If you were to receive a plateful of the first image, you would most likely have an enjoyably delicious snack. However, the second could be fatal, due to the toxic lode of dauricine. If you based your decision of whether to eat this berry only on what you know grapes smell like and look like and the vines they grow on (your schema), there is the possibility your existing schema could prove detrimental.
Recall from earlier in the chapter that a schema, or schemata when plural, is a category of information, a representation or symbolic illustration that forms in the mind when an individual learns information or develops behaviors. Rumelhart (1980) summarized the extensive nature of schemata:
Schemata can represent knowledge at all levels—from ideologies and cultural truths to knowledge about the meaning of a particular word, to knowledge about what patterns of excitations are associated with what letters of the alphabet. We have schemata to represent all levels of our experience, at all levels of abstraction. Finally, our schemata are our knowledge. All of our generic knowledge is embedded in schemata. (p. 41)
Existing schemata are based on experiences, previous knowledge, and beliefs, and these schemata are the stepping stones for organizing material within our memory. In addition, our schemata are ever changing as we experience and learn more over time. Although these schemata can be accessed easily and quickly, such mental connections can also be the reason why learners might consciously and unconsciously accept only new knowledge that aligns with what they already know or believe. Consider what your prior studies taught you about learning. If you did not fully understand a concept or did not have it clearly explained to you, then this clouded information could continue to affect your current studies. Thus, new knowledge acquisition can be a very perplexing process, as it may become associated with inaccurate or underdeveloped schemata.
Because of this, proper schema development has become a key framework within the theory of cognitivism. Prior knowledge as an important basis for learning was introduced by researchers Piaget (1929) and Bartlett (1932). How learners use schemata can affect how, or if, they successfully and accurately acquire new knowledge. In many cases, learners will unconsciously apply schemata. However, this reflexive response can sometimes be problematic, as the nearby images of grapes and moonseed fruit illustrate.
The excerpts in this section are from Hodnik Čadež and Manfreda Kolar (2015). You will learn more about how schemata are formed, how they apply to problem solving, and how instruction is presented to complement the formation of effective schemata. Note that the words schema, mental schema, and cognitive schema are used interchangeably to refer to mental representations of information.
Excerpts from “Comparison of Types of Generalizations and Problem-Solving Schemas Used to Solve a Mathematical Problem”
By T. Hodnik Čadež and V. Manfreda Kolar
Clinical psychologist Jean Piaget (who is known more broadly for his work on children’s cognitive development) is undoubtedly the first name that comes to mind when researching mental schemata. He uses the term structure or a schema to denote a “mature” or developed form of knowledge organization. [. . .]
Applications of Piaget’s work are present in works of many recent researchers, and the definitions of the term schema are interwoven with that of Piaget. Marshall (1995) sees a schema as a mechanism in human memory that allows individuals to organize similar experiences in such a way that they can easily recognize additional similar experience. Chinnappan (1998) uses the term for a cluster of knowledge that contains information about the core concepts, the relations between these concepts, and the knowledge about how and when to use them. Thus, when individuals acquire concepts, principles, and procedures, they organize them into schemata, which provide for the knowledge base for further mathematical activity. Subsequent events contribute to refining and further development of schemata, and knowledge transfer takes place. “Schemata are triggered when an individual tries to comprehend, understand, organize, or make sense of a new situation” (Steele & Johanning, 2004, p. 67). Organization and spread are the two characteristics of understanding schemata (Chinnappan, 1998), whereby organization refers to the establishment of connections between ideas, and spread refers to the extent of those connections.
For example, as you are reading this material about schema development, what comes to mind? Perhaps it is your knowledge about how your life experiences have shaped your beliefs. Hence, how you understand and subsequently organize the information about schema development could be based on your current understanding about belief development. These ideas (your past knowledge about belief development and the new knowledge about schema development) are now connected and thus organized within your mind. If this knowledge is very new to you, your spread may be limited. As you learn more about schema development, your ability to connect it to future new knowledge would advance, increasing your spread.
An individual’s cognitive schemata are constantly being revised and elaborated upon each time the individual encounters new experiences. A schema is structured if it is vertically constructed, known as vertically constructed schema: By adding new layers an individual forms a deeper and more closely connected hierarchy of knowledge; the individual is able to make connections between the new experiences and prior knowledge and assimilate new information. According to Piaget (1952, 1968) assimilation is the process in which the individual acts toward the environment so as to bring it into accord with its existing structures. (In other words, the individual incorporates new information into his or her existing schemata.) The adaptive orientation of an individual is toward the achievement of a more stable equilibrium. Sometimes, this requires not only assimilation, but also accommodation, where the individual has to adjust his or her existing schemata to comply with the objective, outside world. [. . .]
Individuals must make a series of accommodations to the objective conditions imposed by the environment and incorporate these accommodations into their own structure as a basis of their future behavior. Individuals attempt to encompass each new set of accommodations on the basis of their capacity to assimilate objective reality at the existing level of structure. Should this prove impossible, adaptive pressure leads individuals to attempt new accommodations together with their old structure under principles of a higher order. These principles in turn become the basis of a new and a more powerful schema. Tall (1991) defines assimilation as an expansive generalization: One extends the existing cognitive structure without a change in current ideas, whereas accommodation is a reconstructive generalization—it requires reconstruction of the existing cognitive structure. (See Figure 2.1 for an example of assimilation and accommodation.)