Preservice Teachers' Perceptions of Applets for Solving Mathematical Problems: Need, Difficulties and Functions

Article excerpt

Introduction

Background

The use of the internet as an educational medium is now rapidly expanding (Liaw, 2004). Sinclair (2000) points that the internet is becoming an intriguing environment for mathematics education by combining a variety of modes that can be applied to learning. Engelbrecht and Harding (2005) say that there are an increasing number of mathematical sites that use applets to enhance their pages with animated figures and interactive illustrations. They point that these sites include good mathematical applets that are visually of great value and that can be fruitfully used as educational tools. Applets are programs that require a WWW browser or other application to run. Usually these tools represent scientific concepts algebraically and visually, so they enable learners to perceive different representations of the same concept. Examples of mathematical applets can be found at many educational sites, for example the National Council of Teachers of Mathematics' (NCTM) site or the Center of Educational Technology' (CET) site, where the first site includes applets that treat different mathematical topics, while the second site includes applets that treat two topics: linear and quadratic functions. Usually an applet treats a specific topic, for example number factors, decimal fractions, the circle area, etc. So to cover a whole subject one needs different applets, for example one needs to work with applets that treat the following topics to cover the linear function subject: input-output, rate of change, transformations, transformations of straight lines which pass through the origin, addition of linear functions, subtraction of linear functions, forms of linear functions, and functions defined on intervals. The CET's site includes an applet for each topic mentioned above, where the topics are presented in a problem solving context. I've been introducing this environment for preservice teachers for almost 8 years now. Some of them find difficulties working with applets to solve mathematical problems, while others don't find such difficulties, some don't consider applets to be needed in solving mathematical problems, while others are attracted to these new tools and find them helpful in solving the problems. I have always asked myself about the factors that make some learners find difficulties while working with applets while others don't do so, and about the factors that make some learners approve working with applets while others think applets are not needed. This research came to answer these questions.

Literature review

Bolyard and Moyer (2003) say that students in middle grades sometimes need extra help and scaffolding to make the transition from concrete tasks to abstract concepts. They suggest to use contextualized problems with multiple representations that applets can provide as means to help perform this transition. Young (2006) provided a summary of the current literature on applets in mathematics education and described their benefits as found in various articles: (1) their availability on the internet and thus their free and ease of access (2) their focus on specific concepts (3) applets enable learners to do things that are not possible or easy with physical manipulatives, or pencil and paper (4) applets provide students with instantaneous and corrective feedback, so they fit inquiry-based learning and problem solving (5) applets provide multiple representations of a single concept at the same time; thus they can promote the transfer of knowledge from specific ideas to general knowledge (6) applets may be helpful for students with disabilities (7) applets increase motivation and attention in students as well as teachers.

The ability of applets to represent mathematical phenomena in multiple representations and to motivate students' learning of mathematics make them an appropriate tool for solving mathematical problems, especially word problems which students don't look forward to solve them. …