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Additional resources for The Van Hiele Model of Thinking in Geometry Among Adolescents (Journal of research in mathematics education, Monograph, No. 3)
Studentsare then asked to explain again how the coloringon the summarycardtells thatthe sum of the angles is 180 degrees, (including why the saws and ladders are saws and ladders). They are asked if they have learned this fact before, and if so, how. Finally, if studentsdid not complete it earlier, they are again shown the sheet from Activity 1 which shows a triangle with only two angle measurementsgiven. note: This is the first time that studentsare asked explicitly about the sum of the angles of a triangle.
First you had to learn the simple facts such as 2+3=5 and 5+4=9. " This relationis pictured with an arrow,as shown. " 41 SuvY of aoA\Ces of (o tr'i ^a lI is t 0?. %,J The interviewer points to the fact summary cards and says: "Let us return to these geometryfacts we've been discussing. "If necessaryan example is given of how to place an arrowfrom "anglesum of a triangle" to "angle sum of a quadrilateral" cards. Studentsare then asked "Whatcould you say about the angle sum of a five-sided figure, a pentagon?
The transitionto "lengthx width" is made by relating area via strips with area determinedby measuring length (rows) and width(squaresin a row). " To solidify understandingof the rule, the studentis asked 48 to find areasof rectanglesand relatedshapes, explainingwhen the rule applies and when it does not. r 7. i Now an alternate rule, "base x height," is developed, using an L-square device to measurebase and height of cut-outrectangles held upright. note: After the AssessmentActivity 2, studentscan enterthis activity at different places.