Assumptions and Academic Success

Assumptions make up the basic fabric of Mathematics.  Every problem in mathematics makes assumptions.
As a student, when you see a problem on a test or in homework, the first thing you need to do is figure out what assumptions the question writer has in mind.  It may be that a problem has multiple solutions, and knowing the assumptions will allow you a better chance to answer the question in the correct context.  
Many people who are trained in teaching write questions for the ACT or SAT make commonly accepted assumptions without realizing it. They do this because they don't have sufficient training in Mathematics and Logic to understand what assumptions they are making.   Teachers often lack training, and many homework problems make unstated assumptions which confuse students and cause them to fear Mathematics.  In my opinion, a student's fear of Mathematics is often a fear of being tricked by unwarranted assumptions.
As a Mathematics tutor, I see my task as a moderator to comment on the assumptions that are missing in the statement of each problem.  I try to help my students think creatively about a problem - about what assumptions are being made in each problem, and what the possible solutions would be under different assumptions.  
My students are successful because they learn to be smarter than the person who wrote the question.  This is not difficult to do since most students are smarter than most of the people who write the questions. 
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