Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

Why is subsequent recall sometimes better for self-generated answers than for answers obtained from an external source (e.g., calculator)? In this study, we explore the relative contribution of 2 processes, recall attempts and self-computation, to this "generation effect" (i.e., enhanced answer recall relative to when problems are practiced with a…

All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).

Many students and adults feel that algebra is merely the shuffling of symbols. The three interrelated concepts of variable, expression, and equation are central to beginning algebra, and in recent years, helping students understand the idea of a variable has been emphasized. Although graphing calculators help students solve equations, it is also…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied…

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

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

Mathematics games are often used in the classroom as a reward or warm-up activity before the "real" learning takes place. Many teachers have witnessed how useful games are for tuning-in students to the impending mathematics lesson. However, have teachers considered playing games as the central part of the lesson? This article explores…

The author recommends allowing elementary students to use pocket calculators, so that they may concentrate on the sense of a math problem without getting bogged down in computation. He presents calculator activities on place value, estimation, and arithmetic operations, suitable for grades 1-6. (SJL)

Describes three approaches teachers can use to help students understand multiplication and division: calculator explorations, problem solving, and discussion topics. Specific examples are provided for primary and upper grades. (MDM)

Describes three approaches teachers can use to help students understand the computation of numbers: calculator explorations, problem solving, and discussion topics. Specific examples are provided for primary and upper grades. (MDM)

Postulated here is the notion that the exploration of number patterns with calculators is a valuable mathematical learning activity that should be commenced in the primary grades. Various activities are presented that make use of the constant function key, which is available on many of the inexpensive four-function calculators. (JJK)

One teacher's approach to the development of number sense while using calculators is outlined. The relationship between number sense and calculation is discussed. Teaching strategies and two worksheets used in this approach are presented. (CW)