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Productive Failure

See also: teaching, teaching-mathematics, when-to-instruct, desirable-difficulties

Lodge et al (2018)

Productive failure is a way of sequencing learning activities to give students an opportunity to familiarize themselves with a complex problem or issue in a structured environment but without significant instruction on the content of the material to be learned

Echoes of the timms-video-studies findings about Japanese teaching methods

The ETH web page on productive failure offers this definition

Productive Failure (PF) is a learning design that entails the design of conditions for learners to persist in generating and exploring representations and solution methods (RSMs) for solving complex, novel problems. Though such a process may initially lead to failure to generate canonical RSMs, it has a hidden efficacy that is germane for learning provided an appropriate form of instructional intervention follows that can consolidate and assemble student-​generated RSMs into canonical RSMs.

And subsequently identifies two problems with direct instructions

  1. Students don't have the necessary prior knowledge to understand how/why the new RSMs are useful/apply
  2. Presenting RSMs as neat abstractions during DI, students may not understand why they are assembled this way

Hence productive failure has two phases:

  1. Generate and explore multiple RSMs.
  2. Consolidation and knowledge assembly.

Design Principles#

Design Phases Task Participation structures Social surround
1. Generate and explore multiple representations and solutions methods (RSMs) Design tasks that are adequately complex, engaging, and draw on students' mathematical resources Enable collaboration to allow students to elaborate, critique, explain, and evaluate shared work, thereby enriching the shared representation and solution spaces. Create a safe space for students to explore and generate setting appropriate socio-mathematical norms, and providing affective support for persistence
2. Organisation and knowledge assembly Compare and constrast student-generated and canonical ideas Enable student engagement through group presentations and students' participation; teachers act as facilitators paraphrasing student explanations, and drawing attention to critical features Create a safe space to explore the affordances and constrains of student-generated RSMs with a view of improving upon them, and not assessing them as correct or incorrect

Mathematics#

Kapur (2014) compared the two approaches

  1. More traditional direct instruction

    The traditional, most prevailing method is to first teach students the concept and procedures of SD and then get them to solve problems requiring those concept and procedures. This sequence of instruction followed by problem solving is commonly known as direct instruction (p. 1008)

  2. The productive failure sequence

    A contrasting method is one that reverses the sequence, that is, engages students in problem solving first and then teaches them the concept and procedures (p. 1008)

    Arguing that the productive failure sequence "combines the benefits of exploratory problem solving and instruction, thereby mitigating the possibility that students do not discover the correct concepts and procedures on their own" (Kapur, 2014, p. 1009)

Reasons to believe in the effectiveness of productive failure include

  1. Initial problem solving helps activate and differentiate prior knowledge, if students are able to use that prior knowledge to generate suboptimal/incorrect solution to the problem
  2. The difficulty they encounter "can aid encoding and schema assembly" and prepare for subsequent instruction
  3. If students persist in problem solving this provides them with more agency and therefore engagement
  4. Help students notice inconsistencies and limitations or prior knowledge
  5. Prior knowledge activation and differentation may afford greater opportunities comparing student and expert solutions - raising student awareness of and encoding of critical features of the new concept, helping improve their ability to select and apply knowledge & procedures

Results#

In summary

  • Direct instruction students tended to somewhat better on procedural knowledge
  • productive failure students did significantly better on conceptual understanding and transfer

Productive failure students, in spite of reporting greater mental effort than DI students, significantly outperformed DI students on conceptual understanding and transfer without compromising procedural knowledge.1 Evidence therefore supports the hypothesis that the PF method activated and differentiated students’ prior knowledge during the problemsolving phase, which may have prepared them to learn from the subsequent instruction phase. The significant correlation between the number of solutions generated by PF students during the problem-solving phase—a proxy indicator of prior knowledge activation and differentiation—and their conceptual understanding and transfer performance on the posttest lends further credibility to this explanation. (Kapur, 2014, p. 1014)

DeCaro & Rittle-Johnson (2012) found

Exploring problems before instruction improved understanding compared with a more conventional “instruct-then-practice” sequence....Microgenetic analyses revealed that problem exploration led children to more accurately gauge their competence, attempt a larger variety of strategies, and attend more to problem features—better preparing them to learn from instruction

References#

DeCaro, M. S., & Rittle-Johnson, B. (2012). Exploring mathematics problems prepares children to learn from instruction. Journal of Experimental Child Psychology, 113(4), 552--568. https://doi.org/10.1016/j.jecp.2012.06.009

Kapur, M. (2014). Productive Failure in Learning Math. Cognitive Science, 38(5), 1008–1022. https://doi.org/10.1111/cogs.12107

Kapur, M. (2015). Learning from productive failure. Learning: Research and Practice, 1(1), 51–65. https://doi.org/10.1080/23735082.2015.1002195

Kapur, M., & Bielaczyc, K. (2012). Designing for Productive Failure. Journal of the Learning Sciences, 21(1), 45–83. https://doi.org/10.1080/10508406.2011.591717

Lodge, J. M., Kennedy, G., Lockyer, L., Arguel, A., & Pachman, M. (2018). Understanding Difficulties and Resulting Confusion in Learning: An Integrative Review. Frontiers in Education, 3. https://doi.org/10.3389/feduc.2018.00049

Steenhof, N., Woods, N. N., Van Gerven, P. W. M., & Mylopoulos, M. (2019). Productive failure as an instructional approach to promote future learning. Advances in Health Sciences Education, 24(4), 739–749. https://doi.org/10.1007/s10459-019-09895-4