Evaluated effects of a reciprocal peer tutoring (RPT) intervention on arithmetic performance of 12 low-income, underachieving elementary school students. Results indicated that merely teaming students and providing them with positive attention for constructive team activities had no clear effect on arithmetic performance. RPT condition that…

This special section on cognition and mathematics contains an introduction and 13 articles on advances in the psychology of mathematics learning. The articles focus on how students learn to solve mathematics problems, including arithmetic computation problems, arithmetic word problems, and computer programing problems. (SLD)

Identifies four causes of confusion in reading mathematics related to numbers, symbols and sentences, vocabulary, and directionality. Discusses techniques for overcoming each type of the confusion. (YP)

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…

Discusses activities using base-10-block skits to teach number system concepts in first grade classrooms. Describes the students' responses to the activities. (YP)

Discusses ways to incorporate language into the teaching of mathematics and involve students more fully in mathematical processes. Describes classroom teaching practice with and without writing. Lists 11 references. (YP)

Outlined are the weaknesses of traditional, norm-referenced tests which fail to help in making instructional decisions. Presented is a step-by-step series of operations for analyzing and categorizing arithmetic errors, for selecting corrective strategies, and for applying peer-referenced standards to judge the performance of special needs…

Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)

Case studies investigating the effectiveness of procedures undertaken to develop number sense and basic computational skills in (n=12) learning disabled students in a K-1 classroom found that all students were successful in recognizing and matching the numbers 0 through 5 and adding sums to 5. (13 references) (Author/MKR)

Described are the strategies of 44 academic mathematicians on a set of computational estimation problems involving elementary multiplication and division. Discussion centers on the theoretical implications evident from pretest/posttest results in terms of the variety of strategies used and how the choice of strategy changed across the two tests.…

This article offers guidelines for using timed drills to achieve computational fluency in elementary students. It considers the acquisition and practice stages of learning, setting fluency aims and objectives, measuring fluency, research supporting time trials, how to do time trials, and 11 specific guidelines for conducting time trials. (DB)

To determine how middle school students cope with the demands of arithmetic word problems, 140 eighth graders (67 males and 73 females) had to solve problems modeled after those of the National Assessment of Educational Progress. Extraneous information and extra steps reduce the accuracy of students' word problem solutions. (SLD)

Twenty children with left or right hemisphere dysfunction and 10 controls were administered a comprehensive neuropsychological evaluation. Results provide limited support for the hypothesis that the right hemisphere subserves attention and concentration but not for the hypothesis that right-hemisphere deficits are more frequently associated with…

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Postulated here is the notion that the exploration of number patterns with calculators is a valuable mathematical learning activity that should be commenced in the primary grades. Various activities are presented that make use of the constant function key, which is available on many of the inexpensive four-function calculators. (JJK)