Introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. Describes components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies. (Author/MM)

Presents an activity in which students work in cooperative groups and roll balls down inclined planes, collect data with the help of an electronic motion detector, and represent data with a graphing calculator to explore concepts such as mass, gravity, velocity, and acceleration. (Contains 12 references.) (Author/ASK)

Describes various philosophical positions on the teaching of the scientific method in the middle years of the 20th century by examining articles published in this journal. Concludes that there is still no agreement on a definition of the scientific method or the best way to teach it. (MM)

Describes and reviews the book "The Educational Concepts of Secondary School Science Teachers" by Paul Hurd. (MM)

Describes electronic resources designed to illuminate the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics". Provides a vehicle for further discussion of the vision put forth in the Standards. (Author/MM)

Discusses the implications of the National Council of Teachers of Mathematics (NCTM) standards for mathematics curricula and instruction and provides three examples of lessons from problem-based curricula for various grades. (Author/MM)

Discusses the level of knowledge, understanding, and ability relative to mathematics for the college graduate in the 21st century. Focuses on mathematical literacy and abstraction such as the definition of abstraction, difficulties in addressing abstraction, and one approach to helping students learn to address abstraction. (Contains 12…

Traces three major stages in the development of algebraic notation: (1) rhetorical or prose; (2) syncopated; and (3) symbolic. Illustrates the development of a standardized, efficient symbol system by tracing the evolution of some common symbols, including the symbols for equals, addition, subtraction, multiplication, and division. (Author/WRM)

Examines geometry language used in K-6 textbooks and compares the findings to language used in modern mathematics standards documents. Finds a substantial misalignment between the geometry presented in textbooks, the geometry teaching expectations of mathematics education professionals, and the geometry being assessed in student performance…

Describes a lesson that provides an opportunity for students to obtain the equation for a line describing data they have collected, use the equation they have derived to set up an Egg Bungee Jump, and relate the numbers in the equation to the physical properties of the bungee jump. (WRM)

Presents a lesson on the scale of the solar system that focuses on measurement, exponential notation, proportionality, and ratios. (Contains 17 references.) (Author/ASK)

Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…

Presents an activity that integrates mathematics and science and focuses on estimation, percent, proportionality, ratio, interconverting units, deriving algorithms mathematically, energy transformation, interactions of energy and matter, bioavailability, composition, density, inferring, and data gathering through scientific interpretation.…

Some topics in mathematics are unique because they can be explored by learners from the early grades through the advanced grades. An example of such a topic is polygon rings. Presents activities on polygon rings that integrate problem solving, reasoning, and communication. (Author/ASK)

Reviews the historical use of each of the three algorithms used for subtraction in the United States: (1) the equal additions; (2) the decomposition; and (3) the Austrian method. Discusses the modification to the decomposition algorithm and gives a brief overview of the current status of subtraction algorithms. Contains 12 references. (Author/ASK)