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People have biologically primary abilities (e.g., spoken language comprehension, counting, spatial relationships) which have evolved biologically to serve some function related to survival. Constructivist-based instruction works well for these abilities. They also have biologically complex secondary abilities (e.g., reading, Euclidean geometry, complex math) that are culture-related. Constructivism is not sufficient to support these; they need spaced, procedural learning, over time, on different types of problems that the procedure is normally used to solve.
Textbook
Resnick, L. (Ed.). (1989). Knowing, learning, and instruction: Essays in honor of Robert Glaser. Hillsdale, HJ: Erlbaum.
"Coherence refers to the extent to which the sequencing or ordering of ideas in a text makes sense and the extent to which the language used in discussing those ideas makes the nature of the ideas and their relationships apparent" (p. 50). The goal of a text is to assist the reader in developing a representation of a situation that goes beyond the textual information (see Kintsch). The reader must actively construct meaning in the reading process. To help with this process, text should be organized to build toward an understanding of the topic, with individual statements fitting together logically to build the main points or arguments. Connections between points should be well developed and explicit.
"We use the term intentional learning to refer to cognitive processes that have learning as a goal rather than an incidental outcome" (p. 363). In learning through problem solving, learning results from operations applied to knowledge states, in search of a state that satisfies or constitutes an advance toward the goal state (i.e. search the problem space to get to a stated goal). In learning as problem solving, the goal itself is a learning goal, and there is something problematic about achieving this goal (ownership of an authentic goal). "children see learning as an activity, whereas sophisticated adults see it as a goal" (p. 371). Two key aspects of intentional learning are: the extent to which the tendency to engage in this effortful activity depends on one's conception of knowledge and how it is acquired, and the ways in which the instructional situation can either promote or inhibit these tendencies.
Reciprocal teaching was designed to provide a simple introduction to group discussion techniques aimed at understanding and remembering text content. It's based on Vygotsky's ZPD. It takes place in a cooperative learning group that features guided practice in applying four concrete strategies to that task: questioning, clarifying, summarizing, and predicting. (p. 413). The instructor models and externalizes mature comprehension activities, focuses group energies on a clear instructional goal, and provides supportive feedback (suggestions and help). High-level functions are gradually turned over to the students as the instructor removes the scaffolding and fades. The group benefits from the increased range of expertise of its members' combined knowledge. Conflict or criticism forces the group to defend or elaborate solutions, resulting in a more mature resolution.
Expert and poor students encode knowledge differently. Expert students develop rich representations (situational models) of text-based problems that go well beyond the sparse information given in the textbook, linking them to prior knowledge and explanatory material in the textbook. Poor students did not engage in self-explanation, so even if they did have the declarative knowledge to solve the problem, they could not elaborate it to solve the problem. Poor students depended upon the explicit, basic representation of the problem; expert students saw the domain principle behind the problem, so they could derive a solution from general laws.
Basically, they found that the poorer students looked at the surface features of the problems in the textbooks, whereas the better students tried to figure out the principle underlying the solution to the problem. It's the difference between knowing that this is an inclined plane problem vs. knowing that is is a problem in statics, and it can be solved by balancing the forces to zero.
For authors: If students are to rely on worked-out examples, then these examples must specify the complete procedure (with precise elaborations) as well as the conditions under which those actions apply. For students: Students must actively construct an interpretation of each action and relate it to the explanations and principles introduced in the text.
Cognitive apprenticeship, like any apprenticeship, involves not didactic teaching, but observation, coaching, and successive approximation. Lave hypothesizes that observation aids learners in developing a conceptual model of the target task or process prior to attempting to execute it. (see also Hong.) Coaching involves hints, scaffolding, feedback, modeling, reminders, and new tasks aimed at bringing performance close to expert performance. Apprenticeship is embedded in a subculture in which members are all participants in the target skills, resulting in continual access to models of expertise-in-use. Conceptual and factual knowledge are exemplified and situated in the context of their use. The teacher models expert strategies in context. Learners and experts alternate in task performance in a shared, problem-solving environment. Modeling, coaching, scaffolding, and fading are important. So is articulation of reasoning, knowledge, or problem-solving processes (see Chi & Bassok, self-explanation).
Cognitive apprenticeship is appropriate for developing four aspects of expert knowledge: domain knowledge, heuristic strategies (see Suchman), control strategies (metacognition), and learning strategies (e.g., inquiry learning).
Implicitly held knowledge of fundamental principles (e.g., counting) is the beginning of acquisition of arithmetic knowledge (see Geary, 1995). Instruction builds upon this framework to develop competence. Conceptual competence comprises knowledge of principles and constraints: action schemata (domain principles and procedures: "how to do this") and utilization propositions ("when to do this"). Procedural competence means that you are able to generate competent plans that honor the constraints dictated by the knowledge domain AND the constraints dictated by the task and the setting. Interpretative competence is concerned with how to interpret verbal instructions and physical displays to decide which plan is applicable on a given occasion.
Based on the theory of van Dijk and Kintsch (1983), Kintsch deals with textbased and situation models. A textbase model is the mental representation of the text that a reader or listener constructs in the process of comprehension (expresses the esmantic context of the text). A situation model is a mental representation of the situation described by the text (a map, an arithmetic structure, or an operating procedure). (p. 26). In situational models, subjects make inferences that go beyond the propositions explicitly stated in the text. Subjects who worked arithmetic problems did not recall the text directly, but recalled the problem model they had formed from the text. Subjects who drew maps reconstructed the text more accurately, and inferred more, than those who just recalled the text.
Larkin studied students who solved physics problems using the FERMI AI program. Decomposition of quantities and maintenance of invariance can be applied to related fields, provided the related field has enough domain-specific knowledge to identify correctly the quantities involved and the invariances required. General knowledge from the base domain must not be intermingled with domain-specific knowledge in a way that prevents it from being separated and applied in the target domain (p. 302). Knowledge that transfers well includes: strategies applicable in a limited set of related domains, methods for setting useful subgoals, knowledge for task management, and learning skills. These can be imposed deliberately and interpretatively on more than one situation.
Leinhard studied a master teacher, Ms. Patrick, as she taught her elementary school students the procedure for subtracting two numbers. She used the idea of differences, followed by subtraction with regrouping.
Information transmission by a skilled teacher depends on highly implicit procedures. Leinhardt constructed semantic nets for teacher and students, and compared them. The teacher verbally provides the text from which the children must create their mental (situational) models. The children create their own variations on what they have heard. Critical features are: making sure subskills are in place, clarifying (explaining) the nature of the problem, representing the concept in several ways (numeric, manipulables), specifying the conditions and contexts under which a procedure is to be used, identifying the principles that permit the procedure to be used, identifying and checking errors, and connecting new knowledge to old.
Constructivist theory states that students need to construct knowledge through interaction with the environment. They also need to arrive at mathematical truths. Experts already do this, but they have collapsed the procedure to go directly from mathematical language and relationships to exemplification language and relationships, bypassing ordinary language. Learners must have a chance to start with exemplification relationships (cuisinaire rods) to the exemplification language (place 2 and 3 end to end, compare with 5, see that they match) to mathematical language (add them) to mathematical relationships (2 "+" 3 "=" 5). A learning system is based on two components: a knowledge component (an expert's description of the knowledge domain) and an exemplification component (a parallel, illustrative domain for the learner; manipulables). The analogy must be airtight for this to work.
The important competencies that can be transferred are not specific elements of domain knowledge, but rather language comprehension abilities that are carried across domains. There is a distinction between achieving a meaning and an interpretation for text. Text meaning resembles Kintsch's textbase representation; it stays close to the text and requires little inference beyond that provided by the text. Text interpretation requires inference and is more independent of the text. It resembles Kintsch's situation model. Constructing meaning depends on knowledge of the language, not knowledge of the situation described in the text. Word recognition (knowledge of word meanings) and sentence-parsing (syntax) are impenetrable processes (see Geary, biologically primary abilities). General reading ability transfers because the same words and syntactic forms are used in many texts and because the processes are automatic and impenetrable by domain-specific knowledge.
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Lorraine Sherry