January 14, 2009

21st Century Skills and Real World Problems

So how much does possessing 21st century skills compensate for a lack of domain knowledge?

Can you think critically in a domain in which you do not have a deep understanding?

Some in the edusphere think you can.

I think lack of domain knowledge will serious handicap your ability to think critically in that domain.

Instead of arguing and accomplishing nothing, why don't we collect some data.

And I urge everyone in the edusphere who has an opinion in this area to think up their own example.

Below is a simple physics problem that requires some domain knowledge in physics, algebra, and arithmetic to solve. And, unless you've seen a problem very similar to the one below, I think you'll need a somewhat deep understanding to come up with a solution.

At least before the 21st century and the internet.

I've taken 2 years of physics (one in high school and one in college) and a semester of dynamics. I have some domain knowledge in physics. But, I took these courses over 20 years ago and I haven't had much need to solve these kinds of problems since then. However, I still remember how to solve these problems with a little prompting because I solved a few hundred similar problems two decades ago. It's in long term memory at this point.

And, indeed, I was able to solve the problem in about five minutes with a pencil, paper, and a calculator with trigonometric capabilities.

Then I turned to the internet and tried to solve it using knowledge I could extract therefrom. Not unsurprisingly, the internet offered a cornucopia of information that greatly assisted me and made the job of solving the problem much easier. I didn't have to use any algebra nor did I have to do any manual computation. And, the tools I found had brief descriptions of the underlying physics, so I'm thinking a non-expert might be able to use them without really knowing or understanding the underlying physics all that well.

Again, I was able to solve the problem using the internet in about five minutes. But, again, I have domain knowledge.

In theory, the problem can be solved using general critical thinking skills and a basic understanding of how the world works if one has access to the internet.

Let's put that theory to the test.

Here is a simple physics problem that any high school student taking physics is capable of solving. You've probably taken high school physics, but you probably don't remember much of it if you didn't go on to take more physics in college.

See if you can use your critical thinking skills to solve it. Use your 21st century skills to help you solve it. Here it goes.

A ball is kicked from a point X m away from the crossbar, where X is a number between 38 and 39 that you select. The top of the crossbar is 3.05 m high. If the ball leaves the ground with a speed of 20.4 m/s at an angle of 52.2ยบ to the horizontal? (The usual assumptions apply: uniform earth gravity, no drag or wind, the ball is a point)

a. By how much does the ball clear or fall short of clearing the crossbar?

b. What is the vertical velocity of the ball at the time it reaches the crossbar?

Just pick a random number between 38 and 39 and off you go. (I did this so that everyone would get a different answer).

It may be that I picked too simple of a problem. (I always underestimate the amount of math that non-science/engineering majors know and I didn't want to make the problem too hard.) But I think what the problem will demonstrate is that without domain knowledge in physics you will be overwhelmed by the problem and will have much difficulty in doing all the steps needed to answer the questions.

(I did not find any tools that allowed you merely to plug in the numbers and pop out and answer. That would not require any critical reasoning.)

Leave your answers and comments in the comments of this post. Don't forget to tell us what number you selected (between 38 and 39).

And for all of you edusphere bloggers why don't you use your specific domain knowledge and come up with your own critical thinking problems to test and challenge your readers and your own opinions on critical thinking and 21st century skills.

Update: No fair using the pre-21st century skills as asking someone else for help or a complete solution or to learn the specific domain knowledge needed. I wouldn't be able to have chosen such a simple problem if I allowed that and I can certainly have found a more difficult problem in which you could not have learned the domain knowledge in a reasonable amount of time.

Don't spend more than about 20 minutes or so solving the problem.

Also, don't give away too much information in your comments. We don't want other readers using your methodology to find their own solutions. But do tell us the amount of domain knowledge you think you possess. And do tell us if you can't solve the problem within the constraints.

I will make a new post in a few days where you'll be able to leave more detailed information as the discussion gets furthered.


Stephen Downes said...

Why would you suppose critical thinking (or 21st century skills, etc) are used to solve physics problems?

In any case, here's how I would solve the problem using these skills, if I had any genuine need to do so.

I'd write to my friend Daniel, the physicist, and ask him for a solution. He would send it to me.

*This* is how you solve problems using 21st century skills. It is evident by the example that you just don't get that yet.

CrypticLife said...


If that's Downes' definition for 21st century skills, have they stopped penalizing students for "cheating" on tests? (not really cheating now, I suppose). After all, copying from your neighbor is just applying 21st century skills!

Of course, it does give me pause that schools need to spend so much time teaching that.

KDeRosa said...

Why would you suppose critical thinking (or 21st century skills, etc) are used to solve physics problems?

Because the ability to solve problems is a subset of critical reasoning ability.

From the Willingham article: "From the cognitive scientist’s point
of view, the mental activities that are typically called critical thinking are actually a subset of three types of thinking: reasoning, making judgments and decisions, and problem

Critical reasoniong does niot just comprise logic and being able to spot logical fallacies. those are important (and often neglected) areas that should be learned -- a point on which we agree.

I'd write to my friend Daniel, the physicist, and ask him for a solution. He would send it to me.

*This* is how you solve problems using 21st century skills.

You must have missed my update. This is not a 21st century skill. We've had effective communication ofr at least the past 50 years and if time were not critical for much longer than that.

By this reasoning, there's not really much need for formal schooling any more. Why learn to read -- my mother used to enjoy reading me stories when I was a kid, I'm sure she wouldn't continue to do so.

Roger Sweeny said...


If I ask Daniel because knowing who to ask is a 21st century skill, why shouldn't Daniel do the same thing? Why should he have bothered to learn physics when he could just ask someone else?

You see where this is going.

Anonymous said...

Downes answers reminds me of the 20th century story of the physics professor who asked students how to use a barometer to measure the height of a building. (See http://www.snopes.com/college/exam/barometer.asp)

A student, allegedly Niels Bohr, comes up with many alternatives. The final one is: "I would offer the building superintendent a nice new barometer if he will tell me the height of the building."

RMD said...


Why don't we just let all the Chinese, Indians, etc., just do "stuff" for us and we'll send them all our money?

oh, wait, that is 21st century commerce when you have 21st century skills

Evan Abbey said...

This begs the question... are problems like these the key outcome for our educational system? Right now, the answer appears to be yes, for that's what high-stakes testing has emphasized in its accountability structure.

Even though I appear to be in the minority, I posit the answer is no. This isn't an authentic question... it isn't a question that people have to face in the world. Perhaps a better problem would be "Given the downturn in the economy and the un-affordability of college, what steps will you do to ensure your family's well-being and how will you assess your progress?"

That is an authentic question that this year's seniors will be facing. Does deep content knowledge help answer that question? Sure... it never hurts. But knowledge of mathematics and physics are not as vital as creativity, organization, problem-solving, and leadership. I could foresee students answering the question without the former, but not as much the latter.

RMD said...


Unfortunately, striving for amorphous problem-solving, leadership and creativity give educators the green light to do all kinds of things that don't translate into useful knowledge and leave the country with a bunch of generalists, competing against specialists

specific knowledge in whatever field you're discussing helps tremendously to make good decisions (i.e., not just decisions that seem right at the time)

for example, imagine if our president had a true understanding of the Middle East, or energy policy. that would help him or her not only understand the issues, but make better decisions, and involve his or her advisors better

I'm not sure if I'm making sense here . . . I still need my first cup of jo

KDeRosa said...

Evan, I've been meaning to address the points you raise in your 21st Centurey skills blog posts, but I haven't had the time yet.

are problems like these the key outcome for our educational system?

They are, in my opinion, one key outcome. And I believe this regardless of the presence of high stakes tests.

Being able to critically reason within a specific domain has been and continues to be an important skill and source of knowledge. And, I think my example demonstrates that a superficial understanding of the content plus various 21st century skills does not lead to deep understanding of the domain. The lack of content knowledge in ths domainn prevents you from utilizing your 21st century skills. In contrast, someone with domain knowledge would benefit greatly from waht is available on the internet, as I will demonstrate in a future post.

I disagree that this is not an authentic question, but I'll address that later.

Evan Abbey said...


Good points. I definitely agree with your first point. While I say 21st century skills are essential to teach, that doesn't make them easy to teach. I have evaluated many teachers in my school who do use the "ambiguity of these skills" as a shield (see, I must be doing a good job, I'm requiring my students to use problem-solving!)

Job #1 is making these amorphous skills more concrete and tangible, and proponents like me have some work to do in that area.

And yes, I need to be clear... content knowledge can never hurt (it's a good thing). But, I'd argue our president's downfall is not his content knowledge, but rather the skills he uses to make decisions. He doesn't need to be an expert in the Middle East. He does need to know how to synthesize his experts and make the right decision when it's time.

RMD said...

I'm not arguing that he needs to be an expert in Middle East affairs

but a strong knowledge of history of the region will help him evaluate what his advisors are saying. . .

. . .much in the same way that a strong understanding of accounting will help CEOs make better decisions, even though they don't have to be accountants.

emphasizing "creativity" and other such amorphous goals doesn't help children learn content that is going to be very hard or impossible to learn when they are older

also, content knowledge acts as "hooks" for additional information. so when people see events or cultural references, they have some way to put the information into context

I feel like "21st century" is just a way to say "we'll educate your children to whatever lousy and unchallenging standards we deem necessary"

Anonymous said...

Interesting problem. My computation is that if x = 38.5 the ball just barely clears the crossbar and has a vertical speed of almost 14 m/s downward. But I didn’t use the internet. I used my rusty knowledge of physics. And I certainly didn’t do it in five minutes. I spent considerably more time than that just figuring out whether the trig functions on my spreadsheet were set to degrees or radians.

But to imagine anyone without a physics or math background would get a meaningful answer from the internet seems pretty fanciful to me. There’s lots of information on the internet, but few textbooks. And if you do find a physics textbook on the internet, it’s a lot more than a twenty minute job to use it to actually make some sense out of this problem. And it seems to me that anything less than actually making some sense out of the problem is not solving it. It is having it solved by someone else. Is that what we mean by twenty-first century skills? That’s going to make us competitive in a global marketplace?

The idea that the internet will make any knowledge obselete has always seemed very dubius to me. Facts are available on the internet, of course, but not much more. If you need a fact, such as the discharge rate of the Mississippi River into the Gulf, you can find it. And getting on the internet is a lot easier than driving to the nearest library large enough to be of help. But facts are very limited. Perspective is something else. Facts are essential to perspective, but not sufficient. Without perspective you have no idea what to do with the facts.

I think we need to back up one step. The problem you pose would never occur to someone who knew no physics. It’s wonderful to have answers available, but utterly irrelevant if you have no idea what questions to ask. If you let the other guy ask all the questions, you’ve lost already.

In an article I wrote some time ago I divided response levels into “look-say”, (which simply means immediate recall), “ciphering“, (which means figure it out, like a math problem), and “reference” (which means to look it up somewhere). I think this line of analysis is very beneficial and relevant to what we are talking about here. I concluded that the “textbook reference” level is not very meaningful or useful. Here’s a link: http://www.brianrude.com/Tchap14.htm

elke said...

I regret not taking any physics beyond the obligatory high school courses so I had to use my 21st century cheating skills and a java-applet (not in English).
Found it in three seconds.
Critical reasoning to me, as a historian, is: assessing the message, who says what and why.
I had to guess for the last question: perhaps because you think teachers are insufficient in physics and algebra?

Tracy W said...

Evan: This isn't an authentic question... it isn't a question that people have to face in the world.

Why does the authenticity of the question matter? If you can think critically and/or creatively, there's nothing special about applying your critical and/or creative thinking skills to both "authentic" problems and "non-authentic" ones. Einstein fooled around with inauthentic daydreams about travelling at the speed of light. The professional scientists and mathematicians I know are generally happy to play around with silly non-authentic ideas and puzzles.

Actually, ballistics is used in a variety of applications, such as spaceships and rockets.

But knowledge of mathematics and physics are not as vital as creativity, organization, problem-solving, and leadership.

I don't follow. How is knowledge of mathematics and physics not a part of problem-solving? I solve problems using mathematics and/or physics several times a day as part of my job. Algebra is the most valuable problem-solving method I know (this may admittedly reflect the limitations of my education). How do you expect schools to teach problem-solving without teaching mathematics? And why would you want to?

As for the other points - yes, organisation is important. Creativity is nice, but a necessary part of problem-solving is figuring out which creative solutions are actually useful. How would leadership though help your students solve the problem you posit about ensuring "your family's well-being"? I think leadership is important, but it's hardly as vital as a knowledge of mathematics - everyone who is going to deal with money needs to know mathematics, but we can't all be leaders simultaneously, as if we are, there can be no followers. Plus, there's a certain value in being able to strike off in your own independent direction without worrying about whether anyone is following you.

Tracy W said...

I think we need to back up one step. The problem you pose would never occur to someone who knew no physics.

Actually it possibly would if that someone was trying to figure out how to aim his artillery guns [pronoun chosen on purpose].

Anonymous said...

Tracy W-

If I were lucky enough to be Einstein's teacher, I'd have to re-think my curriculum. But the students in my classroom are not Einstein. Which means they learn best with relevant problems.

Artillery guns? You're better off arguing that the problem is good for logic-building than being authentic. There are fewer ballistics experts than hairdressers in America. I suppose we should be teaching styling.

Tracy W said...

But the students in my classroom are not Einstein. Which means they learn best with relevant problems.

Anon, I have several puzzles. Firstly, Evan and I were talking about authentic problems, you here say "relevant problems". Are you defining relevant problems the same as authentic problems or are they something different, and if so, what?

Secondly, your conclusion does not follow from your premise. Einstein needed food. Your students are not Einstein. I would not therefore conclude that your students don't need food. Of course, it is possible that your kids do learn best with relevant problems. Possibly Einstein would have done better in school had he only studied relevant problems. You just haven't given me any rational reason to believe so. And I still can see no reason why a person with critical thinking skills or creative thinking skills or whatever should be any worse at solving inauthentic problems than at solving authentic problems.

As for your comment about artillery guns, what are you going on about? Brian said the problem posed would never occur to someone who didn't know anything about physics, I gave an example of a real world situation where the problem may occur to someone who didn't know physics. Why are you suddenly talking about authenticity and the number of ballistic experts in the USA? Firing artillery may not be a relevant problem to many people today, but it is an authentic problem, in the sense that it's a problem people have needed to solve in the past.