Research in Problem Solving Improving the Progression from Novice to Expert Roxi Finney Abstract This paper presents a review of research in problem solving The first section includes various research papers across multiple disciplines which call for the need to improve the problem solving skills of students and the need to improve the methods of teaching problem solving skills Many arguments are presented for the importance of research in this area The second section defines and describes the various types of problems presented to students and presents research projects dealing with problem types The final section provides information about novice and expert problem solvers including characteristics of each Several research papers are listed which focus on studies aimed to improve the progression from novice to expert Results of this review suggest problem solving skills cannot be improved through explicit instruction in problem solving but may be improved through increased instruction in conceptual chemistry 1 I The Need for Research and Reform Many instructors myself included have believed or hoped that teaching students to solve problems is equivalent to teaching the concepts If as is now being proposed this axiom is not true then we all must rethink our approach to chemical education Sawrey 1990 In 2000 Cohen Kennedy Justice Pai Torres Toomey DePierro and Garafalo published a paper on improving quantitative problem solving in chemistry In this paper the authors address the problems associated with introductory level students engaging in quantitative problem solving activities without having a strong understanding of the algorithms problem solving strategies that may or may not involve mathematical equations or equations they use to solve such problems Without understanding fundamental mathematical concepts used in solving problems such as the meaning of ratios problem solving has the potential of becoming an exercise in mere symbol manipulation as described by Cohen et al For example introductory students may memorize the algorithm for converting moles to grams as such To convert from moles to grams multiply by the formula weight While this algorithm is correct in the sense that it will give the correct answer it shows no understanding of the physical situation at hand An introductory student lacking in conceptual knowledge may not understand why this algorithm works They will however be able to correctly apply this meaningless algorithm to homework and exam questions Using this algorithm without conceptual understanding does not enhance or improve a student s problem solving abilities 2 Cohen et al 2000 respond to this common occurrence by proposing meaningful problem solving in the classroom When students are solving quantitative problems instructors should not be satisfied with numerically correct answers Rather they should require students to demonstrate their conceptual understanding of every aspect of the problem including the equations and ratios used to solve the problem Cohen et al propose that this process of developing conceptual understanding of problem solving should occur at the secondary level as it requires more time than may be available in a college course If a student s first response is to decide which algorithms to use then he or she is not solving a problem at all Frank Baker Herron 1987 Additional publications Bodner 1987 Fortunato Hecht Tittle Alvarez 1991 Frank et al 1987 Halmos Moise Piranian 1975 Nurrenbern Pickering 1987 reiterate the need to supplement the use of algorithms with conceptual understanding of the entire process of problem solving Students should not be taught to rely entirely on algorithms or equations to solve problems Algorithms or equations such as the mole to gram conversion described above are shortcuts to solving commonly encountered exercises These shortcuts lose their value when the student encounters a problem for which their algorithm is not appropriate For example the mole to gram conversion could not be directly applied to a problem requiring the student to convert from gram to mole If the student is equipped with a strong conceptual understanding of this topic stoichiometry they will see the similarity of the two problems and will be able to arrive 3 at a solution with minimal complications On the other hand if the student lacks a solid conceptual understanding of stoichiometry they may not recognize the relationship between the two problems They may seek out and memorize a separate algorithm for converting grams to moles When a student approaches a problem by asking themselves the question Which equation do I use to find the answer that student has not learned good strategies for solving problems By focusing directly on an equation the student bypasses critical steps in the problem solving process such as determining the type of problem or forming valuable problem representations This automatic response to seek out an equation may stem from typical homework assignments such as those found in the back of textbooks where problems are grouped by the algorithm used to obtain the solution This repetitive application of identical algorithms eliminates crucial steps in the problem solving process such as understanding the conceptual nature of the problem This presents students with an inadequate problem solving experience Chemistry teachers have assumed implicitly that being able to solve problems is equivalent to understanding of molecular concepts Nurrenbern Pickering 1987 Chemical educators Nurrenbern Pickering 1987 Pickering 1990 Sawrey 1990 Yarroch 1985 emphasize the need for instructors to recognize the common disconnection between conceptual understanding and problem solving ability In the studies cited above researchers found that students are significantly more successful at solving traditional quantitative problems applying an algorithm or equation than they 4 are at solving conceptual qualitative problems representing a system at the molecular level of a similar level of complexity In separate studies Nurrenbern and Pickering 1987 and Sawrey 1990 found that some students could correctly solve problems pertaining to the ideal gas law without being able to represent the behavior of gases at the molecular level Both studies also found that some students could solve stoichiometry problems without being able to represent the reaction with an illustration Yarroch found that some students could correctly balance