One Important Reason For Students To Explain or Justify Their Work!

 I finally tripped over the answer to "Why students need to explain or justify their work?"  My students see no reason to do any explanations because they got an answer.  Unfortunately, it is not always the correct answer and my students cannot always explain how they got that answer.

What I read, makes so much sense because it is put into a context I can share with them.  In the future, many students will be working at jobs where they are given a problem to solve.

The solution may not be numerical as we get from solving mathematical equations but it will be a solution to the problem.  Usually two or three people will each work towards finding a solution, talking to each other, explaining their thinking, and eventually combining ideas into a solution.  Then one group or many groups will present their solutions to the boss and they have to convince him that their solution is the best.

When we have students draw pictures, or diagrams, it is preparing them to create multiple representations of their solution to a problem at work.  When people prepare a presentation for work, they usually include graphs, diagrams, illustrations, words,  mathematical equations, or tables to convey the information to an audience.  Furthermore, the idea behind these presentations is to convince the audience that the position of the presenter is the best one.  This is done through explanations and justifications of the method chosen with supporting data.

As we all know, more and more of the mathematical calculations are being done by machines via computer programs but people still need to interpret the results to know if the results indicate this choice is the best or if the person is arguing the other way, why it shouldn't be chosen.  Learning to justify or explain prepares people to support their position on the topic.

When the explanations are based on the mathematics, students who have gone through the process of developing mathematical communications are at an advantage over those who have not because they know how to formulate their ideas based on interpreting the results of mathematical calculations so they can argue one way or the other.

This is an important skill to develop.  Many industries rely on people who have excellent communications skills to develop new mines, new products, new ways of doing things.  For instance, when a mining company is looking at developing a new gold mine, they take samples, they do surveys, they determine if the amount of gold will be enough to build the mine, hire the people, pay taxes, and still make a profit.

In addition, many of these same businesses look at amortization tables to determine when a business will break even on the new project so they can account for inflation as part of the process and know if they can break even.  These are all important parts of communication. This is why we need to have students learn to explain and justify their work.  It teaches them an important skill for the future.  Let me know what you think, I'd love to hear.  Have a great day.