The purposes of this study were to assess the differential effects of a single strategy (schema-based instruction; SBI) versus multiple strategies (general strategy instruction, GSI) in promoting mathematical problem solving and mathematics achievement as well as to examine the influence of word problem-solving instruction on the development of…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of…

Five reasons are discussed for teaching estimation involving utility, problem solving, concept formation, calculations, and attitude. Specific types of estimation are analyzed and examples given. (MP)

The study reported is the first in a series of investigations designed to empirically test the hypothesis that calculators reduce quantitative working time and increase computational accuracy, and to examine the relative magnitude of benefit that accompanies utilizing calculators compared to manual work. (MN)

A question as to the number of stitches needed for a particular triangular crocheted scarf gives rise to the use of several methods of solution including arithmetic series. (MN)

Presents and analyzes data on the arithmetic procedures people use when shopping for groceries in American supermarkets. Reports that the way shoppers solve problems is closely related to the way they formulate problems: supermarket arithmetic does not begin with a well-defined problem that calls for a specific numerical answer. (KH)

The article seeks to illustrate that calculators and problem solving complement each other perfectly. (MK)

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Discusses a meaningful experience, conceptually, of multiplication of fractions. (Author/YDS)

Describes a framework to help teachers decide when to use calculators with their students. (YDS)

Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)

Develops computational fluency using a game format. Activities involve a standard deck of playing cards. (Author/NB)

Describes activities that will help students calculate the volume of water carried by a river or stream and how to measure the amount of water wasted by leaky faucets. (MDM)

Presents a mathematical problem on calculating the length of a groove on a long-playing record. Analyzes the problem-solving stages by using two methods of estimation or calculation. (ASK)