Worksheets (aka how I learned to stop worrying and love the bomb)

who: J1 and J2
when: after bath, before bedtime
where: in the bedroom
what: worksheets (gasp!)

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So...Whoever loves worksheets, raise your hands!

You can't see, but my hands are firmly down at the keyboard. In other words, not raised. I'll tell you first why I don't like worksheets and then why we were using them last night.

The bad
My first issue with worksheets is that they (usually) don't facilitate understanding. Take this typical example:

Tiny pic, to contain the evil.
Also, not a worksheet we used!

From these exercises, we don't learn anything about what subtraction is (or isn't), we don't learn anything about how to apply it, we don't connect any additional language with the operation.

The ugly
One danger is that worksheet activities can define "doing math" for kids. They seem so official, so that must be what math is all about, right?  In the usual process, these will be done (alone, silently) given to the teacher, marked up in red pen, and then returned with right and wrong clearly labelled.  This isn't the message I want for my kids.

The good
Having all that written out explicitly, it is pretty clear that each of the weaknesses with worksheets can be addressed.

1. They don't facilitate understanding.
   Two possible fixes here.  First, some worksheets give nice pictures or diagrams that can aid understanding. In the concrete-pictorial-abstract schema, when you are on the picture stage, it is actually a benefit for children to get their own paper with some pictures to investigate.
   The other fix for this is maybe you aren't working on understanding and you need the worksheet for something else. It could be a diagnostic tool too see what the student doesn't understand (facilitated by discussion, see my comments below on grading). Or, it could be pure practice (see the practice point).
    
2. Done alone
   If that's your concern, then have them done together, in pairs or small groups. That also addresses the language issue by encouraging the kids to talk about what they are doing.
 
3. Graded with right and wrong
   At home we, would go over the problems together and talk about them. Sometimes we would take one they did correctly, ask if they are sure of the answer and ask how they got it. Other times, we'll focus on one that wasn't right and ask the same questions. How did you get this answer? Can you draw a picture? Can you use some objects to show me? This is the best way to tease out differences of interpretation, misconceptions, alternative approaches mis-executed, or just a mistake.

Practice
All of those rehabilitation steps aside, at long last I've concluded that there is a role for repetition and practice for our young mathematicians.  However, I think the point at which you can take out a pure practice worksheet in good conscience is when . . . the kid asks for it.

How did J1 ask? Playing Munchkin, actually.

J1 wanted to be faster at calculating so he could easily see whether adding a wandering ancient plutonium dragon to my current combat would let them win. And winning at Munchkin, like all worthwhile things, takes some practice!