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Effects of a mathematics instructional sequence on the conceptual and procedural understanding of algebraic expressions for secondary students with mathematics difficulties
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Type
Thesis
Author
Leong, Swee Ling
Supervisor
Walker, Zachary
Cohen, Libby G.
Abstract
In this study, the researcher sought to determine the effects of an instructional sequence on the conceptual and procedural understanding of the manipulation of algebraic expressions of secondary students with mathematics difficulties (MD). The instruction sequence focused on bridging arithmetic to algebra with direct instruction of the arithmetic laws and algebraic laws in tandem. The instructional package comprised six lesson units on the properties of commutativity, associativity, and distributivity that were designed explicitly for the teaching of the manipulation of algebraic expressions. A multiple methods design was utilized with quantitative data from a single subject design to examine the effects of the explicit concrete-representational-abstract integration (CRA-I) instruction. A group design was used to compare the effects of the representational-abstract integration (RA-I) instruction with abstract (TI) instruction.
Three experiments were conducted within the study. Experiment 1 determined the reliability of the four parallel test forms used as indicators of student proficiency in the manipulation of algebraic expressions. The pretest, posttest, maintenance test, and follow-up test developed, contained 15 target problems on the evaluation and simplification of algebraic expressions. The four test forms were administered to 76 students in Secondary 2 and 3 normal streams, and were found to be reliable measures of the conceptual and procedural understanding of the manipulation of algebraic expressions of students with MD. Experiment 2 was a single subject multiple-probe across participants design that determined the effectiveness of CRA-I instruction for six participants of Secondary 2 normal stream. Results showed that all six participants improved their manipulation of algebraic expressions. Experiment 3 was a pretest-posttest comparison group design with random assignment of two groups of 14 students from Secondary 2 normal stream to treatment conditions RA-I versus TI instruction. Results of this study indicated that participants taught by RA-I instruction performed better than the TI group on posttest. Additionally, both RA-I and TI groups maintained their learning as indicated by positive results on maintenance and follow-up tests.
The results point to the potential of the intervention programme to identify MD in the manipulation of algebraic expressions. The study suggests that both the CRA-I instruction and RA-I instruction are effective in the teaching of the conceptual and procedural understanding of the manipulation of algebraic expressions. This raises the possibility of overcoming the three challenges of abstractness of algebra, the language of mathematical symbols, and characteristics of mathematics structures in learning of algebra concepts for secondary students with MD.
Three experiments were conducted within the study. Experiment 1 determined the reliability of the four parallel test forms used as indicators of student proficiency in the manipulation of algebraic expressions. The pretest, posttest, maintenance test, and follow-up test developed, contained 15 target problems on the evaluation and simplification of algebraic expressions. The four test forms were administered to 76 students in Secondary 2 and 3 normal streams, and were found to be reliable measures of the conceptual and procedural understanding of the manipulation of algebraic expressions of students with MD. Experiment 2 was a single subject multiple-probe across participants design that determined the effectiveness of CRA-I instruction for six participants of Secondary 2 normal stream. Results showed that all six participants improved their manipulation of algebraic expressions. Experiment 3 was a pretest-posttest comparison group design with random assignment of two groups of 14 students from Secondary 2 normal stream to treatment conditions RA-I versus TI instruction. Results of this study indicated that participants taught by RA-I instruction performed better than the TI group on posttest. Additionally, both RA-I and TI groups maintained their learning as indicated by positive results on maintenance and follow-up tests.
The results point to the potential of the intervention programme to identify MD in the manipulation of algebraic expressions. The study suggests that both the CRA-I instruction and RA-I instruction are effective in the teaching of the conceptual and procedural understanding of the manipulation of algebraic expressions. This raises the possibility of overcoming the three challenges of abstractness of algebra, the language of mathematical symbols, and characteristics of mathematics structures in learning of algebra concepts for secondary students with MD.
Date Issued
2015
Call Number
QA159 Leo
Date Submitted
2015