This groundbreaking book looks at the development of mathematical thinking in infants and toddlers, with an emphasis on the earliest stage, from zero to three, when mathematical thinking and problem solving first emerge as natural instincts. The text explores the four precursor math concepts--attribute, comparison, change, and pattern--with an…

Today, schools are introducing STEM education and robotics to children in ever-lower grades. In "Beyond Coding," Marina Umaschi Bers lays out a pedagogical roadmap for teaching code that encompasses the cultivation of character along with technical knowledge and skills. Presenting code as a universal language, she shows how children…

"Invention through Form and Function Analogy" is an invention book for teachers and other leaders working with youth who are involving students in the invention process. The book consists of an introduction and set of nine learning cycle formatted lessons for teaching the principles of invention through the science and engineering design…

"Classroom Discussions: Seeing Math Discourse in Action, Grades K-6" provides preservice and inservice instructors, coaches and facilitators with real, classroom-based video examples that illustrate the principles and practices covered in the authors' best-selling book, "Classroom Discussions: Using Math Talk to Help Students Learn, Grade K-6,…

One of the best tools for sharpening students' problem solving skills can be found in the mystery story, which calls for logical thinking, paying attention to detail, and distinguishing between facts and assumptions. Activities that can help to develop problem solving skills are described along with several references to mystery magazines and…

Three mathematical problems are discussed to point out the need to use problems with more than one solution, but at least one readily available solution. As well as encouraging logical thinking, problems should involve pattern recognition and the generation of guesses to be tested. (MNS)

Three responses from teachers to a problem originally presented in the January-February 1996 issue are shared. The problem concerns sharing a fraction of a meal's price between six diners. Each response reflects a different approach to the problem and to using the problem with a class of students. (AIM)

The purpose of this paper is to demonstrate methods for developing cognitive processes in adult students. It discusses concept formation and concept attainment, problem solving (which involves concept formation and concept attainment), Bruner's three stages of learning (enactive, iconic, and symbolic modes), and visual thinking. A curriculum for…

One pluralistic method for teaching advanced composition reflects the approaches of two texts: Linda Flower's "Problem-Solving Strategies for Writing" and Jeanne Fahnestock and Marie Secor's "A Rhetoric of Argument." Such an approach combines the practical tasks of arguing for consensus proposals with functional rather than…

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…

Presents a problem of tetras made with four cubes, mathematical ideas involved in this problem, and guiding questions for teachers. (KHR)

The National Council of Teachers of Mathematics' (NCTM's) Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly,…

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

Suitable for secondary school students, the workbook provides flowcharting activities to help students understand the logical steps used in problem solving. Before applying the flowcharting procedures to mathematical problems, students are first introduced to familiar non-mathematical problems such as sharpening a pencil or eating peanuts. Section…

Describes three models for teaching effective thinking, but warns against oversimplified approaches. (SRT)