Katharina Loibl

Affect Matters: Exploring the Impact of Feedback During Mathematical Tasks in an Exploratory Environment

We describe a Wizard-of-Oz study that investigates the impact of different types of feedback on students’ affective states. Our results indicate the importance of matching carefully the affective state with appropriate feedback in order to help students transition into more positive states. For example when students were confused affect boosts and specific instruction seem to be effective in helping students to be in flow again. We discuss this and other effective ways to and implications for the development of our system and the field in general.

Productive Failure as strategy against the double curse of incompetence

Learners who lack knowledge often also lack the ability to assess their limited competence correctly. Due to the incorrect self-assessment, they are unlikely to apply strategies that would help them to acquire relevant knowledge. This effect is known as the double curse of incompetence. When students solve problems prior to being taught the canonical solution in a so-called Productive Failure setting (PF), they usually come up with solution ideas that are erroneous or incomplete. Due to this struggle with the problem at hand, they may become aware of the limitations of their knowledge. Demonstrating how typical student solutions fail to solve the problem during subsequent instruction may further help students to assess their competence correctly. Improved awareness of limited competence, in turn, may foster fruitful learning strategies when learning the canonical solution. Indeed, our empirical study showed that students in PF conditions have a more realistic perception of their own knowledge than students in so-called direct instruction conditions (DI), and that they also ultimately learn more. The same pattern was true for students who were confronted with limitations of typical student solutions during instruction.

Discussing Student Solutions Is Germane for Learning when Providing or Delaying Instruction

Recent studies have shown benefits of problem-solving prior to instruction (cf. productive failure) for learning. These findings seem to contradict well-established assumptions of cognitive load theory. However, there are two possible mechanisms in line with cognitive load theory that may explain these beneficial effects: the activation of prior knowledge and intuitive ideas during the problem-solving phase to generate solution approaches and the focusing of attention on relevant components of the canonical solution by comparing and contrasting typical student solutions to the canonical solution during the instruction phase. It is unclear whether the reported benefits originate from the activation of prior knowledge and intuitive ideas during the problem-solving phase or from the specific form of instruction in which student solutions are compared and contrasted to the canonical solution. To investigate this question, we compared three conditions in a quasi-experimental study: standard instruction prior to problem-solving (I − PS), instruction in which typical student solutions are contrasted to the canonical solution prior to problem-solving (Icontrast − PS), and problem-solving prior to instruction in which typical student solutions are contrasted to the canonical solution (PS − Icontrast). I − PS was outperformed by the other two conditions on conceptual knowledge. This finding suggests that student solutions are fruitful learning resources. We argue that the comparison of student solutions and the canonical solution focuses attention on the relevant components of the solution, which leads to deeper processing. Indeed, our cognitive load measures suggest that comparing and contrasting typical student solutions during instruction is germane for learning.