An exploratory study of Grade 8 Albanian students' solution processes in mathemathics word problems
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This dissertation is a case study, which set out to explore Grade 8 Albanian students‟ difficulties in mathematics word problems‟ solution processes. In particular the present study explores the role of two factors, these being the context in which the problem statement is framed, and the provision of ready-made diagram that represent the components of the problem statement and the relation between them. To identify students‟ difficulties on word problems, I used Duval‟s (2006) cognitive approach. In Duval‟s (2006) theory, conversion between different registers and treatment within the same register are considered as two types of cognitive processes (mathematical transformations) that are independent sources of incomprehension in mathematics learning. The research questions addressed are: 1. What evidence of Grade 8 Albanian students‟ conversions and / or treatments is exposed in their solution of mathematical word problems? 1.1 What is the evidence of influence of the inclusion of problem statements in abstract or real world context on students‟ solutions? 1.2 What is the evidence of influence of the inclusion (or omission) of a diagram in problem statements on students‟ solutions? 2. What are the students‟ opinions about the test and their performance? Four different methods including participant observation, a pencil and paper test with word problems, a questionnaire about the test and students‟ performance, and task based interviews are combined to collect data from students‟ engagement with word problems. The results of the study confirm that students have difficulties to solve word problems. The majority of students‟ errors arise in the conversion processes, nevertheless a considerable part of students‟ errors also arise in the treatment processes. Thus, showing that both cognitive processes (conversion and treatment) are sources of difficulty in mathematics word problem‟ solution processes. Furthermore, consistent with Duval‟s (2004, 2006) explanation, the cognitive processes of conversion appear to be the more complex and difficult processes for students. The students‟ responses to both real world and abstract context word problems exposed that problem statement context appeared to have little difference on their performance. Whereas, the students‟ responses to both word problems with and without ready-made diagrams exposed some difference in their performance that might arise from the provision of a diagram. Several possible explanations for the reported results are discussed. The study suggests that students will benefit from instruction in the use of information provided in word problem statements.
Masteroppgave i matematikkdidaktikk- Universitetet i Agder, 2012