The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

Tree diagrams with numbers in a given pattern generate questions related to pattern recognition and number concepts such as binary numbers and exponentials. (MP)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

Describes an activity designed to allow secondary students to practice pattern recognition using the proof-of-purchase scanning lines found on many consumer products. Provided are a list of materials, procedures, and student activity sheets. (CW)

A computer program is presented for the billiard ball problem. It can be integrated into a lesson on inductive reasoning and suggests several ways to do so. (MNS)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Brief articles are included on exploring mathematical patterns, with two computer programs listed for finding happy numbers; a simple periodic function in trigonometry; and comments on humorous student errors. (MNS)

How to find and classify positive integral solutions to 1/a + 1/b = 1/c in beginning and advanced algebra classes is described. The computer finds the solutions, but students practice algebraic manipulation as they analyze the solutions for patterns. Extensions to challenge more capable students are included. (MNS)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)

Described are activities that use a hundred chart to improve student abilities to recognize and describe number patterns, to use variables, to make and informally prove conjectures, and to communicate mathematical ideas to classmates. Included are the directions, four reproducible student sheets, the answers, and extensions. (KR)

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…