Mental models of recursion

African Journal of Research in Mathematics, Science and Technology Education

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.

warwick.ac.uk

In this study, I examine students' appreciation of the relationship between recursion and iteration, including how they perceive the intra-relationship of the components within those processes. My approach is to design a logo-based microworld, which acts as a window on the students' thinking. In this environment, the students model trees and fractal-shape objects. I use a design-based research methodology in order to gain insights into students' understanding and design issues of the software. These early results show that having a clear understanding of the relation between recursion and iteration and of the flow of control are important in understanding the recursion itself. In addition, functional abstraction is a key concept in dealing with recursion. In the light of these results, I am planning to open

Computer Science Education, 2017

Recursion is both an important and a difficult topic for introductory Computer Science students. Students often develop misconceptions about the topic that need to be diagnosed and corrected. In this paper, we report on our initial attempts to develop a concept inventory that measures student misconceptions on basic recursion topics. We present a collection of misconceptions and difficulties encountered by students when learning introductory recursion as presented in a typical CS2 course. Based on this collection, a draft concept inventory in the form of a series of questions was developed and evaluated, with the question rubric tagged to the list of misconceptions and difficulties.

ACM SIGCSE Bulletin, 1999

Recursion is a powerful and essential computational problem solving tool, but the concept of recursion is difficult to comprehend. Students that master the conventional programming construct of iteration in procedural programming environments, find it hard to utilize recursion.This study started as a test of CS College students' utilization of recursion. It was conducted after they have completed CS1, where they studied recursion with the C programming language. The test revealed that students adhere to the iterative pattern of "forward accumulation", due to their confidence with the iteration construct, but lack of trust of the recursion mechanism. These results motivated us to get more insight into the nature of recursion difficulties and ways to overcome them.In this paper we describe the difficulties we observed, and present a declarative, abstract, approach that contributed to overcome them. We question the emphasis that should be put on the basic computing model ...

2014

One of the most challenging topics for both computing educators and students is recursion. Pedagogical approaches for teaching recursion have appeared in the computing education literature for over 30 years, and the topic has generated a significant body of work. Given its persistence, relatively little attention has been paid to student motivation. This article summarizes results on teaching and learning recursion explored by the computing education community, noting the relative lack of interest in motivation. It concludes by briefly discussing an approach to teaching recursion is appealing for students interested in web development.

Proceedings of the thirty-first SIGCSE technical symposium on Computer science education - SIGCSE '00, 2000

Reoursion is a powerful concept, appearing in almost every introductory course in computer-soience (CS). CS ocbwators and eda~cational researohets often refer to diff;oulties in learning recursion, and suggest methods for toaohing recursion. However, the researoh literature barely addresses the unique ways in whioh students relate to this intcrdisciplinmy conoept and the particular learners' language exm~ning reoursive phenomena. The gap is most apparent when seen through a constmctivist lens, where the students' prior knowledge and idiosyncratic conceptions should be referred to and reflected upon in order to serve as a basis for further knowledge construction. This paper reports on a study in which a collaborative classification of several recursive phenomena is used to facilitate the construction of recursion. The students' discourse was analyzed, as a step toward understanding the students" ways of speaking reeursively. Preliminary results indicate some basic aspects of recursion in the student discourse, although the students appanmtly talk a very different lansuag a fi'orn that of the experts, as used by books and tmohcrs.

ACM Sigcse Bulletin, 2000

We propose a gradual approach to teach recursion. Our main assumption is that the difficulty in learning recursion does not come from the recursion concept itself, but from its interaction with other mechanisms of imperative programming. We use this basic idea to propose a new pedagogical approach. On the one hand, recursion is introduced in a gradual way by means of three fields (grammars, functional programming and imperative programming). On the other hand, each instance of recursion is explained so that all of its accompanying mechanisms are clearly identified.

Cybernetics and Information Technologies, 2016

In this article we have presented the results of an empirical study which was carried out on 130 students in Introduction to programming classes. Their initial preference, success rate, comprehension and subsequent preference were studied when dealing with programming tasks which could be solved using either iteration or recursion.

System Visualization of Recursion and Conditions, effectively learning it, 2001

Relevance and formulation of the research problem The growing need to solve more and more ¬complex problems and the rapid development of computer technology make it possible to use recursion as a simple and effective way to solve applied problems in computer science, mathematics, physics and economics and other sciences . Until recently, didactic research related to recursion was not given due attention, and most students became familiar with it only in connection with the recursive feature of subroutines in programming languages or as one of the most common ways to formalize the concept of a computable function in the theory of algorithms. In the works of Professor A.R. Yesayan and his co-authors, a systematic attempt has recently been made to study recursion as a key subject-forming component of a universal method for solving practically oriented problems. Regardless of the inertia of the educational environment and negative ¬comments about the need and possibility of using and applying recursion in education, more and more attention is paid to this topic in higher education. The teacher of computer science in the classroom continues to use various tricks in programming to this day. This gives rise to numerous programming difficulties that are very difficult to notice when debugging, testing and modifying programs. Although there are all kinds of commentators in programs, but with the help of recursion, you can achieve simplicity, clarity and brevity of the text of the program, and also replaces all kinds of commentators with programs, but also allows you to work effectively with them. It is enough to discover and implement ¬the corresponding recursive algorithm for solving the problem, and the excess of the secondary disappears as if by itself. Recursion opens up many possibilities for us, but in didactics it is used and studied very little. All this determines the relevance of the topic of scientific research, which is intended to resolve the contradiction between the need to prepare a new type of information-literate student and the traditionally established inertial system of his training, in which little attention has been paid to recursion and recursive algorithms in computer science. In order for students to sufficiently master recursion as a method for solving applied problems, it is necessary to give them a description of the anatomy of recursion, to explain that recursion is available, achievable, to form a worldview based on a recursive system-information approach. With the formed recursive thinking, a new understanding of the content of the subject and the learning process as a whole is achieved. Having mastered the recursive method of solving applied problems, the student begins to clearly understand the recursive essence of nature and himself in it. In this study, we consider a general approach for building demo programs by recursion, based on the need to visualize the internal mechanisms for implementing recursive calculations. In our opinion, there are two complementary directions here. On the one hand, this is the formation of an extensive set of recursive algorithms from various branches of mathematics with their software implementation. Another direction is related to the demonstration of internal processes that take place during the implementation of recursive algorithms. In accordance with this topic, the object, subject, purpose and objectives of the study were determined. object research is the learning process of recursion. The subject of research is the visualization of recursion. Target research : theoretically substantiate and experimentally test the possibility of recursion visualization. Hypothesis: visualization of recursion when using information technology is possible if: - find out the essence of recursion and recursive algorithms; - identify the reasons for the lack of attention to learning recursion; - determine the place and role of the use of new information technologies in the visualization of recursion; - develop a methodology for combining traditional and information technology education; - formulate criteria for selecting material for the content of the recursion visualization system; - develop general requirements for the visualization of recursion; To achieve the goal of the study and test the hypothesis, the following tasks were set : 1. Based on the analysis of literary sources, clarify the concept of “recursion”. 2. Analyze the facts that negatively affect the learning of recursion; 3. Develop general requirements for training and control software; 4. Develop a methodology for teaching recursion when using new information technologies (NIT); 5. Develop a methodological approach to the use of personal electronic computers (PC) in teaching recursion; 6. Develop computer programs for teaching recursion; 7. Experimentally verify the effectiveness of the proposed methodological approach. The following methods were used in the research process: - analysis of psychological, pedagogical and methodological literature on the research problem; - study of specialized literature on recursion, the role and place of NIT in teaching and programming languages and the structure of computer programs; - monitoring the course of the educational process; - analysis of the quality of assimilation of new material presented by the teacher; - analysis of verification and control work of students; - carrying out diagnostic work, questioning, conversation, testing; - analysis of research results. Stages of research . There are three stages in problem development. At the first stage of the study (1998 - 1999), study and analysis of educational and program documentation, psychological, pedagogical and methodological literature on recursion were carried out. The experience of teachers of secondary schools in Yemen in the cities of Sana'a, Taiz and Aden and teachers of the Tula State Pedagogical University named after LN Tolstoy in the development and implementation of recursion in the educational process was summarized, approaches to solving the problem were studied. The obtained materials made it possible to formulate a research hypothesis, to determine the main goals and objectives. At the second stage (1999 - 2000), the training system "visualization of recursion" was created and tested; developed a technique for its application in the study of recursion. Based on the results of the conducted pedagogical experiment, an assessment of the effectiveness of the developed automated system for teaching recursion and methods of their application was obtained. At the third stage (2000 - 2001) the experimental work was completed, the obtained results were processed and analyzed, adjustments were made to the developed software, the theoretical provisions were refined, the text of the dissertation was drawn up. The scientific novelty and theoretical significance of the study lies in the fact that the concept of “recursion” has been clarified, and all concepts related to recursion used in the didactic system have become explicit, a classification of visual aids has been introduced; a holistic program and methodological approach is proposed and implemented, designed to teach recursion, as well as to control the assimilation of the knowledge gained by students; various approaches to their design are considered; the main requirements for the visualization of recursion with the current level of development of technical means are highlighted; the necessity of developing a new course of recursion as a method for solving applied problems is proved.

ACM SIGCSE Bulletin, 2008

Recursion is an important topic in computer science curricula. It is related to the acquisition of competences regarding problem decomposition, functional abstraction and the concept of induction. In comparison with direct recursion, mutual recursion is considered to be more complex. Consequently, it is generally addressed superficially in CS1/2 programming courses and textbooks. We show that, when a problem is approached appropriately, not only can mutual recursion be a powerful tool, but it can also be easy to understand and fun. This paper provides several intuitive and attractive algorithms that rely on mutual recursion, and which have been designed to help strengthen students' ability to decompose problems and apply induction. Furthermore, we show that a solution based on mutual recursion may be easier to design, prove and comprehend than other solutions based on direct recursion. We have evaluated the use of these algorithms while teaching recursion concepts. Results suggest that mutual recursion, in comparison with other types of recursion, is not as hard as it seems when: (1) determining the result of a (mathematical) function call, and, most importantly, (2) designing algorithms for solving simple problems.