I agree with Z. It’s easier to cook a good meal for friends than it is to plan a menu for 300 people night after night and turn it all into a great business. The most difficult thing for me to do after I’ve thrown out the text book because the problems are bad is to plan something awesome that somehow incorporates the standard. I am more and more successful with more and more experience but I want to write a big text book as much as I want to open a restaurant.

I’m with the other commentors on this one. When I first glanced at this post on my feed, I had to read it twice to find out if this was actual data or if it was supposed to be another example of silly pseudo-context. I mean, I agree that calling measuring the angle of a piano silly, but this question, taken out of context is just as removed from the students.

But there are plenty of ways to pose the same question in a context that the students WOULD be able to connect with, I think even better than if you printed an article about a far away place from the internet:

It costs $200 for a season pass lift ticket, and with this pass, you get discounted ski rentals: $10 per day. A day-pass plus rental costs $45

This type of question writes itself. Others don’t so much.

Good post and I do a similar problem with my students right before I work on simultaneous equations. Some are motivated to do it and some are not. Some see the connection between the traditional problem and the one above and some do not. I will throw in my two cents here. I want a real life example for every topic I teach the students in my class I want a problem that totally gets them motivated, but even my best efforts at this still come up short as it still doesn’t reach all the students. I have a ton of linear examples. They are everywhere. I have a ton of quadratic examples, and I have a ton of exponential examples in the form of biology and finance. For trigonometry we can talk modeling average temperature of cities based on time in months. But even with my best efforts of placing context with at least one problem for each area of math that I teach, in the end we are preparing them for the ACT, SAT State tests etc . . . and the problems on these tests are all psuedocontext so are we going to change the tests that we have to prepare them for? I do not think that is going to happen. So in the end we have to some how make all students motivated to solve psuedocontext. There is no way around it and the only way to have them motivated to solve them is to do them and some how use all the tools at your disposal to get them to see math as its own subject and be motivated to solve x^2+2x+1=0 just because they can. Get them motivated to say “well that problem was easy, I hope there are more of those”. And I think the key to that is to let them play with the problem first let them use guess and check . . . here come my students.

Dan

The question brought up by this news item seems to be, “is it worth it to pay the monthly access fee?” And you don’t need systems of equations for that.

So if you use a question like this to make the kids use equations when there is a simpler way, isn’t that imposing psuedo-solutions?

@Sylvia, I can’t get too worked up over students using a table to solve this. Say they do. It’s going to be a trivial matter (now that this context has been established) to adjust the coefficients to make guessing-and-checking supremely annoying, which will leave a door wide open for systems.

I had my students research a real event and make their own problem based on what they find. For “work problems”, for example, a group of kids made up a pretty funny problem that involved cupcake eating contest which actually happened at a nearby school. They found out the names of participants, teams, number of cupcakes eaten, how fast – everything, and incorporated all of that into a word problem.

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.

@numbat I don’t even see that a table or guessing or even an equation is necessary. The problem is easily solved by just stating that the difference in transaction cost (10 cents) is not worth the fee until you park 17 and half times (1.75/10), so the answer is that if you park 18 or more times a month, the fee is worth it. If not, not worth it. Seems like this problem is a good intro to the concept of “break even” which is a real thing that people deal with in real life all the time.

@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.

I’m not sure about this. The implied algebra problem (finding the break-even point) is reasonably interesting and authentic. 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.

@JimP Pretty short half-life I’d say. Most of the even vaguely relevant problems are starting to smell pretty awful by the time the book is published and delivered. Give it a couple of years in a classroom and they stink pretty badly.