Since Bruner's introduction of discovery learning in the 1960s, there has been an ongoing and intensive debate on the value of inductive teaching methods (e.g., problem-solving followed by instruction, such as in problem-based learning and productive failure) compared to deductive teaching methods (instruction followed by problem-solving, such as…

Contradictory evidence has been reported on the effects of discovery learning approach and the role of instructional explanations. By manipulating the presence of instruction (verbal explanation) and transparency of problem structures, we investigated how effects of instructional explanations differed depending on the transparency of problem…

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain…

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

This paper describes an approach to task analysis which seeks to identify potential sources of difficulty in the self-discovery of improved procedures by students who have been taught simpler procedures. The approach considers novices' procedures in terms of the changes needed to produce an expert procedure; the knowledge required to make those…

Using mathematics as an example, the nature of the confusion between "knowledge" and "coming to know" is elucidated. The range of curriculum choices available to structuralists once the distinction is clarified is larger, and teaching a body of knowledge and teaching by discovery are compatible. (Author/MLF)

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

The exploration mode of content presentation is discussed. (MP)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

The purpose of this paper is to present a conceptual basis for advocacy of an inquiry-based instructional model. Focusing on the teacher as inquirer, the paper discusses the nature of inquiry, presents its conceptual framework and describes in detail the use of question strategies in the preschool program. The definition of inquiry analyzes…

Describes teaching strategies in which children are encouraged to develop computational procedures that are meaningful to them. Authors state that classroom observation reveals most primary students to be capable of developing their own accurate solution procedures for multi-digit addition and subtraction as well as for simple multiplication and…