Introduction

Problem solving forms an important part of teaching critical thinking. Many see problem solving as part and parcel of critical thinking while some consider it synonymous with creative thinking. Many know it to be the antithesis of rote learning, while others understand it to be the basis of problem-based or project-based learning. The existing literature on why problem solving should be taught is clear: learners derive immense benefits from this approach whether it is taught explicitly and whether it is taught in a discipline-specific area. This paper describes some learning outcomes in a course offered to engineering students-EG1413 "Critical Thinking and Writing" (CTW)-in which an assessment format called the position paper makes use of the problem solving technique to teach learners valuable critical thinking skills.

The assessment

Learners are given a broad theme area (e.g. technology and its impact on society) and in groups, investigate a more specific idea that should culminate in a position paper with a well thought-out thesis statement substantiated by appropriate claims and proof. Learners finally forward a solution or solutions to the problem they identify.

Definitions of problem solving

Mathematicians see problem solving as "a situation, quantitative or otherwise, that confronts an individual or group of individuals, that requires resolution, and for which the individual sees no apparent or obvious means or path to obtaining a solution" (Krulick & Rudnick, 1987). The position paper is designed such that learners have no visible means to the solution; they grapple with the problem from day one, and arrive at the solution after an extensive period of research.

The assessment in question sees problem solving as "what you do when you don't know what to do" (Trismen, 1988). This is clearly manifested in the way in which learners are presented with an ill-defined problem whose answer or solution cannot be reached with algorithms or formulae. The solution does not lie with the instructor nor is there a shortcut. Learners pick up problem solving skills by participating actively in the process of problem solving.

Tasks within the problem solving assessment

In the module, learners solve not only one but multiple problems by carrying out many tasks, overcoming difficulties, and learning valuable skills in the process, as shown in Table 1 (see page 7).

Problem solving and learning

Problem solving is an integral part of teaching critical thinking as it encourages learners to find the ways in which they learn best. To cite a few conditions, learners learn best when:

• they discover the answer for themselves
• they contribute the answer
• they have thought out the process through which the answer is achieved
• they come up with possible answers and
• they have surveyed all the data available, and have examined its support, concepts and underlying assumptions.

Overall, through working independently and collaboratively to complete the task, learners learn valuable skills in time management, task or project management, people and resource management. Motivation is high as learners could choose their own topic and the extent of the topic, based on their interests, abilities and pre-knowledge of the interest area.

However, the problem solving approach is not without challenges. Firstly, instructors need to familiarise themselves with the pedagogy of problem solving. To be effective, instructors need to pose open-ended and thought-provoking questions and not 'spoon-feed' learners with information. Secondly, even with assessment criteria, individual performance and contribution can seldom be objective. Additionally, it is difficult to assess a learner's acquisition of problem solving skills simply by looking at the relationship between the product (answer) and the process. Finally, it is not feasible to 'test' if the skill can be applied to a new or another learning situation. Additional cross-modular collaboration and networking among teaching staff will be required to closely monitor learners' 'real' use of the skills.

Table 1. Tasks and skills learnt

Indeed, although the approach poses challenges, it is clearly a rewarding one for learners. Here is what some learners have to say about the practical dimension of and the gain from the problem solving approach:

Made me see problems in society that are not so obvious- made me understand that solutions are not so easy to create (so I whine less when others try and fail to solve society's problems).

I like the research done for my PP [position paper] as I learnt new things related to my topic which otherwise I would not come across in my daily life. PP is a very good opportunity to think issues carefully and logically. It is different from the way how we do math calculation.

References

Krulick, S & Rudnick, J.A. (1987). Problem Solving: A Handbook for Teachers, 2nd Edition, Allyn and Bacon, Inc.

Sternberg, R.J. (2001). 'Teaching Problem Solving as a Way of Life', in Developing Minds-A Resource Book for Teaching Thinking, Arthur L Costa (Ed.). 3rd Edition, Association for Supervision and Curriculum Development.

Trismen, D.A. (1988). 'An Aid to Diagnosis in Mathematical Problem Solving', Journal for Research in Mathematics Education, Vol. 19, pp. 358-361.