By David Fuys, Dorothy Geddes, Rosamond Tischler
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Extra info for The Van Hiele Model of Thinking in Geometry Among Adolescents (Jrme Monographs, Vol 3)
First students are asked what they would choose to measure with, then if and how they have learnedto measureangles in school. ) Once students are able to measure angles in some way, they are shown the diagramof two adjacentangles to the left. They are asked to measure the two angles, then to predict the "outside"one (the sum). ) Studentsare then shown the diagram to the left with three adjacent angles. This leads to discussionof the measureof a straightangle. 31 Finally,studentsare shown a triangle,and are asked to measure angles in it (which are simply recordedfor later reference).
E elvl. 7 The interviewer says "Let's try that guessing game again. You will try to figure out what shape I'm thinkingof, only now you won'tsee any of the shape;insteadI'lljust give you some clues about it. I'll show you the clues one by one--after each tell me all you can. What COULD it be? Could it be anythingelse? " The interviewerslides a piece of paper down the sheet to uncoverclues one by one. At the end the student is asked "Canyou think of other clues I couldput down? " This processis repeatedfor two sets of clues.
If I makeone using parallellines, do you thinkthe angles will always be congruent? " The demonstrationis now repeatedfor a saw. The intervieweruses the ruler to constructa saw with parallellines, and then the studentis asked to constructa saw using only the traced angle. Studentsareled to summarizewhathas been done for saws, and also to summarize againwhatwas done for ladders. note: If studentsdo not recognize the "if-then"natureof this constructionat this point, they are not questioned further,but if they do, they are asked about the converse.
The Van Hiele Model of Thinking in Geometry Among Adolescents (Jrme Monographs, Vol 3) by David Fuys, Dorothy Geddes, Rosamond Tischler