Sequencing items in the stepwise process of acquiring associative knowledge
(from P.A.Wozniak, Economics of Learning)
The most important rule in sequencing items is inherently related to the learning process in general. The progression must go from basic concepts through foundations to more intricate and detailed issues. In all forms of learning, this principle derives from the need for comprehension, which obviously is greatly reduced when the student is thrown at a deep end at once. In application of repetition spacing with low forgetting index, this approach has also another important aspect. As in this form of learning, forgetting plays an insignificant role, the student is likely to experience the phenomenon of new pieces of knowledge nicely slotting in in the already established structure. This might affect the sequencing algorithm by moving it from truly basics-to-details approach to first-comprehended-first-memorized approach which dispenses with the need for full comprehension at the first contact with the newly learned material. This way the student will less likely experience the feeling of getting stuck because of his or her inability to comprehend some concept and, at the same time, reluctance to proceed any further out of fear of snowballing incomprehension phenomenon. Thus, in the first pass of the material, the student will memorize only those components that have been comprehended, and hope that the slotting-in phenomenon will eliminate of comprehension gaps in the second pass.
The basics-to-details approach may be combined successfully with the most-applicable approach, in which the student delves more rapidly into details of those parts of the material which are most frequently referenced in other parts. This enhances the slotting-in phenomenon, which is one of the strongest motivational factors in learning, providing the student with the sense of accomplishment.
There is no cut-and-dried algorithm for optimally sequencing items then, however, in slightly more formal terms, the optimum sequencing might be defined as bicriterial optimization in which the following two factors are considered:
- primitiveness of the considered item, i.e. number of semantic dependencies on other items in the sequenced group
- applicability of the item, i.e. the frequency with which the item appears in semantic dependencies of other items (or if it can easily be quantified, the frequency with which the item is more or less directly referred to in the learning materials accompanying the knowledge system, or even in the daily application of the learned knowledge in real life situations)
As an example let us consider the definition of the concept of production in economics. Production is commonly assumed to be synonymous with manufacturing. However, a more accurate and useful definition of production, from the economic analysis standpoint, is as any activity that creates value. The following item placed in the student’s memory is likely to profoundly affect the students interpretation of the concept:
Q: What is production?
A: any activity that creates value
As it will be shown later, it is always recommended to apply both the ability to associate the name with the concept, as well as the concept with the name; therefore, the following mirror item should also appear in the same knowledge system:
Q: What is the name of an activity that creates value (in economics)?
A: production
In the analysis of the aspects of production in economics, a more precise definition of production maybe useful for the sake of classifying its nature from the cybernetic standpoint. As the above definition provided an intuitive understanding and severed the link between production and manufacturing, the definition presented above, not quite consistent with the previous approach may have greater applicability in cases where the production process becomes the focus of more detailed analysis, esp. using economic models: "production is a series of activities by which resource inputs are transformed through a recipe and technological process into outputs of goods and services". Because of the fundamental nature of the concept, the very exact imprint of the above definition may be considered a valuable asset in building more advanced facets of knowledge of economics. The difficulty with basic concepts is that they are so basic that they cannot be asked for in yet more basic terms. Questions like "what is production?" demanding the by-heart recitation of the definition, as it will be shown later, entirely misses the point of building true comprehension (cf. simplicity of synaptic patterns and specificity of synaptic stimulation). Simplifying the answer to "series of activities" and following it with a number of items that define the "activities" is also inadmissible because of a number of adequate substitutes for "series of activities" like, for example, "any activity that creates value", and many more. Here, a very valuable, and often underappreciated tool of Cloze deletion comes handy. Consider the following wording of items:
Q: Production is a series of ... by which resource inputs are transformed through a recipe and technological process into outputs of goods and services
A: activities
similarly, Cloze deletion should generate items in which the following terms are missing in sequence: "resource inputs", "recipe", "technological process", "outputs", and "goods and services", so that to finally arrive at:
Q: Production is a series of activities by which resource inputs are transformed through a recipe and technological process into outputs of ...
A: services
The question arises if the aforementioned set of items will generate the desired effect which is the comprehension of the concept of production along the definition provided earlier. The experience shows that despite seemingly high degree of dissociation between the particular components of the learned concept, the presented items appear to produce a solid imprint in the students memory that not only provides a firm support for stable comprehension, but also makes it possible to effortlessly recite the entire definition of production. A-factors for such constructed items typically fall into the range from 2.0 to 2.8 depending on other elements affecting memorization with interference as the most prominent factor. Despite a larger number of items, this is a sure guarantee to produce less workload than in the case of cramming the entire definition in the answer with A-factor most likely to drop below 1.5.
For contrast, let as consider the following item that appeared to show a high degree of intractability because of the lack of respect for basics-to-details approach:
Q: What is discount rate?
A: interest rate charged by the FRS on loans to member banks
This item was frequently forgotten because it was not backed up by other items in the same knowledge system that would result in understanding the acronym FRS (Federal Reserve System), and consequently the concept of a member bank. This made the definition of discount rate leave little semantic connotation forcing the student to assume syntactic approach to memorization which is nothing else than mindless cramming with very poor retention prospects.