Lately, there's been a lot of talk in the math educator community about ditching worksheets. Personally, I'm not a "fan" of worksheets but I'm also not about to abandon them either. In fact, I actually spent hundreds of hours over the course of many years developing a piece of open source software that automatically generates math worksheets. I felt compelled to write about my use of worksheets not just for the sake of voicing my opinion, but I also feel it's important to state the purpose of my software.
First, let's be clear on what I mean by "worksheet". A worksheet is a math assignment that only exercises mathematical procedures – no genuine problem solving is required. Often, the completion of a "worksheet" can be done by rote. Second, let me specify exactly what I am defending. It is appropriate to use worksheets sometimes. Worksheets are best used in a classroom where problem solving is emphasized – in other words – in a classroom where the attitude towards learning mathematics was established without worksheets. This is because the overuse of worksheets rewards students for embracing at least three misconceptions: (1) math boils down to a memorized sequence of steps (2) math is about getting the answer (3) there is one way to solve a problem.
The ill effects of worksheets are countered by activities that promote an opposite way of thinking: (1) true problem solving never involves a prescribed procedure (2) the "answer" is in how you solved it and (3) there is more than one answer. There is no shortage of writing about activities that promote this thinking. Much of what I have found lately has been on Twitter, by following #MTBoS (Math Twitter Blog-o-Sphere) or #iteachmath and searching for "worksheets". So let's just assume that these ideas are already established in your classroom. It is in this, and only this, setting that I can stand in support of using worksheets. Under such conditions, the repetition that is exercised when a worksheet is completed (this is also assuming it is completed in earnest, and not copied) offers at least three things, judging from my experience: (1) procedural fluency (2) pattern recognition and (3) perceived consistency of underlying mathematical principles.
I mentioned I'm judging based off "my experience". I was once a student and I am now a teacher. From where I stand today, a worksheet is a disgrace before what has become my profound appreciation of mathematics, but I didn't always have that appreciation. I slowly acquired it by working procedurally through problems whose applications were meaningless to me. I wouldn't fault my teacher for that; I think there really is a way in which doing countless Riemann sums by hand lends to an understanding of a definite integral. I have such vivid memories of the grind of my calculus class, but I truly feel it was a necessary stage toward the mastery that would come much, much later. I'd like to provide more examples from my personal experience but It's difficult to describe the extent to which I can credit worksheets from earlier classes with the algorithmic, symbolic, or quantitative thinking I do as a software developer. In fairness, there may have been a better way to obtain these skills, but I would at least say the years of worksheets were not a detriment. In a similar vein, programminghas "hello world", karate has the kata, acting has line memorization, instruments have arpeggios. For me, it makes sense that a discipline can be learned, exercised, even improved through a practice that is routine and noncreative.
As a teacher, I have witnessed students have a familiarity and comfort in worksheets. I don't always take that as a good sign. Sometimes the comfort is rooted in the perceived ease of finishing with less effort because a worksheet provides a more familiar avenue for copying. Furthermore, students often think the heart of math is in the worksheets. To me, that's like saying you can act because you have memorized your lines or you can program because your computer prints 'hello world'. That just is not tolerable.
But students still need the practice.
So the worksheets I give my students are not collected. They are not graded. But if I announce a skills quiz on material from provided worksheets, (and if I have a reputation for quizzing students according to what I announced) then each student can choose the assignment. If anything, I'm a proponent of student choice.
I designed my software, the OrcMath Worksheet Generator, to make such use of worksheets effortless for me. For something I wasn't grading, I didn't want to spend a lot of time preparing the material. That was the need from which this software was created. They aren't collected and we don't go over it in class, but students still need access to the answers and an explanation. OrcMath is the only worksheet generator that creates step-by-step directions. Furthermore, I wanted to use the application to generate as many worksheets as my students request, so the generator creates unique questions every time – they aren't taken from a library. I even tell students how to download the software on their own.
I may not be a huge fan of worksheets, but I think they can be an effective tool when properly used. It just should consume much of our time or energy.