Discusses three problems preschool teachers should consider when aiming to facilitate children's mathematical activity: (1) How may young children relate to the necessarily abstract basis of mathematics? (2) When is a child's activity mathematical? (3) How may "mathematical" language, concepts, and experiences be appropriately defined?…

Encourages teachers to listen more carefully to what students say. Discusses two modes of reasoning in an effort to understand more deeply what students hear and the styles of reasoning that they might use in mathematics. (Contains 12 references.) (ASK)

Describes students' investigative work that resulted from playing the game Set in an attempt to show how such games can be used to develop mathematical reasoning. (ASK)

A game of noughts and crosses (tic-tac-toe) is used to motivate some mathematical activities. Several "starter" questions for activities are included. (MK)

Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

Presents research findings and teaching implications of mathematics as reasoning and students' reasoning abilities in mathematics. (20 references) (MKR)

Describes four projects that support the transition from an abstract to a concrete notion of the effective use of technology in the secondary school classroom: The Interactive Mathematics Program, Systemic Initiative for Montana Mathematics and Science, University of Chicago School Mathematics Project, and Connected Geometry. (MKR)

An activity in a college statistics class had students go to a field of grass and clover and use a variety of estimation, probability, sampling, distribution, and calculation techniques for determining the number of flowers in the field. The activity focused on the discovery process, encouraged abstract reasoning, and was pleasurable. (MSE)

Simple graphing activity helps primary students make the jump from counting concrete objects to understanding abstract symbols. As part of the activity, students vote for their favorite season, then stand up and become a graph of the data they collect. The activity requires the Graph Club Classroom Kit software program. (SM)

(MDH)

Nine students (ages 7 to 11) with math disabilities were effectively taught using an instructional sequence that moved from the concrete to the semiconcrete to the abstract. Subjects needed between three and seven lessons using manipulative devices and pictures before being able to do abstract-level problems. (Author/DB)

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Compares two approaches to the teaching of mathematics, rote versus reasoning. Discusses the way to teach mathematics as reasoning in elementary classroom as stated in the NCTM Standards. (YP)

This paper reviews special considerations in teaching higher order thinking skills to students with mild disabilities, focusing on curriculum implications; principles of instruction (prior knowledge, connections between new and existing knowledge, self-regulated learning, and impact of social setting); the use of an anchored instructional…

This pamphlet reviews five reports that highlight an emerging consensus among researchers about the value of systematically incorporating cognitive instruction into the elementary school curriculum. First is a comprehensive framework by Robert J. Marzano and C. L. Hutchins for an integrated approach to thinking skills that has been developed and…