Thoughts On Solutions Versus Answers.

 After hearing a speaker at the math conference state the solution is showing how you solved a problem and the answer is the last step of the process, I realized most of us do not think that way.

Most of the textbooks I deal with that the word solution, use it to refer to the answer.  This leads to us instructing students to "Show their work" so we see their steps, otherwise, they only want to put the answer down.

If one assumes the solution is showing how they got from the problem to the answer, then we can ask students to show their solution and know it includes the answer.  I've also seen the term solution set used to express the answer.

I took time to look up the definition of solution on several websites.  Some sites define the solution as the value or values that make the equation true while other sites define it as act of solving a problem.  I'm beginning to think that solution is one of those words that has multiple meanings depending on the context.

I think it is a matter of how its phrased.  If one is asked to find the solution, then it is the process of finding the answer and the work involved in going from the problem to the answer but if asked for the solution, then it is those values that make it true.

I actually spoke with a friend on this topic.  He said we should ask students to solve the problem but I pointed out that as a teacher, I usually have to clarify my instructions with "Show your work" because students believe the word solve means give the answer.  If we use "Find the solution" in and of itself means show the whole process from problem to answer.  He thought about it a minute before agreeing but I suspect my students would argue they found the solution when they write only the answer.

Since many words in mathematics have multiple meanings, this is one of those words we should include since depending on its use will determine which meaning is wanted.  It would be nice to introduce students to finding a solution versus the solution or solutions so student learn to the difference.

I don't know if I fully agree with the solution being the whole process but I do know I want to teach my students that "find the solution" means the same as show how you got your answer and hopefully I won't have to remind them to "Show their work" otherwise I'll get answers only.

Let me know what you think, I'd love to hear.  Have a great day.