Grade 4 mathematics teachers’ development of learners’ mathematical proficiency towards solving algebraic word problems

Abstract

The purpose of this qualitative case study was to explore Grade 4 mathematics teachers’ development of learners’ mathematical proficiency towards solving algebraic word problems. The purpose of the study was guided by two research questions: ‘What are Grade 4 learners’ challenges when solving algebraic word problems?’ and ‘How does a Grade 4 mathematics teacher develop learners’ mathematical proficiency towards solving algebraic word problems?’ This study was prompted by Grade 4 learners’ poor performance when solving algebraic word problems as outlined in the Annual National Assessments report (ANA) reflections on learners’ performance from grades 1–6 (Department of Basic Education, 2014). The reflection on ANA demonstrates that Grade 4 learners have poor understanding and little knowledge of solving algebraic word problems. This qualitative case study used convenience sampling to select participants who are conveniently available with regard to access and location (Lopez & Whitehead, 2013). The study sampled a Grade 4 mathematics teacher and 76 mathematics learners in Grade 4 classes (class A consisted of 41 learners and class B consisted of 38 learners). Classes A and B were taught by same teacher at the primary school where the data were collected. Data were collected by means of observation, written tasks and interviews. A Grade 4 mathematics teacher was observed when attempting to develop learners’ mathematical proficiency towards solving algebraic word problems. Written tasks were administered to Grade 4 mathematics learners to determine the challenges they faced when solving algebraic word problems. Interviews were conducted with the Grade 4 mathematics teacher and the Grade 4 mathematics learners. The Grade 4 mathematics teacher was interviewed to get an insight into how he develop learners’ mathematical proficiency, while Grade 4 mathematics learners where interviewed to find out on how they experienced the lessons and to identify the course of their challenges when solving algebraic word problems. Data were analysed using the three steps proposed by the Merriam (1998) case study, guided by Kilpatrick et al. (2001) theory of mathematical proficiency, which

is characterised by five strands, namely conceptual understanding, procedural fluency, strategic competency, adaptive reasoning and productive disposition. The steps followed were consolidating, reducing and interpreting data. Using content analysis as an analytic strategy, data collected from observations, learners’ written tasks and interviews were initially analysed separately, guided by the strands of mathematical proficiency indicators, and later reconciled the analysis using methodological triangulation. Quality criteria of the study were ensured using the four principles of Lincoln and Guba (1985) to ensure trustworthiness of the qualitative research, namely credibility, transferability, dependability and confirmability. Ethical consideration of the study was achieved by way of voluntary participation, informed consent, anonymity and confidentiality. The findings of the study reveal that in order for the teacher to develop learners’ mathematical proficiency toward solving algebraic word problems, teachers should have rich pedagogical content knowledge (PCK); be a reflective practitioner to reflect on the lesson they taught in the classroom before preparing for the new lesson and devise a new plan of delivering content knowledge; and incorporate discourse-based mathematics instruction within a learning-centred classroom to create an effective environment for learners to develop mathematical proficiency. The findings reveal that a learning-centred classroom incorporated with discourse-based mathematics instruction improved Grade 4 learners’ development of mathematical proficiency towards solving algebraic word problems. The study also revealed that Grade 4 mathematics learners still face great challenges when solving algebraic word problems as they appeared to lack the necessary mathematical vocabulary and conceptual understanding. It is therefore recommended that teachers should intensify discourse-based mathematics instruction within learning-centred classroom to improve Grade 4 mathematics learners’ development of mathematical proficiency towards solving algebraic word problems. It is also recommended that similar studies can be conducted using a sample of more than one mathematics teacher so as to get

the insights into how different teachers develop learners’ mathematical proficiency, and drawing on learners from different primary schools to identify other challenges that they may face when solving algebraic word problems.