Academic journal article International Education Studies

A Study of Improving Eighth Graders' Learning Deficiency in Algebra by Applying a Realistic Context Instructional Design

Academic journal article International Education Studies

A Study of Improving Eighth Graders' Learning Deficiency in Algebra by Applying a Realistic Context Instructional Design

Article excerpt


The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts. Therefore, this study aimed to explore how the "realistic context" instructional design influenced 8th graders' performance on algebraic grade skipping learning of "linear programming". A quasi-experimental design with a post-test was employed in this study. Samples were selected purposely from thirty-six 8th graders of a junior high school as the Experimental Group, while seventy-nine 12th graders of a senior high school were chosen as the Control Group. Data were mainly gathered by the linear programming achievement test after executing the instruction. Statistical analyses were performed to answer the research question. Findings indicated that there was no significant difference between 8th graders (Experiment) and 12th graders (Control) on the performance of the linear programming achievement test. This result indicated that the instructional material with a realistic context design used in this study did help students to learn the abstract algebra effectively.

Keywords: algebra learning, realistic context, instructional design, eighth grader, linear programming

1. Introduction

1.1 Background and Theoretical Framework

In the highly civilized world of 21st century, mathematical knowledge and abilities became basic requirements in our daily lives and careers (Lin, 2003; Polya, 1945; Romberg, 2001). In our daily lives, we actually used the most popular mathematic ideas and theories, not even recognizing that we were living with mathematics. The more one knew about mathematics, the broader one may develop in his career life (Stein, 1999). However, mathematic educators reviewed mathematical teaching materials used in the past and found that they were designed with an emphasis on mathematician and adult thinking approaches. In addition, the instruction emphasized heavily on abstract mathematical symbols and the training of calculation skills (Huang, 2003). The de-conceptualized, de-experienced thinking of the materials also ignored the cognitive principles and the processes of discovering the truth. Since mathematic teachers overvalued symbolic calculations and proofs as well as answers for mathematical questions, students may naturally sense that mathematics was disconnected with real-life situations; and then they may form the habit of insisting more on calculation skills for answers instead of on the process of thinking and reasoning. Thus, more and more students thought that "math was a boring symbolic game which concerned nothing about the real-life", or "math was so difficult to master (learn)" (Wu & Ye, 2002; Zheng, 2003).

According to Piaget's (1970) theory of cognitive development, the junior-high students were at the right developmental period of "formal operational period", and they should be able to practice hypothesis and deduction with abstract symbols (Huang, 2001). Therefore, most of countries put the concept of written symbols into the mathematical curriculum at 7th or 8th grades. However, there were a large number of students facing problems in algebraic learning (Huang, 2001). A possible reason was because students' mathematical learning experience in the past (in the elementary level) was mainly about concrete practices of numbers and graphs. Consequently, when it came to more abstract algebraic content, if the instruction were not designed properly connected with their life experience and prior knowledge, the degree of learning difficulty would be then notably increased.

In recent years, our government endeavored to work on the educational innovations to enhance the civic quality and national competitive ability (Ministry of Education [MOE], Taiwan, 2000). …

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