Bar Model and Table and Arrow Diagram

How can younger students be introduced to algebraic thinking before they are ready for formal algebra?

In discussing multiplicative structures, ergnaud (1988, 1994) argued for less formal representations to make algebraic thinking accessible to younger students.  he introduced table and arrow diagrams to repsent multiplication problems

Vergnaud argued that the table and arrow diagrams are helpful conceptual learning tools - the vertical arrows indicate ratios and the horizontal arrow represent functions

He also claimed that the table and arrow diagram is a pre-algebraic representation  that is less abstract and more accessible to younger students than formal algebra.

In the introduction of the model method in Singapore schools to address students  difficulities in solving word problem, Kho similarly argued that "the model method is less abstract than the algebraic method and can be introduced before students learn to solve algrebraic equation".  In fact students will appreciate better the use of symbols to represent quantities as they have experienced using bars to represent quantities in the model method.