Let Us Now Praise Ditto Marks

Consider the following snippet of a simplification of an algebraic expression.  The left-hand side has the usual notation and the right-hand side uses ditto marks to mean “the same as that part of the expression above.”

Using Ditto Marks in Algebra I

Using Ditto Marks in Algebra I

Notice how the ditto marks allow you to focus your attention on the pertinent part of the current step.  This idea has possibilities.  Next term I intend to try this method when I explain algebraic simplifications in class.  I also intend to allow students to use ditto marks on their tests as a time-saver if nothing else.

When I coach students struggling to understand  chemistry/physics problems or derivations, I always recommend that they look at what changes on each line and then try to understand why.  If they replace what remains the same with ditto marks as I have done below.  It might help.

Using Ditto Marks in Algebra II

Using Ditto Marks in Algebra II

I might have got a little carried away on the second line but it seems pretty clear.



About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
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