Describes a programming environment called Tinker, in which a beginning programmer presents examples to the machine, distinguishing accidental and essential aspects of the examples. Examples of programming in Tinker are presented in which programmers demonstrate how to handle specific examples and the machine formulates a procedure for handling…

The authors hypothesize that a means-end strategy places a load on cognitive processing capacity which retards knowledge acquisition. Three experiments using trigonometry problems with high school students were conducted in which the problem goal was modified to disrupt strategy used by novices. Results supported the authors' hypothesis.…

Identifies procedure to help classroom teachers infuse problem solving into the typical technology education classroom. The five steps involved are (1) set a goal the student can attain, (2) define a task that incorporates new actions and ideas, (3) provide a structure, (4) force the student to choose between several alternatives, and (5) make the…

Presents ideas to improve education, including employing increasingly effective group procedures, teaching techniques of cooperative planning and group problem solving, developing skills of cooperative assessment and self-evaluation, and developing skills of propaganda analysis. (CT)

This report on mathematics education in Soviet elementary schools was prepared by a writer for the Novosti Press Agency in Moscow. It notes that mathematics is taught by subject specialists beginning in grade 4 and provides details on both curriculum and instructional practices. (MNS)

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,…