Carrie posted a link to this story today. The story itself is interesting, but it’s one of the comments to that story that really got me thinking:
Why would a professor give an exam for which the answer can be found by using Google or ChaCha? For example, the only reason to ask someone the square root of 323 is to see if they know how to use standard tools (calculators, spreadsheets, Google) to find it. The exception is if the class is something like calculus and the student is being tested on approximation by using numerical methods or a series – and in that case, the professor needs to see the student’s work; she or he does not care very much about the actual value. When students are working in the real world, all the tools are available, so why make students memorize something that can be looked up in three minutes? All tests should be open-book tests, constructed so that the student can use the textbook, class notes, Google, and any other reference tool. Then test for thought process and methodology. We should no longer be teaching facts to memorize.
Interesting, huh? I have to admit that after reading that, I think it makes sense. I might even agree with it…which is weird because it’s almost suggesting that we teach kids to find the answer, not the solution. Does that makes sense?
Think of it in terms of something like a video game. Maybe there’s aparticularly challenging sequence or something. You could spend a lot of time using trial and error and improving your skills and work your way through it or you could jump online or pick up a magazine or call a friend and get a walkthough showing you how to get through. In both cases the end result is the same, but the method for getting there is vastly different.
The whole thing is even weirder to me because when we first moved to the area and my daughter started school in the fall, they used some form of ‘new math’ that we hadn’t seen taught in any of the previous schools she attended. My exact comment at the time after seeing how they did things was, “They teach the kids to find the answer, not solve the equation.”
I wish I had an example for you, but one is escaping me right now and, oddly enough, the following year they went back to a more traditional method of teaching math.
I guess my point is that I’m torn on the issue. I completely see where the comment I quoted above is coming from, but on the same note still think it’s important to find the solution, not the answer. If we all learn to find the answer, then who is going to find the solution to tell us the answer in the future? (I just blew yer mind!)
On a secondary level, I think it also loosely ties to an idea Jeff touched on in one of his recent posts about the upcoming election:
We don’t have an excuse to be ignorant, but we are anyway. I suppose that in a world where reality TV is watched obsessively, ads that make stuff up or stray from issues work because people find that easier to digest than reading about issues. But what happens when the wisdom of crowds is based on sound bites and charged feelings?
In other words, what happens when people are taught to look for an answer rather than taught to find the solution.
Am I stretching too much there or does someone else see the parallels that I do?
The first thing that struck me about this service is that while it touts the advanced use of technology to get information, on the back end it only consists of a bunch of people who are looking up information. It’s not a big information database that delivers the answers to your questions electronically or anything. I just found that to be kind of funny.
And given that is all this service really entails, a means to ask someone else to get information for you, I think more than anything it helps foster laziness in yet another way. Then again, cheaters are generally lazy, so I guess it stands to reason that this service might be used for that purpose.
But getting to your point, I totally see the connections you’ve drawn. I don’t think it is a stretch at all. I think that teaching people to think is just as important, if not more so, than teaching people to regurgitate information.
The former is what encourages people to think about and learn about important things in life, like political elections. The latter is what leads to people reciting what they’ve heard on the latest newscast.
And let’s be real. The folks who were never taught to think are the ones who can’t figure everyday things out…like how to use the self checkout lane at the grocery store. If no one shows them, they won’t be able to do it.
I think it’s even less clear than what you describe. I get the “new math” thing as it’s being taught in some places, because my brain always worked that way. I’d get in trouble in early grade school because I wouldn’t show my work. 37 + 19 = 56. I’d never “show my work” to carry the 1 or whatever, because in my brain I saw 37 + 20 – 1, which is super easy to process quickly.
But I still get what you mean, and I even talked about it on my tech blog. Trying to stump a kid is stupid. Memorizing something is nearly useless as well. But teaching them how to be analytical and solve problems, that to me is where education should be.
Correct me if I’m wrong, but the example Jeff provides (37+19=56 vs 37+20-1) doesn’t negate the idea that a solution still exists and could be taught/demonstrated. Even when you rewrite the equation you are still adding 37 and 20 to get 57 and then subtracting the 1 to get 56.
There is still a process that could be taught and demonstrated. The only reason to offer the shortcut (i.e. rewriting the equation to something that will “click” easier in your mind) is to get you to the answer faster without reasoning out the solution.
I think the math example is a great example of the problem of teaching this way. Because math is a science of building blocks and you need a foundation to keep building. How does “new math” work for algebra, trigonometry, or calculus?
At some point to succeed at those levels of math you have to have skills in problem solving and analysis. I think you get there by learning to process solutions even at the basic levels.
And that concept is a truism of life.
I think you guys started heading a different direction than me, but Carrie kind of brought it back around with the last comment.
Indeed the foundation is what I feel is missing. Being able to give an answer without understanding why that answer is correct is the problem as I see it.
I really wish I could find some of my daughters old worksheets for specific examples. They were doing Everyday Math (AKA Chicago Math) and honestly, the idea is a lot like Jeff’s example…and that’s fine – once you know the basics. You just don’t ignore the basics and start teaching at that level.
I think we all end up figuring out to do math the way Jeff describes…but we figure it out. And that’s the key.
Too often the new math seemed to skip the fundamentals in lieu of the easier way we all eventually figure out. The kids didn’t know why 57+20-1 worked, they were just told it did. Apply that same way of teaching to concepts more complicated than basic addition and the kids weren’t learning how to solve an equation, they were learning how to find the answer. They knew ‘how’ but not ‘why’ and I think ‘why’ is the key.
That’s where it goes back to the comment from the ChaCha article – this guy argues that the answers are all out there and knowing why the answer is what it is isn’t necessary. It’s more about knowing how to find the answer.
I think you’re looking at it wrong. The “new math” isn’t about short cutting anything, it’s about critical thinking. I’d argue that my example offers a deeper understanding, not less. If a kid learns my example, they’re not losing anything by not carrying the one, they are in fact learning about tens in a different way. They still need the facts surrounding the base of decimal numbers.
Yeah, maybe. I don’t want to turn this into a ‘new math’ discussion. Our school dropped it the following year and a Google search shows plenty of accredited education folks dismissing it. My point isn’t the validity of the new math. (that will have to be another post)
I’m wondering if it’s ok to let kids use a calculator to find the square root because they’ll probably alwys have that tool available as the comment I quoted suggests or if it makes more sense to tech the kids to figure the square root of a number.
Finding the answer vs solving the problem?
I’m really torn on the issue. It makes sense on the surface, but deep down inside I still believe in having to know why the answer is, not just what it is.
I think you’re trying too hard to make it a black and white issue. Using square roots as an example is less helpful because those aren’t something your brain generally can compute anyway. Calculators don’t compute algebraic equations either. You have to teach that technique.
Well, yeah, there is a time and place for using tools to find the answer vs trying to solve the problem yourself. But I think the question remains, is it in your best interest to use tools to find answers just because you can?
I think about this from the perspective of cooking, too. There are a zillion products out there now that make cooking dinner easier to do.
There are even entire meals that you can just peel back the cover on and heat up. But what about the value of a home-cooked meal that is made from scratch? Aren’t we losing something by always turning to the express meals?
And getting to your point, Gonch, (you know, when you blew our minds) what happens when there is no one left who knows how to cook from scratch because everyone learned to make the express meals? Who will create the express meals then for others to make?