2.5 Computational thinking: the overview diagram

The aim of this subsection is to draw together some of the concepts you have encountered so far. Consider once more the diagram illustrating some of Wing’s ideas (Figure 19).

Figure 19 Abstraction and automation

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Three rectangles are laid out as a triangle with one rectangle at the top and two at the bottom. Arrows link the rectangles in a clockwise direction.

The rectangle at the bottom left contains the words ‘physical-world phenomenon’ and is linked via an arrow to the top rectangle called ‘mathematical model’. The arrow between them is labelled ‘create an abstraction’.

The rectangle at the top, labelled ‘mathematical model’, is connected via an arrow to the third rectangle at the bottom right, which is called ‘automation’. The arrow between them is labelled ‘automate’.

Finally, the ‘automation’ rectangle at the bottom right is linked to the ‘physical-world phenomenon’ rectangle at the bottom left via an arrow. The arrow is labelled ‘tells us more about’.

Abstraction and automation

The three main components in the diagram are:

• a physical-world phenomenon
• a mathematical model
• an automaton.

How do these relate to the concepts you met in Section 1, namely:

• real-world problem
• computational problem
• algorithm and data structures?

Let us start with Wing’s use of the term ‘mathematical model’. As we will now explain, Wing’s notion of a mathematical model is linked to that of a computational problem. According to Wing, a mathematical model is an abstraction of the physical-world phenomenon of interest. It ignores irrelevant detail. It also is the point of departure for automation. The fact that it is a mathematical model means that it is sufficiently precise to be used as a starting point for creating an automaton. Now, you may recall that we defined a computational problem as a problem that is expressed sufficiently precisely that it is possible to attempt to build an algorithm to solve it. In other words, Wing’s mathematical model is nothing other than a computational problem.

Wing’s physical-world phenomenon is abstracted by the mathematical model, just like a computational problem provides an abstraction of a real-world problem.

Algorithms and data structures form the link between a computational problem and its automation. Finding algorithms and data structures is part of automating. When these are then implemented as a program and executed, they provide a machine that solves the problem. In Wing’s words, the resulting machine – or automaton – automates the abstraction.

The complexity of the machine, as we have just discussed, is managed by having a series of encapsulated layers.

To sum all this up, we can refine the diagram of Figure 19 as shown in Figure 20.

Figure 20 Computational thinking overview diagram

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This figure is a diagram with three principal items that are arranged as sitting at the corners of a triangle. At the bottom left is a cloud labelled ‘REAL-WORLD PROBLEM’. At the top is a rectangle labelled ‘COMPUTATIONAL PROBLEM’. At the bottom right is a rectangle labelled ‘MACHINE’.

Additionally, in between the ‘COMPUTATIONAL PROBLEM’ and ‘MACHINE’ rectangles sits an item labelled ‘algorithms and abstract data types’. From each of these three items an arrow labelled ‘models’ points to the ‘REAL-WORLD PROBLEM’ cloud.

The ‘MACHINE’ rectangle is linked with the ‘algorithms and abstract data types’ item with an arrow labelled ‘expresses’.

There is also an arrow from the ‘algorithms and abstract data types’ item pointing to the ‘COMPUTATIONAL PROBLEM’ rectangle. This arrow is labelled ‘solves’.

Inside the ‘MACHINE’ rectangle is number of items arranged in a hierarchy. At the top is a ‘program’ and at the bottom is ‘hardware’. The bit in between is not fully specified, as indicated by three vertical dots, but includes ‘machine code’. Each pair of items in the hierarchy is linked with an upward-pointing arrow labelled ‘hides detail from’ and a downward-pointing arrow labelled ‘depends on’.

Finally, moving back to the top level of the diagram, a set of green arrows link some of the items. A green arrow labelled ‘create an abstraction’ points from the ‘REAL-WORLD PROBLEM’ cloud to the ‘COMPUTATIONAL PROBLEM’ rectangle. A green arrow labelled ‘transform’ leads from ‘COMPUTATIONAL PROBLEM’ to ‘algorithms and abstract data types’. From ‘algorithms and abstract data types’ a green arrow labelled ‘implement’ points to the ‘MACHINE’ rectangle. Finally, a green arrow labelled ‘learn more about’ goes from the ‘MACHINE’ to the ‘REAL-WORLD PROBLEM’ cloud.

Computational thinking overview diagram

Whereas the core of this diagram represents artefacts (real-world and computational problems, machines) and their relations (models, solves, and expresses), the green arrows indicate the actions that a computational thinker engages in (i.e. create, transform, implement and learn).