### Clarification of Ambiguous Problems: Effects on Problem Solving Ability and Attitude Towards Mathematics

#### Abstract

Problem solving is now being encouraged to be used as the main activity in all mathematics classes. Students should be encouraged and exposed to work on problems that may take hours, days, and even weeks to solve to develop effective problem-solving ability (Mikusa, 1998). However, it has been observed that students lack the necessary skills to engage in real-life problem solving outside the school setting. This is because students are only trained to work on routine problems that have well-defined goals where all the needed information are given to be able to solve the problem. That is why it is vital to explore other types of problems that can be given as class activities to develop effective problem-solving skills and positive attitude towards mathematics.

The Merriam-Webster online dictionary defines “ambiguous” as “doubtful or uncertain especially from obscurity or indistinctness”, “inexplicable”, and “capable of being understood in two or more possible senses or ways.” Thereare times that problems encountered are fragmented, contradictory, or elicit multiple meanings, which cannot be easily structured and understood. How a person reacts or deals with ambiguous situation or stimulus shows the degreeof tolerance or intolerance he or she has. It can also have a profound impact on his/her educational experiences (Owen and Sweeney, 2002). Recognizing the potential positive effects of developing ambiguity tolerance to problem solving, this research utilized activities involving lateral thinking problems, riddles, and analysis of impossible figures, which encouraged students to think outside the box. As stated by Baroody (1995), solving a problem often depends on looking at the problem in a new way.

In this study, it is hypothesized that ambiguous problems will help improve the problem solving ability and attitude of students towards mathematics. Furthermore, given an ambiguous problem, students will be able to practice analysis of conditions in a problem and clarify rules and goals to come up with an array of sensible answers. Problem clarification can be one of the important skills that a student needs to develop in order to become a proficient problem solver. This hypothesized importance of problem clarification agrees with the observation of Roberts (1995) that the crucial part in problem solving is how to get started with a solution.

The Merriam-Webster online dictionary defines “ambiguous” as “doubtful or uncertain especially from obscurity or indistinctness”, “inexplicable”, and “capable of being understood in two or more possible senses or ways.” Thereare times that problems encountered are fragmented, contradictory, or elicit multiple meanings, which cannot be easily structured and understood. How a person reacts or deals with ambiguous situation or stimulus shows the degreeof tolerance or intolerance he or she has. It can also have a profound impact on his/her educational experiences (Owen and Sweeney, 2002). Recognizing the potential positive effects of developing ambiguity tolerance to problem solving, this research utilized activities involving lateral thinking problems, riddles, and analysis of impossible figures, which encouraged students to think outside the box. As stated by Baroody (1995), solving a problem often depends on looking at the problem in a new way.

In this study, it is hypothesized that ambiguous problems will help improve the problem solving ability and attitude of students towards mathematics. Furthermore, given an ambiguous problem, students will be able to practice analysis of conditions in a problem and clarify rules and goals to come up with an array of sensible answers. Problem clarification can be one of the important skills that a student needs to develop in order to become a proficient problem solver. This hypothesized importance of problem clarification agrees with the observation of Roberts (1995) that the crucial part in problem solving is how to get started with a solution.