We investigate problem solving by analogy in order to see whether solving a similar, easier problem beforehand aids in deciphering a more complicated one, given that the two problems have a similar (homomorphic) problem state. The two problems that have been used in this experiment are the historic Missionary & Cannibals problem (M&C) as well as its visual representation - referred to as "Counter-Moving" (CM) in the following.
The use of analogy in problem solving requires restructuring the problem in order to create an insight - as can be measured by "warmth" ratings - in contrast to problem solving based on trial-and-error learning (mostly common in elementary algebra) as proposed by behaviourists such as Thorndike. The restructuring of the problem relies on mapping from a source domain to a target domain. Since there is an infinite number of possible source domains, many humans have difficulies at spontaneous use of analogy and need its relevance to be highlighted. We have shown that the success rate on the counter-moving problem does differ significantly from the success rate on the M&C problem, which implies that the CM problem is conceptually easier to understand. Hence, we could show that solving a similar, easier problem with a homomorphic problem state does indeed increase the success rate of solving a more complicated one later by comparing the success rates between Groups A and B that solved the problems in opposite orders.
At a glance
- Analysis combines practical-session results from 204 Cambridge psychology students across three years
- Compares the Missionary & Cannibals problem with its counter-moving visual representation
- Compares groups that attempted the two problems in opposite orders
- 10 sources in the bibliography
Contents
1. Introduction
2. Methods
2.1. Subjects
2.2. Materials
2.3. Procedure
3. Results
4. Discussion
5. Conclusion
Objectives and Topics
This practical report investigates whether solving an easier problem first helps people solve a more difficult problem with a similar underlying structure. It compares performance on the Missionary & Cannibals problem and a visual counter-moving version, as well as the order in which the problems are attempted.
- Insight and analogical problem solving
- Problem representation and restructuring
- Homomorphic problem states
- Order of problem-solving attempts
- Statistical comparison of success rates
- Prior knowledge as a potential influence
Excerpt from the Book
1. Introduction
Insight was first studied by Gestalt Psychology, in the first half of the 20th century, partly as reaction to the associationistic view of learning proposed by behaviourists such as Thorndike. [10] The most famous experiments are Maier’s pendulum problem [5] and Duncker’s candle problem [1]. Some proposed potential mechanisms for insight include: suddenly seeing the problem in a new way, connecting the problem to another relevant solved problem (solving by analogy – as investigated here), releasing past experiences that are blocking the solution (overcoming functional fixedness), or seeing problem in a larger, coherent context. [9] One more recent example is Knoblich’s matchstick experiment [4], whereby the constraints of algebra need to be relaxed. This implies that impasses need to be broken by changing the problem representation. This breakage of impasses is crucial for solving insight problems as pointed out by Ohlsson [8]. In the following, we are going to investigate the Missionary & Cannibals problem (M&C) problem state in more detail. This problem has various homomorphic appearances, the first one of which is the jealous husbands problem in the medieval text “Propositiones ad Acuendos Juvenes” (Alcuin), whereby couples of husbands and wifes are considered and the constraint is that no woman can be in the company of another man unless her husband is present. The problem can be translated into a visual representation in a 2D-space, whereby certain vectors lead from one problem state to the next one. One of the main impasses in the two appearances of the problem is a goal-subgoal conflict, in which an intermediate step seems to increase the distance to finding the solution – as in the Tower of Hanoi problem. [7] Hence, problem solving by analogy [2, 3] might be necessary in order to overcome this obstacle.
Chapter Summaries
1. Introduction: The introduction presents theories of insight and problem restructuring, then describes the Missionary & Cannibals problem and its alternative representations.
2. Methods: This chapter describes the participating students, the paired experimental setup, the materials and the timed procedure.
3. Results: The report presents chi-squared comparisons of performance on the two problems and of the order in which they were attempted.
4. Discussion: The discussion considers whether prior teaching about analogical problem solving could have influenced participants and proposes a counterbalanced follow-up design.
5. Conclusion: The conclusion interprets the comparisons in relation to the proposed effect of solving a similar, easier problem first.
Keywords
analogical problem solving, insight, problem representation, problem restructuring, homomorphism, Missionary & Cannibals problem, counter-moving problem, goal-subgoal conflict, experimental psychology, problem order, chi-squared test, transfer of learning
Frequently Asked Questions
What is this report about?
It examines whether solving one problem can help people solve another problem with a similar underlying structure.
What are the main topics?
The report addresses insight, analogy, problem representation, problem-solving order and statistical comparisons of performance.
What is the central research question?
It asks whether attempting an easier analogous problem first helps people solve a more difficult problem.
What research method is used?
The report analyses results from a practical experiment involving two problem-solving tasks and uses chi-squared tests to compare outcomes.
What does the main body cover?
It describes the experimental participants, materials and procedure, presents statistical results, and discusses a potential influence of prior teaching.
Which keywords characterize the report?
Key terms include analogical problem solving, insight, problem restructuring, homomorphism, problem order and chi-squared testing.
Which problems are compared?
The experiment compares the Missionary & Cannibals problem with a visual counter-moving representation of a similar problem state.
How was the order of the tasks investigated?
Two groups attempted the problems in opposite orders, allowing their performance to be compared.
What potential limitation does the discussion identify?
Participants had heard about an analogical problem-solving example before the practical session, which may have affected their awareness of possible analogies.
- Quote paper
- Laura Imperatori (Author), 2014, Problem Solving by Analogy, Munich, GRIN Verlag, https://www.grin.com/document/276480
