Harmful effects of Algorithms

An algorithm is a fancy word for a trick, a shortcut or a rule that very smart people figured out and shared with the world so others didn't have to reinvent the wheel every time we want to go somewhere.

I've written before about how really smart people like to make curriculum that focuses on the "basics". Unfortunately, these "basics" tend to be rules and shortcuts that were manufactured by people after they figured things out the hard way. These very smart people make the (mis)assumption that others can just learn the algorithms (the fabricated shortcuts and rules) in an attempt to expedite the whole learning process. And many many teachers are prepared to eat this up because they've got too much to cover anyways - anything to speed up the inconvenient messiness of learning is seen as an asset.

But there's a problem.

The only reason these really really smart people understand the algorithms is because they worked their tails off trying to figure things out from scratch. They played around in the mud and got their hands dirty trying to figure stuff out. In other words, they constructed their own meaning and made sense of these ideas; hence why they could make the algorithms.

I've been writing in generalities thus far. It's time for a specific example.

I was reading my students the book Twenty and Ten when we found out that the story was taking place in 1944, and World War II was in full force. I stopped the class and informed them that I was not even born during this time. Even though I'm 31, I still get these shocking reactions - "Really, but you're soooo old." (Despite my strict anti-punishment beliefs, I promptly bend these kids over my knee and... just kidding) 

I then explained that my dad (who was born in 1953) was not even born yet. However, I did share with them that my Grandpa Art (here's a hilarious post about my Grandpa and multiple choice tests) was born in 1916 and that he was alive at this time.

I told them he is 94, but then I asked them how old he would have been in 1944. 

Cue the debacle.

Kids stared at each other. I'm pretty sure half the class broke out in cold sweats while the other half couldn't avoid eye-contact with me fast enough. Intimidation. Embarrassment. Confusion.

I asked if someone could come up and show how they could figure this out. Jake was kind enough to come up and show his multi-column subtraction skills - but the whole operation went sideways from the get-go because he promptly placed 1916 on top of 1944 and started to carry and borrow. 

Gentlemen, start your algorithms.

He ended up getting an answer of 1972. I have no idea how, nor did anyone else in the class understand his explanation. I thanked Jake and he sat down. Student after student tried to tackle this mathematical albatross - time and time again, algorithms went up in dust as they tried to spit rule after rule at these despicable numbers. The class was left in a haze of math mumbo-jumbo. 

I was depressed.

After reading Constance Kamii's book Young Children Reinvent Arithmetic, I was all gung-ho to help kids think and reason their way through math, but these kids weren't thinking or reasoning; they were spewing shortcuts and riddling rules that resembled the algorithms you and I have come to understand. 

And there lies the problem. You and I have come to understand these algorithms - single and double column addition and subtraction with healthy doses of carrying and borrowing - but they didn't have a sniff of understanding.

They were just following the rules.

Based on this experience, I totally understand why Constance Kamii warns educators how teaching students algorithms before they make meaning can undermine a child's understanding for place value:

It took centuries for mathematicians to invent, or construct, “carrying” and “borrowing.” When we teach these algorithms to children without letting them go through a left-to-right process, we are requiring them to skip a step in their development. Babies need to crawl before they walk (although a few walk without crawling). Most say “Ball gone” before they say “The ball is gone.” Teaching them to “carry” and to “borrow” makes children skip a stage of development that took centuries for adult mathematicians to invent. Since 1972, Ashlock (1972, 1976, 1982, 1986, 1990, 1994, 1998, 2002, 2006. 2010) has been publishing an astonishing variety of data showing that children do not understand “carrying,” “borrowing,” and the many other computational rules they have been taught in school.

Even if our goal is to just get kids to simply bark "right" answers to questions on tests, Kamii's research shows that students who make meaning out score children who only know the algorithm. Even if you don't differentiate between encouraging children to make meaning with math and pumping out higher standardized test scores, you're still better off teaching meaning and only introducing algorithms after kids construct their own understanding.