Explores students' abilities in mental computation, finds out the strategies they use most naturally, and develops a theoretical framework by giving 60 children a questionnaire and interviewing them on a series of arithmetic operations to be solved by mental computation. Generates a classification of children's strategies. Contains 31 references.…

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Discusses overall mental computation achievement and limits discussion to strategies middle school students used when computing with whole numbers, decimals, and fractions. Suggests that the development of conceptual knowledge of numbers is an important prerequisite for the understanding of mental computation procedures. (Contains 31 references.)…

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

This experimental study compared the use of Belcastro rods with the use of traditional methods in teaching addition and subtraction of whole numbers to five blind students. Results showed a significant difference favoring the use of Belcastro rods. (Contains 30 references.) (MKR)

This study examined the problem-solving strategies and systematic errors of (n=82) preservice elementary school teachers related to place value concepts and decimal representations of rational numbers. Problems were posed in the unfamiliar domain of numeration systems with bases other than base ten. (Contains 13 references.) (MKR)

Analyzes the solution of additive problems involving negative numbers by prospective primary school teachers using surveys. Concludes that students feel no need to use negative numbers in the solution of additive problems and compares results of this study to another study of same content done on secondary school students. (ASK)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

Interviewers asked (n=10) 6th- and (n=10) 10th-grade students to solve nonroutine number problems. Task analysis of perseverers, those students who continued after reaching "dead-ends," found that students who were ultimately successful were more inclined to be flexible in their strategies. (28 references) (MKR)

Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH)

Reports a study to explore student's computational performance on computer-administered testing situations while at the computer. Students from grades 3-6 (n=100) were randomly assigned to treatment order, computer assessment first or paper/pencil assessment first. Significant differences occurred in three areas: completion time, number of mental…

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…