One of the junior high teachers came around a while ago asking if any of us had a good “algorithm” for solving problems. Something which could, with minor tweaking, be allied to things as carried as calculus or fixing your sprinkler system.
He’s the technology teacher, so he’s got some freedom in setting up his curriculum - and he mostly teaches 7th graders, so wants to try and set them up well.
Does anyone here have any ideas for such an “algorithm”?
I don’t think there is really any such general algorithm.
For example, nobody has been able to turn modern science into an algorithm.
And if there were such an algorithm, it would have to depend so much on the environmental input that it would be impossible to understand it abstractly. As an example, maxwell’s equations are four relatively simple equations that lead to an incredibly diverse range of behavior. But because of this very fact, looking at them by themselves is not very enlightening in many ways.
Need a step: “Google how to solve the problem.”
Or, “Google to search for an expert on the subject in your area to solve the problem.”
Also, to the OP: figuring out the algorithm for solving the problem is essentially Step 1 to solve the problem. Tell your teacher friend this. I like “f.k.d.”'s general problem solving algorithm template, but each step needs filled in for the specific problem before tackling the problem.
Here is a quick summary (with “business world” addition in parentheses):
Understand the (real) problem–might need to translate what is requested into what is the real problem to address
Devise a plan
a. Understand what you do know
b. Clarify/determine what you don’t know (and need to know) that relates to the problem to be solved
c. Identify ways to connect what you do know to what you don’t know (you might find more than one path for this)
Execute (one or more of) your plans
Examine the result(s)
a. Do they address the original problem?
b. Are the results reasonable?
c. Should more work be done? (if so; revisit “step 2”)
It might be worth noting that much of “education” is building the toolbox for working in Step 2 (and successful execution in Step 3).
And some of working in Step 2 is exploration of what you do know to see what might be a reasonable path to fully execute. For example, might do some “trial and error” to see what happens. This might lead to a better idea of which other approaches to try (or to exclude).
That is true. Similar to terms like “parameter” and “space”, algorithm has migrated into more general use, and in that context loses a lot of its specificity and, in my opinion, meaningfulness.
In that case, I’d rather use a word like “guidelines.” There are certainly guidelines for solving a wide variety of problems. But then we seem to lose the ability to objectively determine whether the guidelines really “work.”
Im taking a course on problem solving right now. It seems to be mostly basic techniques and general principles then lots of practice problems and hoping for the best.
I.e. Some problems work well with diagrams. Others trying test cases then looking for a pattern. Problems where the solution required isnt in the same units as whats given, but relationships exist, use algebra.