Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

Nonfreshmen business students at two universities (n=333) evaluated two open-ended arithmetic expressions; 14.8% evaluated the first incorrectly and 33.3% the second. More recent high school graduates performed better. A refresher lesson on order of operations was recommended. (SK)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

The investigation of cognitive factors responsible for the arithmetic learning problems of fifth graders found that children with arithmetic learning problems were characterized by very slow operation execution. No support was found for theories that inefficient number encoding or inappropriate strategies are characteristic of this population.…

Probit analysis of arithmetic scores from the Young Adult Literacy Assessment Survey (840 males and 1,077 females) found that quantitative literacy skills are a major factor in the likelihood of full-time employment. Low quantitative literacy appears to be associated with the lower probability of employment among young African Americans. (SK)

Specific suggestions for teaching young children (ages 5-7) mathematical principles are offered, covering such concepts as addition, subtraction, multiplication, division, arithmetical laws, and utilizing a story to teach various mathematical concepts and skills. (DB)

Although ability to solve multistep problems is essential for success in numerous careers, only 6.4 percent of 17 year olds can do such problems. Elementary teachers can help students learn to analyze word problems by encouraging visual conceptualization, juxtaposing identical numbers and varying contexts, emphasizing accuracy over speed, and…

Exemplifies a model of a conceptual-support net in the domain of multidigit addition that provides guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. Presents summaries of several different multidigit addition solution methods that indicate how different quantity…

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…