We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

The theoretical framework of conceptual change has gained growing influence for analysing learning difficulties. The article pleads for combining conceptual change approaches in the learning sciences with established categories from mathematics education research, such as "Grundvorstellungen" and epistemological obstacles. These didactic…

Uses of calculators to teach the concept of exponents are described. Topics covered on activity sheets include powers of two, number systems, and powers as repeated multiplication. Cooperative learning is emphasized. (KR)