Mental models of recursion

Götschi, Tina; Sanders, Ian R.; Galpin, Vashti

doi:10.1145/612001.612004

Cited by 5 publications

(13 citation statements)

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“…The step, return value and algebraic models simply demonstrate various forms of confusion on the part of the student. Sanders et al (2006) corroborated the findings of Götschi et al (2003) as regards the first year students. Subsequent work (unpublished) identified the existence of a risky viable passive mental model of recursion where only the passive flow is shown.…”

Section: Introductionsupporting

confidence: 81%

“…Continuous efforts have been made to determine whether first year students do, in fact, build viable mental models of recursion by studying how students trace recursive functions, analogous to the work of Kahney (1989) and Dicheva & Close (1996). Traces in specific test and examination questions over a number of years were analyzed (Götschi, Sanders & Galpin, 2003;Sanders, Galpin & Götschi, 2006). The students' mental models were then determined based on their representation of the flow of control in the recursive functions.…”

Section: Introductionmentioning

confidence: 99%

“…The students' mental models were then determined based on their representation of the flow of control in the recursive functions. Götschi et al (2003) noted the existence of the copies, loop, magic and odd models, as identified by Kahney (1989), but identified an additional, sometimes viable, model (the active model) as well as additional nonviable models (step, return value and algebraic). In the active model the active flow is explicitly demonstrated but the passive flow is not shown, either because the solution has been evaluated at the base case, or because the passive flow has been implicitly dealt with.…”

Section: Introductionmentioning

confidence: 99%

“…In the active model the active flow is explicitly demonstrated but the passive flow is not shown, either because the solution has been evaluated at the base case, or because the passive flow has been implicitly dealt with. Götschi et al (2003) also showed that the looping and active mental models could be considered as risky viable models: they can result in the correct solution for simple tail recursive functions (like factorial) but do not always lead to the correct solution. Götschi et al (2003) argued that students who demonstrate the magic model have partial understanding of the recursive process as their traces show aspects of the active flow, limiting case and passive flow but with clear errors showing lack of understanding.…”

Section: Introductionmentioning

confidence: 99%

“…Götschi et al (2003) also showed that the looping and active mental models could be considered as risky viable models: they can result in the correct solution for simple tail recursive functions (like factorial) but do not always lead to the correct solution. Götschi et al (2003) argued that students who demonstrate the magic model have partial understanding of the recursive process as their traces show aspects of the active flow, limiting case and passive flow but with clear errors showing lack of understanding. The step, return value and algebraic models simply demonstrate various forms of confusion on the part of the student.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

First year students' understanding of the flow of control in recursive algorithms

Sanders

Scholtz

2012

African Journal of Research in Mathematics, Science and Technol

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Recursion is an important concept for any computer science student to master. Many first year students develop the viable copies mental model of recursion and can successfully trace the execution of a simple recursive function. This article discusses a study focused on determining whether the ability to successfully trace a recursive function means that the student understands recursion or whether they are simply "applying a formula". The research question investigated was thus "To what extent do students with viable trace mental models understand the flow of control of recursive algorithms?" The research followed a phenomenological approach. A group of first year students with viable mental models was identified by classifying the mental models in their answers to test questions. Fifteen of these students were interviewed. The interviews involved the students talking aloud while they tackled various tasks. Each student's understanding of the active flow, the limiting case and the passive flow was assessed. The results show that in most cases even these students have some difficulty with the active flow, are confused about the passive flow and have misconceptions about the limiting case. This implies that more careful thought needs to be given to the examples used in teaching recursion and how the concept is taught.

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Section: Introductionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

First year students' understanding of the flow of control in recursive algorithms

Sanders

Scholtz

2012

African Journal of Research in Mathematics, Science and Technol

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EEG Activities During Program Comprehension: An Exploration of Cognition

Liao

2021

IEEE Access

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This study attempts to explore cognition during program comprehension through physiological evidence by recording and comparing electroencephalogram (EEG) activities in different frequency bands and the eye movements of the participants with high or low programming abilities. An experiment was conducted with thirty-three undergraduate students majoring in Computer Science. We recorded their EEG activities when they were reading two programs with three types of program constructs. At the same time, the participants' eye movements were recorded by an eye tracker to further understand the relationship between the program comprehension process and EEG activities. Experimental results show that the highperformance participants displayed higher performance for working memory (theta power), attention resource allocation (lower alpha power), and interaction between working memory and semantic memory (upper alpha power) in program comprehension tasks of complex constructs, which proves related theories proposed in the existing research on programming and cognition. The results of this study not only offer objective evidence of the roles cognition plays in program comprehension but also provide educators with suggestions for designing suitable pedagogical strategies.

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Algorithm Visualization and the Elusive Modality Effect

Zavgorodniaia

Tilanterä

Korhonen

et al. 2021

Proceedings of the 17th ACM Conference on International Computing Education Research

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The modality effect in multimedia learning suggests that pictures are best accompanied by audio explanations rather than text, but this finding has not been replicated in computing education. We investigate which instructional modality works best as an accompaniment for algorithm visualizations. In a randomized controlled trial, learners were split into three conditions who viewed an instructional video on Dijkstra's algorithm, with diagrams accompanied by audio, text, or both. We find neither a modality effect in favor of the audio condition nor a verbal redundancy effect in favor of using only a single modality rather than both. Taken together with earlier research, our findings suggest that the modality effect is difficult to apply reliably and computing educators should not rush to integrate audio into visualizations in expectation of the effect. We discuss theoretical viewpoints that future research should attend to; these include alternative part-explanations of the modality effect and attention-based models of working memory, among others. CCS CONCEPTS• Social and professional topics → Computing education.

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Mental models of recursion

Cited by 5 publications

References 0 publications

First year students' understanding of the flow of control in recursive algorithms

First year students' understanding of the flow of control in recursive algorithms

EEG Activities During Program Comprehension: An Exploration of Cognition

Algorithm Visualization and the Elusive Modality Effect

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