This paper is a report of a study conducted with preservice elementary teachers at the University of Wyoming during the summer of 1993. The study had two purposes: (1) to observe the effectiveness of using a constructivist approach in teaching mathematics to preservice elementary teachers, and (2) to focus on teaching probability using a constructivist approach. The study was conducted by one instructor in one class, The Theory of Arithmetic II, a required mathematics class for preservice elementary teachers.

Key words: educational methods, teacher education, concept formation, constructivist teaching, preservice teacher education, problem solving, classroom techniques, mathematical concepts, teacher education programs

Purpose: The paper contributes to the naturalization of epistemology. It suggests tentative itineraries for the progression from elementary experiential situations to the abstraction of the concepts of unit, plurality, number, point, line, and plane. It also provides a discussion of the question of certainty in logical deduction and arithmetic. Approach: Whitehead’s description of three processes involved in criticizing mathematical thinking (1956) is used to show discrepancies between a traditional epistemological stance and the constructivist approach to knowing and communication. Practical implications: Reducing basic abstract terms to experiential situations should make them easier to conceive for students.

Key words: foundations of mathematics, concept formation, conceptual semantics

This paper describes some salient aspects of inservice education that focus on constructivist learning/conceptual change. Major issues for inservice education based on the constructivist approach are described. These issues arise from viewing teachers as constructivist learners, and from the assumption that constructivism and conceptual change need to be considered in the saw: way for both teachers and students. The following assumptions are contained in the constructivist theory of learning: (1) inservice education that matters involves conceptual charge on the part of teachers; (2) when the thrust of the inservice program is towards constructivist perspectives on teaching and student learning, the change involves teachers’ conceptions of learning and teaching; (3) conceptual change in teachers is most helpfully considered in terms of whether or not new ideas are intelligible, plausible, fruitful, and feasible; (4) the conceptions held by teachers on entering an inservice program will sometimes include ideas and beliefs about the focus of the program which are in conflict with the ideas and beliefs of those running the program; (5) the inservice must, wherever possible, model but not mimic the strategies and ideas being advanced; (6) different groups will enter inservice programs with different levels of relevant knowledge and experience; and (7) those conducting the inservice program must be sensitive to their own needs to undergo conceptual change. Descriptions of four inservice programs illustrate how one or more of these issues arose and was dealt with in the course of the program.

Key words: attitude change, cognitive dissonance, concept, formation, foreign countries, inservice teacher education, learning processes, program attitudes, teacher attitudes.

Excerpt: It is argued that laboratory experiences may be a worthwhile or essential aspect of science education, but the literature relating to research in this area does not always support these assumptions. While the laboratory may have value for nurturing positive student attitudes and for providing opportunities for students of all abilities to demonstrate skills and techniques (Bates, 1978), it appears that students fare no better with a laboratory experience than without one in developing understanding of chemistry (Novak, 1984)

Key words: educational methods, philosophy, research methodology, instructional design, classroom techniques, concept formation, constructivism, control groups, qualitative research

The subject “energy of chemical reactions” has been referred/reported as a theme in which the students demonstrate several difficulties of an adequate understanding (Johnstone, 1980; Finley, Stewart and Yarroch, 1982; Granville, 1985; Lawrenz, 1987; Shaibu, 1988). Some alternative conceptions in this area have been identified and are discribed (Cachapuz and Martins, 1987; Martins, 1989). For example, high school students may think that in some chemical reactions one of the reactants may play a more important role than the other(s), the so called “principal reactant” (PR) (Cachapuz and Martins, 1988). The idea of “principal reactant” is probably a specific case of a more general difficulty on the part of students in perceiving a chemical system in its entirety and it may be considered as a contemporary version of the duality between the sulphur and mercury principles used by 13th century Alchemists to explain natural phenomena. As referred by historians of science (Caron and Hutin, 1964) the sulphur principle would explain the active and warm properties of materials (hence the idea of “principal reactant”) whereas the mercury principle would explain passive and cold attributes.

Key words: concept formation, teacher education, philosophy, concept formation, misconceptions, concept teaching, teaching for conceptual change, constructivist teaching, constructivism

During the past decade ‘Constructivism’ or one of its many variants has become the dominant ideology in science and mathematics education. A casual, disinterested observer might be shocked at the rate at which this school of thought has permeated research communities across the globe and at the grip that it holds on their work. In this paper, I wish to concentrate on the notion of Constructivism prevalent in science education as defined by the the Generative model of learning (Osborne and Wittrock 1985), Driver’s (1985) account of a constructivist approach to curriculum development and White’s (1988) position on the learning of science.

Key words: philosophy, educational methods, concept formation, epistemology, realism, learning motivations, cognitive style, curriculum design

Excerpt: There are some fundamental questions in relation to scientific knowledge development. What are major components for knowledge construction and how do people construct their knowledge? How is this personal construct assimilated and accommodated into a scientific paradigm? How can one design a computational system to facilitate these processes? This chapter does not attempt to answer all these questions but serves as a basis to foster thinking along this line. A brief literature review about how people develop their knowledge is carried out through a constructivist view. A hydrological modeling scenario is presented to elucidate the approach.

Key words: knowledge discovery, knowledge structure, concept formation, knowledge construction, constructivist view.

This paper reflects on the implications of a five year programme of research and development with non-specialist teachers of science in primary (elementary) classrooms in England. Within a constructivist framework defined by University-based researchers, groups of teachers explored the viability of a range of methods of eliciting children’s ideas prior to helping children to develop their thinking in the direction of conventional scientific understanding. This research led to the development of curriculum materials, (Nuffield Primary Science) generated in a similar manner, with groups of teachers operating under normal classroom conditions. The outcomes and implications of this programme of research and curriculum development are described and critically discussed. Particular reference is made to the needs of teachers wishing to operate within a constructivist orientation, bearing in mind the constraints of normal classroom conditions.

Key words: philosophy, educational methods, concept formation, epistemology, realism, learning motivations, cognitive style, curriculum design.

In this conceptual paper we propose a shift of perspective for parts of AI – from search to model construction. We claim that humans construct a model of a problem situation consisting of only a few, hierarchically structured elements. A model allows selective exploration of possible continuations and solutions, and for the flexible instantiation and adaptation of concepts. We underpin our claims with results from two protocol studies on problem-solving imagery and on the inductive learning of an algorithmic structure. We suggest that a fresh look into the small-scale construction processes humans execute would further ideas in categorization, analogy, concept formation, conceptual blending, and related fields of AI. Relevance: In accordance with von Glasersfeld’s postulate that knowledge is actively built up by the cognizing subject, the paper emphasizes the constructive nature of human intelligence. While problem space models in AI also partly reflect this, the metaphorical language of problem space search lends itself to epistemological misinterpretations.

The implications of constructivist epistemology and conceptual-change ideas have received less attention in teacher education than in the case of teaching science to pupils. However, some paradoxes mentioned in the literature apply to teacher education in special ways: 1. Even if we accept the validity of a constructivist epistemology, does that imply a specific teaching strategy? 2. If we say we want learners to construct their knowledge, but we define success according to whether they change their conceptions in a certain direction, are we trying to have it both ways? These questions have two layers of meanings in the context of teacher education: what to “tell” teachers about instruction, and how to “tell” them. Teachers continually construct their views of the nature of learning and teaching science. These views are major determinants of how they carry out their teaching functions. How the informal and formal experiences of teacher education influence thses views in an important issue.

Key words: teacher education, concept formation, educational methods, constructivist teaching, cognitive restructuring, constructivism, inservice teacher education, preservice teacher education, emppowering students