Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

Under what conditions can a true "science of mental life" arise from psychological investigations? Can psychology formulate scientific laws of a general nature, comparable in soundness to the laws of physics? I argue that the search for such laws must return to the forefront of psychological and developmental research, an enterprise that requires…

Mathematics is an "artificial" deliberately constructed language, supported crucially by: (1) special alpha-numeric characters and usages; (2) extra-special non-alphanumeric symbols; (3) special written formats within a single line, such as superscripts and subscripts; (4) grouping along a line, including bracketing using round brackets,…

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

This article considers steps towards making a numeracy-across-the-curriculum policy. Numeracy means more than the kind of everyday arithmetic a person (a competent independent adult) needs to handle whole number (and simple decimal) calculations; e.g., money, time, and simple measurement. Importantly, aspects of numeracy arise in any everyday task…

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

Activities for teaching mathematics in kindergarten through grade 8 are included in this guide. Both original ideas and ideas gleaned from various sources, including teachers in the district, are presented. The introduction briefly discusses the importance of developing understanding of concepts, processes, and relationships, the need for…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include graphing on a number line, place value, using exponents, flow charts, and Roman numerals. (MK)

This teacher-prepared Learning Activity Package (LAP) for individualized instruction in topics in pre-algebra covers the natural numbers, whole numbers, and integers. The unit contains a rationale for the material, a list of behavioral objectives, a list of resources including texts (with reading assignments and problem sets specified) and tape…

Behavioral objectives are listed for the primary, intermediate and junior high mathematics curriculum in the Mesa Public Schools (Arizona). Lists of specific objectives are given by level for sets, symbol recognition, number operations, mathematical structures, measurement and problem solving skills. (JP)

A set of ten teacher-prepared Learning Activity Packages (LAPs) for individualized instruction in topics in pre-algebra, the units cover the decimal numeration system; number theory; fractions and decimals; ratio, proportion, and percent; sets; properties of operations; rational numbers; real numbers; open expressions; and open rational…

This fifth unit in the SMSG junior high mathematics series is a student text covering the following topics: rational numbers and coordinates; equations; scientific notation, decimals, and the metric system; constructions, congruent triangles, and the Pythagorean property; relative error; and real numbers. (DT)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…