The Van Hiele model - an outline

I reckon this blog isn't a ripe platform for discussing teaching approaches. It's just that the main focus here is to analyse nostalgia stuff that comes to mind at times. But since I've been involved with some teaching projects (in a skewed sort of way), I'd like to present a brief view on an underrated teaching approach which rose to recognition in the 70's to aid teachers who had been clueless about teaching geometry to their pupils. It is none other than the Van Hiele model (Van Hiele niveaus),created by a Dutch couple in 1957 and widely analysed by teachers and scholars alike in the late 70's and early 80's after proof of its core tenets holding true after it was shown that students at the lower levels of the Van Hiele model were unable to understand a single iota fed to them about geometric theorems and equations. It turned out their cognitive level was below the threshold necessary to be able to grasp the staple principles of planes and solid figures. The original work on which the theory is based was Structure and Insight: A theory of mathematical education (author unknown). The model is a classical example of wiskundedidactiek (mathematics education) reference and is specifically used for a didactic approach to teaching geometry at school level. Pierre van Hiele died on 1st November 2010 aged 101 at his home in Haag.

Basisidee
The basic premise behind this model  ,in a nutshell (weergegeven), is that learning geometry is achieved through gradual levels of cognitive awareness (graduele denkniveaus). Besides, the levels through which a student's progress is met bear no ties with their physiological age, although they do have specific eigenschappen (properties) which should become easier to observe following the levels' linear pattern. A specific level cannot be reached without the completion of a previous one, ie the learner's progress (de vordering van de leerlingen) follows the same succession of learnt competences towards utter understanding of the whole picture. Doing otherwise would be chewing more than one can swallow. Each level also makes use of its own language or linguistic symbols (linguïstische symbolen) and accompanying in-content relevance (inhoudbetekenis). It also holds that two students of diverging levels (verschillende niveaus) cannot understand each other. Odd, because the more competent peer is supposed to make sense out of what his inexperienced counterpart means as he was once at the same stage and should recall what what his gripes were at the time (the been there, done that argument).

Niveaus

The Van Hiele model consists of 5 levels, going from 0  to 5.

• Niveau 0 : Visualisatie
• Niveau 1 : Analyse
• Niveau 2 : Ordening of classificatie
• Niveau 3 : Informele deductie
• Niveau 4 : Formeel

Retrieved from:
http://www.fisme.science.uu.nl/wiki/index.php/Niveautheorie_van_Van_Hiele