This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ?) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + ? or 6 + 4 + 5 = ? + 5). Next, they completed an encoding task in which they reconstructed…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

As a unifying feature of this Special Issue, we have asked proponents of each framework to analyse an empirical classroom account of one student's process of solving a mathematical problem. Here, for the case study of "Frank", we give the main data that were available to all authors.

Accurate and accessible expressions for the probability of having a matching birthday are obtained by using Stirling's formula and Taylor series. For interest, the results are applied to the planets of our solar system.

This article explores how different proofs of a solution to the Surfer Problem provide answers to the question "Why"?

This article describes a solution, using CAS, to graph theory problem that was presented in the movie "Good Will Hunting."

This study assessed the effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving. Stratifying within schools, 119 3rd-grade classes were randomly assigned to conventional or validated problem-solving instruction (Hot Math, schema-broadening instruction). Students identified as at…

Teaching mathematics to students with emotional and behavioral disorders (EBD) is one of the most challenging tasks educators face today. Students with EBD are reported to have the most dismal outcomes of any other group of students with disabilities including the lowest grades, the most failing grades, higher retention rates, the highest dropout…

Based on the notions of social and socio-mathematical norms we investigate how these are established during the interactions of pre-service teachers who solve mathematical problems. Norms identified in relevant studies are found in our case too; moreover, we have found norms related to particular aspects of the problems posed. Our results show…

Developed by the ABCs of Construction National Workplace Literacy Project, these curriculum materials for the area of electrical and instrumentation contain a lesson that deals with reading diagrams. The lesson consists of an objective, instruction, and 10 exercises. The objective for the lesson is for the student to learn to locate and apply…

Developed by the ABCs of Construction National Workplace Literacy Project, these curriculum materials for the occupational area of millwright contain a lesson that deals with reading diagrams. The lesson consists of an objective, instruction, and 10 exercises. Three types of problems are provided in each exercise: "try it,""apply…

Developed by the ABCs of Construction National Workplace Literacy Project, these curriculum materials for the occupational area of pipefitting contain a lesson that deals with reading diagrams. The lesson consists of an objective, instruction, and 10 exercises. Three types of problems are provided in each exercise: "try it,""apply…

The National Council of Teachers of Mathematics' (NCTM) "Curriculum and Evaluation Standards" recommends that mathematical connections be made between mathematics and other disciplines. This book presents 35 activities for middle school students that integrate the teaching of mathematical concepts with environmental concepts. An…

Provides descriptions of 44 award-winning computer software packages that are designed to be used in areas such as science, mathematics, computer literacy, creative arts, language arts, social studies, computer tools, and graphics. (TW)