Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

Interviews 53 sixth grade students individually in an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occurs in a purely numerical context. Concludes that students' difficulties with the algebraic structure were also found in purely numerical contexts. (Contains 27 references.) (Author/ASK)

Observes some children as they went through middle school from two perspectives: as a parent, and as a college mathematics teacher. Contemplates why American children learn so little arithmetic in the middle grades. (ASK)

Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation and algebraic manipulation skills. Considers the contribution made by Jean-Baptiste Lagrange to thinking about the role of CAS in teaching algebra. (ASK)

Presents worksheets for students to practice substituting whole numbers into fairly simple symbolic expressions. (MKR)

Introduces some of the basic techniques of cryptography along with examples of how cryptography can be employed in teaching mathematics and used as a cross curricular theme. (Author/ASK)

We conducted a brief computer-based assessment involving choices of concurrently presented arithmetic problems associated with competing reinforcer dimensions to assess impulsivity (choices controlled primarily by reinforcer immediacy) as well as the relative influence of other dimensions (reinforcer rate, quality, and response effort), with 58…

Does a concurrent cognitive task affect the dynamics of bimanual rhythmic coordination? In-phase coordination was performed under manipulations of phase detuning and movement frequency and either singly or in combination with an arithmetic task. Predicted direction-specific shifts in stable relative phase from 0 degrees due to detuning and…

The aim of this research is to devise a cognitive tool for meeting the diverse needs of learners for comprehending new procedural knowledge. A model of affordances on teaching fraction equivalence for developing procedural knowledge for adding/subtracting fractions with unlike denominators was derived from the results of a case study of an initial…

Research on dimensional comparison processes has shown that comparing one's own verbal achievements with poorer results in math leads to a higher self-concept of verbal ability. It has been argued that when observers make inferences about a student's academic self-concept, they do not usually have access to dimensional information. In the present…

We argue that to test preschoolers' understanding of counting, one has to use tasks that relate counting to the goal of doing arithmetic, as counting and arithmetic principles are mutually constrained. A naturalistic study in the preschool classroom led to the development of an ''arithmetic-counting'' task, where counting was being related to the…

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…

This article describes the impact of thinking about addition and subtraction facts instead of rotely memorizing them.

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

Background: Understanding and solving problems involves different levels of representation. On the one hand, there are logico-mathematical representations, or problem models (PMs), which contain information such as "the size of the flock changed from 31 sheep to 42" while, on the other hand, there are more qualitative representations, or…