Last month’s Side Note about developing successful study habits touched on two broad steps that are included in most study guides – (1) understand the problem and (2) devise a plan to solve it.
This month, we’ll look at the two remaining parts of the equation to successful problem solving – (3) implementing the plan and (4) evaluating the plan’s effectiveness.
Implementing the plan.
An observer of organized sport knows that coaches often bemoan a ‘failure of execution’ when describing a play that didn’t go just right. While the plan may have been the right call for the situation, the goal wasn’t achieved because of a player (or players) who didn’t quite perform their role as well as needed.
It is the same with study and solving problems in the academic world.
When studying an assignment or exam problem, students may have prepared ‘a plan’ to look at the problem from different perspectives, to sketch out the elements described in the narrative to better understand relationships of space and time, or to re-write the problem statement in her/his own words to better understand the objective of the exercise.
All good plans - none of which will work if execution falls short.
One element that is often the cause of ‘execution failure’ is a something akin to carelessness – trying to execute a good plan while not paying attention to detail, or, in some cases, just skipping some important step in order to save time.
The need for speed often pushes students to rip through their intended plan as fast as possible, hopefully coming to a solution quickly enough have extra time to solve the next problem (or quickly enough to close the books and get some sleep).
But if a sense of urgency leads the student to misread a critical phrase in the problem statement, to needlessly fumble the direction of a vector, or to botch the simple arithmetic behind a calculated exponent, that accelerated performance resulted in nothing more than the student crashing into a dead end.
When that happens, the unfortunate student realizes that time needs to be spent to figure out where the plan went awry… time that should never have been wasted in the first place.
Successful problem solvers understand that attention to detail, both in how the student approaches a problem statement, and in how the student formulates the steps of a solution, are critical in arriving to a correct solution.
Evaluate the plan’s effectiveness.
Sometimes, plans don’t work.
When that happens, it is important for the student to look back on the exercise to get a better handle on the circumstances the resulted in less than satisfactory performance.
An honest assessment that identifies the most likely causes behind a failed experience.
Generally speaking, a student can come up short short in a task for reasons that fall into any of the following categories:
- The student simply didn’t have the skill needed to be successful
- There was needed information that was missing or overlooked
- Assumptions were wrong
- Carelessness
The first item in the list – a lack of skill – is the reason why any student is, well, a student. Skills will improve with repetition, so in order to improve on needed skills, all that is necessary is to not give in to discouragement and show up the next day for the next assignment, the next problem.
We’ve already mentioned the issue of carelessness, an issue which is actually easiest to deal with through better attention to the discipline needed to pay attention to details.
Which brings us to the more interesting categories behind failed exercises – missing information, and wrong assumptions.
While it may be perceived that a solution is being blocked by missing information, chances are the needed information isn’t really missing, but hidden.
What may first be assumed as some missing relationship that is blocking an algebraic solution, may just be some key that needs to be uncovered with the application of a single trigonometric identity or physical law. When a student recognizes this as a common stumbling block to success, it is important to develop the skill to see beyond the obvious facts presented in the problem statement. More often than not, the ‘missing information’ is something that needs to be filled in by looking past the obvious facts to apply some reasoning or inference that introduces new actors onto the problem-solving stage.
And finally, there is the issue of wrong assumptions.
Sometimes, when dealing with the missing information issue, students try to apply a law, rule, or corollary in order to move a solution forward. While this ability is critical to fill in an information gap, the underlying assumption may not be correct – perhaps the student misinterpreted the problem statement, or misunderstood the nature of mathematical law to apply it correctly to the given problem.
Wrong assumptions lead students to yet another dead end--- or worse, lead to a never-ending road where each step seems to take the student further away from a real solution.
When this happens, it may be useful to back up and revisit the problem, this time, discarding a previous assumption, forcing oneself to approach the problem differently. This new direction often opens up new insights that lead to a better result.
Stay in the game.
The plans a student prepares, whether they involve sketching, rewriting, re-phrasing, or whatever, need to be executed in a patient, disciplined way that pays close attention to detail.
And when plans fall short, due to whatever reason, the student owes it to him/herself to honestly assess where the plan went wrong and map out a path forward that focuses on whatever shortcomings need to be addressed.
Most importantly, it is critical to remember that with practice and persistence, problems can be solved, courses will be passed, and skills will be obtained that enable students of any age and background to be successful.
Next month – the importance of attitude.