Lyrics and Performance by Vicki Young
Original Melody by Vicki Young
There are levels of understanding in everything we do.
First, we start with the basics and then we follow through,
From novice to expert, as each phase goes by,
New skills to conquer, new tasks to try.
van Hiele found five levels for geometry:
With basic visualization, children start to see;
They analyze, deductions make Ė informal to begin Ė
ĎTil formal deduction brings rigor at the end.
Before we go much further, we mustnít forget
These five important properties to know:
The model is sequential; on advancement you can bet;
Itís intrinsic and extrinsic as you go;
Linguistics are essential, with vocabulary set;
And mismatch will cause your progress to be slow!
Each level has five phases so learning can progress:
Inquiry information lets both their views express;
Directed orientation leads to explicated views;
Then free orientation and integration true.
With five skills at each level, our modelís now complete.
Visual and verbal let our students see and speak.
These drawings lead to logic and conclusions to defend,
And concept applications bring each level to its end.