This week we were asked to develop the first draft of a formative assessment. I created a three-act 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).
Using pop cans and a marketing perspective, the lesson is set up to be a problem solving and problem finding task. It 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. To complete the task, learners need to know how to find the volume of each cylindrical can, how to write proportions for unit conversions, and how to interpret their findings. They also need to be able to identify what matters in a problem situation and what information they need to complete the task.
Changing the model of pedagogy to meet the demands of the 21st century is crucial. Learners need the opportunity to learn how to learn, discover and formulate problems, build on other peoples’ insights, and adapt their abilities to various situations. As Polya (1957) states:
“A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.
Here is the link to the first draft of my formative assessment : A Problem Worth Solving