Implementing Proficiency-Based Assessment
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Two 3rd grade geometry tasks are presented that involve patterns of squares or tiles. The first task simply asks students to determine the number of squares in the 25th arrangement, while the revised version asks students to investigate and report on the pattern. The document suggests questions teachers could ask themselves in examining student work, including the mathematical ideas explored, surprises, and implications for practice. A sample of student work is also included that provides observations about the pattern, a sketch of larger figures, methods for determining the total number of tiles, and how to convince others of the solution.
Implementing Proficiency-Based Assessment
- 17. Examining Student Thinking: Geometric patterning tasks Two 3rd grade tasks and associated student work samples Questions to consider: What mathematical ideas do these tasks draw out? What do you notice? What do you wonder? What surprises you? What are the implications for your practice?
- 18. A Typical Algebra Task How many squares will be in the 25th arrangement? Figure Number 1 2 3 Total Number of Squares 5 7 9
- 20. A Revised Version of The Algebra Task Investigate and report all you can about this pattern. Figure Number 1 2 3 Total Number of Squares 5 7 9
- 24. Investigate and report all you can about the following growing pattern. Figure Number observations about the pattern a rough sketch or picture of some larger figures in this pattern some different ways of 'finding' the total number of tile in any figure in pattern (like methods of counting, a table, a graph, a formula or rule) Which figure has 120 tiles? How did you decide? What is another way to determine this? How would you convince somebody else that you are right? 2 3 Total Number of Tile You may want to consider including things like: 1 3 8 15
- 25. 120 Total Number of Tile 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 Figure Number Figure Number Total Number of Tile 1 2 3 3 8 15 4 5 6 7 8 9 10
- 27. Investigate and report all you can about the following growing pattern. Figure Number observations about the pattern a rough sketch or picture of some larger figures in this pattern some different ways of 'finding' the total number of tile in any figure in pattern (like methods of counting, a table, a graph, a formula or rule) Which figure has 120 tiles? How did you decide? What is another way to determine this? How would you convince somebody else that you are right? 2 3 Total Number of Tile You may want to consider including things like: 1 3 8 15
Editor's Notes
- #5: Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
- #6: Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
- #7: Definitions “Continuum of knowledge and skills” means the Oregon Academic Content Standards. “Proficiency” means demonstrated knowledge and skills which meet or exceed defined levels of performance.
- #30: “An ideal learning environment or experience occurs when both teachers and students seek answers to each of these questions” (Hattie and Timperley 2007, 88).