Submitted in fulfillment of the requirements of the Degree of Master of Technology: Language Practice, Durban University of Technology, 2011. / The abolition of apartheid in South Africa in the late 1980s and the advent of democracy in 1994 resulted in dramatic changes in the education system. Of great significance to this study is the freedom African parents were allowed in choosing the medium of instruction to be used at schools. Surprisingly African parents encouraged their children to study through the medium of English mainly due to the education and employment opportunities English will provide them in the future (Mda, 1997). Now, seventeen years into democracy, English as a national language and the preferred medium of instruction has been blamed for poor results among ESL learners (Moreosole, 1998). Taylor, Muller and Vinjevold (2003: 54) point out that the difficulties associated with studying in a language other than one’s home language are more pronounced in mathematics, a subject which is strongly dependent on technical language proficiency. A section in the Grade 8 mathematics syllabus that is generally problematic for ESL learners is that of word problems (Wetzel, 2008). This is because ESL learners lack the language and reading skills needed to comprehend word problems, and the listening skills required to understand the educator’s explanation of the solution (Crandall, Dale, Rhodes and Spanos, 1985). To address the aims and objectives of this study, relevant literature was reviewed and various teaching strategies were examined to determine which strategies may be most effective in helping ESL learners solve word problems. Grounded within the Constructivist Learning Theory, this study was based on Vygotsky’s zone of proximal development and Bruner’s concept of scaffolding. Using a mixed methods approach, this study investigated problems that mathematics educators and ESL learners experience in the teaching and learning of word problems through the medium of English, and also identified strategies that mathematics educators use to teach word problems to ESL learners. iv Analysis of the educator questionnaire and the focus group interviews with learners revealed that ESL learners are experiencing difficulty solving word problems in English and educators are, to a large extent, adapting their teaching strategies when teaching them. The data also indicated that groupwork was considered by the majority of educators to be the most suitable method in the teaching of word problems to ESL learners, but sadly this method was used less frequently compared to whole class discussion and individual work due to discipline problems, the educators’ inability to handle group dynamics and the tendency for learners not to contribute to the group discussion. The findings also suggest that it is necessary for the educator to use a variety of teaching strategies to ensure that ESL learners enjoy success in mathematics. Based on the findings, this study makes recommendations regarding the teaching and learning of word problems and the use of adapted teaching strategies to foster active participation in lessons and group discussions, thereby increasing learner confidence and aiding in the understanding of English terminology used in mathematics word problems.

TITLE: Word Problems in the First and Second Year of Primary School AUTHOR: Pavla Weinzettel DEPARTMENT: Departmement of Mathematics and Mathematical Education SUPERVISOR: PhDr. Michaela Kaslová ABSTRACT: This thesis focuses on word problems in maths books for Year One and Two of primary schools, published by Alter and Prodos. The objective is to analyse the word problems set out in these maths books and to classify them according to the following criteria: context, methods of solution, time management, and non- standard types of maths problems. A partial aim of the thesis is a comparison of the textbook word problem analysis and the analysis of those word problems which the students can create themselves. The conclusions of the work point out the importance of the teacher's role in maths teaching and learning. Teachers should use their judgement when using the published maths books and endeavour to expand on them, taking into consideration the above mentioned criteria in order to increase the students' eagerness to not only to solve the maths problems but also to understand as to why they solved them the way they did. The thesis recommends practical tools for teaching material evaluation and for assessing to what extent the students understand what the purpose of word problems is. KEYWORDS: word problem,...

Made available in DSpace on 2016-04-27T16:57:50Z (GMT). No. of bitstreams: 1 EDM - Vera Lucia da Silva.pdf: 1384460 bytes, checksum: 3234ebd8c11c96412594a6df13e184cf (MD5) Previous issue date: 2006-11-16 / Secretaria da Educação do Estado de São Paulo / This research is about a teaching project aiming at mastering abilities and concepts related to the solution of problems of Cartesian product. The selected population were students of 4th Grade from a State School in the eastern region of the city of São Paulo. Our reference is the G. Vergnaud Conceptual Fields Theory and we took in consideration theoretical elements from researchers interested in studying the multiplicative reasoning. Data were collected from continuous observation and evaluation of the students performance, from the analyses of the materials produced by them and from interviews. The activities were designed with the intent of establishing connections between adding and multiplying processes and the processes involved in the determination of all the pairs of the Cartesian product. These connections become evident when represented by means of spatial relations promoting the evolution of non-conventional representations, produced by the students, to conventional representations, in Cartesian graphics and tree diagrams. The major contributions of this research for understanding the cognitive operations involved in solving Cartesian product problems are the repertory of non-conventional processes, employed by the selected group of participants, and their justification, and the analyses of the phenomena that occur in the passage from one to the other of the different representations of the Cartesian product. This research also offers contribution for the training of elementary education teachers / Nesta pesquisa, desenvolvemos uma proposta de ensino voltada ao domínio de competências e conceitos, relativos à resolução de problemas de multiplicação cartesiana. A população selecionada foi constituída por alunos de uma classe de 4a série do Ensino Fundamental, de uma Escola Estadual localizada da zona leste do Estado de São Paulo. Tomamos como referência a Teoria dos Campos Conceituais, de G. Vergnaud, e consideramos elementos teóricos de pesquisadores que desenvolvem pesquisas sobre o pensamento multiplicativo. Os dados foram obtidos por meio de registro e avaliação contínua do comportamento dos alunos no desenvolvimento das atividades, da análise do material produzido por eles e de entrevistas, entre outros. No desenvolvimento das atividades, buscamos estabelecer conexões entre procedimentos aditivos e multiplicativos e os processos envolvidos na determinação de todos os pares do produto cartesiano. Essas conexões foram ressaltadas ao serem representadas por meio de relações espaciais, promovendo a evolução de representações não convencionais, produzidas pelos alunos, para representações convencionais, em gráficos cartesianos e de árvore . Como principais contribuições desta pesquisa para a compreensão das operações cognitivas envolvidas na resolução de problemas de produto cartesiano, ressalte-se: o levantamento de um repertório de procedimentos não convencionais empregados pela classe selecionada e suas justificativas, a análise de fenômenos ocorridos na passagem de uma para outra das diferentes representações do produto cartesiano. A pesquisa oferece, igualmente, contribuições para a formação de professores do ensino fundamental

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg. December 2014. / The National Curriculum and Assessment Policy Statement document (CAPS) (Department of Basic Education, 2012: 4) outlines some of the salient skills related to the modelling of word problems that Mathematics learners are expected to acquire during the course of their learning. One such critical skill is the learners' ability to represent and describe situations in algebraic language, formulae and expressions. In line with this broad objective, the present study investigated learners' linguistic knowledge and skills in translating from word to linear algebraic representations. Particularly focussing on errors learners made during the translation process, a class of 40 Grade 11 learners at one school in Gauteng West District were selected and given a written test on word problems. To gain access to learner misunderstandings leading to the observed errors and their sources, five learners were selected for interviews that were audio recorded. A Mixed-method Sequential Explanatory Design was used in the study. The major finding of this present study was that learners committed more semantic errors than syntactic and schematic errors suggesting that they (learners) had challenges in understanding the language used in the word problems. The major sources of semantic errors were found to be learners' lack of vocabulary knowledge, inexperience in interacting with expository text structures and their lack of syntax awareness. In addition to the above finding, learners exhibited limited metacognitive skills essential in word problem solving as well as their inability to reflect on the appropriateness of their written algebraic representations for all categories of word problems. The study concludes by providing recommendations on how errors committed in word problem solving can be attended to

Vi som har skrivit arbetet har haft olika erfarenheter kring läsning av matematiska textuppgifter. Intresset växte, då vi blev intresserade kring varför det kan vara svårt att läsa en matematisk text. Syftet med studien är att undersöka hur elevers läsförståelse binds samman med läsning av matematiska textuppgifter samt se vilka inre och yttre faktorer som påverkar förståelsen. Kvalitativa intervjuer tillsammans med en kombination av fallstudier och observationer ligger till grund för metoden som använts i studien. I undersökningen deltog 63 elever och fyra lärare. Totalt gjordes studien i fyra klasser, varav två klasser i årskurs 2 och två i årskurs 3. Resultatet visar att många elever blev oroliga över att se textuppgifterna. En del av eleverna visade ett engagemang för att klara uppgifterna, men uppgifternas struktur och nivå var allt för krävande för dem. Pedagogerna i intervjun är övertygade om att för lite kunskap kring ämnet och stress är bidragande orsaker till att matematikförståelsen hämmas vid läsning av matematiska textuppgifter. Slutsatsen är att det är svårt med läsning av matematiska textuppgifter, och elever bör besitta en större kognitiv förmåga samt ha ett brett ordförråd för att kunna förstå matematiska texter. Textens struktur spelar roll vid förståelse, och det är pedagogens ansvar att hjälpa eleverna med matematiska textuppgifter.

Specific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.

Title from first page of PDF document. Includes bibliographical references (p. 35-37).

The diploma thesis consists of two parts, the theoretic part and practical part. Theoretic part is focused on terms of unique mental dificiencies of learning and discalculation, ways and methods of solutions word problems. The aim of the practical part is finding influence of terms of unique mental dificiencies of learning on succesfull solution of word problems at students of basic school. The enclosure contains a few worksheets, which can be used to reeducation of difficuilties.

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))