Generating Mathematical Activity in the Classroom

This report contains examples of fifteen mathematical inquiries carried out by a class of eleven year old students and is designed to demonstrate that it is possible to teach in a way which encourages students to begin to ask their own questions, to control the direction of their investigations, to make conjectures and think how to test them, to make and agree on definitions and equivalences, to search for patterns, to make generalisations and to seek reasons for what seems to be happening. Each activity is described and contains written records of students' inquiries, some write-ups and some thoughts jotted whilst working. The activities covered are mediators of triangles, the greatest number of intersections, making magic squares, fractions of a rectangle, sending cards, splitting decominoes, questioning tessellations, producing number patterns, triangle numbers, odd numbers of factors, quick tests of divisibility, bases eleven and twelve, beginning the 'lost region' problem and subsets of the set of letters of the alphabet.