Describes some basic difficulties in early algebra and their causes and presents some strategies for overcoming them. Lists five areas as being essential foundations for learning algebra: (1) seeing the operation, not just the answer; (2) understanding the equals sign; (3) understanding the properties of numbers; (4) being able to use all numbers;…

Compares the effects of two types of feedback on mathematical reasoning in a computerized Israeli sixth grade class. Metacognitive feedback (MF) is based on self-regulation learning using metacognitive questions that serve as cues for understanding the problem, and results feedback means giving cues that pertain only to the final outcome.…

Explores parallels in children's moral and mathematical judgments. Considers how children coordinate these judgments with concepts of authority, particularly when using conventionally determined symbol systems to convey logical and social meanings. (JPB)

Discusses ways for middle school teachers to encourage their students to discuss mathematical concepts in the classroom. Considers setting up the classroom environment to facilitate mathematics discussion, the role of the teacher, small group discussions, whole-class discussions, and student presentations. (JPB)

This article argues that the reason the mathematics performance of students with mild disabilities is so limited is the mathematics. Using illustrations from subtraction, the article proposes number sense be a primary goal and that within the realm of number sense, big ideas be included among the dependent variables. (Contains references.)…

Two experiments investigated how child and adult speakers of English and Kannada (Dravidian) interpret scopally ambiguous sentences containing numerally quantified noun phrases and negation. Results showed that 4-year-olds' interpretations were constrained by the surface hierarchical relations (the c-command relations) between sentence elements…

Third-graders showing negligible mastery of multiplication combinations were randomly assigned to two groups which practiced different subsets of combinations. Retest results were inconsistent with Siegler's (1988) proposal that item-specific computational practice is necessary to change error patterns and promote mastery. Results suggested that…

Describes and explains a procedure for photographing the chaotic scattering of light. (WRM)

Observed gesture and speech to investigate patterns of change in third and fourth graders' strategies for solving mathematical equivalence problems before and after an intervention. Children who received instruction were more likely to generate new strategies. Gradual change was more common. Abrupt strategy change was more common in children who…

Tested 3- to 7-year-olds' ability to calculate with whole numbers, fractions, and mixed-numbers, in a task in which an amount was displayed, then hidden. Subjects were to determine the hidden amount resulting when numbers were added or substracted. Found that, although fraction problems were more difficult than whole-number problems, competence on…

The purpose of this study, grounded in near-transfer theory, was to investigate relationships among music sight-reading and tonal and rhythmic audiation, visual field articulation, spatial orientation and visualization, and achievement in math concepts and reading comprehension. A regression analysis with data from four high schools (N = 98) in…

This article describes an investigation making connections between the time on an analog clock and the angle between the minute hand and the hour hand. It was posed by a middle school mathematics teacher. (Contains 8 tables and 6 figures.)

This article describes how two middle school teachers incorporated algebraic thinking into their textbook-based geometry lessons. One teacher embedded algebraic concepts within an existing textbook lesson while the other teacher elicited algebraic thinking by extending a textbook lesson. (Contains 5 figures.)

This article describes a hands-on activity in which students convert decimals to fractions, measure, make scale drawings, use algebraic formulas, and use visualization to construct a three-dimensional physical model of a portion of the seafloor. In the process, they learn about sound, speed, and ocean exploration. (Contains 2 figures.)

This article contrasts relational and instrumental understanding and the consequences on the application of mathematics learning. (Contains 3 endnotes.)