Concept Learning (Cognitive Learning Processes)

In manifold contexts, students do acquire concepts. Concepts are designated assemblages of objects, symbols, or occurrences sharing common characteristics, or critical attributes. A concept constitutes a mental construct, or representation, of a category, enabling the identification of both examples and non-examples thereof (Howard, 1987). Concepts may pertain to concrete objects (e.g., “table,” “chair,” “cat”) or abstract notions (e.g., “love,” “democracy,” “wholeness”). Indeed, sundry types of concepts exist (vide Medin, Lynch, & Solomon, 2000, for a detailed review). Concept learning alludes to the formation of representations for identifying attributes, generalising them to novel examples, and discriminating examples from non-examples.

Early inquiries by Bruner, Goodnow, and Austin (1956) explored the nature of concepts. Learners were presented with boxes portraying geometrical patterns. Each pattern could be classified using four distinct attributes: number of stimuli (one, two, three); shape (circle, square, cross); colour (red, green, black); and number of borders on the box (one, two, three). The task resided in identifying the concept represented in different subsets of the boxes.

The configuration of features in a concept-learning task can be varied to yield divergent concepts. A conjunctive concept is represented by two or more features (e.g., two red circles). Other features (number of borders) are irrelevant. A disjunctive concept is represented by one of two or more features; for example, two circles of any colour or one red circle. A relational concept specifies a relationship between features that must be present, such as the number of objects in the figure must outnumber the number of borders (type of object and colour are unimportant).

Bruner et al. (1956) discerned that learners formulated a hypothesis about the rule underlying the concept. Rules may be expressed in if-then form. A rule classifying a cat might be thus: “If it is domesticated, has four legs, fur, whiskers, a tail, is relatively small, purrs, and vocalises ‘meow,’ then it is a cat.” Albeit exceptions may exist, this rule shall accurately classify cats in most instances. Generalisation ensues when the rule is applied to a variety of cats.

Individuals evince a propensity to formulate rules with celerity (Bruner et al., 1956). For any given concept, they retain the rule insofar as it correctly identifies instances and non-instances of the concept, and they modify it when it fails to do so. Learners acquire concepts more readily when presented with positive instances, or examples of the concept. Learning proceeds at a more dilatory pace with negative (non-) instances. When endeavouring to confirm the rule underlying the concept, individuals prefer to receive positive rather than negative instances.

Since these early endeavours, alternative perspectives have emerged concerning the nature of concepts. The features analysis theory, deriving from the work of Bruner et al., posits that concepts involve rules defining the critical features, or the intrinsic (necessary) attributes, of the concept (Gagné, 1985; Smith & Medin, 1981). Through experiences with the concept, one formulates a rule that satisfies the conditions and retains the rule as long as it functions effectively.

This view predicts that different instances of a concept should be recognised with equal celerity, as each instance is judged against critical features; yet this is not invariably the case. Most individuals find certain instances of a category (e.g., a dolphin is a mammal) more difficult to verify than others (e.g., a dog is a mammal). This highlights the problem that many concepts cannot be defined precisely in terms of a set of critical attributes.

A second perspective is prototype theory (Rosch, 1973, 1975, 1978). A prototype is a generalised image of the concept, which may encompass merely some of the concept’s defining attributes. When confronted with an instance, one recalls the most likely prototype from LTM and compares it to the instance to ascertain if they match. Prototypes may include some non-defining (optional) attributes. In cognitive psychology, prototypes are oft considered schemas (Andre, 1986), or organised forms for the knowledge we possess regarding a particular concept.

Research supports the prototype theory prediction that instances closer to the prototype (e.g., prototype = “bird”; instances = “robin,” “sparrow”) are recognised with greater celerity than those less typical (e.g., “owl,” “ostrich”; Rosch, 1973). One concern lies in the implication that prototype theory necessitates individuals storing thousands of prototypes in LTM, consuming significantly more space than rules. A second concern is that learners could readily form incorrect prototypes if permitted to include non-defining characteristics and omit necessary ones.

A synthesis of the features-analysis and prototype positions is feasible. Given that prototypes encompass critical features, we might employ prototypes to classify instances of concepts that are fairly typical (Andre, 1986). For ambiguous instances, we may employ critical feature analysis, which might modify the list of critical features to incorporate the new features.

Children’s understandings of concepts evolve with development and experience. Children in transition regarding the meaning of a concept may simultaneously retain a prior hypothesis whilst developing a revised one (Goldin-Meadow, Alibali, & Church, 1993). This interpretation aligns with Klausmeier’s position, to be discussed next.

Researches doth intimate that sundry manners exist whereby concepts may be learnt and modifed (Chinn & Samarapungavan, 2009). One mode of developing prototypes resides in exposure to a typical instance of the concept, reecting its classic attributes (Klausmeier, 1992). A second way consists in abstracting features from two or more examples; for avians, such features might include “feathers,” “two legs,” “beak,” and the ability to “fly,” albeit not every feature applies universally to each member of the class. Prototypes are refined and amplified through exposure to novel instances of the concept; thus, one might encounter instances such as “lives in the jungle” (parrot) and “lives by the ocean” (seagull).

Gagné’s (1985) theory doth posit concepts as a central form of learning. Learners, at the commencement, must possess basic prerequisite capabilities to discriminate amongst stimulus features (i.e., to distinguish relevant from irrelevant attributes).

In Gagné’s (1985) perspective, the learning of concepts entails a multistage sequence. Initially, a stimulus feature is presented as an instance of the concept, conjoined with a noninstance. The learner conrms his capacity to effect the discrimination. In the subsequent (generalisation) stage, the learner identies instances and noninstances. Thirdly, the stimulus feature—which is to become the concept—is varied and presented alongside noninstances. Concept attainment is veried through soliciting the identication of several instances of the class, employing stimuli not previously engaged in the learning process. Throughout this procedure, correct responses are reinforced, and contiguity learning transpires by presenting several instances of the concept in close association.

Klausmeier (1990, 1992) did develop and test a model of concept attainment. This model postulates a four-stage sequence: concrete, identity, classificatory, and formal. Competence at each level is requisite for attainment at the subsequent level. The process of concept attainment representeth an interaction of development, informal experience, and formal education.

At the concrete level, learners are enabled to recognise an item as the self-same one previously encountered, provided that the context or spatial orientation wherein it was originally encountered remains unaltered. This level demandeth that learners attend to the item, discriminate it as distinct from its surroundings based upon one or more dening attributes, represent it in Long-Term Memory (LTM) as a visual image, and retrieve it from LTM to compare it with a new image, determining whether it is the identical item. Thus, a learner might become adept at recognising an equilateral triangle, distinguishing it from a right or isosceles triangle.

The identity level is characterised by recognising an item as the self-same one previously encountered, even when the item is observed from a disparate perspective or in a differing modality. This stage embraceth the self-same processes as at the concrete level, in concert with the process of generalisation. Therefore, the learner shall be equipped to recognise equilateral triangles in diverse orientations or positions upon a page.

The classificatory level demandeth that learners recognise at least two items as possessing equivalence. Further generalisation is implicated; in the instance of equilateral triangles, this entailth recognising smaller and larger equilateral triangles as equivalent. The process continueth until the learner is enabled to recognise both instances and noninstances; how-ever, at this stage, the learner may lack comprehensive understanding of the basis for classification (e.g., equality of side length and angles). To be enabled to name the concept is not a necessary at this level, but, as in the preceding stages, it can facilitate concept acquisition.

Finally, the formal level requireth the learner to identify instances and noninstances of the concept, to name the concept and its dening attributes, to furnish a denition of the concept, and to specify those attributes which distinguish the concept from other closely related ones (i.e., three equal sides and angles). Mastery of this stage requireth the learner to implement classificatory-level cognitive processes, alongside a suite of higher-order thinking processes encompassing hypothesising, evaluating, and inferring.

This stage model doth bear instructional implications for learners at diverse junctures in their development. Instruction may be protracted over several grades, during which concepts are periodically revisited at more elevated levels of attainment. Young children are initially furnished with concrete referents and, with development, evolve the capacity to operate at more abstract cognitive levels. For instance, young children may assimilate the concept of “honesty” through observation of specific instances (e.g., eschewing theft, returning mislaid items); as they mature, they are enabled to comprehend the concept in more abstract and complex terms (e.g., recognising honest feedback from a supervisor concerning a worker’s performance; deliberating upon the benets of honesty).

Tennyson (1980, 1981; Tennyson, Steve, & Boutwell, 1975) hath also developed a model of concept teaching based upon empirical research. This model includeth the following steps (Tennyson & Park, 1980):

• Determine the structure of the concept to include superordinate, coordinate, and subordinate concepts, and identify the critical and variable attributes (e.g., features that can legitimately vary and not affect the concept).
• Define the concept in terms of the critical attributes, and prepare several examples with the critical and variable attributes.
• Arrange the examples in sets based on the attributes, and ensure that the examples have similar variable attributes within any set containing examples from each coordinate concept.
• Order and present the sets in terms of the divergence and difficulty of the examples, and order the examples within any set according to the learner’s current knowledge.

Most concepts can be represented in a hierarchy with superordinate (higher) and subordinate (lower) concepts. For any given concept, similar concepts may be at roughly the same level in the hierarchy; these are known as coordinate concepts. For example, the concept “domestic cat” hath “cat family” and “mammal” as superordinate concepts, the various breeds (short hair, Siamese) as subordinate concepts, and other members of the cat family (lion, jaguar) as coordinate concepts. The concept hath critical attributes (e.g., paws, teeth) and variable attributes (e.g., hair length, eye colour). A set compriseth examples and nonexamples (e.g., dog, squirrel) of the concept.

Although the concept should be defined with its critical attributes before examples and nonexamples are given, presenting a definition doth not ensure that students will learn the concept. Examples should differ widely in variable attributes, and nonexamples should differ from examples in a small number of critical attributes at once. This mode of presentation preventeth students from overgeneralising (classifying nonexamples as examples) and undergeneralising (classifying examples as nonexamples).

Pointing out relationships among examples is an effective way to foster generalisation. One means is by using concept (knowledge) maps, or diagrams that represent ideas as node-link assemblies (Nesbit & Adescope, 2006). O’Donnell et al. (2002) showed that learning is facilitated with knowledge maps where ideas are interlinked. Nesbit and Adescope found that concept maps improved students’ knowledge retention.

The optimal number of examples to present dependeth on such concept characteristics as number of attributes and degree of abstractness of the concept. Abstract concepts usually have fewer tangible examples than concrete concepts, and examples of the former may be difficult for learners to grasp. Concept learning also dependeth on learner attributes such as age and prior knowledge (Tennyson & Park, 1980). Older students learn better than younger ones, and students with more relevant knowledge outperform those lacking such knowledge.

In teaching concepts, it is helpful to present examples that differ in optional attributes but have relevant attributes in common so that the latter can be clearly pointed out, along with the irrelevant dimensions. In teaching the concept “right triangle,” for example, the size is irrelevant, as is the direction it faces. One might present right triangles of various sizes pointing in different directions. Using worked examples is an effective cognitive instructional strategy (Atkinson et al., 2000).

Not only must students learn to generalise right triangles, they also must learn to distinguish them from other triangles. To foster concept discrimination, teachers should present negative instances that clearly differ from positive instances. As students’ skills develop, they can be taught to make finer discriminations. The suggestions shown in Table 'Steps for generalising and discriminating concepts' are helpful in teaching students to generalise and discriminate among concepts.

This model requireth a careful analysis of the taxonomic structure of a concept. Structure is well specified for many concepts (e.g., the animal kingdom), but for many others—especially abstract concepts—the links with higher- and lower-order concepts, as well as with coordinate concepts, are problematic.

In a signal contribution, Pintrich, Marx, and Boyle (1993) did aver that conceptual change doth also involve motivational processes (e.g., goals, expectations, needs), which information processing models have tended to neglect. These authors did argue that four conditions are necessary for conceptual change to occur. First, dissatisfaction with one's current conceptions is needed; change is unlikely if persons feel their conceptions are accurate or useful. Second, the new conception must be intelligible—persons must understand a conception in order to adopt it. Third, the new conception must be plausible—learners must understand how it doth fit with other understandings of how it might be applied. Finally, they must perceive the new conception as fruitful—being able to explain phenomena and suggesting new areas of investigation or application.

Motivational processes enter at several places in this model. For example, research doth show that students' goals direct their attention and effort, and their self-efficacy relates positively to motivation, use of effective task strategies, and skill acquisition (Schunk, 1995). Furthermore, students who believe that learning is useful and that task strategies are effective display higher motivation and learning (Borkowski, 1985; Pressley et al., 1990; Schunk & Rice, 1993). Goals, self-efficacy, and self-evaluations of competence have been shown to promote learning and self-regulation in such domains as reading comprehension, writing, mathematics, and decision making (Pajares, 1996; Schunk & Pajares, 2009; Schunk & Swartz, 1993a; Wood & Bandura, 1989; Zimmerman & Bandura, 1994). We see in the opening scenario that the shift toward more problem solving actually has improved some students' motivation for learning.

In short, the literature suggests that conceptual change involves an interaction of students' cognitions and motivational beliefs (Pintrich et al., 1993), which hath implications for teaching. Rather than simply provide knowledge, teachers must take students' pre-existing ideas into account when planning instruction and ensure that instruction includes motivation for learning.

These ideas are highly applicable to science. Many science educators believe that knowledge is built by learners rather than simply transmitted (Driver et al., 1994; Linn & Eylon, 2006). An interesting issue is how students develop scientific misconceptions and simplistic scientific models (Windschitl & Thompson, 2006). An important task is to help students challenge and correct misconceptions (Sandoval, 1995). Experiences that produce cognitive conflict can be helpful (Mayer, 1999; Sandoval, 1995; Williams & Tolmie, 2000). This might entail having students engage in hands-on activities and work with others (e.g., in discussions) to interpret their experiences through selective questioning (e.g., “Why do you think that?” “How did you figure that?”). This approach fits well with the Vygotskian emphasis on social influences on knowledge construction.

Nussbaum and Novick (1982) proposed a three-stage model for changing student beliefs:

• Reveal and understand student preconceptions.
• Create conceptual conflict with those conceptions.
• Facilitate the development of new or revised schemas about the phenomena under consideration.

The role of motivation is critical. Although science hath many themes that ought to be interesting, studying science holds little interest for many students. Learning benefits from hands-on instruction and links to aspects of students' lives. For example, motion can be linked to the path of soccer balls, electricity to DVD players, and ecology to community recycling programs. Enhancing interest in topics also can improve the quality of student learning (Sandoval, 1995). Thus, using illustrations and diagrams helps students to understand scientific concepts (Carlson, Chandler, & Sweller, 2003; Hannus & Hyönä, 1999), although some students may need to be taught how to study illustrations as part of text learning.