MATH 329 Productive Failure I

The errors made on this diagram stemmed from misunderstanding properties of specific polygons and also from rushing at the end to move on to the following problems. Looking at the mistake we made with parallelogram, I have no idea how I, or either of my group members, did not catch our incredibly obvious error. The definition of a parallelogram is literally- "A quadrilateral with two sets of parallel sides". My group members and I were so focused on where the kite fell within this diagram however, that I believe we simply skimmed through the definiton of a parallelogram and quickly set it outside of the circle with the kite and trapezoid without going back in our notes and looking at the definiton of a parallelogram. The reason we did not put the parallelogram under "quadrilaterals with 2 sets of parallel sides" was because we thought a kite was a parallelogram. We knew a kite did not have two sets of paralles sides so concluded that if a kite was a parallelogram, then a parallelogram could not be placed under the "quadrilateral with 2 sets of parallel sides". We also knew that there were certain parallelograms that did not have equal diagonals, resulting in us placing the parallelogram outside of the venn diagram. After looking back at our reasoning, it becomes clear to me that the mistake made simply came from confusion on the properties of a kite. I believed for some reason that a kite was a parallelogram and that since a kite did not have two sets of parallel sides, then a parallelogram could not be placed under the section of "a quadrilateral with 2 sets of parallel sides".

The error made with our placement of the rhombus also stemmed from not knowing all the properties of a rhombus. I had believed that since a rhombus could be a square, then the rhombus must be placed in the "quadrilaterals with equal diagonals", since a square has equal diagonals. Now looking at the diagram again however, I see that we do account for the small portion of rhombii's that have equal diagonals with the center overlap circle which contains the square and the rectangle. When looking at the description "A quadrilateral with two sets of parallel sides", I was just picturing the typical diamond shaped rhombus and thinking that the two sides were not parallel. Once drawing a rhombus out however (even the typical diamond) , I now see that opposite sides of a rhobmus are indeed parallel to one another.

The errors made on this diagram came from simple misunderstanding on the definition and properties of polygons. From this I have definitely learned how important it is to not only have the correct definition written down in your notes, but also how important it is to understand the fundamentals and properties that make up each polygon. Since there are so many properties among the various polygons, a diagram like the one to the left is extremely helpful; but first, we must make sure we understand where to place each polygon and why each polygon is placed where it's placed.