Considering its relationships with real life and mathematics, mathematical modeling is one of the most effective ways of learning and teaching mathematics. In this study, the effect of teaching with mathematical modeling on students' mathematics achievement was examined using the meta-analysis method. An effect size of 51 was achieved with 45…

Educational strategies have evolved over the years, due to research breakthroughs and the application of technology. By using the latest learning innovations, curriculum and instructional design can be enhanced and strengthened. The "Handbook of Research on Driving STEM Learning with Educational Technologies" is an authoritative…

Models for developing addition, subtraction, and multiplication with integers are given. (MNS)

A model, easily constructed by students, is used to assist in seeking basic Pythagorean identities used to prove more complex ones. (MNS)

The "positive-negative charge" model is described and demonstrated with all four operations on integers. Its major advantages are that it is both concrete and complete. (MNS)

Describes several activities of the Data and Chance program involving third and fourth graders. Students use real-life situations to investigate probability. (MKR)

Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…

Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Presents an activity in which the subject is the identity of the team in the greatest jeopardy of becoming the big loser in a basketball tournament. Explores several facts about the big loser, offering them in a hierarchy appropriate for creating various short- and long-term projects for a high school mathematics class. (ASK)

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

Describes the instructional strategies and activities used to illustrate the essential features of mathematical modeling to a group of infant and junior high school teachers. The intent was to involve the group with some number work, elementary algebra, and some simple work on arrangements by way of tree-diagrams. (JN)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)