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Designing A Multimedia-based Cognitive Tool for Solving Word Problems
Involving Fractions
Azlina Ahmad, Siti Salwah Salim & Roziati Zainuddin
Faculty of Computer Science and Information Technology
Universiti Malaya, Malaysia
Abstract
Various studies have indicated that many students
in the world faced difficulties in solving word problems especially when the problems involve fractions. A study
conducted on Malaysian students shows that they too
are facing similar problems. This paper describes the
results of the study, its analysis and its implication on
the design of a cognitive tool to solve fraction word
problems. With multimedia technology today, we
believe that the development of a multimedia-based
cognitive tool can help improve students’ performance
in solving word problems.
1. Introduction
Solving mathematical word problems is an essential
skill that should be acquired when learning
mathematics. Various studies have indicated that many
students worldwide faced difficulties in solving this
type of problem. The situation became worse when the
word problems involve fractions. Since multimedia
and computers have played a big role in improving
quality of education today, we propose the
development of a cognitive tool for solving word
problems involving fractions, which can organize,
restructure, and represent what they know.
2. The Results of Study on Malaysian
Students Ability in Solving Problems
Involving Fractions
The study involved fifty-seven seventh grade students.
One of the main focus of the study is to identify the
types of error made by students when solving fractions
word problems. We categorized these errors into four
types as listed below:
• Type I error – Errors that occur when forming
the correct equation at the first step of problem
solving process
• Type II error – All procedural errors such as
computation in addition, subtraction,
multiplication and division of fractions.
• Type III error – All other errors such as error
when fraction number in student’s answer not in
the correct form. (improper fraction)
• Type IV error – For unanswered questions.
One of the observations we made from the study is
that percentage of Type I errors made by the students
was higher than Type II errors. This clearly indicates
that students are having more difficulties in problem
representation. We also found that many students were
poor in communicating in mathematics. In addition to
this problem, many students did not obey the syntax
and grammar of mathematics.
3. Problem Solving
Problem solving involves various steps. For each
step of problem solving, different kinds of knowledge
are required. Mayer, Richard E. [5] described five
types of knowledge in problem solving. They are
linguistic, semantic, schema, procedural and strategic
knowledge. We will apply the model of problem
solving process as shown in Figure 1. Problem
representation phase of problem solving requires the
linguistic, semantic, and schema knowledge. From our
Proceedings of the Fifth IEEE International Conference on Advanced Learning Technologies (ICALT’05)
0-7695-2338-2/05 $20.00 © 2005 IEEE
observation, this phase is the most difficult for
students.
Figure 1. Model of problem solving process
4. Toward An Instructional Design Model
of the Cognitive Tool
Jonassen and Reeves (1996) proposed that cognitive
tools are best used as reflection tools that amplify,
extend, and even reorganize human mental powers in
order to help learners construct their own realities and
complete challenging tasks. Cognitive tools should
support cognitive processes, such as, memory and
meta-cognitive processes ([2] Lajoie, 1993).
We model our instructional design based on the
behaviorist-cognitivist-constructivist approach. We
believe that this combination of learning theories is the
most effective way of developing problem solving
skills since one need to have different types of skills
and knowledge to solve a problem.
• Behaviorism stresses the importance of presenting
knowledge in gradual steps.
• Cognitivism believes that learning results when
information is stored in memory in an organized,
meaningful way
• Constructivism emphasizes on students to construct
and externalize their mental models
The behaviorist-cognitivist- constructivist approach of
our model includes the following constructs:
Multimedia-based Information Visualization – .
Using animation, graphics, audio and text, students at
the comprehension level to visualize the word problem.
Exploratory – Students solve problems on their
own. They are free to select the support tools they need
to solve the problem.
Scaffolding – The usage of certain support tools
can be stopped once students have developed certain
skills.
Reflection – Students can reflect on the concepts
and procedures of fraction calculation.
Self –paced – Students control their own learning
and repetition of steps is allowed.
5. Conclusion
Solving word problems involving fractions is an
essential skill that certainly needs to be improved
among Malaysian students. Since problem solving
requires higher order thinking skills with different
types of knowledge, we believe that a carefully
designed cognitive tool for solving word problems
involving fractions can provide students the
opportunity to develop and enhance this skill.
6. References
[1] Jonassen, D.H. & Reeves, Thomas C. Learning with
Technology. Using computers as Cognitive Tools. Handbook
of Research for Educational Communications and
Technology. Bloomington, Indiana, Association for
Educational Communications and Technology, 2001.
[2] Lajoie, Susanne P. & Derry, Sharon J. Computers as
Cognitive Tools, New Jersey, Lawrence Erlbaum Associates,
Publishers, 1993
[3] Mayer, Richard E. (1983). Thinking, Problem Solving,
Cognition. New York. W.H. Freeman Co.
Reading and understanding given word problem
Identifying problem type
Identifying situational characteristics of problem
Listing down given information- variables and/ or keywords
Identifying what need to be solved
Forming the required equation/s
Check calculations
Selecting and applying appropriate algorithm
COMPREHENSION
EXTRACTION
CONSTRUCTION OF EQUATION/S
SOLVING OF EQUATION/S
ANSWER
PROBLEM REPRESENTATION
Proceedings of the Fifth IEEE International Conference on Advanced Learning Technologies (ICALT’05)
0-7695-2338-2/05 $20.00 © 2005 IEEE
