Productive failure in learning the concept of variance

@article{Kapur2010ProductiveFI,
  title={Productive failure in learning the concept of variance},
  author={Manu Kapur},
  journal={Instructional Science},
  year={2010},
  volume={40},
  pages={651-672}
}
  • Manu Kapur
  • Published 22 March 2012
  • Education
  • Instructional Science
In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical formulation of variance taught to them, PF students generated a diversity of formulations for variance but were unsuccessful in developing the… 

Comparing Learning From Productive Failure and Vicarious Failure

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students generated solutions to a complex problem

Productive Failure in Learning Math

The results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem-solving attempts or those of others before receiving instruction as alternatives for better math learning.

Classroom-based Experiments in Productive Failure

Results challenge the claim that that direct instruction alone is the most effective approach for teaching novel concepts to learners and question whether there is little efficacy in having learners solve problems that target novel concepts they have not learnt yet.

Preparatory effects of problem solving versus studying examples prior to instruction

  • Gog
  • Education
  • 2021
The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to instruction – at which point they typically fail. Yet, research on PF shows that students who are involved

Preparatory effects of problem solving versus studying examples prior to instruction

The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to instruction – at which point they typically fail. Yet, research on PF shows that students who are involved

Probing boundary conditions of Productive Failure and analyzing the role of young students’ collaboration

This study adds to the mixed results regarding the superiority of problem solving prior to instruction for young students, thus opening the discussion about age-related prerequisites as boundary conditions for PF.

A further study of productive failure in mathematical problem solving: unpacking the design components

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics

Errors During Exploration and Consolidation—The Effectiveness of Productive Failure as Sequentially Guided Discovery Learning

Posttest results indicate that including erroneous solution attempts in the instruction phase can be beneficial for learning units in which most students fail to come up with a correct solution themselves, but only if students are prompted to compare the erroneous solution Attempts with correct solutions.

When Problem Solving Followed by Instruction Works: Evidence for Productive Failure

When learning a new concept, should students engage in problem solving followed by instruction (PS-I) or instruction followed by problem solving (I-PS)? Noting that there is a passionate debate about
...

References

SHOWING 1-10 OF 41 REFERENCES

Classroom-based Experiments in Productive Failure

Results challenge the claim that that direct instruction alone is the most effective approach for teaching novel concepts to learners and question whether there is little efficacy in having learners solve problems that target novel concepts they have not learnt yet.

Designing for Productive Failure

The design principles undergirding productive failure (PF) are described and findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability.

Productive failure in mathematical problem solving

This paper reports on a quasi-experimental study comparing a “productive failure” instructional design (Kapur in Cognition and Instruction 26(3):379–424, 2008) with a traditional “lecture and

A further study of productive failure in mathematical problem solving: unpacking the design components

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics

Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction

Two studies on teaching descriptive statistics to 9th-grade students examined whether invention activities may prepare students to learn found that invention activities, when coupled with subsequent learning resources like lectures, led to strong gains in procedural skills, insight into formulas, and abilities to evaluate data from an argument.

The Equivalence of Learning Paths in Early Science Instruction

It is found not only that many more children learned from direct instruction than from discovery learning, but also that when asked to make broader, richer scientific judgments, the many children who learned about experimental design from direct Instruction performed as well as those few children who discovered the method on their own.

Direct instruction vs. discovery: The long view

D. Klahr and M. Nigam (2004) make a case for the superiority of direct instruction over discovery learning in students' mastery of the control-of-variables strategy central to the scientific method.

Productive failure in CSCL groups

Additional analyses revealed that neither preexisting differences in prior knowledge nor the variation in group outcomes (quality of solutions produced) seemed to have had any significant effect on individual near and far transfer measures, lending support to the idea that it was the nature of the collaborative process that explained productive failure.

Designing for productive failure in mathematical problem solving

Designing for Productive Failure in Mathematical Problem Solving Manu Kapur & June Lee National Institute of Education, Singapore solving problems without the provision of support structures. While