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Tuesday, January 18, 2011

Algebra in the Third Grade?

I got the NASCO 2011 catalog in my mailbox this morning. If you haven't dealt with them, they are a pretty typical school supply catalog - prices are double what you can find if you search diligently or ten times the scrounger's price. What it is really good for is as a wish list, a source for ideas. "How does that toy work? I could do that in the garage for $2 in materials."

My problem with them is that sometimes they really miss the mark. Here's the cover:




Really? Third grade and up? I rail all the time about my students arriving in 9th grade without a clear grasp of fractions and clueless about operations with fractions (sans calculator), limited fluency with percents and decimals, and an unsteady grasp of their multiplication tables and other basic stuff. I had usually blamed the 3rd through 6th grade teachers for not really understanding arithmetic and passing on any math phobias, but this seems like a major problem right here.

If the expectation is that this kind of thing is possible for 3rd grade and up, maybe it shouldn't be a surprise that fractions and arithmetic aren't getting as much attention.

My questions:
  • Is this typical? Do third grade teachers really do this?
  • Is it just a stupid cover by a catalog desperate to sell overpriced AlgeBlocks to a gullible school system?
  • Shouldn't we be solidifying knowledge to the point of automaticity instead of spreading algebraic materials ever lower?
  • I'm pretty sure that a few third graders could get this but is it appropriate for that level? 
  • Is it possible without manipulatives at this age?
 Then, there's the other debate:
  • Are manipulatives appropriate? 
  • Does the use of something tangible and obviously fixed in size get in the way of learning an abstract idea about a variable?

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