Should We Teach Students To Use Tricks And Shortcuts?

 

As a high school teacher, I get students who ask me which way the alligator bits when referring to inequality signs.  I usually give them a funny look because I've never figured out how the alligator thing is supposed to work.  When I was younger, I developed my own visual clues to help me remember which one was the less than.  I decided the less than sign was the letter L slumped over to become <.  That helped me but if a student is asking me about the alligator, that tells me they never learned the basics originally.

I'm assuming the thing about the alligator is a trick to help students remember which one is less than and which one is greater than.  Then there is the trick of adding a zero to the number when multiplying it by 10.  Yes it works but when students rely on shortcuts and tricks too much, they never actually learn the concept, only the process.  Once a student has mastered a concept, the shortcut becomes more useful because they know what is happening.

In addition, when a student learns a shortcut before learning the concept, they often are unable to apply it properly or are unable to do a problem if it is presented in a different way. Furthermore, when they do not learn the concept instead relying on the shortcut, the missing understanding of the concept becomes a learning gap in the student's knowledge.  

Unfortunately, shortcuts may not always apply to a every situation.  Returning the idea that if you multiply  any number by 10, you add a zero at the end only applies if it is a whole number such as 5 x 10 = 50 but it does not apply if you multiply a decimal such as .056 x 10 is 0.56, not 0.0560 as one might assume without knowing the concept, proving the shortcut does not help with students learning the knowledge conceptually.

Another reason for not teaching shortcuts till after students have established conceptual understanding is that they often try to apply the shortcut without fully reading and thinking about the problem.  One needs to take time to determine if it applies to the situation for instance, we always teach students the order of operations using PEMDAS or Please Excuse My Dear Aunt Sally but there are times when it is better to divide before adding or subtracting, or that minus 5 is the same as adding a negative 5 so you can apply certain rules you couldn't before.  

In addition, teaching students shortcuts before they understand the concept and regular rules means they are not using their critical thinking skills, the same skills needed when problem solving.  When I teach binomial multiplication, I don't focus only on the FOIL method with the letters, I actually show students 5 different ways to multiply ranging from multiply just like we do a two or three digit number to a distributive method, to a pictorial method because not all students understand the FOIL method.

I do use rise over run when discussing slope because those are the terms they are used to but I equate rise to the change in Y, and run to the change in X along with a pictorial method to try to tie it all together and help students gain better conceptual understanding.  Oftentimes in high school math, I have to work on conceptual understanding by starting with the trick they learned earlier in their school career.  Let me know what you think, I'd love to hear.  Have a great day.