This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

A method is described for working multiplication problems by counting on fingers. (DT)

The representation of a binary number by a row of people sitting or standing by their chairs is reviewed. The representation is extended into a counting activity and then directions are given for combining the counters into an automatic "machine" which will add, subtract, multiply, and divide. (DT)

Discusses children's concept of number and number operations and describes activities which help to develop number concepts and skills. (JP)

Counting and dividing activities for 5- and 6-year-old children, using base ten multibase arithmetic blocks, are described. (DT)

Teachers asked students to write down as many names for their favorite numbers as they could. The results were surprising, with many students performing better than their teachers had expected. (SD)

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)

Artistic configurations can be built using a rectangular array of points and number concepts or principles. (SD)

This column discusses problems involving a paper folding game for bicimals, the sum of exterior angles of polygons and polyhedra, solving quadratic equations in finite arithmetics, nomograms, and cube folding patterns. (DT)

Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)

After noting that accurate calculation is not the only reason for teaching arithmetic, innovative activities providing practice with basic facts, pattern spotting,'' and exploration are presented. (MS)

Using arrays of dots and grids many numerical concepts can be illustrated for students. (SD)

While repairing a sleeping bag, the author observed that the quilt stitching was unicursal. This led to development of a classroom activity relating the stitching patterns of quilts to the highest common factor of the numbers of "bumps" in each direction. (SD)

The first article describes students' activities with tiling patterns and tessellations; the second discusses the use of balances and weights as an approach to number concepts. (DT)