”How old will you be next time?” I asked the child. “Four”, he answered and showed me four fingers. “Four, you said?” I asked and showed him four fingers held together two by two. “No, that is not four, that is two twos!” the child replied thus insisting upon what exists, bundles of twos, and two of them. Likewise, preschool children have no difficulties counting in other units than ten, even if they only learn how to count in tens. This observation motivates the following question:

*What kind of mathematical learning takes places when children count in bundles less than ten?*

The methodology comes from the two Enlightenment republics by mixing French skepticism and American pragmatism. First postmodern contingency research will deconstruct the ruling traditions by uncovering hidden differences that might make a difference when tested by designing different micro-curricula, in this case for the last year in preschool mathematics.

When testing the design in a group of students, grounded theory resonating with Piaget assimilation/ accommodation is used to gather observations and create categories. Finally, the categories are validated or refined by tests in other student groups.

BundleCounting and NextTo Addition Roots Linearity and Integration

Proposal for a Research Project in BundleCounting and NextTo Addition

Counting and Recounting before Adding