To explore the impact on performance and affect of explaining and correcting worked examples that include errors compared to practicing problem solving.
Erroneous Examples and Misconceptions
Erroneous examples, or worked-out solutions to an example problem that include at least one incorrect step, have been studied as a way to address misconceptions. Misconceptions can be hard to remedy with direct explanations. Instead, it is often more effective to allow the learners to uncover the logical flaw that disputes a misconception.
For instance, a common misconception in biology is that trees grow from nutrients that they pull from the soil. If an instructor explained that trees grow by breathing in CO^2 from the air, retaining the carbon, and breathing out O^2, a biology student is likely to forget the correct explanation. Instead, if the instructor asks what trees are made out of (carbon), what a tree breathes in (CO^2), and what a tree breathes out (O^2), then the student makes the conclusion that trees grow from carbon in the air and is more likely to remember the correct explanation long term.
Despite intuitions that giving students erroneous examples can foster misconceptions, the research suggests the opposite. Asking students to correct erroneous examples prompts them to explain why incorrect steps are wrong and why correct steps are right. By directly addressing incorrect steps, students are more likely to remedy misconceptions and better understand example solutions. Of course, there are more and less effective methods of using erroneous examples, and Richley et al.’s study sought to explain the mechanisms that drive efficacy of erroneous examples. They also sought to explain the impact on confusion and frustration, or confrustion (Liu et al., 2013), that working with erroneous examples had on students compared to practicing problem solving. Prior work is conflicted about whether confrustion predicts better learning outcomes or not.
Richley et al. explored the short-term and long-term effect on performance and confrustion of correcting erroneous examples compared to practicing problem solving. Students learned about decimals in math, a concept that has several well-documented misconceptions. Their sample was 598 students in 6th grade math, and they used log data collected from computer-based tutoring systems.
Performance was measured with three isomorphic (problems are the same, but the numbers are different), 46-item tests given before using the tutor (pre-test), immediately after using the tutor (post-test), and one week after using the tutor (delayed post-test). Confrustion was measured through affective state detectors based on interactions with the tutoring systems. These detectors are imperfect but highly scalable compared to more accurate physiological sensors.
Performance: After accounting for pre-test score, there was no difference between the erroneous-example and problem-solving conditions on the post-test. Students who worked with erroneous examples, however, performed better than those who practiced problem solving on the delayed post-test one week later, F(2, 595) = 15.83, p < .001, d = .27.
Confrustion: Students working with erroneous examples experienced more confrustion than those practicing problem solving, F(2, 595) = 43.0, p < .001, d = .54. Further analysis suggested that the erroneous-example condition also experienced longer periods of confrustion than the problem-solving condition. Confrustion levels declined throughout the instructional materials, though not by a large degree, F(3, 27334) = 210.85, p < .001, η^2 = .0075.
Performance and Confrustion: Student with lower pre-test scores had higher levels of confrustion. After accounting for pre-test scores, higher confrustion still predicted lower post-test and delayed post-test scores. Despite this general finding, there was an interesting interaction with condition. Higher confrustion had less of a negative impact on post-test and delayed post-test scores for the erroneous example group.
Why this is important
Besides introducing me to the term confrustion, this paper is valuable because it adds nuance to our understanding of the role of confrustion in learning. The results seem to contradict themselves because high confrustion correlated with low performance, but correcting erroneous examples resulted in both higher confrustion and higher delayed post-test scores than practicing problem solving. However, further analysis suggested that not all confrustion is created equal. High confrustion while correcting erroneous examples was not as harmful to performance as high confrustion while practicing problem solving. The authors argue that intentionally confrusting students within the erroneous example framework was more beneficial than the unintentional confrustion that often accompanies early problem solving attempts, especially for a topic with many common misconceptions.
I particularly liked this paper because I just finished reading Reshma Saujani’s Brave, Not Perfect book about resisting the urge to stay in our comfort zones where we can perform perfectly and bravely push into new territory where we might have to fail before we flourish. She argues that girls in particular are encouraged to perfect existing skills while boys are encouraged to try, flounder, and persist in learning new skills. Erroneous examples seem like a good tool for all students to practice persisting in the face of confrustion to achieve ultimately better learning.
Liu, Z., Pataranutaporn, V., Ocumpaugh, J., & Baker, R. (2013, July). Sequences of frustration and confusion, and learning. In Educational Data Mining 2013.
Richey, J. E., Andres-Bray, J. M. L., Mogessie, M., Scruggs, R., Andres, J. M., Star, J. R., … & McLaren, B. M. (2019). More confusion and frustration, better learning: The impact of erroneous examples. Computers & Education.
Saujani, R. (2019). Brave, Not Perfect: Fear Less, Fail More, and Live Bolder. New York, NY: Penguin Random House.
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