Assessment is not a spreadsheet or score, it is a conversation.
This week in CEP 813 we were asked to revise and further the development of a formative assessment we first started back in June. For my formative assessment, I created a Three Acts Math Task designed for 8th grade math students who are learning to apply the volume formula for cylinders to solve real-world and mathematical problems. The lesson is designed for students who have already worked with the surface area and volume of 3-Dimensional solids, so they are familiar with how to approach and solve related computational math problems; however, this lesson goes beyond math computation and requires the students to think critically and wrestle with an indirect problem. That is, this lesson requires learners to formulate and solve mathematical reasoning problems (i.e. problems that require application of math processes in the world around us). Thus, while this formative assessment requires learners to be profiecent in certain skills & standards, it’s focus is on measuring learners’ mathematical modeling skills as part of the problem solving process. Although, the summative assessment at the end of the unit will take a step back and measure those computational skills embeded in this task, that is not the purpose of this design.
The job of the dramatist is to make the audience wonder what happens next. Not to explain to them what just happened, or to suggest to them what happens next.
Storytelling requires empathy, an understanding of an audience’s expectations, their current knowledge, and their prior experience. As you saw in Version 1.0, this formative assessment task was carefully designed to ensure learners are able to identify the problem, accurately communicate their thinking, apply reasoning skills, make connections to prior knowledge, and understand complexities in various forms. By using multimedia to present the lesson, the learners are able to consider much more complex concepts on their own terms. They are able to address real world problems and present real world solutions. They are able to see how their math computation skills can be applied to real world processes realistically, such as how surface area and volume effect producer and consumer choices. Most importantly, digital media allows for learners to be involved in the process of mathematical abstraction, tackling the problem in its most concrete form first and building towards the abstract form. As a result of the design, students will show that they are able to transfer their knowledge regarding volume of cylinders to real world scenarios as they work through the task. “Transferability is understanding revealed: The performers must figure out which knowledge and skill is needed on their own, without simplifying teacher prompts or cues, to solve the real problems of performance” (Wiggins & McTighe, 2005, p. 156). As the problem unfolds and is developed, the learners will identify what information is necessary to solve the problem on their own and will use their networked device to find information as needed. The most rewarding thing that an assessment task like this have to offer is seeing the creativity learners bring to mathematics. Processing information, making connections, reflecting, and learning through constructivism are qualities of creative problem-solvers and innovative learners and define the educational ideology of the 21st century.
Building on the framework and design I established in Version 1.0, my second draft will provide a more detailed outline and plan for integrating Three Acts Math as a formative assessment in an 8th grade math class, check out the second draft: Formative Assessment Design 2.0 of my Formative Assessment Design.
Wiggins, G.P. & McTighe, J. (2005). Understanding by design. Alexandria, VA: Association for Supervision and Curriculum Development.