Paint Bucket Polygons

Paint Bucket Polygons
Teaching Children Mathematics
http://my.nctm.org/eresources/view_media.asp?article_id=9163

Summary
This article is presented as the combined efforts of intermediate-level school teachers and college methods instructors. The group worked together to determine a series of lessons that would help the students develop a more sophisticated understanding of geometric concepts. In this particular lesson the fifth grade class was attempting to build an understanding of polygons and what the characteristic of a polygon are. The goal of the lesson: to use the pain bucket function of popular photo editing software, which is also located in the paint application of virtually every computer, to allow students to explore and build an understanding of polygons. The intent was the students would understand if a shape was not closed due to the fact that the paint would “spill out” and color not only the shape but also the background. Also if a shape had intersecting lines inside the shape only part of the image would be colored. As a result, the students would build an understanding of the closed and similar shapes.
The students gathered together and worked with several prototypes and non prototypes. In this instance popular prototypes are triangles, squares, rectangles and pentagons. Typical non prototypes are crescents and circles. While this can be a useful tool it can greatly limit students thinking and the intent of the lesson was to introduce the shapes and quickly graduate to more complex and less typical shapes. However, there was a more difficulty than expected. The students spent much more time than expected defining the word polygon and had considerably difficulty with distinguishing the prototypes and non prototypes.
Eventually the students were able to get to the main focus of the lesson, the use of the software to explore the attributes of polygons. The students were clearly able to understand the distinction of simple and closed using the software but there were limitations of the software and still areas which would need to be addressed using another medium.

Application
This article brings to light a problem that exists in many instances across Mathematics curriculum. Terms and definitions are used in student text books that are ambiguous and vague. Some texts use language that is clearly not student friendly or is all together too broad. When the authors of this article researched 80 different curricula they identified over 21 different definitions. This is clearly a point of confusion and dissension. If students are going to understand the concepts they need an understanding of the vocabulary and precise, student-friendly definitions. While, I like this lesson as a whole, I am surprised by the general tone of the lesson. The authors present the paint tool like a wonderful, unheard of, very creative approach. I consider paint to be old software and I am surprised by the notion that this is a new or novel idea. As soon as I get to school on Monday I want to see if the same tool can be used on the Smart Board, as I believe it can, as that could be another way to teach this lesson. Furthermore, with software like Geometers Sketchpad and other more student oriented applets and programs I feel that the approach is outdated. Like we’re discussed in class, manipulatives and software can not save the subject if it is to be held back by poorly written definitions, text books and lack of inventiveness with upcoming software and technology.

Edwards, M. & Harper, S. (2010). Paint bucket polygons. Teaching Children Mathematics. 16(7) 420.