Mental models of recursion revisited

Sanders, Ian; Galpin, Vashti; Götschi, Tina

doi:10.1145/1140123.1140162

Cited by 22 publications

(24 citation statements)

References 6 publications

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“…Götschi [7] y Sanders [16] identificaron modelos mentales para recursividad empleando una metodología basada en la inspección visual de exámenes manuscritos. La metodología de análisis de protocolos verbales [9][10] (grabaciones de voz mientras se realizan programas) ha permitido observar que si la intención al analizar un programa fuente es leer-para-recordar (documentar un programa), el enfoque es el texto y su forma, en cambio, si la intención es leer-para-hacer (reutilizar un programa), el enfoque es la secuencia de pasos para lograr las metas del programa y el modelo mental usado es más profundo.…”

Section: Aspectos Cognitivos Y Educacionalesunclassified

“…Algunas se orientan a los aspectos cognitivos del aprendizaje [7][8][9][10][11]16] y otras a desarrollar herramientas de evaluación automática. Sistemas tales como TRY [4], PSGE [3], TRAKLA [12], CourseMaker [13], y AutoLEP [2] usan mecanismos para ejecutar los programas de los estudiantes sometiéndolos a diferentes casos de prueba, en un ciclo que permite varios intentos.…”

Section: Introductionunclassified

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Una plataforma de evaluación automática con una metodología efectiva para la enseñanza/aprendizaje en programación de computadores

Reguera¹,

Rivas²,

Leiva³

2011

Ingeniare. Rev. chil. ing.

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RESUMENAprender a programar computadores es un proceso difícil para los estudiantes novatos y un desafío a las metodologías empleadas por los docentes. En este artículo se presenta una plataforma de evaluación automática que apoya el proceso de enseñanza/aprendizaje en cursos introductorios de programación de computadores para estudiantes de ingeniería de la Universidad de Concepción. Esta plataforma utiliza mecanismos que combinan análisis estático/dinámico y aplican evaluación de comprensión/análisis en línea, permitiendo una retroalimentación personalizada a los alumnos. En este trabajo se presentan los criterios usados para crear secuencias didácticas de problemas y una forma de aplicarlas efectivamente mediante la evaluación automática. Los resultados obtenidos después de seis años de aplicación muestran que la evaluación automática afecta positivamente la motivación, el desempeño y la autoeficacia de los alumnos. La metodología utilizada para estudiar la efectividad de la plataforma incluye análisis cualitativo y cuantitativo. Los aspectos cualitativos se extraen mediante la observación del comportamiento de los estudiantes durante el proceso de aprendizaje, mientras que el análisis cuantitativo está basado en los datos de los estudiantes registrados por la plataforma. Con el fin de acumular información cuantitativa, aplicamos distintos experimentos basados en grupos de estudiantes de control y grupos experimentales.Palabras clave: Evaluación automática, aprendizaje activo, autoeficacia, modelos mentales, análisis estático. ABSTRACT Learning to program is a difficult process for novice students and challenging for teaching methods. In this paper we present an automatic evaluation platform and a methodology to support the teaching/learning process in computer programming introductory courses for engineering students at the Universidad de

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Section: Aspectos Cognitivos Y Educacionalesunclassified

Section: Introductionunclassified

Una plataforma de evaluación automática con una metodología efectiva para la enseñanza/aprendizaje en programación de computadores

Reguera¹,

Rivas²,

Leiva³

2011

Ingeniare. Rev. chil. ing.

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“…In a recent pair of papers Sanders et al study various mental models of recursion that students develop [6,10]. The second of those papers opens with the statement, "Students struggle to understand recursion and we need to find good ways to teach the concept.…”

Section: Introductionmentioning

confidence: 99%

Teaching strategies for reinforcing structural recursion with lists

Goldwasser

Letscher

2007

Companion to the 22nd ACM SIGPLAN Conference on Object-Oriented Programming Systems and Applications Companion

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Recursion is an important concept in computer science and one that possesses beauty and simplicity, yet many educators describe challenges in teaching the topic. Kim Bruce champions the early use of structural recursion in an objectoriented introductory programming course as a more intuitive concept than traditional (functional) recursion. He uses many graphical examples for motivation (e.g., nested boxes, a ringed bullseye, fractals), providing concreteness to the recursive concept. Internally, most of those examples are disguised forms of a basic recursive list pattern. Recursive lists are important in and of themselves and a mainstay within the functional programming paradigm. However, further challenges exist in providing a tangible presentation for pure lists when disassociated from a graphical structure.We describe an active-learning exercise in which students play the roles of distinct objects that together comprise the structure of a single, recursive list. This activity establishes intuition that we later use when developing a complete implementation of a recursive list class. Our approach demonstrates a rich set of recursive patterns involving several distinct forms of a base case and varied use of parameters and return values.

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“…In the School of Computer Science at the University of the Witwatersrand (Wits) we have for a long time been concerned about how we can assist our students with recursion [4,1,3]. One thrust of our research is the study of the mental models of recursion (c.f.…”

Section: Introductionmentioning

confidence: 99%

“…The students' traces from two recursive algorithms were categorised into the mental models previously observed [1,3] by identifying how the student deals with the active flow, base case and passive flow in their trace and then by combining this information into an overall categorisation of the trace for that algorithm . Overall the results are in line with our previous results which showed that the copies model is the dominant model for a recurrence relation type of recursive function but that for list manipulation problems some students showed an active or looping model.…”

Section: Introductionmentioning

confidence: 99%

Students' mental models of recursion at wits

Sanders

Galpin

2007

Proceedings of the 12th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education

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Recursion is a concept which all computer scientists should understand and be able to use but novices find it difficult to master. In the School of Computer Science at the University of the Witwatersrand (Wits) we have for a long time been concerned about how we can assist our students with recursion [4, 1, 3]. One thrust of our research is the study of the mental models of recursion (c.f. Kahney [2]) which our first year students develop.Most of our students encounter recursion for the first time in our Fundamental Algorithmic Concepts (FAC) course. When we originally investigated the mental models of our students we noted that although many of them seem to develop the viable copies model there are still many that develop models which are non-viable (i.e. that cannot be relied on to lead to a correct result) [1]. Thus we adapted the way in which recursion was introduced in FAC in 2003, 2004 and 2005 by introducing more complex recursive algorithms earlier to help in the development of the copies mental model. We then compared the mental models developed by the 2003, 2004 and 2005 students to those developed by the earlier group [3]. The results indicate that more of the students were developing viable mental models of recursion and thus that the changes to our teaching were benefitting our students.In 2006 we changed the programing language in which our students implement algorithms to Python (from Scheme). In essence the programming language was the only change made as the course was still taught in a "functional" style to emphasize the link between the formal specification of a problem, the solution to the problem and the program. We did, however, feel it was important to assess the impact of the change on our students' mental models of recursion. We thus did a similar study on the 2006 students to that on earlier cohorts.The students' traces from two recursive algorithms were Copyright is held by the author/owner(s). ITiCSE'07, June 23-27, 2007, Dundee, Scotland, United Kingdom. ACM 978-1-59593-610-3/07/0006.categorised into the mental models previously observed [1, 3] by identifying how the student deals with the active flow, base case and passive flow in their trace and then by combining this information into an overall categorisation of the trace for that algorithm . Overall the results are in line with our previous results which showed that the copies model is the dominant model for a recurrence relation type of recursive function but that for list manipulation problems some students showed an active or looping model. These results indicate that our teaching approach, even with the switch to Python, is assisting our students in developing a viable copies mental model of recursion. Such a mental model is more likely to lead to correct traces of recursive algorithms. An interesting new result was the emergence of a passive mental model. Here the students recognised that the recursive algorithm would somehow get to the base case and then used the base case plus the implicit definition of the functi...

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Mental models of recursion revisited

Cited by 22 publications

References 6 publications

Una plataforma de evaluación automática con una metodología efectiva para la enseñanza/aprendizaje en programación de computadores

Una plataforma de evaluación automática con una metodología efectiva para la enseñanza/aprendizaje en programación de computadores

Teaching strategies for reinforcing structural recursion with lists

Students' mental models of recursion at wits

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