Dave: But an individual driver would have no need for this information. She would simply calculate the cost of each option, based on how often she expects to park downtown, and select the cheaper option.

But I don’t know exactly how many times I expect to park downtown. I could throw out a few numbers that seem plausible, but more helpful for me is to know this break-even point. I’m not sure how many times I’ll park downtown but I know it’ll be less than 17, so I’ll pass on the monthly access fee.

sylvia, So I’m curious, are you saying you would you pump up the reality and make the problem more complex to force the issue? At some point, some people will give up on tables and that would be a good time to talk equations — but at this simple level, I don’t think anyone would get to that tipping point.

Yeah, this is basically it. I wouldn’t feel great about it, but I’d fabricate a news clipping from another city where the difference between surcharges wasn’t a multiple of ten and then another one where both plans featured a flat monthly fee. The pseudocontext is obviously picking up speed but it’s mitigated by a) the reality of the first example and b) the students’ confidence with the first two examples.

And I’d still keep an eye out for a better example of systems of equations.

@dan As you say, if you give the leeway to solve the problem with multiple means, you are naturally going to see solutions that don’t involve systems of equations, which may defeat the purpose of using a simple (yet real) problem like this to do systems of equations.

So I’m curious, are you saying you would you pump up the reality and make the problem more complex to force the issue? At some point, some people will give up on tables and that would be a good time to talk equations – but at this simple level, I don’t think anyone would get to that tipping point.

In other words, would you agree that your anti-pseudocontext stance doesn’t mean that you have to find an actual verbatim problem, but instead, you are advocating that the context would appear to be real and within the student’s realm of experience. Would you fudge the actual circumstances a bit to build problems that are more complicated to create annoyance and induce students to beg you to help them do it in an easier way than guessing or tables? Would you start with this problem and then ramp it up? Start with a harder problem and use this as practice? Introduce equations only when they beg for an easier way?

I’m mostly interested in hearing how you think this would unfold with kids.

@Numbat I went to a talk two years ago where an instructor had built a table top demonstration building with three rooms. He used light bulbs as a heat source. Using thermal conduction to set up a system of equations, he calculated equilibrium temperatures for each room. He would then measure the temperatures directly. I can’t find the conference program on-line (KYMATYC must have taken it down), so I can’t give the instructor credit. His target audience is two year, non-transfer students (AAS). They have no tolerance for pseudocontext.

This has worked for me with varying success – sometimes, they get really excited about what they find. Other times, they just don’t care, and I’ve learned to accept it and move on.

YOINK!