What can we do for science education?

[DrRocket]

There's a difference between a course actively promoting misconceptions and one which gives the students a poor conceptual understanding of the subject -- though they are quite capable of memorizing equations and grinding out answers -- and leaves them to fill in the conceptual gaps with their own intuitions and invention. I suspect we see far more of the latter. Students learn all about the physics terms, but have little understanding of how they connect to reality and how they can be applied to physical situations.

 

If you'd like to see the examples from the research, here's the citation:

 

McDermott, L. C. (1984). Research on conceptual understanding in mechanics. Physics Today, 37(7), 24. American Institute of Physics. http://physicstoday....d/v37/i7/p24_s1

 

If you can't get a full-text copy easily, I can send you a PDF.

 

I don't think the blame can be placed solely on the students. Somehow, we're designing courses which students can pass easily with little conceptual understanding, and we're teaching them in a way that encourages them to simply memorize steps to solving problems. We could blame this on the students all we want, but how do we fix it?

 

Here's my take on that article.

 

1. Although it dates from 1984 I doubt that the situation is any better today. I would guess that it is worse.

 

2. I am not particularly surprised that students made conceptual errors in applying mechanics to real-world examples. Besides the obvious lack of mastery of the subject there are some issues not identified in the study: 1) The desired responses are based on idealizations of the real-world scenarios. Unless students recognize the expected idealization they may miss the point or give incorrect answers. 2) Some familiarity with the experimental apparatus (e.g. dry ice pucks and air hoses) is necessary to make sense of the problem presented, and non-ideal behavior may introduce confusion.

 

3. The difficulty in identifying forces in a given situation does not surprise me, if the students were taught mechanics in a physics class. I have seen a Ph.D. student (nuclear physics) have difficulty with this in a very elementary setting. On the other hand engineering students are taught very early on about "free body diagrams" and don't seem to have such problems. (When I showed the technique to the physics Ph.D. student, the response was instant understanding and "That's neat.").

 

4. The study correctly recognized that "Of particular concern is the apparent failure of universities to help precollege teachers develop a sound conceptual understanding of the material they are expected to teach." I think getting understanding implanted in secondary school teachers is the real solution, but that is easier said than done.

5. Some of the problems presented and the expected reasoning are actually rather sophisticated and require an ability with abstract mathematics that relatively few students really have. The problem asking if two rolling balls ever have the same speed is such a problem -- it is an existence proof in essence (It was slower here there and faster there so it must have been equal somewhere in between.)

 

6. The problems seem to be world wide. So no particular educational system is indicted, or exonerated.

 

7. The study paper was by a lady in the U. of Washington Physics department and referenced work by her students for Ph.D. dissertations. If Ph.D. degrees in Physics (rather than psychology or Ed.D degrees in education) were awarded for such work then I am appalled.

 

Aside: Back in my undergraduate days, mechanics was taught to engineers by the Engineering Science Department. They complained that physics students who took their classes "Were great at theory, but couldn't solve the problems." This still baffles me. You simply cannot really understand a theory but not be able to apply it. Equally you cannot apply something unless you understand the underlying theory. What this tells me is that people can somehow "get by" through regurgitation of what some view as "theory" without having any real understanding. I don't know how that is possible except through rote learning and canned testing. This makes me really appreciate Moore method classes and seminar courses where student participation dominates. I hate pure lecture courses.

[rktpro]

My Physics Teacher(PH D in Geophysics and earlier a researcher) almost threw me out of the class. I would like to copy his own words when I asked this to him this.

He said in the beginning,"Anyone who wants to ask a question may come to me." I wanted to ask the question again because this time I had my notebook on which I had made the ray diagram and the derivation. He saw me and said,"Look at that fellow. He wants to know mathematical modelling. Brother, that would yield to you nothing. Okay come to me again with it."

When I went to him, he didn't listen to the question. His mood and his expression were a sort of-'What the heck he wants to know.'

And the most baffling thing he said was," Why don't you go to your maths teacher?"

 

What would you say now? A physics teacher asking you to go for a maths teacher(who I doubt even know something about reflection) is a reality with me.

 

Get a look at the thread please.

[Cap'n Refsmmat]

Not surprising.

 

I have been told by students that they had no interest in understanding the theory, but rather just wanted to "plug and chug". I saw a lot more of this attitude in industry and there it is scary because you get people who are good at manipulating sophisticated computer codes, but don't understand what those codes really tell you or what the limitations are.

I see this all the time assisting for a physics course. Mid-semester, we passed out an anonymous survey in class to ask what students thought of the course, whether certain things were helpful, etc. Everyone complained that the homework did things which they didn't cover in class, as though the point of homework is to ensure you can memorize and repeat everything the professor said.

 

Fortunately, our professor responded with this:

 

And yes, that means that I expect a typical HW of length 6 problems requires >9hrs to complete. This is not a first-year physics class in which all solutions have a single equation solution – plug and chug and you’re done.

 

...

 

Some of you have expressed concern that the solutions required mathematical tricks – I’m glad that you observe this, because I am indeed hoping you will start using math beyond arithmetic to solve physics problems.

 

Students today have the same basic genetics that students have always had, plus ready access to a vast amount of information. If they are weak on critical thinking and deep understanding it is because such has not been demanded of them. Critical thinking is not "taught", it is developed through exercise, and with that excercise comes understanding. One can demand exercise.

Agreed. I think, though, that this is partly the point of interactive and inquiry-based classes such as the ones in the papers I linked to. They're halfway to the Moore method, I suppose.

 

3. The difficulty in identifying forces in a given situation does not surprise me, if the students were taught mechanics in a physics class. I have seen a Ph.D. student (nuclear physics) have difficulty with this in a very elementary setting. On the other hand engineering students are taught very early on about "free body diagrams" and don't seem to have such problems. (When I showed the technique to the physics Ph.D. student, the response was instant understanding and "That's neat.").

I think the current AP physics curriculum requires free-body diagrams. There's often a free-response question requiring the student to label the forces on a particular object in a problem.

 

What I often see, though, is students confused about the normal force, or who draw the current velocity of the object as a force, as though it needs some impetus to keep it in motion. They refer to it as "the force of the object" or something like that.

[DrRocket]

 

Agreed. I think, though, that this is partly the point of interactive and inquiry-based classes such as the ones in the papers I linked to. They're halfway to the Moore method, I suppose.

 

 

Anything that requires student involvement and significant intellectual participation is a step in the right direction.

 

The Moore method, per se, is rather strict. Collaboration and any use of references are strictly forbidden. The student is expected to do all of the work on his own.

 

Many faculty do not like the Moore method. It has the drawback that one cannot cover nearly the amount of material that can be covered if a text is employed, and very difficult material can become esssentially impossible. So there are a lot of less stringent methods that can be successfully employed. For instance you can use a text but require that each student not only read it but come prepared to explain the material to the class. Or you can assign the text as reading and spend class time with student presentations of (often challenging) homework problems.

 

But in my opinion virtually anything beats a straight lecture except for very specialized and advanced subject matter when no good text or readable papers exist.

 

But lectures can provide the platform for some great horse play: We had one algebraist who lectured and also used the students must be ready to lecture themselves technique. He was a great guy, but had a somewhat dour demeanor (which contributes to this story). In any case there were a couple of new Asian students who were advised by one of the older grad students that " When Professor X says something that you don't quite understand, the proper procedure to ask for clarification is to jump up from your desk and shout 'Bullshit !' ". When this happened, Professor X wheeled around, but noticed the older grad student rolling on the floor, unable to breathe, and figured out what was going on.

[A Tripolation]

When students can't do simple arithmetic calculations quickly in their head they have no hope of being able to follow a lecturer in a derivation of nearly anything. It is a BIG problem in terms of understanding.

 

Simple example: Students often have trouble with fractional exponents -- because they can't add fractions.

 

Based on this quote and this post, it seems that you have a problem with calculators. Not to deviate too far from the OP, but I don't understand this. I see a calculator as a tool. And like any tool, it can be used to create or destroy. I'm good at "plugging and chugging", but I struggle with abstract math. I often use a calculator or a program like Mathematica to obtain a final result.

 

Once I do this, I'm able to think, "Now how did they get this?" and work backwards to a solution. It may not be the most elegant way to go about doing math. However, I find that it helps me to see how different techniques may be applied in different situations. It taught me to make substitutions that seem outright ridiculous at first. So in this way, I feel that calculators are vital to students. I do not think they are indicative of "lack of thought", as it were.

[Schrödinger's hat]

Based on this quote and this post, it seems that you have a problem with calculators. Not to deviate too far from the OP, but I don't understand this. I see a calculator as a tool. And like any tool, it can be used to create or destroy. I'm good at "plugging and chugging", but I struggle with abstract math. I often use a calculator or a program like Mathematica to obtain a final result.

 

Even using a calculator as a crutch can be beneficial.

Using it to get the answer so you can be more confident of your understanding is, more often than not, good.

Using it to get the answer and leaving it at that is a good way to lose any progress you've already made.

 

 

<mandatory car analogy>

Calculators are tools, just like cars.

And in the same vein they are very useful. I'll happily use a CAS to do tedious algebra that I can learn nothing new from, or use a computer when I want to add more than a few numbers. Just like I'll use a car when travelling more than 2km and want to get there quickly.

 

The problem comes when the calculator is the first thing you reach for.

If you use the car for every tiny thing like going to the letterbox to collect your mail, you'll become increasingly unfit. When you get to the base of a mountain which the car can't climb or get stuck in somemud, you'll be completely helpless.

</mandatory car analogy>

[DrRocket]

Based on this quote and this post, it seems that you have a problem with calculators. Not to deviate too far from the OP, but I don't understand this. I see a calculator as a tool. And like any tool, it can be used to create or destroy. I'm good at "plugging and chugging", but I struggle with abstract math. I often use a calculator or a program like Mathematica to obtain a final result.

 

 

Calculators are very useful and appropriate tools in a physics or engineering class. They are useful in mathematics classes to avoid having to spend a lot of time with trig tables or log tables, or tedious arithmetic. They are useful to professional mathematicians for doing tedious calculations and balancing the check book.

 

But calculators and computers are detrimental to learning how to think about mathematics in most situations not listed above. Your struggle with abstract math is a good example of why you in particular ought not use a calculator in a mathematics class. You will not learn to understand abstract mathematics except by struggling with the concepts using nothing but your brain. Plugging and chugging is detrimental to your intellectual health, as is any other mindless reliance on a tool that you don't really understand.

 

So it is not that I have a problem with calculators. You have the problem, and apparently calculators contribute to it.

 

In an industrial setting it doesn't matter how you find a useful answer, so long as it is correct, or at least close enough. But to get to that point you first need to understand the basic theories of mathematics, physics, chemistry and perhaps biology. There is no substitute for thoroughly understanding the fundamentals, and that means theory.

[Appolinaria]

Looking back at high school, I have to laugh. The use of calculators at my high school was just ridiculous. We'd frantically trade them amongst each other in the hallways between tests. Cram formulas into loopholes overlooked by teachers. I used my cellphone on tests all the time, too.

[superball]

What can we, as people in the science community, do? What can educators do to change this? We can't just make the tests harder -- they'll all fail. There's something structurally wrong with how we teach high schoolers.

 

Greetings all. there are allot of great posts I read through. I recently did a study in my own thought process relating to cognitive thinking.

The study of analyzing my own process of behavior, and patterns of drawing on what I had learned in my younger years.

 

I am happy to see teachers looking for a way to solve the problems of higher education on a high school level. A time in a persons life that does not allow for play.

We all like to play, and are sometimes preoccupied struggling for memory retention in our later years.

 

For me, I had struggled very much through high school, less time for homework, play time, work time, free time, and relationship.

What comes later in life are Social skills, character, sports, hobbies home life, parents etc..

 

I truly believe, higher education needs to be introduced in the early years of the students development. To this day I still struggle with the basics, because of the preoccupied mind.

It is well know in the early development stages a child mind performs like a marshmallow, absorbing and expanding, learning language, and taking in there surroundings.

Curiosity, and learning is highly increased, creating life long connections to retrieve information in there later years.

 

If we could blow up the mind like a balloon in that stage of development, many more nerve connections, and pathways will develop. This would allow for shrinkage as we get older, for memory retention. smile.

Second languages, musical arts, mathematics, you name it. The process will lead to high society, virtue, etiquette, social skills, and much more.

 

You may try the word association game, because what options are you left with?

For me as a 9th grade high school student, my favorite class was earth science, although I had struggled with history, language, social study, and you guessed it mathematics.

 

So yea, early introduction would indeed help the situation. Life long skills could also be introduced allowing for stronger more technology based working class.

Open book testing may prove to be a viable resource, enabling the high school student to grasp the concepts needed for future retrieval of information.

When I had taken a class for a drivers course the lecturer had gone over every question, and answers that would be on the test allowing for questions from the student driver.

I have to admit I pass with flying colors, and retained the information also.

You may try setting a time after school, 45 minutes over the course of a week to test my proposal, and learn if student score higher on closed testing averages.

 

Sincerely super-ball.

 

Edited November 22, 2011 by superball

[Cap'n Refsmmat]

Looking back at high school, I have to laugh. The use of calculators at my high school was just ridiculous. We'd frantically trade them amongst each other in the hallways between tests. Cram formulas into loopholes overlooked by teachers. I used my cellphone on tests all the time, too.

A friend and I wrote a series of programs in TI-BASIC to solve problems in our algebra class. We even programmed it to show its work, make useful plots, and everything.

 

Sometimes I think it counts as cheating, but I justify it by pointing out that we had to understand the math to write a program to do it.

 

The people we shared it with, on the other hand...

[Appolinaria]

A friend and I wrote a series of programs in TI-BASIC to solve problems in our algebra class. We even programmed it to show its work, make useful plots, and everything.

 

Sometimes I think it counts as cheating, but I justify it by pointing out that we had to understand the math to write a program to do it.

 

The people we shared it with, on the other hand...

 

If you're capable of creating a trick, you should be able to use it

[DrRocket]

A friend and I wrote a series of programs in TI-BASIC to solve problems in our algebra class. We even programmed it to show its work, make useful plots, and everything.

 

Sometimes I think it counts as cheating, but I justify it by pointing out that we had to understand the math to write a program to do it.

 

And you either learned the theory prior to writing the program or increased the depth of your understanding by writing it. I would not call it cheating.

 

 

The people we shared it with, on the other hand...

 

Learned nothing and preserved that state by using the canned program instead of their brain. They were cheating.

[A Tripolation]

So it is not that I have a problem with calculators. You have the problem, and apparently calculators contribute to it.

 

I haven't seen any direct link between my use of a calculator and and my ability, or lack thereof, to use eigenvectors to solve for systems of DE's. We aren't allowed to use calculators on tests. So why would being dependent on one be beneficial to me? I think that they have helped me to understand how to solve more advanced mathematics.

[superball]

And you either learned the theory prior to writing the program or increased the depth of your understanding by writing it. I would not call it cheating.

 

 

 

 

Learned nothing and preserved that state by using the canned program instead of their brain. They were cheating.

 

The problem with this determination is, did the people you shared with actually apply the program, and use it on a consistent basis? Not important.

 

If your dealing with public schooling, and the norm is no student left behind, how would you apply this premise? No student was left behind?

 

Cheating is OK if you want to educate. By cheating with cheat sheets is wrong. By cheating the mind into thinking it is actually learning is a process leading to learning, and retention.

 

Lets say you have 20 kids out of 40 willing to learn, and stay after school. You review the steps necessary to grasp the principles. Give 10 questions, and include in depth explanation. Answer all questions by asking any questions. Participation is part of the learning process. You had already given all the answers on the quiz. Give quiz either at the end of the class, or wait a few days adding more, and more review.

You may also break it down to as little as three questions per day, and wait till the end of the week for the test. It would prove retention, and also grasping process of how it was derived.

 

 

You may end up with more than you had bargained for. You will also see the progress made by the students who had participated, and those who did not.

 

I hope you give the technique an honest try. You may find it useful, even practical bringing up the average scores of the student state wide.

 

Sincerely super-ball

[TonyMcC]

This may be contentious but I think one important factor not yet considered, and which may not be realised by people who do not teach, is the personality of the "good teacher". Many people either choose to teach or are persuaded to teach because they have an exceptional understanding of their subject. One point made during my own teacher training was that such people tended to be introverted whereas teaching really requires an extrovert personality, one not afraid of putting on a show to grab attention. Teaching as a career has quite a lot of similarity to stage acting as a career. Many people who start a teaching career actually find doing it surprisingly stressful.

[ewmon]

Many people either choose to teach or are persuaded to teach because they have an exceptional understanding of their subject [yet tend] to be introverted

The introverted science/math teacher

as exemplified by Ben Stein's Mr Cantwell

in the TV sitcom The Wonder Years.

Somewhere came the concept that, apart from the other subjects, math and science must be taught in a controlled, methodical, and detached manner. Having tutored students from grade six through graduate level in math and science, I know that there's a time to spell things out plainly or discuss things logically, and there's a time to do something interesting either on paper or in real life. I'm not saying that every math/science teacher must be another Richard Feynman, but to truly register with the students, after theory must come application ... something like MythBusters and definitely NOT like Beakman's World (maybe that's why America has become so scientifically dumbed-down).