är att synliggöra lärares erfarenheter av undervisningsutformning när de lär ut problemlösning genom blockmodellen på mellanstadiet. Tidigare forskning har visat att blockmodellen är en framgångsrik problemlösningsmetod med både för- och nackdelar. Studien anses relevant då det inte finns mycket forskning om blockmodellen i svenska sammanhang. För att samla in data användes individuella semistrukturerade intervjuer och materialet analyserades genom en tematisk analys. Fem lärare som är verksamma på mellanstadiet intervjuades med fokus på vilka hinder och anpassningar de erfarit i sin undervisning med blockmodellen. Studiens teoretiska utgångspunkt är sociokulturell teori med fokus på hur elever tar till sig kulturella redskap. Resultatet visar fyra teman som kunde identifieras i lärarnas utsagor. I resultatets två första teman hanteras hinder som lärarna beskriver i samband med problemlösningsundervisning med blockmodellen. I resultatets två sista teman hanteras anpassningar som lärarna beskriver i samband med problemlösningsundervisning med blockmodellen. Samtliga lärare har en positiv inställning till blockmodellen som problemlösningsmetod men de är överens om flera utmaningar som behöver hanteras när undervisningen med metoden utformas. / The purpose of this study is to make teachers’ experiences of instruction design when teaching problem solving with the bar model in middle school visible. Previous research has shown that the bar model is a successful method for mathematical problem solving with both pros and cons. The study is considered relevant since there has not been much research conducted on the bar model in Sweden. Individual semi-structured interviews were conducted in order to collect data which later was analysed through a thematic analysis. Five active middle school teachers were interviewed with focus on the obstacles they have experienced and the adaptations they have implemented while teaching with the bar model. The theoretical framework used in this study is sociocultural theory with focus directed at how pupils assimilate cultural tools. The result shows four themes that could be identified from the teachers’ responses. The teachers’ descriptions of obstacles connected to teaching using the bar model are compiled in the first two themes. In the two following themes teachers’ descriptions of adaptations are compiled. All the teachers share a positive attitude towards using the bar model when teaching mathematical problem solving. They are however in agreement about several challenges that needs to be handled when designing instruction for problem solving with the bar model.

The study explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)

The study explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)

In this study, the role of the problem-based approach on the performance of Grade 9 learners in solving word problems is investigated. Traditional approaches have produced learners whose performance in mathematics is not satisfactory and who are not sufficiently equipped with critical and problem skills that are necessary in this dynamic world. Problem-based approach is among the current reform efforts recommended for teaching and learning mathematics. For this approach to be successful, learners need vital tools such as problem solving strategies, which many learners in this country lack. The emphasis in this study was therefore on exposing learners to a variety of problem solving strategies through the problem-based approach. Problems solved throughout the investigation were non-routine, word problems. The results show that awareness of these strategies improves learners' problem solving performance and attitudes towards mathematics. Based on this investigation, recommendations are made concerning effective implementation of this approach to the teaching and learning of mathematics. / Educational Studies / Thesis (M. Ed. (Specialisation in Mathematical Education))