Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep features of the target content, which prepares them to better process the subsequent instruction. Unclear is whether this effect results from merely changing the order of the learning phases (i.e., instruction or problem solving first) or from additional features, such as presenting problem-solving material in the form of cases that differ in one feature at a time. Contrasting such cases may highlight the deep features and provide grounded feedback to students’ problem-solving attempts. In addition, the effect of the order of instruction and problem solving on procedural fluency is still unclear. The present experiment (N = 181, mean age = 14.53) investigated in a 2 × 2 design the effects of order (instruction or problem solving first) and of contrasting cases in the problem-solving material (yes/no) on conceptual understanding and procedural fluency. Additionally, the quality and quantity of students’ solution attempts from the problem-solving phase were coded. Regarding the learning outcomes, the ANOVA results suggest that for procedural fluency instruction prior to problem solving was more beneficial than problem solving prior to instruction. Merely delaying instruction did not increase conceptual understanding. The contrasting cases did not affect the quality of solution attempts, nor the posttest results. As expected, students who received instruction first generated fewer, but higher-quality solution attempts.

中文翻译：

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在教学之前和之后解决问题期间对比案例的效果

对生产性失败的研究表明，与在解决问题之前接受指导相比，在指导之前尝试解决问题有助于概念理解。这些假设是，在解决问题的阶段，学生可以激活自己的先验知识，意识到自己的知识空白，并发现目标内容的深层特征，从而为他们更好地处理后续的指导做准备。尚不清楚这种效果是由仅改变学习阶段的顺序（即首先是指导或解决问题）还是由于其他特征（例如，以一种情况下一次呈现出不同特征的案例形式呈现问题解决材料）引起的。与此类案例进行对比可能会凸显其深层特征，并为学生解决问题的尝试提供扎实的反馈。此外，指令顺序和问题解决对程序流畅性的影响尚不清楚。目前的实验（N  = 181，平均年龄= 14.53）在2×2设计中研究了顺序（指示或解决问题的先例）和问题解决材料中对比案例（是/否）对概念理解和程序流畅性的影响。此外，还对从问题解决阶段开始的学生解决方案尝试的质量和数量进行了编码。关于学习成果，方差分析结果表明，对于在解决问题之前进行程序流利的教学，比在解决问题之前进行问题解决更为有益。仅仅延迟教学并不能增加概念上的理解。对比情况既不影响解决方案尝试的质量，也不影响测试后的结果。不出所料，首先接受指导的学生生成的尝试次数较少，但尝试的质量较高。