This action research study examined the influence mathematical strategies had on middle school students' mathematical ability. The purpose of this action research study was to observe students mathematical abilities and to investigate whether teaching students problem-solving strategies in mathematics will enhance student's mathematical thinking and their ability to comprehend and solve word problems. The study took place in an urban school in Orlando, Florida in the fall of 2004. The subjects will be 12 eighth grade students assigned to my intensive math class. Quantitative data was collected. Students' took a pre and post test designed to measure and give students practice on mathematical skills. Students worked individually on practice problems, answered questions daily in their problem solving notebook and mathematics journals. Results showed the effectiveness of the use of direct instruction and problem-solving strategies on at-risk students.

När elever står inför uppgifter inom problemlösning är det ett flertal steg som eleven ska ta sig igenom: Förstå uppgiften, göra någon form av plan, sedan genomföra planen och i bästa fall även gå tillbaka till uppgiften och reflektera över lösning och svar. Syftet med studien var att undersöka och belysa lösningsstrategier inom problemlösning ur ett elevperspektiv. För att besvara syftet har en kvalitativ ansats varit till grund för studien, som bestod av två datainsamlingar: ett elevtest och efterföljande gruppintervjuer. Resultatet för den första datainsamlingen analyserades med ett begreppsligt ramverk som definierar och begreppsliggör lösningsstrategier. Det visade att eleverna till stor del valde mellan algebraisk lösning och blockmodellen. Elevperspektivet har belysts genom att elever efter ett genomfört test ombetts reflektera gällande deras val av lösningsstrategi. Intervjuerna analyserades utifrån en induktiv ansats där data tematiserades och påvisade fem centrala motiveringar till att elever väljer de strategier de väljer. Dessa var: enkelhet att tolka, tid spenderad på varje uppgift, erfarenhet och självförtroende, uppgiftens karaktär och lärarens undervisning. / When students face tasks in problem-solving, there are several steps they need to go through: understanding the task, devising some form of plan, executing the plan, and ideally, revisiting the task to reflect on the solution and answer. The purpose of the study was to investigate and illuminate problem-solving strategies from a student perspective. To address this purpose, a qualitative approach was employed, consisting of two data collection phases: a student test followed by group interviews. The results of the initial data collection were analyzed using a conceptual framework that defines and elucidates problem-solving strategies. It was found that students largely chose between algebraic solutions and block modeling. The student perspective was illuminated by having students reflect on their choice of solution strategy after completing the test. The interviews were analyzed using an inductive approach where data were themed, revealing six central motivations for why students choose the strategies they do. These were: simplicity of interpretation, time spent on each task, experience and self-confidence, the nature of the task, and teacher instruction.

När elever står inför uppgifter inom problemlösning är det ett flertal steg som eleven ska ta sig igenom: Förstå uppgiften, göra någon form av plan, sedan genomföra planen och i bästa fall även gå tillbaka till uppgiften och reflektera över lösning och svar. Syftet med studien var att undersöka och belysa lösningsstrategier inom problemlösning ur ett elevperspektiv. För att besvara syftet har en kvalitativ ansats varit till grund för studien, som bestod av två datainsamlingar: ett elevtest och efterföljande gruppintervjuer. Resultatet för den första datainsamlingen analyserades med ett begreppsligt ramverk som definierar och begreppsliggör lösningsstrategier. Det visade att eleverna till stor del valde mellan algebraisk lösning och blockmodellen. Elevperspektivet har belysts genom att elever efter ett genomfört test ombetts reflektera gällande deras val av lösningsstrategi. Intervjuerna analyserades utifrån en induktiv ansats där data tematiserades och påvisade fem centrala motiveringar till att elever väljer de strategier de väljer. Dessa var: enkelhet att tolka, tid spenderad på varje uppgift, erfarenhet och självförtroende, uppgiftens karaktär och lärarens undervisning. / When students face tasks in problem-solving, there are several steps they need to go through: understanding the task, devising some form of plan, executing the plan, and ideally, revisiting the task to reflect on the solution and answer. The purpose of the study was to investigate and illuminate problem-solving strategies from a student perspective. To address this purpose, a qualitative approach was employed, consisting of two data collection phases: a student test followed by group interviews. The results of the initial data collection were analyzed using a conceptual framework that defines and elucidates problem-solving strategies. It was found that students largely chose between algebraic solutions and block modeling. The student perspective was illuminated by having students reflect on their choice of solution strategy after completing the test. The interviews were analyzed using an inductive approach where data were themed, revealing six central motivations for why students choose the strategies they do. These were: simplicity of interpretation, time spent on each task, experience and self-confidence, the nature of the task, and teacher instruction.

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))

TITLE: The influence of the order of information in word problems on their difficulty for lower secondary pupils AUTHOR: Bc. David Hennlich DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: doc. RNDr. Naďa Vondrová, Ph.D. ABSTRACT: Research has shown an influence of various parameters of word problems on their success rate and solving strategies that are used by pupils. In case of the order of information variable, most of research has focused on word problems, in which the order of information corresponds, or not, with the order of events described in the problem statement. This thesis differs from them by aiming at word problems without the sequence of this kind in their situational models. Two sets of problems solved by ninth grade pupils of four secondary schools situated in Prague were analysed. In order to recognize the influence of the analysed parameter, the combination of qualitative and quantitative approach was used. Item Response Theory (IRT) was used to analyse the parameter from the quantitative point of view. The written solutions of pupils were also analysed in a qualitative way and later amended by additional interviews with pupils. No influence of the parameter was found on either success rate or solving strategies in any of the analysed word problems. There was...

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))

The major purpose of this study was to investigate the effects of using animal organ dissection in general, and its use specifically in problem-solving as a teaching strategy in Grade 11 Life Sciences education. A multiple methods research design was used for this study. The data collection methods for the quantitative approach were the pre-test, post-test and a questionnaire. The pre-test and post-test had predominantly problem-solving questions. The questionnaire and the tests were administered to 224 learners from four Pretoria East secondary schools from different environments. The data collection methods for the qualitative approach were the interviews with the Grade 11 Life Sciences teachers of the selected schools, lesson observations and relevant document analysis. The interviews were conducted with six Grade 11 Life Sciences teachers teaching at the four selected schools. Findings from both the quantitative and the qualitative approaches were integrated to give an in-depth understanding of the study. The findings show that there were significant differences between the means of the pre-test and the post-test for the total for the whole group of 224 learners. The variables in which the tests were categorised were the rote learning, problem-solving and three learning outcomes of the National Curriculum Statement (NCS). The way in which the learners answered the questions in terms of terminology they used, the confidence they displayed, the level of answering and the explanations they gave when they wrote the post-test were significantly different from when they wrote the pre-test. The significant differences between the means of the pre-test and the post-test may possibly have been due to the intervention. This showed the effectiveness of the intervention which was animal organ dissection in problem-solving. The study also showed that most teachers are not well-acquainted with problem-solving strategies which made it challenging for them to use animal organ dissections to develop problem-solving skills in learners. The attitudes of the teachers and learners towards animal organ dissection and its use in problem-solving as a teaching strategy were predominantly positive with less than a quarter of the whole group being negative due to a variety of reasons which include: moral values, religion, culture, blood phobia, squeamishness and being vegetarian. The majority of learners acknowledged the importance of animal organ dissections in developing skills like investigative, dissecting and problem-solving skills. This acknowledgement resulted in them being positive towards the use of animal organ dissections in problem-solving. One can conclude that animal organ dissections can be used in problem-solving as a teaching strategy in Life Sciences education. The level of learner engagement with animal organ dissections can determine the level of development of problem-solving skills as was evidenced by the differences between the mean scores of the four schools. The study recommended that the teachers should be encouraged to use animal organ dissections more frequently where it is applicable to develop problem-solving skills in learners and not merely let the learners cut, draw and label the organ. Teachers should also focus on problem-solving in general and develop this as a prime strategy. All activities should be prepared by the teacher and implemented in class to encourage and develop problem-solving skills. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Science, Mathematics and Technology Education / restricted

In the thesis, results of a research focused on monitoring strategies used by students during problem solving are presented. It follows previous studies conducted with the use of think- aloud method. Due to limitations of this method, an eye-camera is used. The record of the camera is used not only to analyse student's problem-solving process, but also as a tool eliminating one of the RTA limits - inaccuracies due to forgetting. The strategies were investigated among economics-oriented vocational school students in the first grade. They solved indicator tasks from the Methodical Comments and Tasks for Educational Standards in Lower-Secondary Education. The research sample was selected based on a pre-test composed of the selected tasks. According to the results, the students were divided into four categories, two students of each category were selected for the research. They solved a second set of the tasks. Based on eye-tracking and think-aloud data, their problem- solving processes were mapped and false-positive results were eliminated. The research results show that the students used the most expansive strategies, mainly work with the periodical table. However, in most cases, these strategies did not lead to a correct solution, due to the students' problems during solving. In these cases, they...

Syftet med studien är att bidra med kunskap om hur sju elever i årskurs tre löser matematiska problem och varför de väljer att göra så. Syftet uppfylls genom tre frågeställningar som berör vilka strategier eleverna använder, hur den valda strateginanvänds och vad som påverkat elevernas val av strategi. Metoden som använts för att samla in data är semistrukturerade intervjuer, eleverna har vidare fått lösa matematiska problem i samband med en aktiv observation. Den data som samlades in klassificerades utefter Lesters (1988) syn på problemlösningsstrategier. Vidare skapades kategorier utifrån vad som påverkade elevernas val av strategi utefter den insamlade datan. I analysarbetet identifierades fyra strategier, gissa och pröva, rita en bild, ekvationer och tabeller. Eleverna visade på olika nivåer av strukturerat och systematiskt arbete och olika sätt att använda strategierna på har identifierats. Undervisning, lärare och syskon är vad som framkom som påverkansfaktorer på elevernas val av strategi. I den avslutande diskussionen lyfts bland annat hur eleverna använt sig av strategierna på olika sätt. / The purpose of the study is to contribute knowledge about how seven students in yearthree solve mathematical problems and why they choose to do so. The purpose is fulfilled through three questions that concern which strategies the students use, how the chosen strategy is used and what influenced the students' choice of strategy. The method used to collect data is semi-structured interviews, the students have also solved mathematical problems in connection with an active observation. The collected data were classified according to Lester's (1988) view of problem-solving strategies. Furthermore, categories were created based on what influenced the students' choice of strategy based on the collected data. In the analysis work, four strategies were identified, guess and try, draw a picture, equations and tables. The students showed different levels of structured and systematic work and different ways of using the strategies have been identified. Teaching, teachers and siblings are what emerged as influencing factors on the students' choice of strategy. In the concluding discussion, it is highlighted, among other things, how the students have used the strategies in different ways.

Syftet med den här kunskapsöversikten är att undersöka vikten av kreativt tänkande, dess relation till problemlösningsförmågan och den relationella förståelsen. Problemlösningsförmågan är en förmåga som understryks i läroplanen för matematik årskurs 4-6, därmed undersöker vi relationen mellan det kreativa tänkandet och problemlösningsförmågan. Undersökningen har gjorts genom att initialt skapa tre frågeställningar och därefter söka data från olika peer-reviewed forskningsartiklar på engelska mellan årtalen 2019–2023 från databaser som ERC, JSTOR, ERIC från olika delar av världen. Forskningen har granskats och sammanställts för att ge svar på frågeställningarna. Under den systematiska sökningsprocessen har vi stött på nya begrepp som open ended och heuristik som visat sig ha en nära relation till problemlösningsförmågan samt det kreativa tänkandet. Utöver det har Skemps lärandeteorier om instrumentell och relationell förståelse satt grunden för vår systematiska sökprocess. Resultatet påvisar att det kreativa tänkandet utvecklas efter arbete med problemlösningsförmågan samt öppna frågor. Det kreativa tänkandet kan i sin tur relateras till en relationell förståelse. De empiriska studierna påvisar att lärare brister i sin kunskap om hur man kan utforma matematiska problem som utvecklar ett kreativt tänkande hos eleverna. De valda empiriska studierna är genomförda i utlandet och Sverige skulle dra nytta av liknande forskning för att stötta pedagogerna i elevernas utveckling mot ett kreativt tänkande som står emot den snabbt utvecklande värld som väntar efter avslutad skolgång.