The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

Suggests that problems designed for classroom use should include such factors as ways to introduce the problem, the skills to be developed, the mathematical prerequisites for the problem, key questions, extensions, and solutions. An example is provided which illustrates these and other points. (JN)

Critical thinking skills that can be applied to reading can be developed through means other than reading. Teachers can launch class discussions of popular films, such as "E.T.," to nurture these skills, a technique especially helpful for children who have difficulty with the printed word. (PP)

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

This study explores students algebraic and geometric approach in solving tasks in functions and the relation of these approaches with complex geometric problem solving. Data were obtained from 95 sophomore pre-service teachers, enrolled in a basic algebra course. Implicative statistical analysis was performed to evaluate the relation between…

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

The integration of History in the educational practice can lead to the development of a series of activities exploiting genetic "moments" of the history of Mathematics. Utilizing genetic ideas that developed during the 14th century (Merton College, N. Oresme), activities are developed and mathematical models for solving problems related to uniform…

The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

The Malaysian educational system tends to take a clear instructionally-focused approach to the teaching of mathematics. This means that many students gain a good procedural command of areas of mathematics. This paper explores one outcome of a teaching experiment in which one area of mathematics (differentiation) was taught in a radically different…

This paper presents the design and some results of a series of teaching experiments. The design was created to develop a model for everyday math lessons, that describes the conditions which foster or hinder the construction of new mathematical meanings. The development process includes the students' epistemic processes, their social interactions,…

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use…

This paper presents preliminary hypotheses about a common core of faculty beliefs about how their students learn to solve problems in their introductory courses. Using a process of structured interviews and a concept map based analysis, we find that faculty appear to believe that students learn problem solving primarily through a process of…

The purpose of this study was to investigate the effects of the Casio 9850 and the TI-85 graphing calculators on college students' procedural skills and conceptual understanding in two different developmental mathematics courses. The courses used in this study were Elementary Algebra and Intermediate Algebra. Both the non-graphing calculator group…

This book addresses questions of multiple representations in human reasoning and learning. Computational approaches to learning with multiple representations are introduced, and the role of multiple representations in teaching is discussed. The following chapters are included in Part I: Multiple Representations in Learning Concepts form Physics…

This book attempts to review and extend current knowledge and perspectives on scientific problem solving by utilizing the framework of cognitive science. While the focus of the monograph is toward problem solving, its ultimate goal is the improvement of science teaching. Twelve chapters address problem solving in a variety of science content…