Understanding Notional Machines through Traditional Teaching with Conceptual Contraposition and Program Memory Tracing

Abstract

A correct understanding about how computers run code is mandatory in order to effectively learn to program. Lectures have historically been used in programming courses to teach how computers execute code, and students are assessed through traditional evaluation methods, such as exams. Constructivism learning theory objects to students’ passiveness during lessons, and traditional quantitative methods for evaluating a complex cognitive process such as understanding. Constructivism proposes complimentary techniques, such as conceptual contraposition and colloquies. We enriched lectures of a “Programming II” (CS2) course combining conceptual contraposition with program memory tracing, then we evaluated students’ understanding of programming concepts through colloquies. Results revealed that these techniques applied to the lecture are insufficient to help students develop satisfactory mental models of the C++ notional machine, and colloquies behaved as the most comprehensive traditional evaluations conducted in the course.

Effects of oral metaphors and allegories on programming problem solving

“…It would be very interesting if these studies investigate the long‐term effects of allegories on other variables as well, such as understanding, motivation, learning, problem solving, and transfer of skills. We conjecture that qualitative methods, such as colloquies, may be very valuable for evaluating these effects .…”

Engage Against the Machine: Rise of the Notional Machines as Effective Pedagogical Devices

“…There is a long history of tools for visualizing the internal memory state while a program runs, which can have a positive impact while teaching [23]. While these tools have always had an implicit notional machine as their basis for representation, it is only recently that some focus has shifted to explicitly describing notional machines and how the visualization supports them, makes them easier to comprehend, or more useful [6,8,17]. In this paper we continue this separation of visualizations from notional machines.…”

“…Although introduced in the 1980s by DuBoulay et al [12,13] it wasn't until around 2008 that work on notional machines started to appear in the literature with focus, for instance [8,28]. The work of Sorva was influential in this period [29][30][31] followed by other authors through 2019, including [3,4,6,7,10,14,17,21,26,34,35].…”

Fostering Program Comprehension in Novice Programmers - Learning Activities and Learning Trajectories

“…In CER we describe such simplification in terms of a Notional Machine (NM), a term introduced by Benedict du Boulay [85] where he describes the "difficulties associated with understanding the general properties of the machine that one is learning to control, the notional machine, and realizing how the behavior of the physical machine relates to this notional machine." While most previous CER works refer to du Boulay's definition of NM (e.g., [367,257,71,145,158]), some recent works have presented similar but simplified versions of it. For example, Berry and Kölling [27] define an NM as "an abstraction designed to provide a model to aid in understanding of a particular language construct or program execution", while Kohn and Komm describe the NM as "a model of the machine that conceptually executes the program code" [170].…”

“…Most authors agree that there is no single NM that satisfies a spectrum of programming languages or a computer in general. However, some authors (e.g., [145]) state that each programming language provides a single NM.…”