Math Shortcut or Conceptual Understanding?

Image by:  Renjith


There are “tricks” or “shortcut” techniques that many teachers have in their tool belt when it comes to teaching mathematics.  These techniques are often memorized by students to be used later on some type of assignment.  I’m not saying that these types of techniques are good or bad, but often students come away with little conceptual mathematical understanding of the concept being taught via the shortcut. Click on the picture below for more information on conceptual understanding.

© 2007 – 2012 Regents of the University of California

Without that understanding, students are not necessarily being prepared to apply the concepts later in middle school/high school.  A very small sample of the short cut techniques I’m referring to are below.


PEMDAS – order of operations

King Henry Died Drinking Chocolate Milk – Metric System

FOIL Method – Algebra

Negative Multiplied by a Negative = Positive

Gallon Guy/Gal = Capacity


Students generally remember the shortcuts and utilize them on assignments/tests.  Is that a bad thing?  I can almost hear math teachers around the world grumble.   If the students truly have a conceptual understanding of the concept then why not use these techniques?  Many of these types of shortcuts are used at the late elementary level. When students understand the technique – such as King Henry .. but don’t understand the concept (differences between the units of measurement and in what context they can be applied) then students/teachers run into problems.  Students are expected to be able to apply the concepts in multiple situations. Middle school teachers are then are held responsible to deepen the mathematical understanding of the concepts behind the techniques that were briefly utilized at the elementary level.  This topic has been on my mind lately, and finally made it’s way into this post based on this post.  Elementary teachers, as most teachers do,  attempt to use innovative and engaging methods to produce excitement related to learning and school. That motivation is often contagious and beneficial.  Whether teachers use these techniques or not (obviously, it’s up to you!) students should understand the concepts before memorizing nifty sayings that don’t really relate to the concept itself.  I’m not blaming teachers for using these techniques to engage students, but ensuring that students have a mastery of the concepts should be near the top of the priority list.

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