An effective metacognitive strategy: learning by doing and explaining with a computer‐based Cognitive Tutor

A mathematical model of Aleven and Koedinger's data provides evidence that non-verbal procedural and verbal declarative knowledge of the same content can co-exist and that different mixtures of such knowledge can yield identifiable patterns of performance across multiple assessments.

“A mathematical model of their data provides evidence that non-verbal procedural and verbal declarative knowledge of the same content can co-exist and that different mixtures of such knowledge can yield identifiable patterns of performance across multiple assessments.”

Aleven and Koedinger (2002) provide evidence of non-verbal procedural knowledge in geometry students who were more correct on making geometric inferences than on matched explanation items.

“Aleven and Koedinger (2002) provide evidence of non-verbal procedural knowledge in the performance of geometry students who were more correct on making geometric inferences than they were on matched explanation items.”

Adding prompts for self-explanation to tutored problem solving practice, without adding extra instructional time, produced greater explanation ability and conceptual transfer to novel problems while maintaining performance on isomorphic problems.

“They found that adding prompts for self-explanation to tutored problem solving practice (without adding extra instructional time) produced greater explanation ability and conceptual transfer to novel problems while maintaining performance on isomorphic problems.”

Much research on self-explanation indicates that prompting students to provide verbal explanations of actions, whether their own or ones given in a worked example, can often aid robust learning.

“Much research on “self-explanation” indicates that prompting students to provide verbal explanations of actions (whether their own or ones given in a worked example) can often aid robust learning (Aleven & Koedinger, 2002;Chi et al., 1994;Graesser, McNamara, & VanLehn, 2005;Hausmann & VanLehn, 2007).”

In geometry, many students implicitly induce a rule that when angles look equal in a diagram, they are equal.

“In geometry, many students (implicitly) induce a rule that when angles look equal in a diagram, they are equal (Aleven & Koedinger, 2002).”

Non-verbal induction can lead to a situation in which students can correctly perform mathematics that they cannot explain.

“Non-verbal induction can lead to a situation in which students can correctly perform mathematics (e.g., find a correct angle in a geometry problem by subtracting from 180°) that they cannot explain (e.g., indicating that the target and given angle form a line; Aleven & Koedinger, 2002).”

Integrated variable-variable KCs to be learned in both non-verbal procedural and verbal declarative form imply instruction that prompts for self-explanations.

“Integrated variable-variable KCs to be learned in both non-verbal procedural and verbal declarative form (e.g., math and science principles) imply instruction that prompts for selfexplanations (Aleven & Koedinger, 2002).”

Prompting students to self-explain each step of a worked example or each line of a text usually causes higher learning gains than having them study the material without such prompting.

“When students are given a worked example or text to study, prompting them to self-explain each step of the worked example or each line of the text usually causes higher learning gains than having them study the material without such prompting (e.g., Aleven & Koedinger, 2002;Chi, de Leeuw, Chiu, & LaVancher, 1994;Renkl, Stark, Gruber, & Mandl, 1998), but exceptions are discussed below.”