Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…

Developed by the Initial Learning in Mainstreaming Project, the manual presents an instructional program to teach mainstreamed handicapped elementary school students multiplication with multipliers of up to three digits. In addition to detailed teaching instructions and text of tape recordings for students, the manual includes tests, worksheets,…

This study compares the effectiveness of an electronic calculator, programmed as an immediate feedback device, with the effectiveness of pencil-and-paper exercises without immediate feedback for the learning of the 100 basic multiplication combinations. These two methods were also compared with regular classroom procedures. Subjects were…

The use of peers to provide instructional control was investigated in two studies. The first determined the reliability with which students identify multiplication fact errors. The second investigated the effectiveness of a peer-mediated drill procedure for instruction on multiplication facts. (Author/RK)

A method is discussed for learning the multiplication tables that avoid repeating tables everyday or memorizing a large body of facts at the same time. (MN)

A method for obtaining the least common multiple and the greatest common factor of a pair of numbers without using prime factorization is examined. (JT)

Using factoring as an aid to mental multiplication is illustrated. Other suggestions for teaching mental computation are also included. (MNS)

This study involved 48 students ages 9 to 12. The 29 experimental group students, divided into small groups, performed learning exercises designed to improve skills in analyzing and processing expressions frequently included in addition and multiplication problems. The exercises helped significantly to improve problem-solving performance. (MNS)

Presents a technique for multiplying two-digit numbers whose tens digits are equal and whose units digits have a sum of 10. Then various mental calculations with other types of two-digit and larger numbers are discussed. (MNS)

Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)