Teachers’ Perceptions & Practices of Teaching Math Through Problem Solving in Senior High School
Teachers’ Perceptions & Practices of Teaching Mathematics Through Problem Solving in the Senior High School
Student Information
Student Name: Elvis Owusu
Student Number: 8110110016
Course Name: MPhil Mathematics Education
Department: Mathematics
Supervisor: Dr. M.J. Nabie
Chapter 1: Introduction
Overview
This chapter provides context for the study, outlining the background, problem statement, purpose, significance, research questions, delimitations, and limitations.
Background of the Study
Mathematics is a cornerstone of the Ghanaian pre-university education system. Recognizing its importance, various governmental initiatives have aimed to enhance mathematics education quality. These include the 2003 teacher education curriculum review, which upgraded teacher training colleges to diploma-awarding institutions, and collaborations with international agencies like JICA, USAID, and DFID on mathematics projects. The 2007 educational reforms further emphasized skill development, creativity, inquiry, and problem-solving in the senior high school (SHS) mathematics curriculum.
Despite these efforts, challenges persist in students’ ability to solve non-routine problems, as evidenced by the West African Examination Council (WAEC) chief examiners’ reports. This underscores the need to investigate teachers’ perceptions and practices regarding problem-solving as a pedagogical approach.
Problem Statement
While research suggests a positive correlation between relatable, real-life mathematics instruction and student performance, Ghanaian students often struggle with practical and non-routine problems. This difficulty may stem from teachers’ perceptions and practices related to problem-solving. Understanding these perceptions and practices is crucial for improving mathematics instruction and student outcomes.
Purpose of the Study
This study aims to explore the perceptions of mathematics teachers in Ghanaian SHS regarding teaching mathematics through problem-solving. It will investigate how these perceptions influence their teaching practices and contribute to students’ ability to solve non-routine mathematical problems.
Objectives of the Study
The study’s objectives are to explore SHS mathematics teachers’:
- General perceptions of teaching through problem-solving
- Factors that may affect problem-solving
- Role in teaching through problem-solving
- Influence on students’ performance in mathematics
- Ability to teach through problem-solving
Research Questions
This study seeks to answer the following questions:
- What are the general perceptions of teachers on teaching mathematics through problem-solving?
- What practices affect teaching mathematics through problem-solving?
- What differences exist between teaching mathematics through problem-solving and without problem-solving?
- To what extent do teachers’ perceptions of teaching through problem-solving influence their practices of teaching mathematics?
Significance of the Study
This study will contribute to the understanding of mathematics teaching and learning, inform further research, and provide insights for policymakers and educational planners. It will shed light on teachers’ perceptions of problem-solving and its potential to improve student performance in mathematics.
Delimitations
This research will focus on SHS mathematics teachers in the Greater Accra Region of Ghana, specifically within the Accra Metropolis. The study will involve approximately 100 SHS and 40-item questionnaires will be distributed to teachers.
Limitations of the Study
The study’s geographical focus on urban schools in the Greater Accra Region may limit the generalizability of findings. The mixed research design may also present challenges in data analysis and interpretation.
Chapter 2: Literature Review
Overview
This chapter examines the theoretical framework of the study and reviews existing literature on problem-solving techniques in teaching mathematics. It also includes a critique of related work.
Theoretical Framework
This study draws upon the theoretical framework of constructivism in mathematics teaching and learning, emphasizing the active role of the learner in constructing knowledge through problem-solving experiences.
Problem Solving as a Context, Skill, and Art
The literature highlights three key themes related to problem-solving in mathematics education:
- Problem Solving as Context (PSC): Using real-world problems to motivate and engage students in learning mathematical concepts.
- Problem Solving as Skill (PSS): Teaching specific problem-solving skills and strategies as a separate topic in the curriculum.
- Problem Solving as Art (PSA): Developing students’ abilities to become independent and creative problem solvers.
Constructivism in Mathematics Teaching and Learning
Constructivism emphasizes the importance of active learning and the construction of knowledge through experience. Problem-solving is seen as a key component of constructivist pedagogy.
Teachers’ Perceptions in Quality Mathematics Teaching and Learning
Research on teachers’ perceptions highlights the influence of beliefs and attitudes on teaching practices. Studies have explored teachers’ perceptions of curriculum reforms, students’ cognitive-metacognitive skills, and the use of problem-solving approaches.
A Problem-Solving Approach in Teaching and Learning of Mathematics
The literature advocates for a problem-solving approach that emphasizes relating, experiencing, applying, cooperating, and transferring (REACT) knowledge in meaningful contexts.
Factors Inhibiting Quality Mathematics Teaching
Factors such as inadequate teacher training, lack of support, and a focus on low-level skills can hinder the quality of mathematics instruction.
A Brief Critique of a Related Work
This section critiques a study that argues against inquiry and problem-solving teaching methods, highlighting the importance of guidance and support for novice learners.
Chapter 3: Methodology
Overview
This chapter outlines the research design, population and sample, data collection instruments, procedures, and analytical methods used in the study.
Research Design
This study employs a mixed research method, combining quantitative and qualitative data collection and analysis techniques.
Population and Sample
The target population consists of all mathematics teachers in SHS in the Accra Metropolitan District of Education. A sample of 100 teachers from 20 selected schools will be used.
Data Collection
Data will be collected through questionnaires, interviews, and observations.
Analytical Methods
Quantitative data will be analyzed using statistical procedures such as t-tests, ANOVA, and cross-tabulation. Qualitative data will be analyzed through coding and thematic analysis.
Instrumentation
The study will utilize questionnaires, interviews, and observation checklists.
Validity and Reliability of Instruments
The instruments will be reviewed by experts and piloted to ensure validity and reliability.
Trustworthiness
The study will employ strategies to ensure credibility and dependability, including triangulation of data sources and member checking.
Procedures
This section outlines the steps involved in data collection, analysis, and reporting.
Summary
This chapter provides a comprehensive overview of the methodology used in the study.
References
This section lists the references cited in the study.
Appendices
This section includes the questionnaire, interview questions, and observation checklist used in the study.