Investigates the calculation strategies used by female students in Grades Two and Three to solve word problems. Findings indicate that students used three main intuitive models: (1) direct counting; (2) repeated addition; and (3) multiplicative operation. Concludes that children acquire an expanding repertoire of intuitive models and the model…

Describes five basic understandings involved in rational counting: (1) groupings of same or different items may be counted; (2) there is a stable order of the counting numbers; (3) one-to-one correspondence; (4) it does not matter which item is counted first; and (5) the cardinal principle. Discusses the importance of rational counting ability and…

Encourages teachers to allow opportunities for students to present alternative algorithms, whether the students invent them or learn them, then lead a discussion about the meaning of the operations with the goal of students understanding why the algorithm works. Teachers with students of similar racial and ethnic backgrounds should encourage the…

Presents a problem involving fractions for discussing and sharing of student responses to the problem at a later date. (KHR)

Describes how a 2nd grade class learned to add and subtract effectively by packing and unpacking "Aunt Mary's candies." (KHR)

Presents the Perfect-Square Geometry Partners problem to teach students about patterns. (Author/NB)

Presents an activity using a number grid to challenge second grade students' concepts related to counting change. (KHR)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Focusing on linear interpolation, an accurate method of implementing parallel analysis, this article contains tables of 95th percentile eigenvalues from random data than can be used with sample sizes of 50 to 500 subjects and between 5 and 50 variables. An empirical example illustrates how to obtain the eigenvalues. (SLD)

Presents a historical overview and summary of research conducted on simple arithmetic in the past 20 years. Presents two seemingly different directions in current research, one on the role of working memory in mental arithmetic and one on the possible cognitive consequences of mathematics anxiety. Contains 108 references. (MKR)

Suggests using the holes in the tear-strip edges of continuous-feed computer paper to convey the magnitude of one million. (MKR)

Two experiments studied preschool children's ability to infer numerosity from correspondence between two sets. Found that children were able to make inferences as early as three years of age. However, differences between the two conditions suggest production deficiencies in young children's use of counting as a problem-solving strategy when they…