Problem solving within mathematics is important as children need to apply and transfer their learning of how to solve calculations into everyday situations. Enabling children to deduce what algorithm is required in a given situation is important and the way in which a problem is approached (NCTM, 1989) is an essential skill, in addition to arriving at a correct answer. Furthermore the NCTM (1980) recognised that teaching problem solving to children develops the skills and knowledge that are used in everyday life whereby the inquiring mind, tenacity and receptiveness to problems are developed.
One area of problem solving is word problems which Jonassen (2003) summarises in his research that “Story problems are the most common kind of problem encountered by students in formal education.” (p. 294). Given that word problems are the most frequently visited type of problem solving the type of instruction and modelling of approaching and solving word problems must be carefully considered and as Haylock (2010) comments, the teachers need to “… focus on children’s grasp of the logical structure of situations…” (p. 95).
A review of the literature associated with solving mathematical based word problems showed a vast array of research examining the instruction of how to approach and solve word problems. In particular two different approaches to problem solving: general based instruction (GSI) and schema-based instruction (SBI).
GSI uses metacognitive and cognitive processes. Pólya (1957) details in his book How to Solve it, four principles in approaching a given problem (i. understand the problem, ii. devise a plan, iii. carry out the plan and iv. reflect). Pólya (1957) elaborated on the principles with each step including smaller steps. The first step is that the learner has to “understand the problem” (Pólya ,1957, p. xvi). Understanding the problem requires the learner to decide what calculation is required, what stages are involved in the problem and whether the problem provides all of the relevant information required. Following on from understanding is devising a plan which requires the learner to draw on previous experiences and use these experiences to define a strategy to solve the problem. At this point students should also look at the problem to assess whether the problem can be redefined or expressed in other words. Similarly Rich (1960) describes this stage as the representational stage or, as Garofalo and Lester (1985) described, this stage as the orientation stage whereby the student needs to comprehend what processes or calculations are required to arrive at an answer.
The second stage requires the student to generalise and draw upon previous learning experiences whereby they need to assimilate previously learnt procedural knowledge to devise a plan of how they can solve the problem, devise a plan (Pólya, 1957), translation, (Rich, 1960) and organisation (Garofala and Lester, 1985).
However many students may misinterpret the...