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

Presents a historical overview of learning theories in mathematics education applied to the teaching of integers. Theories discussed are meaning vs. rote learning; direct vs. incidental; discovery vs. exposition; concrete vs. abstract; and construction vs. transmission. Includes a reproducible activity sheet and 19 references. (MKR)

The introduction of addition, subtraction, multiplication, and division to children is seen to require a compatible and sequential methodology. The sequence of learning is seen as: (1) physical action; (2) emotional involvement; and (3) conceptual learning. A learning sequence should involve the following steps: (1) connectinq number experience to…

Described is an activity where base-10 blocks are used to develop students' skills in reading, writing, and visualizing large numbers. An activity sheet that helps students with decimal points is included. (KR)

This book is the result of the collaborative effort of nine AYA National Board Certified Teachers in Mathematics. Experiencing Mathematics, is a compilation of teacher-tested activities that prompt high school students to explore, conjecture and reflect on their mathematical adventures--thus "experience mathematics." The relevant nature of the…

Four worksheets are given to enhance the understanding of and facility with numerical concepts and relations for students in grades seven through nine. The focus is on enhancing deductive reasoning abilities with Venn diagrams and arrow diagrams. Teaching ideas are included. (MNS)

Problem solving that both requires and develops higher-order thinking skills is illustrated in the EQUATIONS Challenge Matches program, which consists of computer diskettes at the elementary, intermediate, and advanced levels plus a multi-level diskette. Samples of computer output are given, with the results of various types of experimentation…

This book is directed toward increasing students' ability to analyze problems and comprehend what they read and hear. It outlines and illustrates the methods that good problem solvers use in attacking complex ideas, and provides practice in applying these methods to a variety of questions involving comprehension and reasoning. Chapter I includes a…

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

The looseleaf binder contains a series of 268 learning packages for gifted and talented elementary school students, divided into 13 subject area sections, including art, chess, general, health, language arts, literature, mathematics, perception, reading, science, social studies, study skills, and thinking skills. Two additional sections include…