An Exploration of Effective Pedagogical Practices for Mathematics Learning in the Nigerian Context

Abstract

<p>In recent years, mathematics teachers and educators in Nigeria and other countries have expressed concerns about the superficial teaching and low student achievements in mathematics, which hinder students from transferring mathematical knowledge to solve practical, real-life problems. One major cause of these problems is the pedagogical practices embraced by teachers in mathematics classrooms. Numerous studies have highlighted the importance of pedagogies connected to the van Hiele theory and the cognitive load in enhancing students' mathematical learning and, subsequently, their achievements. The pedagogies associated with the van Hiele theory and the cognitive load theory which this study focused on are the van Hiele teaching phases and the worked examples instruction respectively. The researcher explored and compared these two pedagogical approaches (the worked examples and the van Hiele teaching phases) to enhance students' learning and achievements in mathematics at the secondary education level. The exploration further considered how the pedagogical approaches contributed to students' retention of mathematical concepts, procedural understanding and conceptual mathematical understanding. </p> <p>The research included 157 first-year senior school students, aged 14 to 15, and two mathematics teachers from Nigeria. Data collected in the experimental phases (pre-testing, intervention, post-testing and delay testing) of this study were analysed utilising a qualitative approach based on the Structure of Observed Learning Outcomes (SOLO) model and quantitative statistics in accordance with the Rasch model and Statistical Package for Social Sciences (SPSS). The results of the investigation showed that there was a significant difference between the effectiveness of the van Hiele teaching phases and that of the worked examples strategy, in favour of the van Hiele teaching phases. The van Hiele teaching phases significantly enhanced students' mathematical knowledge acquisition and retention, and had significant positive effects on students of low and high mathematics abilities, and on both male and female students. Conversely, the worked examples significantly aided students' acquisition of mathematical understanding" however, the acquired understanding is not retained beyond three weeks. Furthermore, the worked examples instruction favours only the low-ability students, and students' gender has no influence on the main instructional effect.</p> <p>In terms of the procedural and conceptual understanding demonstrated by the students, the van Hiele teaching phases helped students to acquire more conceptual understanding than procedural understanding, whereas the worked examples strategy facilitated greater procedural understanding than conceptual understanding. Overall, the procedural and conceptual understanding acquired and retained by the van Hiele group is significantly greater than its worked examples strategy equivalent. These findings indicated that the van Hiele theory, which was originally designed for geometry could be applied to a different mathematical area. Lastly, the use of van Hiele teaching phases and an emphasis on conceptual understanding as opposed to the explicit instruction of worked examples is likely to lead to better and more sustained learning outcomes. Therefore, mathematics teachers should focus more on building conceptual understanding if deeper understanding of mathematical concepts, improved retention and greater transfer of mathematical knowledge are desired. </p>