To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

The Mathematics Fluency and Calculation Tests (MFaCTs) are a series of measures designed to assess for arithmetic calculation skills and calculation fluency in children ages 6 through 18. There are five main purposes of the MFaCTs: (1) identifying students who are behind in basic math fact automaticity; (2) evaluating possible delays in arithmetic…

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. The main difference between these standards and most of the others is…

This study was conducted to obtain information related to mental computation from students in Years 3, 5, 7, and 9 in Western Australia. The numbers of subjects were 163, 163, 163 and 152 in years 3, 5, 7, and 9, respectively. The research was designed to provide three different perspectives of mental computation: (1) a survey of the kinds of…

A calculation method using the 10 fingers to perform the four basic operations with whole numbers can be an introductory and supplementary approach to math instruction for handicapped children. Using the finger calculation method to learn arithmetic is supported by J. Piaget's stages of cognitive development. Studies showing the worth of this…

Introduces a collection of papers presented at a symposium on the situationally-specific character of problem-solving practices. Reports that findings provoke speculation about relations among social contexts, knowledge and activity, and relations between school-learned problem-solving techniques and those used in other settings. (KH)

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)

Presented is a historical treatment of computational devices that use counters on a checkerboard. The discussion includes works of John Napier, Walter Minto, and Nicholas Saunderson. (MP)

Thirty students (ages 7 to 18) with moderate intellectual disabilities were interviewed individually and their counting skills and number concepts assessed. Results showed a significant difference among the three age groups on all number skills assessed, and learning patterns were similar to those of students with normal intelligence.…

Analyzes and refutes the arguments made by "back-to-basics" proponents against the use of calculators and for traditional instruction in the algorithms of pencil-and-paper arithmetic. Argues for the value of mental arithmetic in achieving all the aims and more of the traditional curriculum. (Author/ASK)

A program is presented which enables a programable calculator to become a device to check the arithmetic computational skills of students. (MP)

A case is made against the major argument which implies that the use of a calculator for arithmetic problems that can be done by hand will prevent a student from being able to do arithmetic when the calculator is absent. (MN)

The article offers an interpretation of "specially designed instruction" in arithmetic computation for learning disabled students which challenges overreliance on paper-and-pencil methodologies, rule-oriented procedures, and traditional sequences. Long division is used as an example of developing conceptual understanding to undergird computation.…