Computational Thinking and Notional Machines: The Missing Link

Abstract

In learning to program and understanding how a programming language controls a computer, learners develop both insights and misconceptions whilst their mental models are gradually refined. It is important that the learner is able to distinguish the different elements and roles of a computer (compiler, interpreter, memory, etc.), which novice programmers may find difficult to comprehend. Forming accurate mental models is one of the potential sources of difficulty inextricably linked to mastering computing concepts and processes, and for learning computer programming. It is common to use some form of representation (e.g., an abstract machine or a Computational Agent (CA)) to support technical or pedagogic explanations. The Notional Machine (NM) is a pedagogical device that entails one or more computational concepts, originally described as an idealised computer operating with the constructs of a particular programming language. It can be used to support specific or general learning goals and will typically have some concrete representation that can be referred to. Computational Thinking (CT), which is defined as a way of thinking that is used for [computational] problem solving, is often presented as using a CA to carry out information processing presented by a solution. In CT, where the typical goal is to produce an algorithm or a computer program, the CA seemingly serves a purpose very similar to an NM. Although it changes through the different stages of development (of the learner and of the curriculum), the roles of CAs and NMs can be seen as versatile tools that connect a learner’s mental model with the conceptual model of a program. In this article, we look at this relationship between CAs and NMs, and indicate how they would look at different stages of learning. We traverse the range of definitions and usages of these concepts, and articulate models that clarify how these are viewed in the literature. This includes exploring the nature of machines and agents, and how historical views of these relate to modern pedagogy for computation. We argue that the CA can be seen as an abstract, simplified variant of an NM that provides a useful perspective to the learner to support them to form robust mental models of NMs more efficiently and effectively. We propose that teaching programming should make use of the idea of a CA at different stages of learning, as a link that connects a learner’s mental model to a full NM.