Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

This is a worksheet with background material to facilitate tabulation of water and energy use at home. (MCO)

This study demonstrated the effectiveness and efficiency of a constant time delay procedure (four seconds) to teach five elementary students with learning disabilities multiplication facts. Learning generalized to a paper-and-pencil task, to a different presentation orientation, and to reverse facts. (DB)

Describes two main categories of mental activity used by students in mathematics classes: mental mathematics and mathematical thought. Calls for the continuation of teaching mental mathematics and asks for the inclusion of mathematical thought in the national curricula. (MKR)

The results of this case study of a 15-year-old dropout indicate the potential usefulness of incorporating process mnemonics, particularly in the form of allegorical characterizations and stories, within mathematical instructional strategies for the learning disabled. (15 references) (JJK)

The simple physics behind the mechanism of the toy are explained. Experimental and mathematical steps are given that help in understanding the motion of the doll-pair. The geometry of the setup is described. (KR)

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

The amount and placement of instructional time devoted to various types of computation are crucial. Reviews messages regarding what and how computation should be developed in elementary school mathematics and offers a proposal for a K-8 computation curriculum. (ASK)

Discusses science evaluation studies that seek to determine quantitatively the contribution of different authors, departments, or countries to the whole system, and suggests that different scoring methods can yield totally different rankings. Presents formulas for counting procedures, nontrivial examples of anomalies, and possible solutions.…

A study investigated the arithmetic performance of 197 students (grades 3-8) with mild disabilities and 937 controls and data are discussed in terms of student achievement and implications for standards. The mathematics vocabulary of students with mild disabilities was less developed and they had lower performance scores on computation. (Contains…

Twenty-seven children (ages 7-10) with learning disabilities and 42 controls were tested on three different mathematics tasks. Significantly more controls abstracted composite unit structures suggestive of operational logic on modified nonverbal and associativity of length tasks. On a flash card task, children with learning disabilities achieved…

In the current study, a constant time delay (CTD) procedure was embedded in classroom activities and routines to teach counting to three preschool children with speech and language delays. CTD was effective in teaching numbers to all three children. One child out of two also was able to acquire non-target information. (Contains references.) (CR)

From Aesop to Sun Tzu, the importance of working together has long been acknowledged. Yet as long as cooperation has existed, so have the difficulties associated with it. Pooling two fields might mean twice the power, but this union also brings twice the jargon, twice the competing theories, and twice the head butting. Nonetheless, in this…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…