Glossary

Desirable difficulties

Challenges in learning that ultimately allow learners to better encode and retrieve information in the long run (Wichmann & Timpe, 2015; Schweppe & Rummer, 2016; Kachergis et al., 2017; Weissgerber & Reinhard, 2017; Fyfe & Rittle-Johnson, 2017; Diehl et al., 2018).

Fyfe, E. R., & Rittle-Johnson, B. (2017). Mathematics practice without feedback: A desirable difficulty in a classroom setting. Instructional Science, 45(2), 177–194. https://doi.org/10.1007/s11251-016-9401-1

Diehl, B., Dy-Boarman, E. A., Bottenberg, M. M., & Mobley-Bukstein, W. (2018). Utilizing desirable difficulties for sterile compounding training in a skills-based laboratory course. Currents in Pharmacy Teaching and Learning, 10(4), 469–472. https://doi.org/10.1016/j.cptl.2017.12.018

Kachergis, G., Rhodes, M., & Gureckis, T. (2017). Desirable difficulties during the development of active inquiry skills. Cognition, 166, 407–417. https://doi.org/10.1016/j.cognition.2017.05.021

Schweppe, J., & Rummer, R. (2016). Integrating written text and graphics as a desirable difficulty in long-term multimedia learning. Computers in Human Behavior, 60, 131–137. https://doi.org/10.1016/j.chb.2016.02.035

Weissgerber, S. C., & Reinhard, M.-A. (2017). Is disfluency desirable for learning? Learning and Instruction, 49, 199–217. https://doi.org/10.1016/j.learninstruc.2017.02.004

Wichmann, A., & Timpe, S. (2015). Can dynamic visualizations with variable control enhance the acquisition of intuitive knowledge? Journal of Science Education and Technology, 24(5), 709–720. https://doi.org/10.1007/s10956-015-9554-8

Failure driven memory

By encoding why failure occurred through a self-reflexive process, learners will be able to avoid similar failures in the future (A. Tawfik & Jonassen, 2013; Darabi et al., 2018).

Darabi, A., Arrington, T. L., & Sayilir, E. (2018). Learning from failure: a meta-analysis of the empirical studies. Educational Technology Research and Development, 66(5), 1101–1118. https://doi.org/10.1007/s11423-018-9579-9

Tawfik, A., & Jonassen, D. (2013). The effects of successful versus failure-based cases on argumentation while solving decision-making problems. Educational Technology Research and Development, 61(3), 385–406. https://doi.org/10.1007/s11423-013-9294-5

Ill-structured problems

Problems in which the learner does not have a clear path to complete the task (through ill-defined goals, unclear or unknown solutions) (Bogard et al., 2013; A. Tawfik & Jonassen, 2013; A. A. Tawfik, 2017).

Bogard, T., Liu, M., & Chiang, Y. V. (2013). Thresholds of knowledge development in complex problem solving: a multiple-case study of advanced learners’ cognitive processes. Educational Technology Research and Development, 61(3), 465–503. https://doi.org/10.1007/s11423-013-9295-4

Tawfik, A. A. (2017). Do cases teach themselves? A comparison of case library prompts in supporting problem-solving during argumentation. Journal of Computing in Higher Education, 29(2), 267–285. https://doi.org/10.1007/s12528-017-9136-2

Impasse-driven learning

If learners are unable to complete a procedural problem, they can either repair or seek help, allowing them to learn from their failure (Blumberg et al., 2008; A. A. Tawfik et al., 2015; Darabi et al., 2018).

Blumberg, F. C., Rosenthal, S. F., & Randall, J. D. (2008). Impasse-driven learning in the context of video games. Computers in Human Behavior, 24(4), 1530–1541. https://doi.org/10.1016/j.chb.2007.05.010

Tawfik, A. A., Rong, H., & Choi, I. (2015). Failing to learn: towards a unified design approach for failure-based learning. Educational Technology Research and Development, 63(6), 975–994. https://doi.org/10.1007/s11423-015-9399-0

Intelligent fast failure

Learners are encouraged to destigmatize failure by trying as many ideas as possible in a short period of time (Anderson et al., 2018).

Anderson, C. G., Dalsen, J., Kumar, V., Berland, M., & Steinkuehler, C. (2018). Failing up: How failure in a game environment promotes learning through discourse. Thinking Skills and Creativity, 30, 135–144. https://doi.org/10.1016/j.tsc.2018.03.002

Invention activities

Learners invent methods to capture meaningful properties of data provided to them before receiving instructions on canonical methods (Roll et al., 2012).

Roll, I., Holmes, N. G., Day, J., & Bonn, D. (2012). Evaluating metacognitive scaffolding in Guided Invention Activities. Instructional Science, 40(4), 691–710. https://doi.org/10.1007/s11251-012-9208-7

Knowledge gaps

Limitations in one’s knowledge (Loibl et al., 2017; Loibl and Rummel, 2014).

Loibl, K., & Rummel, N. (2014). Knowing what you don’t know makes failure productive. Learning and Instruction, 34(34), 74–85. https://doi.org/10.1016/j.learninstruc.2014.08.004

Loibl, K., Roll, I., & Rummel, N. (2017). Towards a theory of when and how problem solving followed by instruction supports learning. Educational Psychology Review, 29(4), 693–715. https://doi.org/10.1007/s10648-016-9379-x

Known unknowns

Being consciously aware of the limits of one’s knowledge (Otto & Mandorli, 2018).

Otto, H. E., & Mandorli, F. (2018). A framework for negative knowledge to support hybrid geometric modeling education for product engineering. Journal of Computational Design and Engineering, 5(1), 80–93. https://doi.org/10.1016/j.jcde.2017.11.006

Learning from errors

Analysis of errors committed during the completion of a task (Otto & Mandorli, 2018).

Negative knowledge

A type of meta-knowledge in which one knows what not to do (Gartmeier et al., 2011).

Gartmeier, M., Lehtinen, E., Gruber, H., & Heid, H. (2011). Erratum to: Negative expertise: comparing differently tenured elder care nurses’ negative knowledge. European Journal of Psychology of Education, 26(2), 301–302. https://doi.org/10.1007/s10212-011-0057-6

Negotiable failure

Moves away from binary of success and failure, encourages learners to actively negotiate what counts as failure (Trninic et al., 2018).

Trninic, D., Wagner, R., & Kapur, M. (2018). Rethinking failure in mathematics education: A historical appeal. Thinking Skills and Creativity, 30, 76–89. https://doi.org/10.1016/j.tsc.2018.03.008

Open-ended projects

Like ill-structured problems, these projects may lack clear canonical solutions but offer opportunity to engage with tools and concepts (Searle et al., 2018).

Searle, K. A., Litts, B. K., & Kafai, Y. B. (2018). Debugging open-ended designs: High school students’ perceptions of failure and success in an electronic textiles design activity. Thinking Skills and Creativity, 30, 125–134. https://doi.org/10.1016/j.tsc.2018.03.004

Problem-based learning

Student-centered learning using ill-structured problems in which students engage in self-directed and collaborative problem-solving (Swan et al., 2013; A. A. Tawfik, 2017).

Swan, K., Vahey, P., van’t Hooft, M., Kratcoski, A., Rafanan, K., Stanford, T., Yarnall, L., & Cook, D. (2013). Problem-based Learning across the curriculum: Exploring the efficacy of a cross-curricular application of Preparation for Future Learning. The Interdisciplinary Journal of Problem-Based Learning, 7(1), 91–. https://doi.org/10.7771/1541-5015.1307

Productive confusion hypothesis

Confusion offers the learner an opportunity to think, analyze, and invent which supports engagement and frustration but not boredom (D’Mello & Graesser, 2012).

D’Mello, S., & Graesser, A. (2012). Dynamics of affective states during complex learning. Learning and Instruction, 22(2), 145–157. https://doi.org/10.1016/j.learninstruc.2011.10.001

Productive failure

Two-phased learning design: learners grabble with a difficult problem followed by learners receiving direct instruction (Kapur, 2008, 2014b; Kapur & Rummel, 2012; Loibl et al., 2017).

Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424. https://doi.org/10.1080/07370000802212669

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

Kapur, M., & Rummel, N. (2012). Productive failure in learning from generation and invention activities. Instructional Science, 40(4), 645–650. https://doi.org/10.1007/s11251-012-9235-4

Productive struggle

Expending effort and applying prior knowledge to challenging new tasks to make sense of something not immediately apparent (Chen, 2022; Fries et al., 2021; Warshauer, 2019; 2014).

As distinguished from unproductive struggle (Chen, 2022; Jairam, 2020; Anderson, 2006; Weaver, 1949).

“Struggle” on its own may, depending on context, connote productive struggle (as in the classic works of Dewey, 1933, Weaver, 1949, and Piaget, 1972) or unproductive struggle (as in the recent work of Celedón-Pattichis et al, 2022).

Anderson, T. D. (2006). Uncertainty in action: Observing information seeking within the creative processes of scholarly research. Information Research, 12, 283–298. http://InformationR.net/ir/12-1/paper283.html

Celedón-Pattichis, S., Kussainova, G., LópezLeiva, C. A., & Pattichis, M. S. (2022). “Fake It Until You Make It”: Participation and Positioning of a Bilingual Latina Student in Mathematics and Computing. Teachers College Record, 124(5), 186–205. https://doi.org/10.1177/01614681221104106

Chen, Y.-C. (2022). Epistemic uncertainty and the support of productive struggle during scientific modeling for knowledge co-development. Journal of Research in Science Teaching, 59(3), 383–422. https://doi.org/10.1002/tea.21732

Dewey, J. (1933). How we think: A restatement of the relations of reflective thinking to the educative process. DC Heath. https://openlibrary.org/books/OL6295188M/How_we_think

Fries, L., Son, J. Y., Givvin, K. B., & Stigler, J. W. (2021). Practicing connections: A framework to guide instructional design for developing understanding in complex domains. Educational Psychology Review, 33, 739– 762. https://doi.org/10.1007/s10648-020-09561-x

Jairam, A. E. (2020). Attending to uncertainty in the design and implementation of DGE tasks to engage mathematics students in productive struggle. Unpublished doctoral dissertation. The Pennsylvania State University.

Piaget, J. (1972). Intellectual Evolution from Adolescence to Adulthood. Human Development, 15(1), 1–12. https://doi.org/10.1159/000271225

Warshauer, H. K. (2014). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18(4), 375–400. https://doi.org/10.1007/s10857-014-9286-3

Warshauer, H. K., Starkey, C., Herrera, C. A., & Smith, S. (2019). Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematics Teacher Education, 24(1), 89–121. https://doi.org/10.1007/s10857-019-09451-2

Weaver, W. (1949). Recent contributions to the mathematical theory of communication. In C. E. Shannon & W. Weaver (Eds.), The mathematical theory of communication (pp. 94–117). The University of Illinois Press.

Productive success

Short-term achievements which support long-term learning (Kapur, 2016; Darabi et al., 2018).

Kapur, M. (2016). Examining Productive Failure, Productive Success, Unproductive Failure, and Unproductive Success in learning. Educational Psychologist, 51(2), 289–299. https://doi.org/10.1080/00461520.2016.1155457

Reflective learning

A learning process that involves student review of their decisions made in previous work. In a failure context, assesments ask students to explore the assumptions which led to a self-made or external failure (Heemsoth and Heinze, 2016) .

Heemsoth, T., & Heinze, A. (2016). Secondary school students learning from reflections on the rationale behind Self-Made Errors: A field experiment. The Journal of Experimental Education, 84(1), 98–118. https://doi.org/10.1080/00220973.2014.963215

Resiliency

A multi-faceted construct with a range of definitions, most of which emphasize an adaptive relationship to adversity or challenge (Cassidy, 2015): e.g., the ability to learn from failure and bounce back from challenges.

An alterable process or mechanism that can be fostered and developed, as opposed to a fixed attribute (Waxman et al, 2002).

In management and business training, often associated with discourses of “grit” and “positivity” (Berg & Pietrasz, 2017; Avey, Luthans, & Youssef, 2010; Avey, Hughes, Norman, & Luthans, 2008; Avolio, 2006). Like these discourses, may neglect consideration of structural/systemic contexts and constraints.

Avey, J. B., Hughes, L. W., Norman, S. M., & Luthans, K. W. (2008). Using positivity, transformational leadership and empowerment to combat employee negativity. Leadership & Organization Development Journal, 29(2), 110–126. https://doi.org/10.1108/01437730810852470

Avey, J. B., Luthans, F., & Youssef, C. M. (2010). The Additive Value of Positive Psychological Capital in Predicting Work Attitudes and Behaviors. Journal of Management, 36(2), 430–452. https://doi.org/10.1177/0149206308329961

Berg, P., & Pietrasz, C. (2017). Turning classroom failure into student success: The value of integrating resiliency building activities in the academic classroom. Management Teaching Review, 2(4), 299–311. https://doi.org/10.1177/2379298117710780

Cassidy, S. (2015). Resilience Building in Students: The Role of Academic Self-Efficacy. Frontiers in Psychology, 6, 1781–1781. https://doi.org/10.3389/fpsyg.2015.01781

Luthans, F., Avolio, B. J., & Youssef, C. M. (2006). Psychological Capital: Developing the Human Competitive Edge. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195187526.001.0001

Waxman, H. C., Gray, J. P., & Padrón, Y. N. (2002). Resiliency among Students at Risk of Academic Failure. Teachers College Record (1970), 104(10), 29–48. https://doi.org/10.1177/016146810210401002

Self-regulation

Self-awareness and control over setting appropriate goals, maintaining motivations, and evaluating progress (Bogard et al., 2013).

Simulation-based learning

Engineered situations which rely on low stakes conditions to promote the creative application of prior knowledge (Chernikova et al., 2020).

Chernikova, O., Heitzmann, N., Stadler, M., Holzberger, D., Seidel, T., & Fischer, F. (2020). Simulation-Based Learning in higher education: A Meta-Analysis. Review of Educational Research, 90(4), 499–541. https://doi.org/10.3102/0034654320933544

Unproductive failure

Short-term failure not followed by any benefits of sustained learning (Darabi et al., 2018; Kapur, 2016; Kapur & Rummel, 2012).

Kapur, M., & Rummel, N. (2012). Productive failure in learning from generation and invention activities. Instructional Science, 40(4), 645–650. https://doi.org/10.1007/s11251-012-9235-4

Vicarious failure

Learning by evaluating peers’ solutions before receiving instruction (Kapur, 2014a).

Kapur, M. (2014). Comparing Learning From Productive Failure and Vicarious Failure. The Journal of the Learning Sciences, 23(4), 651–677. https://doi.org/10.1080/10508406.2013.81900