I wholeheartedly agree that solving these types of problems requires little if any mathematical understanding beyond the mechanics of solving the equation, and is certainly not the type of problem that one would have to solve in a real-life context.

And I agree that regardless of the amount of information that is given to a student, the problem should at least be something that an engineer or mathematician would be interested in.

My question is, does a well defined, concrete, “unreal-world” problem have any value? Do you think that it is helpful for some students to work through a few problems like this in order to help them understand how the math relates to a physical model?

It is not always a guarantee for the effectiveness of Math’s learning. Thanks again for raising this debate.

I just want to add that this issue is known way back to the 19th century. For example, from the revolutionary approach to Geometry teaching of a French mathematician (Alexis Claude Clairaut, 1871).

From one of his greatest works – Elements of Geometry – he pointed out that teaching Geometry to young students beginning with highly abstract concepts is too arid a way to invite and inspire them into the beauty of Math.

After that, if you simply infuse your lessons with possible practical uses of those abstract concepts in the ”real-world”, you just get students bored about the Theory and confused about the Practice.

His work has been widely cited by other great and innovative Math educators as E. Castelnuovo, who’s been in turn cited and appreciated many times by C. Gattegno.

Robert.

@robert I have been thinking about this and I think we can easily calculate how meaningful most math is to students’ everyday lives: zero.

Even worse, I have another measure for you: if we somehow get them 60% excited about the relevance of math, how much better will they do at simplifying x^2+x-2 over x-1? Kersplat goes the enthusiasm.

When we answer the relevance question we are setting ourselves (and the students) up for failure.

I like Arthur Benjamin’s “math is cool” message as one answer to “why math?”: http://youtu.be/SjSHVDfXHQ4

But the kids won’t fall for that either. :) The biggest win will be when we get better at teaching pure math, by which I mean students get better at learning it. When all students experience the fun of math that many of us experienced, they will not even ask why they have to learn it.

You are right to bring the students back into the discussion. The real problem is that many of them are not learning a very learnable subject: pure algebra. We should be working on that.

I now wonder (and ask for inspirations):
– is it possible to give an estimate of how much a topic, or a single problem is “meaningful” for a commonly-not-engaged-in-math-teenager-student?
– if so, how?
– is it possible to set about a way to connect Math to students personal interests? We speak about Math all the time, but rarely about students.

We teach students much more that we teach Math.

Thank you for your comments.

One of the students, realizing that once the formulas are put in the calculations happen automatically when numbers are changed, said: “Now I get it! Algebra is like cheating for math!”

Let’s see, a direct mailing of 20k is this much postage, the list of addresses costs that much, the printing and mailing, then the orders come in: the increased wages to my part-time fulfillment helper, the revenue, my estimated income taxes, the step-function in which I have to re-order inventory 2,000 boxes at a time… I was impressed by the size of the sheet when I got done.

Those are pretty simple formulas but a bunch of them and expressing them all would be a good exercise — self-corrected by the spreadsheet software running the calculations for them.

The algebra is not so hard, but the real-world thing is clear and students are generating the formulas as long as the description is word-problemish and does not give away the formula.

jes thinkin out loud.

This does remind me however, of a previous post as it seems connected (and also connected to a post on Michael Perhsan’s blog). I wonder if one of the significant flaws of fake world math problems is that they are, at their heart, easy. All we are asking students to do is plug in values and calculate… not very challenging just time consuming. Side note: I do acknowledge that making sense of the diagram (reading the problem if you will) is challenging but that doesn’t mean the mathematics and problem solving are challenging also.

We just finished a unit in which we collected data and fit different functions (linear, power, exponential, etc) to the data to find the best model. It isn’t really the breaking point that is the engaging part, I guess, but maybe the process of collecting data in order to create a function that described the relationship between weight applied and displacement of the board for various widths or positions of the board.

You’ve identified an enormous part of the problem with the task as written: the model is pre-determined and we don’t know how it was determined. It contributes to a student’s sense that math is a neverending black box.

Here is a real-world scenario that is “real-world” in the sense that my fiance had to do this calculation by hand the other week during her job as a project manager at a green building firm:

She had one site that was 3/4 an acre and a price from that site for $54,000 for some work. Then she had another site that was 2.5 acres and needed to know how much that same work would be for the larger site.

In fact, what she ended really needing to know was how much 1 acre was worth, so she could scale it to all her other jobs. To scale it she had initially multiplied 54,000 by 1.25 and that didn’t work and she wanted to know why it didn’t work. I think that could be a good question for a student.

Real-world guarantees nothing, but teachers being able to express the reason someone needs the “real-world” math is a factor worth looking at.