Teaching Abstractions

From E-Learning Faculty Modules


Contents

Module Summary

Abstractions are a critical part of higher education learning. They enable the capturing of more general features of objects, and they enable their categorization. They enable theorizing and transferring learning from one specific context to other similar ones. They enable modeling of relationships and the inference of what may occur next. They enable predictivity. As such, they are important to learning. However, abstractions are by nature difficult to learn because they tend to be elusive, often complex, easily confused with instantiating examples, and often not fully explicated.

The teaching of abstractions—as equations, models, theories, concepts, and others—are a common part of higher education. This module describes some basic challenges to teaching and learning abstractions, and it suggests some ways to effectively teach abstractions in a higher-education-based online teaching and learning context.


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Takeaways

Learners will...

  • consider what informational contents are “abstract” vs. “concrete” and why abstractions may be harder to convey than concrete examples
  • explain why abstractions are important for teaching and learning and list what some common types of abstractions are in higher education learning online (and why abstractions may be harder for younger learners, such as in K-12)
  • consider effective and ineffective methods for teaching learning abstractions in online learning contexts
  • review why it is important to use empirical data to measure the efficacy / inefficacy of the teaching and learning for abstract understandings
  • Describe some effective ways to assess understanding of abstractions (such as by using these to reason, project into the future, to predict, and to form new concepts)


Module Pretest

1. What sort of informational content is “abstract”? What sort of informational content is “concrete”? Why are abstract concepts more difficult to convey to others? Why are abstract concepts harder to acquire?

2. Why are abstractions important to teach and learn? What are some common types of abstractions in higher education learning? K-12 learning? (Why are abstractions often harder for younger learners, say in K-12?)

3. What are some effective methods to teaching and learning abstractions in online learning contexts? Why? What are ineffective methods to teaching and learning abstractions in online learning contexts? Why?

4. Why is it important to use empirical data to measure the efficacy or inefficacy of the teaching and learning for abstract understandings?

5. What are some effective ways to assess understanding of abstractions? Why is it important not only to be able to describe abstractions but also to use these to reason, to project into the future, to predict, and to form new concepts?


Main Contents

1. What sort of informational content is “abstract”? What sort of informational content is “concrete”? Why are abstract concepts more difficult to convey to others? Why are abstract concepts harder to acquire?

An abstraction vs. a concretized object. An “abstraction” is a generalization, a concept, an idea, a model, a theory, or a construct; in other words, it is a conceptualization of a phenomenon that may or may not exist, a perception of a signal that might or might not be real. Abstractions may exist as micro, meso, and macro levels of specificity, or they may exist in even more granular levels of abstraction. Abstractions may be used for categorizing hierarchical or non-hierarchical levels of a thing.

A “concrete” piece of informational content is directly observable or able to be experienced. It can be measured on a range of dimensions or attributes. Physical samples of this may be gathered (or created or induced) and studied. Concrete examples are “real” and “tangible.”

Sourcing . Where do abstractions come from? Well, people think them up. They reason their way to some of them. They experience their way to some others. They draw them; they write them. Or they use a combination of methods to create abstractions. They induce them from machine learning. Abstractions are “sourced” in a variety of ways. Most often, abstractions are built from particulars; however, different people may look at the same set of particulars and emerge with different concepts and abstractions, and these concepts may be diametrically opposed with each other. In various complex contexts, a wide range of interpretations (abstracted knowledge) are possible. In a research context, the next steps are to devise ways to test the various theories to see if one concept is more accurate in understanding the issue than another, and along the way, some of the theories are debunked. The one / the few / the none that survive are left to stand until a better abstraction is created.

Teaching abstractions. One common human cognitive limit is labeled WYSIATI (“what you see is all there is”) by Dr. Daniel Kahneman, a research psychologist, in “Thinking Fast and Slow.” (2011 ) In this cognitive limit, people tend to assume that what they see is the totality of a phenomenon, and often, they do not look further. Abstractions, by definition, are not particularly visible. It takes effort to find and understand abstractions. For many, particularly those who prefer to trust their physical senses and are less comfortable with concepts, they will pursue the explanation that most aligns with their senses when much of reality is beyond the limits of direct senses. (Unaided human eyes can only see a small part of the light spectrum; unaided human ears can only perceive a small part of the sound wave spectrum… Much of the world may be at macro-size, such as the universe, and micro-size, such as atoms and microbes…so humans have to be able to perceive and abstract beyond their perceptions to actually engage the world.)

For teachers, abstract concepts are more difficult to convey because they may or may not exist. There is a risk of reifying a concept that may have no basis in reality. They are often complex, and their full implications may not be seen. Some abstract concepts are not falsifiable; they cannot theoretically or practically be proven or disproven. (And often, at any one time, there are going to be numbers of people who will affirm such unfalsifiable concepts.)

For learners, abstract concepts may be difficult to grasp for a number of reasons. The learners may not have had exposure to the idea before. The abstractions may be complex and difficult to understand. The abstractions may be interpreted and used in different ways in the world, so there is not one accepted definition. The abstraction itself may not be clearly defined. There may be insufficient examples and insufficient ranges of examples.

An abstraction may also be an untested or limited proposition or theory. It may be in the realm of belief without evidentiary backup. They may exist in a realm of uncertainty, while in competition with other theories and competing ideas.


2. Why are abstractions important to teach and learn? What are some common types of abstractions in higher education learning? K-12 learning? (Why are abstractions often harder for younger learners, say in K-12?)

Abstractions are important for teaching and learning because they are a core of transferable learning. (Singular examples / exemplars are not often very transferable.) One researcher writes:

“Learning of substance that will be valuable to learners and will enrich their lives involves the learning of abstractions, referred to by psychologists as ‘concepts’, of principles, of physical skills, and the effective manipulation of learned abstractions which may be referred to as ‘thinking’. When applied to resolving complexities in one’s environment or to cop8ing effectively with novel situations, this activity may be referred to as ‘problem-solving’. (Stones, 1989, p. 8)

So abstracting is a basic requirement for effective problem-solving. Language itself is an abstraction of reality. People can use writing to explore ideas, to find meaning, to troubleshoot and problem-solve, and to document. Abstracting is also a core part of thinking through writing. One researcher writes:

“Writing, by its very nature, encourages abstraction, and in the shuttling process from the past to the present, from the particular to the general, from the concrete to the abstract, we seek relationships and find meaning.” (Irmscher, Oct. 1979, p. 243)

Abstractions are often created by using specific examples and details, and generalizing from “ground up” (Irmscher, Oct. 1979, p. 243). It is also possible to conceptualize abstractions from the general and to apply them to the specific. Even with the proper words, though, explaining abstractions can be difficult. In history, images, art forms, sculptures, paintings, and others have been used to explore the abstract—whether these are ideas of the supernatural or the religious or others. Beyond language, particularly in the present age, there are multimodal digital means to abstract ideas. These include diagrams, imagery, maps, doodles, audio files, singing, vocalizing, video, simulations, immersive virtual worlds, and others.

Some common types of abstractions in higher education include those in fields that deal with realities that cannot be directly experienced through sensory means: math, physics, astrophysics, biological sciences (some aspects), health sciences, food sciences, and others. They may involve all fields that involve theorizing and modeling.

In K-12, some common examples of abstractions include the understanding of shapes, math, budgeting, value systems, logical reasoning, and others. Young learners have been observed to struggle with abstraction more than older learners (and those with high cognitive capabilities among adult learners).


3. What are some effective methods to teaching and learning abstractions in online learning contexts? Why? What are ineffective methods to teaching and learning abstractions in online learning contexts? Why?

Abstractions are generally considered a capability that occurs at a later stage in the development of a subject domain. In general, people have explored a phenomenon based on what is observable and then developed ideas, categories, rules, models, and such, based on that learning. Once the abstractions have been created, though, they can be used as an entry point to learning in a field. (The old sequence of starting with examples for discovery…does not have to be the sequence used in teaching novice learners to the issue.)

In another related conceptualization, the ability to abstract an idea is a part of human intelligence, such as “logical-mathematical intelligence.”

In this section, first, there will be discussions of methods used in a higher education context, and then, methods used in a K-12 context. There will be a short follow-on paragraph about how the online nature of the teaching and learning may affect the teaching and learning approaches.

In higher education. An abstraction, by definition, is conceptual and somewhat elusive. One major strategy for conveying a concept is to provide in-depth details about the concept, such as through the following:

  • define it in depth (both directly and directly)
  • provide a range of examples that support the concept and explain how these examples support the concept
  • offer appropriate analogical thinking
  • use multimodal means to describe the abstraction (visuals, audio, video, and other mixed and multimedia)
  • provide the history to the evolution of the concept
  • explore the implications of a concept
  • use the concept to solve problems
  • use the concept to reason

Another approach is to use multimodal means to describe the concept: text, visuals, video, simulations, and so on.

The level of the abstraction should be described, where relevant. Is the abstraction at a macro level? A meso? A micro? Or are there other more effective ways to set up levels of the abstraction?

Sequencing. Also, there are several different sequences that are under debate in the research:

  • Is it better to fully directly define an abstraction before supporting examples are given?
  • Is it better to approach indirectly and provide a range of examples from which an abstraction may be inferred?
  • Is it better to share stories that suggest the abstraction indirectly?

One researcher suggests that offering examples too early to support an abstraction is a teaching mistake because learners may mistake the examples for the concept:

”Another problem relates to teaching abstractions, in which form most or all of the concepts reach their fullest and richest potential. The urge to use exemplars too early is difficult to resist. For example, half-way through filling out the richness of a concept, a case or example may be offered. The frequent response of the student is "Oh, now I get it." What has been discovered is that the student quickly reifies the exemplar. The consequence is that it is hard to push further to fill out the concept for the student. The problem related to abstraction is particularly difficult in the early stages of the course. A useful technique is to steel oneself toward retaining the conceptual focus, continue to engage the student as he attempts to master a concept and fight the urge to give an example too early. In my experience, students do get used to the abstract, conceptual level of the material.” (Dailey, Spring 1975, p. 28)

From a different perspective, a different researcher suggests that abstractions can be offered to learners in general ways from the beginning, even when the concepts are not directly familiar. It is possible to start with the unfamiliar and move that to the familiar as a legitimate teaching approach. He writes:

”My suggestion here is that at least an inchoate level of meta thought is possible at the outset of learning, and that an early introduction to this more sophisticated way of knowing, which avoids climbing through names and definitions, provides students with an easier path to navigate, thereby increasing the odds that they will indeed become “committed” knowers. Students can understand—at the highest levels—a concept before they can name or define it; indeed, the context in which we apply, analyze, synthesize, and evaluate may make more sense if one is not burdened with the definition beforehand. Thus, both ends of the spectrum benefit from the top-down approach: not only do definitions make more sense within a context, but the context is itself rich in higher level learning. Speaking in more general epistemological terms, Dewey perhaps puts it best: Any subject is cultural in the degree in which it is apprehended in its widest possible range of meanings. Perception of meanings depends upon perception of connections, of context. To see a scientific fact or law in its human as well as in its physical and technical context is to enlarge its significance and give it increased cultural value. (1922, 336).” (Lindsay, July 2011, p. 609)

A researcher who may take a different approach to the teaching of abstractions refers back to different teaching maxims, including the need to “proceed from the known to the unknown” and “the simple to the complex” and the “concrete to the abstract” and the “particular to the general” (Ramesh, 2014, pp. 51 – 53).

Also, it is important to expose learners to the abstractions in different contexts, so that they do not inadvertently learn context dependency (fallaciously linking the generality to a context only).

K-12. In the K-12 teaching and learning context, one research team has suggested that the objects used for the teaching and learning should be properly abstract, without too much complexity. They write:

“…children who learned with simple objects were able to generalize according to shape similarity, typically relevant for early object categories, better than those who learned with complex objects” (Son, Smith, & Goldstone, 2008, p. 626)

In other words, the abstraction should not include excess information. The authors continue: “Abstraction is in part simplification because it requires the removal of irrelevant information. At the same time, part of generalization is ignoring irrelevant differences. The resulting prediction is this: simplification may enable generalization” (Son, Smith, & Goldstone, 2008, p. 626). The shared objects for learning have to be at the proper level of abstraction, and the children’s attention has to be directed to the relevant aspects of the generalized example. Younger learners and novice ones are unable to pick out what is relevant from the available information, so having cognitive scaffolding may enhance their learning and performance.

In the online learning context, whatever the basic teaching strategy and tactic are, they can be applied in a reproducible and accessible way. The multimodal approach is especially easy to design and develop in the online learning context. Learning efficacy is not so difficult to actualize given the data collection that is a part of the running of the learning management system.


4. Why is it important to use empirical data to measure the efficacy or inefficacy of the teaching and learning for abstract understandings?

It is important to assess the teaching and learning by actual learner knowledge, attitudes, and performance—both in contexts where the learning contents are abstract and where the learning is concrete. In the assessment, the work should be towards both confirming and disconfirming the learning hypotheses…in order to capture the most objective and verifiable information.

Actual mastery of an abstraction may be to include the following:

  • defining the abstraction
  • describing the origination of the abstraction
  • articulating the relevance of the abstraction in the field
  • describing the implications of the abstraction
  • describing interrelationships within the abstraction
  • troubleshooting with the abstraction
  • problem-solving with the abstraction
  • reasoning with the abstraction
  • building on the abstraction, and others


5. What are some effective ways to assess understanding of abstractions? Why is it important not only to be able to describe abstractions but also to use these to reason, to project into the future, to predict, and to form new concepts?

At the most basic level, those who are learning an abstraction need to be able to describe it accurately, explain its history and evolution, and understand some implications of it. Higher level uses of abstractions include the ability to use these to reason, to anticipate the future, to predict something, and to even create new concepts.

The simplest way to describe how to create assessments for abstractions is as follows:

If the learning was designed based on learning objectives, and the design and development track closely with those objectives…and the aligned learning outcomes, then the assessments should be designed to the learning outcomes. Generally, if the abstraction is a small part of the overall learning, simple assessments will do: multiple-choice, sorting, short-answer, and short essays.

More complex learning may take the abstractions out of the original learning context and ask questions in a different context. Even more complex methods may include scenarios, problem-solving, story-completion methods, as well as others. There may be small-group projects that serve as assessment.

There are a lot of right ways to do this, depending on the context.

Examples

One commonly relatable abstraction may be weather systems, which involve complex phenomena with complex interaction effects. Often, weather systems are depicted in the following ways:

  • maps (such as live radar maps)
  • digital models
  • simulations

These are augmented by expert explanations orally and via text…and line-based annotations.

How To

Creating a pedagogical plan for the teaching of abstractions to a particular learner group depends on a variety of factors:

  • What do the learners know? What are their beliefs? What are their naïve understandings?
  • What is the abstraction that needs to be conveyed? How did this abstraction originate? How did it evolve?
  • How can understandings of the abstraction (and its variations) be conveyed to these learners, given what learners already know? What are some hurdles that have to be overcome for the accurate conveyance of the abstractions?
  • How can the learning be designed to learner needs? What sorts of augmentations may be created to support learner needs?
  • How will learners’ understandings be assessed accurately?
  • How can the design of the learning be assessed for efficacy?

Given the differing specifics of different learning contexts, it is harder to generalize than to offer a set of questions (above).

Possible Pitfalls

What are some pitfalls in the teaching of abstractions? A major pitfall is a misunderstanding of the abstraction and a misfocus on the wrong parts of the generalization. Reasoning with generalizations can also be difficult since a range of abstractions are at play.

Module Post-Test

1. What sort of informational content is “abstract”? What sort of informational content is “concrete”? Why are abstract concepts more difficult to convey to others? Why are abstract concepts harder to acquire?

2. Why are abstractions important to teach and learn? What are some common types of abstractions in higher education learning? K-12 learning? (Why are abstractions often harder for younger learners, say in K-12?)

3. What are some effective methods to teaching and learning abstractions in online learning contexts? Why? What are ineffective methods to teaching and learning abstractions in online learning contexts? Why?

4. Why is it important to use empirical data to measure the efficacy or inefficacy of the teaching and learning for abstract understandings?

5. What are some effective ways to assess understanding of abstractions? Why is it important not only to be able to describe abstractions but also to use these to reason, to project into the future, to predict, and to form new concepts?


References

Dailey, D.M. (1975, Spring). A learning paradigm for the teaching of social work research. Journal of Education for Social Work: 11(2), 25 – 31.

Irmscher, W.F. (1979, Oct.) Writing as a way of learning and developing. College Composition and Communication: 30(3), 240 – 244. National Council of Teachers of English.

Lindsay, P. (2011, July). Abstract teaching for a concrete world: A lesson from Plato. The Teacher (section). Political Science and Politics: 44(3), 605 – 610.

Ramesh, P. (2014) Principles of Teaching. Orientation Programme for newly Recruited Faculty of KVAFSU, Bidar. 48 – 56.

Son, J.Y., Smith, L.B., & Goldstone, R.L. (2008). Simplicity and generalization: Short-cutting abstraction in children’s object categorizations. Cognition: 108(2008), 626 – 638.

Stones, E. (1989). Pedagogical studies in the theory and practice of teacher education. Oxford Review of Education: 15(1), 3 – 15.


Extra Resources