Why do so many math worksheets?

I read this article this morning: 

Why Johnny Can't Add Without a Calculator

http://www.slate.com/articles/technology/future_tense/2012/06/math_learning_software_and_other_technology_are_hurting_education_.html

and I could not help but think that it does a better job at articulating the EdBoost philosophy than we often do.

From the kids we hear:

  • Why do I have to do so many worksheets?
  • What?  I finished my math homework and now you're giving me more?
  • Why can't we play games instead?

From teachers and afterschool programs, we hear:

  • Why aren't there more game?
  • Can't we have more hands-on activities?
  • Do you feel bad giving kids so many worksheets to do?

And we reply, as this article explains, that math requires practice.  It's all fine and good to give students only 5 math problems for homework.  It makes them very happy!  But when we (as tutors and homework assistants) have to help them through 3-4 of those 5 questions, we wouldn't be doing our job if we didn't give them extra practice.  Math requires practice.  And, most math skills don't do you any good if you don't have mastery.  So, we practice.  And, yes, it's fun to play computer games with math, but when you spend 80% of the game time firing at a shooting star (or whatever the object of the game is) and only 20% doing math, you're not using your practice time efficiently.  Essentially, a student needs to play the game for five times as long as another student would need to spend doing a worksheet to get the same amount of practice.  I'd like the kids to finish their practice and go out and play, so I say, let's do the worksheet and get it over with.

Many people contend that there's less intrinsic reward to math work than, say, reading work.  This is sort of true.  Once you can read, you get stories.  And, the better you read, the better stories you get.  In math, you don't get stories as you improve, you just get harder math.  But it feels amazing to me able to do that harder math well. Kids love to "win" and getting math right means that they win.  Doing math quickly and efficiently means that they win.  Being able to work through homework easily makes them feel smart.  Easily learning new concepts makes they feel brilliant.  And that's the best part about math.  If you take it one step at a time, and actually master each step as you go along, it's easy to do well.  So, it's easy to feel smart at math (and it puts you way ahead of the curve as most people do not feel smart at math).

When is it impossible to feel smart at math?  When you skip the foundational skills (which, by the way, often require rote memorization and tedious practice).

Let's say you want to factor the quadratic equation: $x^{2}+13x+42$

A student who doesn't know how to factor a quadratic equation thinks it's Greek. That's ok.  That student probably hasn't learned this skill yet.  

A student who knows how to factor a quadratic and knows times times, easily factors it into: $(x+7)(x+6)$

A student who knows how to factor a quadratic but doesn't not know times tables stares at this problem for a long time, probably writes a ton of scratch work and either gives up for finally gets it after much frustration.  That problem should only take about 10 seconds.  For a student who doesn't know times tables, it can easily stretch into several minutes.  Multiply that by a long homework assignment.

So, a student can master 8th grade algebra and get completely hung up by 3rd grade times table facts.

There's nothing worse than watching 8th graders count up on their fingers.

So, that's why we have students do worksheets.  We want them to see factor $x^{2}+13x+42$ as if it's easy and feel smart.  Worksheets (and all of the practice that goes into them) is one of the fastest ways to get there.