Date of Award

2013

Degree Type

Thesis

Degree Name

Doctor of Philosophy

School

School of Education

Faculty

Education and Arts

First Advisor

Dr Christine Ormond

Second Advisor

Professor Mark Hackling

Abstract

At both the junior and senior secondary school levels in Nigeria, student performance in mathematics examinations has been poor. Within the context of large classes, with inadequate facilities, and teaching and learning in a second language, algebra and algebra word problems are introduced to students during their first year of junior secondary school. The transition from primary school arithmetic to the use of the algebraic letter is challenging to students and it is important that teachers should know the likely difficulties and misconceptions students may have as they begin algebra (Welder, 2012).

In this study, the impact of a teacher professional learning program on teachers’ knowledge, beliefs and practice was examined. The impact on students’ ability to solve word problems in beginning algebra was also investigated. To do this, a multiple case study was designed and data were collected using quantitative and qualitative methods. Thirty teachers of first year junior secondary students completed a questionnaire and this provided general information about the teachers’ beliefs and algebra teaching practice. After this, 12 of the teachers actively participated and collaborated in a professional learning workshop designed as an intervention program. The program focused on enhancing the teachers’ knowledge of student misconceptions about variables, expressions and equations, and language-based teaching strategies. Four teachers and their classes, two each from public and private schools, served as case studies and provided further data about the impact of the intervention program. Before and after the intervention program, lessons were observed, students completed algebra tests and some of them were interviewed using the Newman interview protocol. The data for each case study were analysed and the key findings generated from each of them were used for a cross-case analysis.

The study revealed that these Nigerian teachers had mainly traditional beliefs about mathematics teaching and that teacher-talk dominated the classroom practice. Prior to the intervention, the teachers had limited knowledge of students’ algebra misconceptions and the students’ main difficulty was that they did not understand the questions. The professional learning increased the teachers’ knowledge of algebra, their pedagogical content knowledge and their awareness of algebra misconceptions. The teachers used more student-centred and language-based teaching strategies when working on algebra problems. There was a significant improvement in students’ problem-solving success on the post-test because more students were able to understand the word problems and displayed fewer misconceptions. The incidences of ignoring the algebraic letter, believing that the algebraic letters cannot have the same value and confusing product and sum reduced. However, the use of the letter as an object or a label and a belief that the algebraic letter had alphabetical positioning persisted.

The study demonstrated the effectiveness of the professional learning model used in this study and it should be considered for more widespread implementation with in-service teachers. There is also an implication for pre-service teacher education. Mathematics education programs should ensure that student teachers are aware of common algebra misconceptions and the language-based strategies needed to support school students’ transition from arithmetic to algebra.

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