1 BACKGROUND AND RESEARCH RATIONALE
In our efforts to investigate the problem-solving skills of first-year students enrolled in the engineering-mechanics course at the University of Auckland's Faculty of Engineering, we seek to address the following research questions:
1. Designing a problem-solving heuristic framework --based on how both experts and proficient first-year students solve problems, what are the key elements of engineering-mechanics that might not be visible to beginners?
2. Measure the effect of a structured problem-solving strategy--(a) how can we measure the strategy's affect on an engineering-mechanics' problem-solving skills? and (b) what improvements can we observe as a result?
3. Designing a more effective problem-solving pedagogy--based on the measured results, how could the activities and instructions be made more effective?
Engineers are problem solvers that use their intellectual, analytical and mathematical abilities. This often involves finding effective solutions for problems that occur in our everyday lives. In the 21st century, these skills have become increasingly essential.
The objective of engineering education is to develop conceptual knowledge and problem-solving skills with all students. From a national survey in higher education learning communities within New Zealand, many first-year engineering students commented how they expect to produce a high standard of work, and to learn problem-solving and many facts at university (Cronjie & Coll, 2008). This is consistent with expectations from the University of Auckland, Faculty of Engineering, first-year students (Paton, 2009). Indeed, problem-solving is one of the most significant types of cognitive processing that occurs during teaching and learning in higher education (Frederiksen, 1984; Reif et al, 1976). This view is also supported by Christiansen & Rump (2007), who argued that it is vital that engineering programs address not only problem-solving skills but also the conceptual development from novice beginner to experienced engineer. Consequential, it is important for any in-course interventions to address both the development of conceptual knowledge and problem-solving skills. This will be explained further in subsequent sections.
At the University of Auckland, one of the main goals of the first-year engineering courses is to help students learn how to solve problems effectively. Often lecturers in the first-year engineering courses communicate to their students that they will be tested on their ability to solve problems (Paton, 2009), and about how they are expected to produce clear, effective and structured solutions. In particular, this is communicated further through course materials, online learning activities and assignments. The key goals of first-year engineering courses could be summarised as follows:
1. Students will acquire problem-solving experience and gain familiarity with expert problem-solving strategies.
2. Students will develop both a conceptual and procedural understanding of engineering, physics and mathematics.
3. Students will observe and employ the connections between multiple external representations of physical systems.
4. Beyond repeating theory and formulas, students will understand how to apply their engineering, physics and mathematics knowledge to different situations and challenges.
In an engineering context, a problem is a situation where the steps required are initially unclear or fuzzy, and sometimes remain so throughout the process of finding a solution. The problem might be to answer a question, design a structure to meet specifications or reduce the number of electronic components in a circuit. Often, in order to find the way forward in the process, one needs to make assumptions and approximations that enable the problem to be solved in parts. Clearly, these assumptions need to be relevant to the described situation. …