Understanding transfer from a dynamic system approach: Two studies of children using problem-solving tasks

Figures & data

Figure 1. Schematic design of study 1.

Figure 2. Schematic design of the repeated and overlapping procedure used in study 2.

Table 1. Number of key elements provided by each solving problem task

Study	Task	# Key elements	Total Elements per Task
Study 1 Archimedes Task	T1—Bird	3	18
	T1A—Vase	3	18
	T2—Tank	3	18
	T2A—Ships	3	18
	T3- Toys	3	18
	T3A—Flowers	3	18
Study 2 Air Pressure Task	T1, T1A—Connected Syringes	3	7
	T2, T2A—Platform Lift	3	7
	T3, T3A—Two platforms	3	7

Figure 3. Percentage of achievement on Archimedes’ task. T# = Type of task, A = second presentation of the task.

Figure 4. Percentage of achievement on t Air pressure task. T# = Type of task, A = second presentation of a task.

Figure 5. Trajectories of criteria used to solve the problem in Archimedes’ task. NK: not using a key element, PK: using a key element of a previous task which is incorrect for the current task, and CK: using a correct key element for the current task. T# = Type of task, A = second presentation of the task.

Figure 6. Trajectories of criteria used to solve the problem in Air Pressure task. NK: not using a key element, PK: using a key element of a previous task which is incorrect for the current task, and CK: using a correct key element for the current task. T# = Type of task, A = second presentation of the task.

Figure 7. Trajectories of criteria used to solve the problem per task and attempt in Archimedes’ task. NK: not using a key element, PK: using a key element of a previous task which is incorrect for the current task, and CK: using a correct key element for the current task. T# = Type of task, A = second presentation of the task.

Figure 8. Trajectories of criteria used to solve the problem per task and attempt in Air Pressure task. NK: not using a key element, PK: using a key element of a previous task which is incorrect for the current task, and CK: using a correct key element for the current task. T# = Type of task, A = second presentation of the task.

Table

Task 1 (T1)Connected Syringes	Task 2 (T2)Lift		Task 3 (T3)Platforms
Criteria	Task 1 (T1) Connected Syringes	Task 2 (T2) Lift	Task 3 (T3) Platforms
Goal	To push the plunge out until the red mark	To lift the weight until the edge of the wooden wall	To push the platform up until the “bee” mark
Target syringe/ Size of the Syringe to solve the problem	Medium size	Small size	Big size
Considerations to solve the task	The size of the added syringe affects the result of the task→ The solution of the task requires to use the same size of the target syringe. The shape of the tubes affects the result → The “Y” shape tube does not work to solve the task. The air scape from one of the disconnected tips. In contrast, a straight tube directs all the air to the target syringe. Both, short and long straight tubes contribute to solve the task. The size of the tube does not affect the result → The size of the tube does not contribute to solve the task.