70ff949d_Conceptual_Framework___English__Description
[Mental model] Arithmetical facts, e.g. 7 x 8 = 56, 56 ÷ 8 = 7 and 56 ÷ 7 = 8 [Description] 
These three number facts are combined as part of a bigger mental model for me - someone who was successful at memorising multiplication tables from an early age. An external representation would be in the form of a concept map relating the three numbers 7, 8 and 56 as nodes with directional arcs labelled with the relevant mathematical operations. The full model takes in all the factors up to 12 - in my day you learnt up to the 12 times table - and some other exceptional numbers beyond. A relationship with other number facts ( 70 x 80 = 5600) where other rules and patterns extend the basic multiplication table. I have no idea how this material is actually formulated in my mental model, it is recalled unconsciously, but I believe it is both parsimonious and effective for me because of its cross connections. The mental model helps me both predict and explain arithmetical results, estimate calculations and solve numerical problems. Externalised conceptual models which are often drawn include number squares, but the graphics do not make clear all the patterns and connections held in a complete mental model.
Theoretical & Conceptual Framework — English
Description