Reasoning Without Arithmetic
A collection of situations in which learners young and not so young can reason mathematically without requiring arithmetic fluency.
Secret PlacesSecret Places (homage to Tom O'Brien):
One of the places at the table has been chosen secretly. In the applet, if you click on a place it's colour changes to

Qualitative Queuing showing 'facts' and deduced Queue with one rejected 'fact'. The 'facts' are generated randomly.
Quantitative Queuing showing 'facts', deductions and check with original Queue
Queuing in 2D showing some 'facts'. There is a randomly chosen grid to be deduced. A second version has no predetermined grid.

QueueingDesigned for primary school use especially, these applets provide sequential information about people in a queue. As each 'fact' is revealed, the user has to decide whether it is consistent with what they know already, or whether it should be rejected as inconsistent.
Quantitative Queuing gives information of the form "A is 3 places ahead of B". Qualitative Queuing gives 'facts' of the form "A is dead of B" and "A is behind B"; or "A is between B and C"; or both types mixed. Qualitative 2D Queuing starts with grid and gives 'facts' of the form "A is above (or below) B and to the left of (Right of) B" The applets stimulate reasoning i trying to persuade others that what a new 'fact' adds to or contradicts 'facts' accumulated so far. Queuing Reasoning.zipIncludes notes
