Abstract
This study attempted to develop a literature-informed discourse-based instructional approach and evaluated its effects on eleventh-grade students’ conceptual and procedural understandings in probability and statistics. To this end, a quasi-experimental study that involved two control groups and one experimental group was used. One-way analysis of variance of the baseline data showed that the three groups were comparable at the start of the experiment. After the intervention, the Kruskal-Wallis test analysis performed on the posttest data showed significant differences in conceptual understanding and procedural understanding. Pairwise comparisons of the three groups using Dunn’s test as post-hoc analysis showed that students who underwent discourse-based instruction demonstrated a better understanding of probability and statistics compared to those students who received traditional instruction. The analysis of survey data about students’ learning mathematics through discourse provided an insight into how the intervention strategy helped students improve their learning. Overall, the main finding of the study is that discourse-based instruction enables students to develop a better understanding of mathematical topics when appropriately orchestrated interactive discourse practices occur. The study contributes a discourse-based instructional design framework and empirical evidence to the field of knowledge of teaching approaches. The findings may motivate educators to examine students’ textbooks for mathematical discourse considerations. A possible recommendation for future research would be conducting longitudinal studies to explore the relations between students’ conceptual understanding and procedural understanding in a specific domain of mathematics and to examine how discourse-based instruction affects the relations between conceptual and procedural knowledge.
Highlights
Over the past three decades the teaching of mathematics for mathematical understanding continues to be among the major research focuses in mathematics education literature (Simon, 2016)
Summary and discussion of the findings Over the past two decades, a growing body of research literature in mathematics education has been consistently promoting the use of mathematical discourse as a powerful instructional approach for developing students’ understanding of mathematical topics and problem-solving capacity (Lampert & Blunk, 1998; Linell, 1998; Ryve, 2004; Sfard et al, 1998; Smith, 2018)
Discourse-based learning opportunities are thought to be powerful instructional strategies because they (a) promote active student learning based on interactive participation in disciplinary mathe matical discourse practices by allowing students to share and listen to each other’s ideas, compare and justify their solution methods, challenge one another’s reasoning, construct convincing argu ments, and reflect on and clarify their thinking, (b) provide meaningful contexts that nurture the culture of classroom participation, (c) create a supportive and inclusive learning environment for all students to construct knowledge by fostering interactive mathematical communications (Bell & Pape, 2012, 1996; Harbour & Denham, 2021; Lampert & Blunk, 1998; Steeley, 2017)
Summary
Over the past three decades the teaching of mathematics for mathematical understanding continues to be among the major research focuses in mathematics education literature (Simon, 2016). Researchers and curriculum designers have been constantly accentuating mathematical understanding to be the most desirable instructional goal (Haapasalo, 2003; Hiebert & Lefevre, 1986; Kadijevich, 2018; Rittle-Johnson & Schneider, 2015; Rittle-Johnson et al, 2015; RittleJohnson & Star, 2007; Simon, 2016; Star & Stylianides, 2013) Despite it is receiving a primary emphasis, studies showed that students’ poor performance in mathematics, an indica tion of lacking mathematical understanding and problem-solving skills, remains a concern to many countries (Cai, 2016; Johansson & Strietholt, 2019), which indicates the question of how mathe matics should be taught for developing students’ understanding concepts and procedures remains a major focus in educational research (Cruz & Antonio, 2008; Garfield, 1995; Li & Schoenfeld, 2019; Shaughnessy, 2007). All the literature evidence shows that researchers should continually look for alternative instructional methods that support the development of both conceptual and procedural understanding of mathematical topics (Rittle-Johnson & Schneider, 2015)
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