The general purposes of a model are discussed, then seven papers are presented which demonstrate several different facets of the problems associated with constructing and using models of mathematics learning. In the first paper, the task addressed concerns how to incorporate developmental psychology into perceptions of what is happening in the…

The author discusses the impact of mathematical developments around the turn of the century, and historical concerns and development of mathematics education. This article is a continuation of SE 515 504. (SD)

Using a great variety of word problems drawn from many contexts can make multiplication and division rules more relevant to the student's needs. (SD)

The author describes a technique for teaching various aspects of the subtraction algorithm (e.g., regrouping, borrowing) by relating them to the use of money. (SD)

The "basic fact bug" is a diagrammatic device for use in reinforcing addition or multiplication skills. It is self-checking. (SD)

After considering the mathematical system common to various types of measure, the author argues that instruction needs to reflect the common aspects of measure systems as well as the distinctive attributes of different systems. (SD)

The fraction concept was analyzed to yield 16 subconcepts which are hypothesized to be hierarchically ordered. This ordering was tested using subjects in grades 4 through 6, and 18 of 23 dependencies hypothesized were confirmed. (SD)

Worksheets are provided for activities involving associating numbers with letters (as on the telephone dial) to compute values for words. Other activities involve systematic counting of telephone numbers. (SD)

The algorithms for finding cube roots is approached by slicing a cube. (SD)

In these 20 activities for grades 1-6, children translate from numbers to words. Five language objectives focus on quantitative expression, comparisons, sequence, logical continuity, and elaboration. Each objective includes a math exercise followed by a related language experience. (Author/SJL)

Similar rectangles are the basis of a set of activities using newspaper. Topics arising include infinite series and Pythagorean theorem. (MP)

Discovering 3 by 3 magic squares, using numbers 1 through 9, is presented as a learning activity on three different levels. (MP)

These worksheets deal with sums of numbers. Students are asked to find the relationship between the last number in the series, the number of addends, and the sum. (MP)

The main problem of this study was to attempt to determine the source of adults' nonconservation error as well as to explain young children's apparent success. Subjects were 188 children from elementary school, high school, and college. (Author/MP)

Four articles are presented in this monthly column: dealing effectively with metric conversions; teaching how to round numbers; why a false statement implying a false statement is true--a discovery explanation; and a third-grade puzzle with interesting implications. (MP)