Learning to debug is a difficult, yet essential, aspect of learning to program. Students in this multi-institutional study report that finding bugs is harder than fixing them. They use a wide variety of debugging strategies, some of them unexpected. Time spent on understanding the problem can be effective. Pattern matching, particularly at the…

I describe how data pooling and data visualization can be employed in the first-semester general chemistry laboratory to introduce core statistical concepts such as central tendency and dispersion of a data set. The pooled data are plotted as a 1-D scatterplot, a purpose-designed number line through which statistical features of the data are…

A three-page questionnaire was modified to a one-page format. Questionnaires were administered in classroom groups to 300 middle school students. Classrooms were randomly divided into two groups, with one group receiving the original three-page format and the other receiving a single-page version of the same questionnaire. The visual layout of the…

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Four worksheets for levels one-eight are included. Practice on addition, multiplication, fractions and decimals, and integers is provided through activities involving puzzling patterns. (MNS)

Three worksheets are given that use calculators to free students from computational restrictions and allow them to focus on the recognition of patterns and the application of numeration concepts in the development of their estimation skills. (MNS)

Presented are problem-solving experiences with area, volume, and algebraic expresssions resulting from data collection. Three worksheets are included for students in grades 7-12. (MNS)

Four worksheets designed to be used with calculators are presented. For levels 1-2, counting is the focus; levels 3-4, estimation; levels 5-6, use of memory keys; and for levels 7-8, patterns. (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)

Practice on computation is provided using new and novel situations, with discovery of number patterns a bonus of the computation. Activities with disguised addition and multiplication tables for whole numbers and integers are presented for varying levels. (MNS)