Since my area of specialty is secondary mathematics, the answer to this question is not simple. Of course, the question is not simple so why should an answer be simple?
Typically, mathematics is treated with a drill and kill, quiz and test, repeat methodology which I find unfortunate. I mean, I hate tests. I'm not convinced that tests are an effective means to assess a complex issue, that being what a student has learned and what a student can do with that learning. From this perspective, portfolio assessment has great value.
But we're still talking mathematics which is not the kind of topic that screams "portfolio." So that means to me that I have to step outside the standard view of mathematics to implement something like a portfolio for assessment. But how?
Is it possible that mathematics has been drilled down to its most basic piece parts in an effort to make standardized testing effective? Is it possible that the beauty and power of mathematics has been lost, or killed, by the standardized testing? If so, portfolio assessment in mathematics has immense value.
Imagine a school in which the basics of mathematics are taught, but the use of mathematics is required. Imagine a school in which it is not enough to simply add, subtract, multiply, divide, know the Pythagorean theorem, and figure the probability of pulling a blue marble out a sack. In this school, you will find all the piece parts of mathematics taught. But instead of filling bubbles, the student will demonstrate knowledge with projects that span the piece parts and make them into a coherent whole. The student will work to explain to peers what the math means, not simply what the manipulations are. And these projects and works of the student will be compiled into a portfolio.
Indeed, portfolio assessment has great value in mathematics.
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