Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

Two procedures significantly improved multiplication skills in six students (nine to 12 years old) with learning disabilities. The procedures were writing out multiplication problems and saying problems aloud while working. (CL)

Introduces addition, subtraction, multiplication, and division of fractions using area models such as rectangles and circles, or linear models such as the number line and fraction strips. (ASK)

Presents problem situations that support students when discovering the multiplication principle, permutations, combinations, Pascal's triangle, and relationships among those objects in a concrete context. (ASK)

Discusses the interpretation given to the multiplication symbol ("x") in elementary school textbooks, the meaning of multiplication, and how it should be introduced to children. Also considers several aspects of multiplication, including: (1) equal steps on a line; (2) the array; (3) equal groupings; and (4) allocation (rate). (JN)

The article describes the oral interview, a mathematics assessment technique in which the learning disabled adolescent's thinking stragegies are examined. Both efficient and inefficient thinking strategies related to multiplication are discussed, and implications for instruction considered. (Author/CL)

By providing children with both the tools to learn basic facts and access to facts not yet learned, teachers give children the freedom to attend to the meaning of algorithms and word problems, which play an important role in the application of mathematics in daily life. (MP)

The study investigated types of errors made by learning disabled children by analyzing written responses to multiplication and division problems. Error classifications are discussed, and possible causes are suggested. The importance of thorough investigation of errors by teachers is stressed. (Author/DB)

Use of an ancient method of mental calculation with aliquot parts is illustrated. Other tips for helping children reason are also included. (MNS)

The article describes learning activities incorporating movement, storytelling, and music with instruction on multiplication facts and concepts for elementary special education students. The author explains that such an approach can alleviate boredom and frustration. (CL)

A teacher describes ways in which learning disabled students can learn through tactile-kinesthetic approaches devised by the teacher. Examples are given of multiplication instruction by counting on fingers, and grammar and long division instruction through movement. (CL)

Two games and one activity designed to be used with a hand-held calculator are presented. (MK)

A description is given of a game used to give a continuous review of multiplication facts and illustrate certain properties. (MP)

A method of multiplying using fingers is described and an explanation given. The method is then generalized to other number bases. (MP)

Detailed instructions are given for presenting a number of activities that serve to tie measurement and multiplication together. The activities involve length, weight, area, volume, and capacity. (MP)