<Li> Free orientation: students do more complex tasks enabling them to master the network of relationships in the material . They know the properties being studied, but need to develop fluency in navigating the network of relationships in various situations . This type of activity is much more open - ended than the guided orientation . These tasks will not have set procedures for solving them . Problems may be more complex and require more free exploration to find solutions . (A teacher might say, "How could you construct a rhombus given only two of its sides?" and other problems for which students have not learned a fixed procedure .) </Li> <Li> Integration: students summarize what they have learned and commit it to memory . The teacher may give the students an overview of everything they have learned . It is important that the teacher not present any new material during this phase, but only a summary of what has already been learned . The teacher might also give an assignment to remember the principles and vocabulary learned for future work, possibly through further exercises . (A teacher might say, "Here is a summary of what we have learned . Write this in your notebook and do these exercises for homework .") Supporters of the van Hiele model point out that traditional instruction often involves only this last phase, which explains why students do not master the material . </Li> <P> For Dina van Hiele - Geldof's doctoral dissertation, she conducted a teaching experiment with 12 - year - olds in a Montessori secondary school in the Netherlands . She reported that by using this method she was able to raise students' levels from Level 0 to 1 in 20 lessons and from Level 1 to 2 in 50 lessons . </P> <P> Using van Hiele levels as the criterion, almost half of geometry students are placed in a course in which their chances of being successful are only 50 - 50 .--Zalman Usiskin, 1982 </P>

First 3 van hiele levels of geometric thought