Teacher Commentary Developing Geometry Skills Through Manipulatives Stetson Middle School, Philadelphia SLC: Visual and Performing Arts Teachers: Mindy Elliot, Montik Goodwin, Phyllis Siermine School Phone: 215-291-4720

Unit of Study Summary This unit of study engaged students in the use of a variety of manipulatives. Students used pattern blocks, tangrams, pentominoes and geoboards to explore a variety of geometric skills. We had hoped that by working with manipulatives on a consistent basis, students would learn to identify properties of geometric figures, improve their visual perception and spatial problem solving skills, and construct geometric patterns. As each manipulative was introduced, students were engaged in whole group and small group activities led by the teacher. Manipulatives and activities were then placed in the teachers' learning centers so that students would have daily access to them. At the conclusion of the unit of study, students were asked to develop a geometric design and produce a quilt. Students' work was assessed using a task specific rubric which was developed by participating teachers during our team meeting time. What should students know and be able to do? School District of Philadelphia Standards: Mathematics Content Standard #3-Understand space and dimensionality concepts; use them appropriately and accurately and communicate the results clearly. What were students asked to do? Students were given a choice of using pattern blocks, tangrams, or pentominoes to create original designs/pictures. Students who chose pattern blocks, as this sample shows, were instructed to design a quilt pattern using the pattern block tracers provided by the teacher. The rubric was shared with students, and teachers verbally explained to them, and visually showed them with manipulatives on an overhead, the expectation for an exceptional piece of work. What story does the work tell? The sample of student work was assessed using a 10 point task specific rubric developed by the teachers who worked on the unit. This sample was scored as an "8" according to the rubric. The student did not use their design to fill up the entire quilt paper. This student also lost one point because she did was only able to incorporate of the six pattern block shapes into her design. This student did demonstrate a good understanding of lines of symmetry. Unlike many other students who created quilts, this student did not chose to create a closed design. A closed design was defined as a design which formed a polygon such as a square or hexagon. This student was able to align her repeating design on a horizontal plane, but not on a vertical plane. This is demonstrated by her partial design at the end of the quilt. How can your analysis guide further instruction? Though not apparent by examining this particular piece of work, upon examination of a larger sampling of work, it was clear that many students had difficulty grasping the concept of a line of symmetry. Geoboards were introduced to students after their projects had been started. In the future, I believe that using the geoboards earlier in the instructional process will help students to grasp this concept easier. Additionally, on reflecting on the unit as a whole, we have found that we would do differently is add a writing component to the project.

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