Student test scores related to mathematical word problems have been declining in a rural school district in western Louisiana. Word problems constitute a major component of the Algebra 1 End of Course examination, which students must be able to pass to graduate. Mathematics teachers have struggled to find appropriate strategies to teach students to answer constructed response questions (CRQs) effectively. The purpose of this study was to investigate the perceptions of math teachers about effective teaching strategies for improving student performance on CRQs. Guided by Piaget's constructivist theory, which is characterized by an emphasis on learner control of the learning process through active engagement and activation of prior knowledge, this study investigated teachers' perceptions and practices in relation to teaching the skills needed for CRQs. The research questions focused on math teachers' perceptions of current teaching practices, instructional effectiveness, and professional development needs. A case study design was used to capture the insights of 8 participants through semistructured interviews and observations. Emergent themes were identified from the data through a code-recode approach, and findings were developed and validated through triangulation and member checking. The key results were that math teachers expressed a need to collaborate with their colleagues to develop effective strategies that would incorporate literacy and hands-on learning. A project was designed to engage teachers in collaboration and planning to prepare students to think critically and problem solve. This study may promote positive social change by providing teachers with the tools necessary to improve students' thinking skills, problem-solving skills, and learning strategies.

In this study, I investigate how successful provided response questions, such as multiple choice questions, are as an assessment format compared to the conventional constructed response questions. Based on the literature on mathematics assessment, I firstly identify an assessment taxonomy, consisting of seven mathematics assessment components, ordered by cognitive levels of difficulty and cognitive skills. I then develop a theoretical framework, for determining the quality of a question, with respect to three measuring criteria: discrimination index, confidence index and expert opinion. The theoretical framework forms the foundation against which I construct the Quality Index (QI) model for measuring how good a mathematics question is. The QI model gives a quantitative value to the quality of a question. I also give a visual representation of the quality of a question in terms of a radar plot. I illustrate the use of the QI model for quantifying the quality of mathematics questions in a particular undergraduate mathematics course, in both of the two assessment formats – provided response questions (PRQs) and constructed response questions (CRQs). I then determine which of the seven assessment components can best be assessed in the PRQ format and which can best be assessed in the CRQ format. In addition I also investigate student preferences between the two assessment formats. / Thesis (PhD)--University of Pretoria, 2009. / Mathematics and Applied Mathematics / unrestricted