By David Fuys, Dorothy Geddes, Rosamond Tischler
Read or Download The Van Hiele Model of Thinking in Geometry Among Adolescents (Journal of research in mathematics education, Monograph, No. 3) PDF
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Extra resources for The Van Hiele Model of Thinking in Geometry Among Adolescents (Journal of research in mathematics education, Monograph, No. 3)
If the student found the area in other ways, he/she is askedto show the otherway it would fit into a family tree. Activity 7. Trapezoids As in the two previousactivities,this one deals with ways of findingthe areaof a particularshape,namely, a trapezoid. (a) (c) (b) Divide the figure into a rectangle and two right triangles. Divide the figure into two triangles. Divide the figure into a parallelogramand a triangle. " The activity assesses the students' ability to sort accordingto propertiesof a shape, to discover and explain the area rule, and to relateit to otherrulesvia family trees.
Anotherperson says the areaof this cover is 24. , "length times width") is asked to explain why one multiplies here and whether the rule works for other shapes (non-rectangles). This type of assessment is repeated for cut-out right triangles, parallelograms,and trapezoids, if the studentknows a rule. If not, the student uses a gridto figureout the area. note: In this activity the intervieweris carefulnot to provideinstructionon area, but simply to assess whatthe studentknows. Assessmentis not pushedbeyondwhat a studentseems to be able to do.
Studentsare led to see how to make a quick drawingusing two familiesof parallellines. 33 / Students are then given parallelogramtiles, andaskedto use themto make a tiling. Again they are led to first constructand then drawa tiling which contains two families of parallel lines. Next students are given two right triangles (more are available, but having just two at first helps them see the relation to a rectangle). "Haveyou ever seen trianglesused as tiles? Try these ones. " When the tiling is complete, studentsare shown a rectanglegrid.