Problem Solving

Problem-Solving
Postscript
Portable Document Format

Problem solving is a process by which the learner discovers a combination of previously learned rules that he/she can apply to achieve a solution. (Holroyd 1985)

In this section, research papers relating to problem solving are presented. These include papers on problem types, strategies to improve problem solving abilities, and investigations which show that students who can solve a given problem may do so without conceptual understanding.

General paper

Fuller 1982

Fuller, R. G, Solving Physics Problems-How Do We Do It?. Physics Today, 35(9), 43-47, 1982.

A general discussion on physics problem solving in the light of the information processing (see Section 14.5) and constructivist (see Section 14.4) theories is presented in this paper. The four stage problem solving strategy of (Reif et. al 1975) is also presented.

Tsaparlis et. al. 2000

Tsaparlis, G. and Angelopoulos, V., A Model of Problem Solving: Its Operation, Validity, and Usefulness in the Case of Organic-Synthesis Problems. Science Education, 84, 131-153, 2000.

In this paper, a problem solving model, based upon working memory theory, (Topic 9) is presented. The authors report that the model was more useful in the case of students without previous training and for those students who were not field-dependent (see Topic 10) for a discussion of field dependency.

Reid and Yang 2002

Reid, N. and Yang, M., The Solving of Problems in Chemistry: The More Open-Ended Problems.. Research in Science and Technological Education, 20(1), 83-98, 2002.

Provides an overview of research into problem solving with some 70 references to the literature.

Reif et. al 1975

Reif, F., Larkin, J. H. and Brackett, G. C., Teaching General Learning and Problem Solving Skills. American Journal of Physics, 44(3), 212-217, 1975.

In this paper the authors present a simple, four stage, problem solving strategy. In addition, there is an exposition of their efforts to teach a general learning skill, designed to help students gain a good working understanding of any new relation.

Bolton and Ross 1997

Bolton, J. and Ross, S, Developing Students Physics Problem Solving Skills. Physics Education, 32(3), 176-185, 1997.

In this paper the authors discuss aspects of problem solving and present an evaluation of the Open University's problem solving booklet and multimedia.

Problem Types

Johnstone 1993

Johnstone, A. H., Introduction. In Wood, C. and Sleet, R. (Eds.), Creative Problem Solving Chemistry, London: The Royal Society of Chemistry, 1993.

In the introduction to this book Johnstone provides a classification of problem types. He suggests that associated with all problems are three variables: the data provided, the method to be used and the goal to be reached. By looking at the extremes of these variables (known and unknown) eight problem types can be identified (see, Table 7.1)

Table 7.1: Problem Types

Type	Data	Methods	Goals/ Outcomes	Skills bonus
1	Given	Familiar	Given	Recall of algorithms
2	Given	Unfamiliar	Given	Looking for parallels to known methods
3	Incomplete	Familiar	Given	Analysis of problem to decide what further data are required. Data seeking.
4	Incomplete	Unfamiliar	Given	Weighing up possible methods and then deciding on data required
5	Given	Familiar	Open	Decision making about appropriate goals. Exploration of knowledge networks.
6	Given	Unfamiliar	Open	Decisions about goals and choices of appropriate methods. Exploration of knowledge and technique networks.
7	Incomplete	Familiar	Open	Once goals have been specified by the student these data are seen to be incomplete.
8	Incomplete	Unfamiliar	Open	Suggestion of goals and methods to get there; consequent need for additional data. All of the above skills.

Factors Effecting Success in Problem Solving

Gabel and Bruce 1994

Gabel, D. L and Bruce, D. M., Research on Problem solving: Chemistry. In: D. L. Gabel (Ed.), Handbook of Research on Science Teaching and Learning: A Project of the National Science Teachers Association. New York: Macmillan, 1994.

Following 12 years of research, into the chemistry problem solving ability of students, these authors proposed that success in problem solving appears to be influenced by three factors:

1. The nature of the problem and the underlying concepts upon which the problem is based: including the problem style and conceptual understanding.
2. Learning characteristics: including an individual's cognitive style, developmental level and knowledge base.
3. Learning environmental factors: including problem solving strategies/methods, and individual or group activity.

Herron and Greenbowe 1986

Herron, J. D. and Greenbowe, T. J., What Can We Due About Sue: A Case Study of Competence. Journal of Chemistry Education, 63(6), 528-531, 1986.

In this paper Herron and Greenbowe suggest that successful problem solvers exhibit four characteristics:

1. have a good command of basic facts and principles.
2. can construct appropriate problem representations.
3. can use general reasoning strategies that permit logical connections between problem elements.
4. can apply several verification strategies.

Furthermore, they suggest 4 ways in which problem solving abilities can be fostered in students. However, they do point out that their suggestions are largely untested.

Bodner and Domin 2000

Bodner, G. M. and Domain, D. S., Mental Models: The Role of Representations in Problem Solving in Chemistry. University Chemistry Education, 4(1), 22-28, 2000.

Bodner and Domain suggest that it is often helpful to produce an external representation of a problem in order to solve it. They define:

• The internal representation as ``the way in which the problem solver stores the internal components of a problem in his or her mind'' and,
• The external representation as ``the physical manifestation of this information'': a drawing, an equation or list of information.

They conclude that a characteristic difference between successful and unsuccessful problem solvers is the number and kinds of representations used whilst attempting to solve a problem. They suggest that students, whilst attempting to solve a problem, should be encouraged to move away from only using verbal/linguistic representations, to also using symbolic representations.

A Network Approach to Problem Solving

Ashmore et. al. 1979

Ashmore, A. D., Fraser, M. J., and Casey, R. J., Problem-solving and Problem-Solving Networks in Chemistry. Journal of Chemistry Education, 56(6), 377-379, 1979.

In this paper a problem-solving network approach to solving problems is proposed: a problem is reduced to a network of unitary pieces of information from which interconnections, between pieces of information, can be seen. These pieces of information fall into three categories (1) stated in the problem, (2) retrieved from memory or, (3) via reasoning. A particular problem-solving network can, either be used to solve the problem or, help a teacher perceive student difficulties in solving the problem.

Fraser and Sleet 1984

Fraser M. J., and Sleet R. J., A Study of Students' Attempts to Solve Chemical Problems. European Journal of Science Education, 6(2), 141-152, 1984.

Using the network approach (Ashmore et. al. 1979) Fraser and Sleet attempted to identify and ascertain why some students could solve sub-problems (of the network) but were unable to solve the complete problem. They discovered that students did not have a plan to solve a particular problem. Moreover they lacked confidence, becoming confused when confronted with unfamiliar data or overly long questions. They suggest that problem solving strategies, summarising, drawing diagrams and breaking down a problem into sub-problems, should be taught so as to reduce the load on their working memory (see Topic 9 for a discussion and references on working memory).

Conceptual Understanding and Problem Solving

Nakhleh 1993

Nakhleh, M. B., Are Students Conceptual Thinkers or Algorithmic Problem Solvers? Identifying Conceptual Students in General Chemistry. Journal of Chemistry Education, 70(1), 52-55, 1993.

In this study, using five paired (algorithmic versus conceptual) general chemistry questions, approximately one thousand students were tested for their competence in solving algorithmic and conceptual problems. It was found that conceptual problem solving ability lagged far behind algorithmic problem solving ability.

Nurrenbern and Pickering 1987

Nurrenbern, S. C. and Pickering, M., Concept Learning Versus Problem Solving: Is There a Difference?. Journal of Chemistry Education, 64(6), 508-510, 1987.

In this study the authors found little connection between a students ability to solve an algorithmic type problem and their understanding of the underlying chemical concepts.

Nakhleh and Mitchell 1993

Nakhleh, M. B. and Mitchell, R. C., Concept Learning Verses Problem Solving: There is a Difference. Journal of Chemistry Education, 70(3), 190-192, 1993.

Following Nakhleh's earlier study (Nakhleh 1993), similar research, using paired exam questions (conceptual and algorithmic), showed that more than 50% of students are poor conceptual problem solvers whilst 85% of students are good algorithmic problem solvers. Furthermore, following interviews with six students, they concluded that most students rely on algorithms to solve problems, even problems specially designed for a conceptual solution.

Phelps 1996

Phelps, A. J., Teaching to Enhance Problem Solving; Its More Than Numbers. Journal of Chemistry Education, 73(4), 301-304, 1996.

In this paper Phelps focuses on conceptual problem solving which rarely had numerical answers. He discovered that non-science students showed more enthusiasm for their chemistry course, whilst the science students became insecure because this approach was not consistent with their expectation of the nature of chemistry. In the later case, students past experience instilled in them the belief that chemistry problems had a right answer and that they should know it. However, after adjusting their expectations, the science students appreciated spending more time developing conceptual understanding.

Cooperative problem solving

Qin and Johnson 1995

Qin, Z. and Johnson, D. W., Cooperative Versus Competitive Efforts and Problem Solving. Review of Educational Research, 6(2), 129-143, 1995.

Qin and Johnson examined 46 studies published between 1929 and 1993 to ascertain the relative impact of cooperative and competitive efforts on problem solving success. During their investigation six independent variables were considered: [Group]

• Cooperation versus competition.
• The type of Problem solving tasks, for example linguistic, nonlinguistic, well-defined and ill-defined.
• The age of the participants.
• The year of publication.
• The duration of a particular piece of research.
• The quality of research methodology.

The authors present 63 findings to which clear evidence is shown that cooperation, rather than non linguistic and ill-defined problems. However, this difference is dependent upon age with older students showing the greatest difference.

Tingle and Good 1990

Tingle, J. B. and Good, R., Effects of Cooperative Grouping on Stoichiometric Problem Solving in High School Chemistry. Journal of Research in Science Teaching 27(7), 671-686, 1990.

Here the suggestion is that cooperative groupings are a viable strategy for chemistry problem solving. That is, an active, rather than receptive, learning environment is fostered and as a result students' problem solving abilities are enhanced. Moreover, they provide evidence that students are able to teach group members through modelling, asking questions, and by using analogies during group discussions. [Group]

General Books on Problem Solving

There is a whole cornucopia of books relating to the field of problem solving, a small selection of which are presented here. The first three books present a multitude of problems for the students to solve, whilst the remaining two are concerned with problem solving theories and teaching methods.

Wood and Sleet 1993

Wood C. and Sleet R., Creative Problem Solving in Chemistry. London: Royal Society of Chemistry., 1993.

This book is designed to foster good problem solving skills in students working in group situations. The skills that it claims to foster include data seeking and selection, choice of method, balance of criteria, awareness of error, discussion and presentation, and is aimed at 16 to 18 year olds. [Group]

Gnädig et. al. 2001

Gnädig, P., Honyek, G. and Riley, K., 200 Puzzling Physics Problems. Cambridge University Press, 2001.

Presents 200, generally open ended, problems in physics. Ideal for group work, with or without a teacher/lecturer. [Group]

Harte 1985

Harte, J., Consider a Spherical Cow: A course in Environmental Problem Solving. Los Alto: William Kaufmann, Inc., 1985.

Drawing from the physical and biological sciences this environmental science problem solving book is designed to teach students how to transform a realistic, qualitatively described problem into a quantifiably solvable form and to arrive at an approximate solution. An additional aim is to teach environmental science

Watts 91

Watts C, The Science of Problem solving: a practical guide for science teachers. Cassell Educational, London, 1991.

This book presents the skills, processes and methods of problem solving.

Randell and Lester 1982

Randell, C. Lester, F., Teaching Problem Solving: what, why and how. Palo Alto: Dale Seymour Publications, 1982.