There are many typologies for understanding social behaviour. This one uses the concept of vertical and horizontal teaching methods. It might benefit from comparison with the Cultural Theory approach to similar social phenomena. Vertical teaching is Hierarchical and horizontal teaching methods are Egalitarian. But Cultural Theory would suggest that there are four basic cultural biases and these are expressed institutionally. Individualist teaching methods emphasise personal project work and self directed learning. This third approach is neither horizontal nor vertical, but it is identified and described by cultural theory. Then there is a fourth ideal type. Anyone who has attended a school will probably have a personal experience of what Fatalist education might entail.
Horizontal vs. Vertical: An International Comparison of Teaching Methods – http://www.freakonomics.com/2011/10/25/horizontal-vs-vertical-an-international-comparison-of-teaching-methods/
Four Cultures 