Ask most adults in the room about checking their checking account and credit card statements and most should admit to checking them religiously (even the online versions). One ALWAYS double-checks (and maybe even triple checks) their IRS tax computations to ensure that mathematical errors are not present. Such errors are a red flag for an IRS penalty or audit. Ensuring that our mathematical computations are accurate is something that has been an integral part of our adult lives for years.
Ask many pre-college students about checking their math homework and you may be surprised that, “checking” has dropped off many a student’s radar screen. This sets the stage for not checking one’s work in college and in the workplace.
Whether it is a time factor or just being lazy, far too many students are sacrificing grades for expediency.
The other day, during a tutoring session, the issue of checking surfaced. It seemed that one student was using the answer key in the back of the book (odd problems) to provide the correct answer for a homework problem, even if his work didn’t justify the answer.
The student was using the answer key in reverse order to guide him toward finding a solution to the homework problem (not necessarily a bad idea). If one knows where to go, it can be easier to trace steps backwards than finding one’s pathway enroute to someplace unknown.
The problem here was that the pathway was incorrect and the student did not use the incorrectness as a way to recognize errors, go back to check his work and find his error before we met.
While the easy solution would have been to assign even numbered problems (no answers provided), that wouldn't have addressed offering a way to find the solution and instilling checking into the solution process.
So, I created the following, “checking your math work” checklist to better help one verify his/her answers BEFORE a tutor, a teacher or a parent finds the error first. As I tell my tutees, their teacher has all the points. Their teacher can give them lots of points or they, the student, can give points back to the teacher. “Why,” I ask them, “would you want to do that?”
Here are some checking rules to get started. I reserve the right to edit this listing because the process I have begun is a, “work in progress.” I welcome feedback and ideas from anyone – student, teacher, parent and tutor.
Note that the steps below require that the student has completed the problem, step-by-step, showing all his/her work. Not all suggestions below work for every type of problem. Use the listing appropriately.
Whether one knows the correct answer (odd numbered problem or your teacher has provided the answer key), always
• Think about the answer one has arrived at and be sure it MAKES SENSE. For example, if the problem involves finding a missing angle in a right triangle and one determines that angle is greater than 90 degrees (i.e., it is obtuse), it should be evident that the answer is incorrect. If one finds that the length of a side in a parallelogram can be 6 or -10, it should be clear that -10 is not a viable answer.
• Verify that the problem has been copied onto a homework or test worksheet correctly.
• Plug the answer back into the ORIGINAL equation or mathematical statement to ascertain if it yields a correct solution. A correct solution usually means that the original problem evolves into an equality (i.e., 7 = 7).
• If the solution does not yield an equality, then go back through the steps and look for an incorrect operation, a sign error, or other miscue. Note that the error could be in the checking process itself. Sometimes, the error could be as simple as writing a “6” instead of a “9” or failing to perform the same operation for each term in an equation. Always check signs. Note that most algebraic problems involve using reverse operations to move numbers, letters and/or terms from one side of an equation to the other.
• If not already done, graph the equation or draw a figure to better visualize the problem/solution. Use of a graphing calculator is always a good way to CHECK one’s answer.
• If the problem involves an inequality (e.g., y > x + 3), graph the solution and shade in the solution area. Then pick three points (one on the line, one above the line and one below the line) to verify the solution area is shaded correctly.
• If the graph involves a second degree or higher polynomial, check end behavior rules.
• Employ other rules or relationships (math textbooks are full of these) to further check one’s answer.
If one uses these and other checking rules and procedures, one can expect higher scores on math homework assignments, tests, quizzes and SAT/ACT exams. The points one earns will be far more valuable that one can imagine.
© 2014 H. Michael Mogil