January 2012 Volume 15 Number 1 - Educational Technology ...

Huang, T.-H., Liu, Y.-C., & Chang, H.-C. (2012). Learning Achievement in Solving Word-Based Mathematical Questions
through a Computer-Assisted Learning System. Educational Technology & Society, 15 (1), 248–259.
Learning Achievement in Solving Word-Based Mathematical Questions
through a Computer-Assisted Learning System
Tzu-Hua Huang, Yuan-Chen Liu 1 and Hsiu-Chen Chang 2
Graduate School of Curriculum and Instruction, National Taipei University of Education, No.134, Sec. 2, Heping
E. Rd., Da-an District, Taipei City 106, Taiwan (R.O.C.) // 1 Graduate School of Communication and Technology,
National Taipei University of Education, No.134, Sec. 2, Heping E. Rd., Da-an District, Taipei City 106, Taiwan
(R.O.C.) // 2 Longtan Elementary School, No.71, Yulong Rd., Jiaoxi Township, Yilan County 262, Taiwan
(R.O.C.) // anteater1029@mail2000.com.tw // liu@tea.ntue.edu.tw // jane@ilc.edu.tw
ABSTRACT
This study developed a computer-assisted mathematical problem-solving system in the form of a network
instruction website to help low-achieving second- and third-graders in mathematics with word-based addition
and subtraction questions in Taiwan. According to Polya’s problem-solving model, the system is designed to
guide these low-achievers through the parts of the problem-solving process that they often ignore. The
situations of verbal questions are visualised to walk the students through the course of thinking so they can
solve the question with proper understanding of its meaning. We found that the mathematical problemsolving
ability of experiment group students was significantly superior to that of control group students.
Most of the participants were able to continue the practice of solving word-based mathematical questions,
and their willingness to use the system was high. This indicates that the computer-assisted mathematical
problem solving system can serve effectively as a tool for teachers engaged in remedial education.
Keywords
Low-achiever, Problem-Based Learning (PBL), Polya’s Problem-Solving Process, Word-Based Mathematical
Questions
Introduction
In traditional teaching, assessment of whether students had understood a mathematical problem was based on
whether they could describe the correct arithmetic procedure. However, it was not enough to evaluate students’
mathematics concepts and abilities of solving math problems merely depending on their writing. Some oral
interpretation and explanation should be considered from multiple assessment points of view (Hwang, Chen &
Hsu. 2006). Several researches also pointed out that good problem solving skills are the key to acquiring a
successful solution in learning mathematics (Gagne, 1985; Mayer, 1992). The cognitive thinking process, as well
as abstract mathematical concepts and representations, is often extremely difficult for middle-school and
elementary students. Many efforts have been made to explore alternative ways of teaching mathematics by
creating curricula and didactic material incorporating new tools, pedagogical approaches, and models or methods,
to engage learners in a more pleasant mathematical learning process (Szendrei, 1996).
Fleischner and Marzola (1988) indicated that the mathematics learning achievement of about 6% of all middleschool
and elementary students were severely flawed. In one of Polya’s speeches (1962), he expounded on
learning, teaching and learning to teach. He stated the fact that only 1% of the students would need to study
mathematics, 29% would need to use mathematics in the future, and 70% would never need knowledge of
mathematics beyond the elementary level in their daily life (Mayer, 1992). Obviously, if a student could
successfully solve a math problem by arithmetic calculation, that did not mean the student really understood it.,
Many students and teachers have found the learning and teaching of solving verbal questions to be the most
challenging part of mathematics education (De Corte & Verschaffel, 1993). Cardelle-Flawar (1992) discovered
that, in order to help these low-achievers sharpen their problem-solving skills; their verbal ability must be
improved first to enable them to identify the core of the problem.
Problem-Based Learning (PBL)
Problem-based learning (PBL) is considered to be one of the most appropriate solutions to increase students’
learning motivation and to develop practical skills. It is a student-centered instructional strategy, and
students can solve problems collaboratively and reflect on their experiences. It also can help students
develop skills and acquire knowledge (Bruer, 1993; Williams, 1993). Polya’s Mathematics Problem-Solving
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