Titration Calculations-A Problem-Solving Approach Robin E. L. Waddling Falmouth School, Cornwall, England The calculations that form a necessary part of every volumetric exercise can prove to be a daunting prospect for many secondary level students. Such calculations require skills that some students find difficult to grasp ( I ). While students of differing abilities are able to develop, with practice, equally good practical techniques, less-confident students find it more difficult to improve their calculation work. Students in the latter category are still a t the Piagetian concrete stage of cognitive development and have not yet learned to cope adequately with formal operations, such as those encountered in titration calculations. Johnstone (2) has suggested that the thinking that is demanded of pupils in similar calculations involving reacting masses, require an appreciationof proportionality, which is a skill that is not properly developed until the age of sixteen, when the student can he expected to think formally. The students who have not yet built up the interlinked cognitive structure needed to tackle such problems, experience an information overload as their workina memories are flooded. This in turn accentuates the perceived difficulty of the problem in the mind of the student and further undermines his confidence ( 3 ) . If we as teachers are to overcome the situation in which our weaker students approach these calculations with trepidation, uncertainty of where to start, and in the forlorn hope that the M1V1Inl = M2V2/n2relationship will save them, we must help these students develop a systematic approach to solving such problems. Mihkelson has suggested that the structuring of questions reveals to students who are not formal thinkers. the reasoning that is required to obtain the solution of a prdblem (4). I t nossihle to lead the students through the thinking orocesses. step by step, from one level to the next. In this w a i we are not only facilitating the means to an end but are also training the student in the methodology of logical thinking. I t is common to find students who are comoetent a t the various steps in a titration calculation; however, i t is not unusual to find a larae number of students unable to link uu these steps. It is th;'hridgingz between existing knoyledge and skills that is needed to lead to successful problem solving. A four-stage (logical) model for problem solving has been proposed by Fraser et al. (5).They have nsed this approach to derive problem-solving networks by the breaking down of problems into unitary pieces of information and reassembling them to show how the various pieces of information have to he connected to arrive a t the solution to the problem. Their networks show diaerammaticallv. the interconnections between the informaiion supplied in the formulation of the urohlem, the information that the student should be able to supply from memory, and that obtained by reasoning processes durina the solvina of the oroblem. ~imilarly,Xramers-P~ etSa f have addressed themselves to the task of uroblem analvsis and thev have devised a Pro(6).This lists, in a sysgram of ~ c t i o n and s ~ e t b d d (PAM) s tematic manner, the desired actions that have to be executed to ohtain a solution. They have constructed problem-solving charts and worksheets to further aid the student.
