In this article, the authors describe how a Java applet can help to build learners' intuitions about basic ideas of algebra. "Matchbox Algebra" is a Java applet the authors have designed to enable learners to grasp a key idea in learning algebra: that the letter "x" may be thought of as representing an as-yet-unknown number. They describe the "MLT" triad, a model commonly used in mathematics education. It sets out the main elements that comprise mathematical learning: the mathematics (M), the learner (L) and the teacher (T). All three are set in some sort of "environ", which represents the physical, social and psychological contexts within which the learning takes place. The authors discuss how the mathematical education of learners can be supported by ICT, an element that can be incorporated into the diagram by reinterpreting the T as the "teacher with technology". They present three ways of interpreting algebraic letters: (1) letter as object; (2) letter as specific unknown; and (3) letter as generalised number. (Contains 7 figures, 1 table, and 1 note.)