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How 'Productive Failure' In Math Class Helps Make Lessons Stick

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 (Amanda Lucier)

Learning from failure has become a popular idea in education recently, partly because it feels like common sense to many people. In a general way, the idea of “picking yourself up after a fall” has long existed in American culture as in many other parts of the world. Teachers are hoping that if they can instill this idea in their students, the small, everyday setbacks inherent to learning new things won’t feel so emotionally charged to students, who might instead see them as part of the path to greater understanding and ultimate success.

But turning the difficult experience of failure into a positive isn’t as easy as telling students to change their mindsets; it takes careful lesson design, a strong classroom culture and an instructor trained in getting results from small failures so his or her students succeed when it matters.

Manu Kapur has been studying what he calls “productive failure” for most of his career, attempting to turn the general advice to “learn from mistakes” into a clearly defined, specific pedagogical design process that yields strong learning results. Now a professor of psychological studies at the Education University of Hong Kong, Kapur has conducted both quasi-experimental and randomized controlled trials on how teaching through productive failure measures up to both direct instruction as well as more constructivist problem-solving approaches.

For Kapur, productive failure is not just a maxim about persisting through challenges; it's an effective teaching strategy that enables students to not only do well on short term measures of knowledge, like tests, but also affords better conceptual understanding, creative thinking, and helps students to transfer learning to novel situations.

“Learning from failure is a very intuitive and compelling idea that’s been around for ages, but teachers may not know how to use it,” Kapur said. He has run enough experiments both in lab settings and in real classrooms to have a fairly good idea of how to structure lessons that include failure up front, followed by consolidation of understanding through instruction.


The general idea is to develop tasks that students will not be able to solve, but require them to call upon their preexisting knowledge to try to solve the problem. That knowledge can be of the subject itself, as well as the informal insights students bring from their lives. The students will inevitably fail -- as the teacher expects them to -- but that failure is framed as part of learning and so is not seen as shameful. This process primes students’ brains to learn the new concept from their instructor after the initial failure.

“It is failure-based activation of knowledge to prepare them to learn,” Kapur said.

It might seem like this process would frustrate kids until they stop trying, but Kapur’s studies found that instead of feeling bad about their inability to solve the problem, students’ interest in the concept spiked. “I think that’s a great place to get students to before we teach them something,” Kapur said.

After students experience failure in their own discovery and problem solving process, the teacher facilitates a discussion that highlights various student attempts and teaches the new concept, consolidating students’ understanding of the processes required to complete the task.


  • Tasks must be challenging enough to engage learners, but not so challenging they give up.
  • Tasks must have multiple ideas, solutions or ways to solve so that students generate a multitude of ideas. It cannot be a closed task with only one path to finding a correct answer.
  • The task must activate prior knowledge, and not just formal learning from a previous lesson. “If you design a task where a student only displays their prior class learning it’s not good because then you aren’t tapping into their intuitive reasoning,” Kapur said. Intuitive reasoning is a big part of how students transfer knowledge to new situations.
  • While the task should activate knowledge, it should be designed so that the knowledge students have is not sufficient to solve the problem. They should hit a roadblock that they can’t get around. “It makes the child aware of what he or she knows, and the limits of what he or she knows, and that creates a motivation to figure out what it is they need to know to solve this problem,” Kapur said.
  • It helps if that task as an “affective draw,” in that it’s related to something students care about or is concerns something with which they identify.

Kapur has tested productive failure teaching strategies with students of varying abilities in Singapore and has found it to work with all students, regardless of ability. “Initial pre-existing conditions between students do not predict how much they learn,” Kapur said. “How they solve the initial problem is what predicts how much they learn.”

Singapore tracks students into ability-based schools after primary school, which makes it easy to conduct research that compares low, middle and high achievers. However, Kapur has also tested productive failure in Indian schools in which students were not grouped by ability. He saw good results there as well. “The task is open enough that kids from different abilities can work together,” Kapur said.

Part of Kapur’s research has been to show that teaching with productive failure doesn’t harm students’ ability to perform on tests, but does improve knowledge transfer and conceptual understanding. In the process he’s discovered an interesting element of creative thinking in math that appears to disprove the generally held notion that students need basic content knowledge before they can move on to more creative uses of the information.

“We’ve found that creativity actually suffers if you teach kids something too early,” Kapur said. When students who have been taught with direct instruction are later asked to generate as many ways of solving the problem as they can, many can’t go beyond the method they have already been taught.

“They were locked into that way of thinking,” Kapur said. “When we start with generating or exploring we find that students still learn the material later on, but the knowledge was more flexible.” This finding tells Kapur that creativity is itself a function of how students’ acquire information.


Kapur’s research on productive failure has convinced Singapore’s Ministry of Education to use the pedagogical model for the statistical portion of it’s A-level curriculum. Statistics make up about one third of the Cambridge A-level exam, Kapur said. All university-track junior-college students in Singapore are in school to pass that exam (junior-college in Singapore is like high school in the US).

Although Singapore’s education system is very test-based, its Ministry of Education is interested in research-proven pedagogical approaches that lead to lasting learning beyond the test. “There is a very strong policy emphasis on changing how we teach,” Kapur said of Singapore. “Just because there are tests does not mean we can’t teach in ways that lead to very deep learning while doing well on the tests.”

Kapur was able to show that productive failure worked well with students at the least prestigious of Singapore’s 20 junior colleges, which provided a compelling proof of concept to scale up to all students studying for the Cambridge A-levels. Kapur and his team have designed a curriculum of tasks that use productive failure, and are training Singapore’s teachers in the method.

The concept is new to many Singaporean teachers and Kapur says the first part of his training focuses on helping teachers understand the problems with direct instruction. He uses the analogy of watching a film. The average viewer focuses on plot, and perhaps pays some attention to acting ability or cinematography. When a director watches the same film, on the other hand, she is likely noticing nuances of camera placement, shot selection, and much more. That’s the difference between what a novice sees and what an expert sees.

“No matter how engaging, entertaining or logically structured the new information is, the novice by definition is not going to see the same thing as the expert in the presentation,” Kapur said. He works to help teachers understand the flawed assumption that students will understand after a concept has been told to them, explaining that direct instruction doesn't prime students’ brains to process the new information.

“We won’t make the assumption that you’re prepared to learn yet; what we will do is activate your formal and informal knowledge systems,” Kapur said.

The teacher training program also focuses on improving teachers’ content knowledge. Working with student ideas and misconceptions requires the instructor have a deep understanding of the subject matter. Finally, Kapur helps teachers improve on important pedagogical aspects of this model like facilitating group work and consolidating ideas after students have grappled with a problem and failed.

“Your job as a teacher is to first prepare them, to give them the proverbial eyes to be able to see what is important, and then show them what is important in interesting and engaging ways,” Kapur said.


Singapore’s Ministry of Education has agreed to give Kapur’s team four years to build teachers’ capacity in this new style of teaching before evaluating its effectiveness. Kapur sees this as a huge gift, knowing that the effectiveness of any program lies in its implementation and that it takes time to get people up to speed.

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