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?


  1. Dollars will get you donuts that the company that puts out the catalog is just feeding off their (probably correct) assumption that schools are competing to be able to claim that they're teaching the important parts of math (i.e. everything except basic arithmetic operations, fractions, decimals)at an early age.

  2. In New York State we (math teachers) argued with the state to no avail just a few years ago, trying NOT to bring algebra standards into grade 5.

    Grade 3 is not much of a stretch from there.

    Look, leave the word "algebra" aside, all of this math stuff is a series of abstractions. But using a variable?

    I think that adding fractions is the biggest abstraction, the biggest leap from concrete reality, that any kid should be normally making in math before something like 6th or 7th grade.

    But I am never in a rush with math. Deeper, with mastery, that's the better way.

    When it comes to mathematics curricular questions, I am unabashedly conservative.