Matchstick task is one of the two task experiments planned for our project.
The second one being Programming Tree task.
This experiment will examine the effect of transfer regarding certain mental representations. Using a matchsticks problem solving tasks we will investigate whether creating a mental representation and learning effective strategies leads to a negative (unwanted) transfer in a similar task, so that other representations and strategies are overlooked.
We expect that creating a particular mental representation can enhance positive transfer in subsequent tasks that support this mental representation and create negative transfer in similar tasks that do not.
Solving a problem is simpler for the second time. This is common knowledge and is directly attributed to learning. Well-learned or practiced people often perform better at certain activities (including problem-solving) and hence the great importance our society puts on learning. The learning process has been widely researched in psychology through many different tasks that focus, each on one small portion of the whole process. The following experiment falls into this category as well, focusing on rarely researched effect of mental representations on the problem-solving process.
We aim to investigate whether mental representations have any effect on our problem-solving process and how strong this effect is. Especially in this experiment, we are interested in the transfer feature of mental representations. (Knowledge) Transfer marks how well are subjects able to solve subsequent problems after solving the initial ones - transfer can be positive, meaning that subjects perform better having solved the initial tasks, or negative, meaning that subjects perform worse. The term 'transfer' is used in problem-solving research field and can be (overly-)simplified as a combination of learning a task and applying the knowledge to a next task. Following Simon's work (Kotovsky & Fallside, 1988)), mental representations can have significant effect on transfer. We aim to extend their study on a set of new tasks and with more variables, to further increase our understanding of the role of mental representations.
Subjects will be asked to solve simple matchstick tasks, where they are presented with a false equation, created by matchsticks, and are asked to move as few matchsticks as possible to make a correct equality equation. They are also asked to do so as quickly as possible. We have identified two different mental representations in such matchstick tasks. By studying this experiment we want to know if subject, that is given a task with one optimal mental representation and learns it and its effective strategies, performs better or worse in a similar task, that has the other representation optimal. We want to know if subject will find it hard to switch mental representations as this point. This experiment will enable us to better understand the transfer amongst tasks and how it is effected by mental representations.
An example of a matchstick task with 4 distinct solutions.
We do not accept the bottom right solution as the equality must be preserved.
For more information on matchsticks: Matchstick background
Creating a mental representation and learning effective strategies leads to an effective transfer in a similar task.
According to EU regulations, not confirmation from ethics committee is required.
A single signed document, that states that subject made an informed decision to participate in this experiment, suffices.
See the following study agreement
Study agreement - matchstick experiment.odt
(This is the temporary version of the agreement and thus it is prone to change)
When the subject signs the agreement, the experiment can begin.
Subjects will be asked to solve simple matchstick tasks, where they are presented with a false equation, created by real (physical) matchsticks, and are asked to move as few matchsticks as possible to make a correct equation. They are also asked to do so as quickly as possible and told that inequality (solutions with inequality sign: ≠) solutions are not acceptable (there are just too many solutions this way). We have identified two different mental representations in such matchstick tasks. This does not mean that there are not more representations available and although, we are pretty sure about this, we will still be on a lookout for signs that subject has created a previously unknown mental representation.
Subjects will assigned into one of the tree groups (two groups get assigned each a dominant mental representation - groups A and B -, and the third group is control - group AB) and be subjected to 4 parts of this experiment. While reading, please consult the picture below for better clarification. In the first part, subjects will be trained on creating a single mental representation that is assigned to their group on 6 matchstick tasks. Subjects in groups A and B will be asked to solve tasks that have the dominant representation the one that was assigned to their group, and subjects in the group AB get assigned tasks that are solvable by both representations. In the second part, all subjects get tasks that are solvable by both representations. In the third part, subjects will be asked to solve tasks which are solvable by both representations, but the mental representation of the opposite group is more optimal (tasks for group A can be solved by the learned mental representation, but it is more optimal to solve them by mental representation of group B). And finally, in the fourth part subjects will be presented with tasks that are only solvable by the mental representation of the opposite group. Tasks basically remain the same type throughout the experiment for the group AB. This procedure will enable us to fully test the transfer amongst tasks and have a great control group.
Schema of the matchstick experiment. (Special thanks to MG).
At the end of the experiment, subject will be asked to describe his/her understanding of tasks and report on which tasks he/she struggled more.
A single task is just a simple valid (all the symbols are numerals, operators or comparators, and are in an order that resembles a standard equation), but not correct (the left and right side of the equation are not of the same value) equation, that the subject has to transform to a correct equation. Subject can use move actions, that require of them to pick up a matchstick from the equation and put it back somewhere else. Each task is solvable in 1 move (*). Subjects have unlimited number of move actions at their disposal, but are told to use as few of them as possible - while trying to solve the task as quickly as possible.
Tasks are separated into 5 task groups, that contain equations with similar features of solutions. They are grouped according to the actions needed to solve the task-equations. Each group is presented below with detailed description, use cases (according to above experiment schema) and files, providing the actual task-equations.
| Group NN |
Group NO |
Group ON |
Group OO |
Group B |
|
| Description |
Equations are solvable in one and two moves only by moving matches between numeral elements. Equations are not solvable in one move! |
Equations are solvable in one move by only moving matches between numeral elements. And in two moves by moving matches between either numeral or operator elements. |
Equations are solvable in one move by only moving matches between operator elements. And in two moves by moving matches between either numeral or operator elements. |
Equations are solvable in two moves only by moving matches between operator elements. Equations are not solvable in one move! |
Equations are solvable in one move by moving matches between either numeral elements or operator elements. |
| Use cases |
6 initial tasks for X, Task U (Group B) |
3 tasks Y, but optimal X, All 6 tasks |
3 tasks X, but optimal Y, All 6 tasks |
6 initial tasks for Y, Task U (Group A) |
6 initial tasks for X and Y, Task T, Task U (Group C) |
| Data file | Group NN | Group NO | Group ON | Group OO | Group B |
| Alternative file |
Equations are solvable in one move only by moving matches between numeral elements. And in two moves by actions that include numerals. |
Equations are solvable in one move only by moving matches between operator elements. And in two moves by actions that include operators. |
Important!
The data that will be collected:
The data will be collected using an application:
Representation and Transfer in Problem Solving.pdf
MATCHSTICKS_Constraint_Relaxation_and_Chunk_Decomposition_in_I.pdf