What types of tasks I use in my class
I prefer to use rich tasks that promote reasoning and problem solving as opposed to memorization of algorithms or 'drill and kill' procedural practice. Often I will ask students to make connections between different representations of math - tables, graphs, equations, real world stories, etc. - so as to encourage deeper conceptual understanding. Procedural practice is then used as an extension of our explorations into mathematical concepts to help solidify those concepts.
I strive to choose tasks with a "low threshold, high ceiling." The "low threshold" means that all students can enter into the mathematics of the class regardless of their current skill level in math. The "high ceiling" means that the task can be extended as high or as far as the students' abilities can take it -- in other words, students who are gifted at math will be able to grow their mathematical understanding as well.
In addition to tasks or activities that focus on mathematical concepts, some tasks or activities serve to help students learn how to learn. Whenever a new class begins, I intentionally choose math activities that will also provide an avenue for me to teach students how to be successful in the class -- such as behavior norms for working in a math group, study habits for math, test-taking strategies for math, etc.
Because students learn best when they are interested in the content, I work hard to make our tasks interesting. Obviously, when we ourselves have fun with the content, then the students enjoy themselves as well. From using kinesthetic or artistic methods to teach math, to taking the time to weave in humor and pop culture, I enjoy working to make individual activities 'fun' to students.
However, an even stronger source of motivation is grounding the content in the real world – why are we learning this and how will we use it? When we make these connection explicit, students often respond with a greater willingness to try, to attempt the work. When we go one step beyond that, to show how math will empower them to influence their future and the future of those they love, then students become more persistent at sticking at the work when it gets tough. To me, that's the best source of motivation I can provide because it will stay with them long after they leave my classroom!
Examples of Tasks/Activities
- After students had begun to explore the relationships between right-triangle trigonometry and the unit circle, I wanted them to reinforce their budding understanding by using technology to explore how the two were related in a more dynamic way. I found an activity for the TI-Nspire that had almost the technology I wanted but their worksheet did not fit. I downloaded their .tns file, modified the code to fit what I wanted to happen, and wrote my own worksheet to guide students (in pairs) through the exploration. You can download my .tns file here.
- One semester my Advanced Algebra (Algebra II) students needed a review of how to evaluate and graph linear equations. They expected a boring worksheet, but instead I took them through a review that required them to kinesthetically graph the equations with their bodies.
- Students often ask for extra credit, and what they typically want is something quick and easy. When I taught geometry, my extra credit options typically required them to digest the concepts to the point that they could creatively and clearly apply them to a project of their choice.
- Not all formal assessments have to be quizzes or tests. When I recently collaborated with a group to write a brief unit on sine, cosine, and their transformations, we chose to have a summative project where students could demonstrate their understanding using topics that could be fun or serious as they wished. I drafted the lessons and models to go along with the project.