Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

Data were collected from 727 entering kindergarteners in the St. Louis, Missouri area by application of the Comprehensive Mathematics Inventory (CMI). Test items and the portion of pupils correctly answering the questions are shown in four tables, divided into subgroups. Data obtained can be used by teachers in planning appropriate learning…

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and…

A variety of suggestions for making the mathematics curriculum more meaningful and interesting to students are described. Activities that incorporate real-world situations are provided for verbal items, common and decimal fractions, estimations and rounding off numbers, large and small numbers, geometry, probability, and statistics. (KR)

Suggestions for outdoor mathematics activities include six each for primary-age and intermediate-age children. (MK)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

Pascal's triangle can be used as early as grades five and six to teach children to recognize mathematical patterns. Children can be guided to discover patterns or sequences of numbers if they begin with pictures or physical objects which they can manipulate and count. (Author/BB)