Provide feedback in the problem-solving phase to foster negative knowledge and multiple solution attempts¶

Strategy · All strategies
Evidence · 6 claims (5 mixed, 1 against) · 1 study (1 causal), q3 · 1 of 1 report an effect size · 6 claims rest on one study

Description¶

As a lesson from the failed replication, the authors recommend that "the problem-solving phase should include implicit (Nathan, 1998; Roll et al., 2014) or explicit feedback to facilitate the acquisition of negative knowledge and to prompt the generation of further solution attempts." In this study, students were satisfied with a single initial attempt because the case design gave no hints that solutions without normalization were incorrect. Feedback via contrasting cases can push learners beyond their prior knowledge and prepare them for subsequent instruction.

Design Implications¶

Context¶

Requirements¶

• Problem-solving tasks or contrasting cases that make the limits of students' initial solution attempts apparent

Constraints¶

• The article notes a challenge in structuring the problem-solving phase so it still allows valid and complex problem-solving processes

Target Learners¶

• undergraduate teacher students learning statistical or probabilistic reasoning

Target Learning Goals¶

• acquiring negative knowledge and generating multiple solution attempts prior to instruction

Claims¶

• In the Bayesian-reasoning problem-solving phase, most students generated only one solution attempt, far fewer than in the original variance study [-W]
• Students' generated solutions rarely matched the erroneous solutions included in the explicit instruction phase [~W]
• No significant interaction between order of phases and type of instruction on conceptual knowledge in the Bayesian-reasoning replication [~W]
• In a Bayesian-reasoning replication, problem-solving prior to instruction (PS-I) showed no significant advantage over instruction-first (I-PS) on conceptual knowledge [~W]
• No significant effect of order of phases on procedural knowledge in the Bayesian-reasoning replication [~W]
• Including typical student solutions in explicit instruction showed no significant effect on conceptual knowledge in the Bayesian-reasoning replication [~W]

Related Strategies¶

• Include student solutions in explicit instruction that are actually typical for the taught sample
• Explicitly guide students to use contrasting cases as grounded feedback by prompting intuitive predictions
• Productive Failure
• Have learners develop their own problem-solving templates instead of replicating instructor templates

Examples¶

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Key Sources¶

• Loibl, K., & Leuders, T. (2024). Can failure be made productive also in Bayesian reasoning? A conceptual replication study. Instructional Science. https://doi.org/10.1007/s11251-024-09670-y