Rich Mathematical Tasks
A teacher told me recently, "There is no way I can present students with every possible type of problem that might show up on the assessments they take. The best way I've found to prepare them is to present them with non-routine problems on a regular basis. This way they learn to think about, work through, and solve problems whether they have seen it before or not".
I think one of the more powerful teaching strategies you can use in the mathematics classroom is the use of rich mathematical tasks. Like so many phrases and buzz words we use these days, you always need to know what definition the person is using for the phrase in question. What do I mean by "rich", by "mathematical", and by "task"?
To Be RICH !!
* It is aligned to the standards/objectives you are teaching
* It has a low floor. That means that everyone can find a way to get started.
------- The student can start with concrete examples
------- There are a variety of starting points with some being more simple
------- There is a common knowledge or experience where students get the necessary background.
* It has a high ceiling. That means that beyond the essence of the task there are ways to extend the task through more elegant/advanced solutions, different solutions, or unique solutions.
* The students find it engaging enough to want to stick with it.
To Be MATHEMATICAL !!
* The task will require the student to use important mathematical concepts and ideas. That means, for example, that it is not a science problem/task where the only mathematics involved is the arithmetic necessary to crunch the numbers.
* These do not necessarily have to be advanced mathematical concepts. A quote I have often used is, "In the mathematical classroom we have students use sophisticated mathematics to solve elementary problems. In the real-world we are usually required to solve sophisticated problems with elementary mathematics." (author unknown)
To Be A TASK !!
* For me, this means the task in set in a real-world context. Point of interest - "real-world" appears 52 times in the CCSS Mathematical Standards document. Why should we subject students to artificially contrived mathematical situations when there are so many real or pseudo-real problems we can attack instead. This is where I differentiate between a rich problem and a rich task. (A rich problem to me is an interesting puzzle, mystery, riddle or other conundrum. Rich problems are not bad - just different than a task for me.)
* A task is not always well defined in the beginning. Real-world problems do not always have all the necessary information given and only the necessary information given. These tasks should allow the problem solver to discern the information needed, the mathematics necessary, the tools to facilitate, and the presentation manner to communicate the solution.
For some web resources with various tasks (and problems) click on the GRAPHICS below.
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(you must be an NCTM member to access) |
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