navigatr85 wrote:Let's clarify what we mean here. My understanding of the term "snake oil" is a situation in which a salesman lies about a product in order to sell it. Or maybe the salesman doesn't lie outright, but he uses deceptive language and marketing techniques to make the product seem better than it actually is. If that's not really what you meant by "snake oil", please let me know. In order to determine whether a salesman is lying or not, I don't think it's always necessary for a customer to to fully understand the physics/science of a product, including mathematical descriptions.
Not just lieing -- I'm including "seller doesn't know their product is garbage".
The rather random case I was pointing out was a (set of devices) to measure a subjects macro metabolic activity while engaging in exercise. Noticing that it "gives bigger numbers when the person is exercising" is easy: determining if the bigger numbers mean
anything requires mathematics well above algebra.
And this is in a field that most would consider not that mathematically heavy.
For a more pedestrian example, the specs of a flat screen TV. Understanding them as more than "this number big good, this number small good" helps. Of course, most people stop at that level: "this number bigger gooder, this number smaller gooder".
You probably own a cell phone. Before you bought it, did you take time to learn about the physics of it, like the transmission of electromagnetic waves? Did you solve equations to prove to yourself that the phone really does what the salesmen said it does? No, of course you didn't. You probably did what normal people do: read reviews of phones written by other customers, try out an in-store model before you buy it, and so on.
Nope -- I bought possible snake oil. The phone could actually be a device that allows the police to track my position without my knowledge or permission, as an example of a feature which I honestly have no clue how it works.
Note that my science/math education does give me a far more informed opinion on "does it cause cancer". I'm still trusting experts not to sell me snake oil here, but less than others.
In addition, the pricing plan for the cell phone is far more attackable via mathematics than the mechanics of the cell phone (understanding a cell phone's inner workings requires far more than high school mathematics).
Finally, I buy cell phones as a sheep -- I am not, really, making a decision about how it works. I'm just doing what other people do, and presume that the results of doing so will be similar to the other sheep's results.
[quote[Can you give me a specific example of a situation in which it would be necessary for a customer to use science, along with higher-level math, to determine if a product is snake oil? By the way, when I say "higher-level math", I mean algebra and above. I can definitely see how some pre-algebra might be useful. And I know what you're thinking, algebra is actually not high-level to you or me. But remember that I'm looking at this from the students' perspective.[/quote]
Here are some consumer problems (and thus have wide applicability). "Producer" problems (when you are actually doing something useful for the rest of the humans on earth) will be far more domain specific:
Someone comes to your door offering you a fixed price on electricity.
You are offered 3 different mortgage options when you buy a house. A car. A television set.
You are deciding if you want to buy a geothermal heating/cooling system to replace your oil furnace.
A news report makes any use of statistics, at all. Is the news spewing bullshit?
A news report talks about nuclear waste management and half lives. Is the news spewing bullshit?
A doctor wants to use radioactive tracers to diagnose something. Do you consent?
A health care provider makes a claim. Is the health care provider spewing bullshit? How can you tell?
Murder rate changes. Is it a crime wave?
Do you do X, or Y, or Z, to reduce your taxes?
You are offered stock options in exchange for a lower salary. Is it worth it?
What percent of your investments do you put into stocks vs bonds?
An investment advisor says you should buy X and sell Y. Is the advisor right?
You watch a financial analysis television show for a year. Does the show contain any useful information?
How much time should you spend worrying about a given financial question?
Someone shows you a way to win at a gambling game. Are they telling the truth?
You are offered two different, reasonably complex pricing options to do two different, yet similar things. Compare them. Determine when one is better than the other. Catch your own mistakes.
As noted, these are consumer/pleb oriented. If you have active control over something that matters (ie, you are more than a wage slave), more applications can show up, but they will be more narrow to the domain.
In many of the above cases, you can go the sheep route (do what everyone else does), the trusting fool way (find an expert and trust the expert), the gut feeling route, etc.
navigatr85 wrote:Like I was saying in the first post in this thread, most word problems are very contrived. In my opinion, most of the word problems in textbooks don't even fall under the category of "applications".
Quite often they are really, really easy problems. They are attempting to stress the math, instead of using math you are presumably mastered last year and doing applications with it.
Doing both a hard problem, and new and hard math, at the same time is hard.
For example, I'd say the ball-throwing problems that I mentioned in my first post are not really an application, because an average person isn't very likely to come upon a situation where he needs to calculate something like that.
Ball-throwing comes from the real-world application of aiming ballistic weapons, by the way. This was and is a major low-end application of the calculus.
Interestingly, American infantry mortars have computers that do this for you. This increases the price (and lowers the reliability) of the mortar significantly, but allows a mathematically illiterate person to use the mortar.
I guess, in a way, the word problems have to be contrived. For some math concepts that we teach, it's very difficult to come up with a real-life situation that uses that particular math concept AND will be encountered by an average person. But if it is difficult to come up with a way for the average person to use a concept, isn't that a good reason to just remove that concept from the curriculum completely? Note that I'm only talking about removing it from the list of "core" requirements. In other words, removing it from the list of topics that EVERYONE has to know. Courses could still exist which teach these things, but they wouldn't be required for every single student.
First, core math education doesn't include anything like calculus. Algebra requirements are exceedingly trivial to get a high school diploma.
Here is what you need for a high school diploma in Ontario:http://www.edu.gov.on.ca/extra/eng/ppm/graduate.html
# 3 credits in mathematics (1 credit in Grade 11 or 12)
So here is the highest level of mathematics that a high school diploma requires:
Course Name: Mathematics for Work and Everyday Life
Course Type: Workplace
Course Code: MEL3E
Prerequisite: Grade 9 Principles of Mathematics, Academic, or Grade 9 Foundations of Mathematics, Applied, or a Grade 10 Mathematics LDCC (locally developed compulsory credit) course
Here are the topics covered:
A. Earning and Purchasing
B. Saving, Investing, and Borrowing
C. Transportation and Travel
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Of course, someone taking a university bound course is expected to be able to figure that stuff out while learning the foundation for even more advanced math later on
I think we're in agreement here, somewhat. You seem to be saying that the current system doesn't do a good job of covering applications, but there's just not enough time/effort/resources to do a serious job of fixing it.
No, I'm saying that covering applications heavily is a cost. Applying math you have mastered isn't that hard of a problem: in effect, covering applications is about hand-holding and providing motivation to the student.
There are non-academic streams that do such hand-holding (at least in the local curricula), but they move far slower.
I was confused by the last part of Yakk's post. It says that the post was edited by JHVH, who I'm assuming is one of the forum moderators. It looks like that moderator deleted part of Yakk's post, and replaced it with that comment in square brackets. Is that right? I'm curious to know what Yakk wrote before the moderator deleted it. Something related to the discussion about political decisions?
No, moderator text is in red.