A case study of selected Grade 7 learners using Argumentative Frames for solving word problems

Abstract

The absence of talk in the classroom shows a gap in the level of syntactic knowledge which relates most centrally to mathematical modes of inquiry and the kinds of practices that point towards the practices of Mathematics as a discipline. Issues of learners’ abilities of word problem-solving, abilities of sense making, the art of argumentation and discussion in mathematics classrooms emerged as issues of concerns too, and were explored in this study. This study sought to explore the use of argumentative writing frames (AWFs) in a case of G word problem-solving in Grade 7 classrooms, and how it influenced the learners’ academic performance in Mathematics. This study followed an interpretive mixed-method case study design. I sought to explore the case of learners’ utterances as they solved word problems in their natural setting (classroom). Within the mixed method approach, I also used a pre-test – intervention – post-test (PIP) making use of quantitative and qualitative data. The data collection strategies used in this study included tests experimental group [42]) and (comparison group [n=36], learners’ focus groups with the experimental group [n=11], and intervention (video and exercise books) with the experimental group in Montshiwa Township in the North-West Province. The study is methodically underpinned by the pragmatic paradigm that asserts the construction of knowledge and meaning from different perspectives (researchers and participants), multiple realities, and values attached to the study findings, participants’ utterances, and the use of triangulation, requiring interpretivist and positivist approaches. Data analyses were conducted in an integrated fashion where concurrent triangulation was followed. Data generated from pre- and post-tests, learners’ focus group interviews and the intervention suggest that the interventional strategy appeared to enhance talk (discussions and argumentation), to improve learners’ abilities to solve word problems as well as sense making in the experimental group where there was minimal talk before the intervention. Talk enabled learners to engage in effective discussion and argumentation during teaching and learning. The findings of this study also suggest that the experimental group performed better than the comparison group in the post-test. The experimental group demonstrated a tendency to include reality when solving multiplicative word problems in particular, and consequently improved sense-making abilities. The statistical analysis of Wilcoxon-Mann-Whitney test delineated statistical significance regarding the intervention: the experimental group (n=42), obtained a bigger median of 15.50 in the post-test from a median = 8, higher than the comparison (n=35) which obtained a median = 13 in the post-test from a median = 8 in the pre-test. The experimental group’s performance in the post-test of item 2.4 was higher (p=0.0100) as compared to the comparison group (p = 0.3613). In item 2.2, the experimental group had a higher performance as it managed to perform the same as the comparison group that earlier demonstrated a significant difference over the experimental performance. The mean of the experimental group (16.78571) and the comparison group was (14.91529) and the difference (1.87042) in favour of the experimental group in the post-test. The experimental group had an observed higher mean and median after the intervention. This implied that the intervention seemed to have favoured the experimental group. Analysis of learners’ interviews suggest that the use of AWFs improved the learners’ comprehension of language in word problems where they felt that teachers should also code-switch when teaching. Learners confirmed that the use of AWFs brought about success or improvement in their performance as far as word problem-solving and taking reality into consideration was concerned. This study has shown that issues of talk, (discussion and argumentation), word problem-solving and sense-making seem to be of utmost importance in the teaching and learning of multiplicative word problems in particular in mathematics classrooms. The reflection from the implementation of the intervention suggests that the use of AWFs yields somewhat positive benefits in the academic performance of a participating group. It is on this basis that any study that investigates on the influences of AWFs can have all types of word problems involved. In addition to this, the nature of the impact of the use of second language learning on learners’ academic performances in word problems should be studied within the contexts of using English as the primary language of learning and teaching in the majority of South African schools. The findings of the study strongly suggest using the AWFs in mathematics classrooms when any topic related to solving (multiplicative) word problems is taught. In doing so, there exists a likelihood of improved talk during the lessons, which may result in better learners’ academic performances in word problems generally. Both the quantitative and qualitative data analysed appeared to suggest that promoting more talk (discussion and argumentation) in the teaching and learning of multiplicative word problems influenced learners’ argumentation and problem-solving abilities and sense making. In addition, mathematics teachers may be equipped with an alternative pedagogy to employ when dealing with story problems in mathematics curricula, which may improve how word problems are dealt with in the classroom.