Effects of manipulatives on the learning of algebra

Teck, Wee Kim (2012) Effects of manipulatives on the learning of algebra. PhD thesis, Universiti Malaysia Sarawak.

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Abstract

This study aimed to investigate the effects of using manipulatives on students' algebraic achievement, attitudes toward algebra, manipulatives preferences and conceptual understanding of algebra in Malaysian secondary schools. This research employed a non-equivalent quasi-experimental pretest-posttest design. A total of 207 form four arts stream students from three secondary schools in Kuching and Samarahan divisions participated in the study The students learned quadratic expansion and factorization using either virtual manipulatives (treatment group) or physical manipulatives (control group) as the instructional method. The virtual manipulatives were developed using Dreamweaver and Java applet based on the guidelines from past studies such as Durmus and Karakirik (2006) and Moyer, Bolyard, and Spikell (2002). The data collection in each school was conducted over a two-week time period during regular school hours. For the first session involving quadratic expansion, group one worked with physical algebra tiles while group two worked with virtual algebra tiles. For the second session involving quadratic factorization, group one worked with virtual algebra tiles and group two worked with physical algebra tiles. Several research instruments were used to collect the required data in this study. The quadratic expansion and factorization pretests and posttests were used to measure the impact of physical and virtual manipulatives on students' algebraic achievement. Kolb's learning style inventory was used to establish the students' learning style preferences. The manipulative preferences questionnaires were used to identify students' manipulatives preferences. The attitude inventory was used to measure students' attitudes toward algebra. Lastly, the conceptual understanding task sheets were used to measure the impact on students' conceptual understanding of algebra. In addition, another 15 students were purposively selected for semi-structured interviews based on the conceptual task sheets. Statistical analyses revealed that students showed progress in algebraic achievement in both instructional methods with virtual manipulatives having more positive impact than physical manipulatives for students with concrete learning style. The analysis also showed that female students performed better than male students when physical manipulatives was used as the instructional method. When the groups were examined for attitudes toward algebra, both instructional methods were equally effective in improving students' attitudes toward algebra. However, the results also showed that male students exhibited more positive attitudes than female students in motivation and enjoyment toward learning algebra. Further result indicated no statistical significant differences in students' preferences toward manipulatives. Finally, analysis showed that physical manipulative and virtual manipulatives performed equally well in promoting students' conceptual understanding of algebra. The findings of this study indicated that the three stages of Bruner's learning theory; enactive, iconic and symbolic could be implemented using virtual manipulatives as the instructional method to promote students' conceptual understanding of algebra. The study showed that secondary school students also benefited from using virtual manipulatives. In general, these findings on virtual manipulatives concurred and supported past findings on positive impact of virtual manipulatives in the learning of mathematics such as studies by Reimer and Moyer (2005), Smith (2006), and Suh (2005). It was recommended that teachers should use more virtual manipulatives in classrooms to promote conceptual learning. Hence, the Ministry of Education should recommend policies that include the use of virtual manipulatives in the teaching of mathematics by providing support such as in-house training for teachers and develop more software on virtual manipulatives. Further research could be carried out to extend the findings of this study by allowing more time for treatment, using larger sample size other than form four arts classes, investigating wider mathematics contents besides algebra, and by comparing the effectiveness between two and more virtual manipulatives to further illuminate greater understanding of the effect of virtual manipulatives on students' conceptual learning.

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