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Old 09-25-2008, 05:07 PM
 
268 posts, read 983,134 times
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If you look at most natural science (especially chemistry and physics) curricula in high schools and 1st- and 2nd-years in colleges, I think you will agree that you will find that students are being taught how to solve problems. In this sense they are being asked to apply already known knowledge to specific problem sets. This is deductive reasoning. We're teaching them to go from the general (the fundamental knowledge) to something specific (the problem to be analyzed).

However, science is not about being deductive. Science is inductive. The practicing scientist goes from the specific experiment or phenomenon and generalizes to some overarching theory. And yet, we are not training our students to be able to come up with their own ideas or have the kind of critical thinking necessary to be good scientists.

No doubt, the current crop of students may become good applied scientists or engineers, but if they become good scientists - it would be despite (not because of) the way we've taught them.

Worse, there is a growing body of evidence that shows that students who are taught to solve problems - and are successful at solving such problems, generally do not even understand the underlying concepts that were necessary to solve those problems in the first place. All they've done is learned to apply a protocol, an algorithm, a step-by-step process. They've memorized the way to solve a particular problem - that's not even really thinking.

This is an issue with many variables: textbooks that are written this way, standardized tests, how gradeschools prep for higher learning, current teachers who have been taught this way and therefore tend to teach this way, the socio-polical climate . . . but what's to be done???
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Old 09-25-2008, 11:23 PM
Rei
 
Location: Los Angeles
494 posts, read 1,664,392 times
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Quote:
Worse, there is a growing body of evidence that shows that students who are taught to solve problems - and are successful at solving such problems, generally do not even understand the underlying concepts that were necessary to solve those problems in the first place. All they've done is learned to apply a protocol, an algorithm, a step-by-step process.
For me, solving problems were what taught the fundamentals and concept. This is coming from someone who hated math and science in HS, but became a structural engineer with adv degree.
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Old 09-26-2008, 04:24 AM
 
Location: Los Angeles Area
3,306 posts, read 3,622,898 times
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Mathematics education has the same problems. They focus far too heavily all what amounts to computation, the vast majority of High School mathematics can be done on a 50 buck calculator.

They never put much focus on how Mathematical ideas are discovered, why they are important, nor how to prove mathematical claims.
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Old 09-26-2008, 07:43 AM
 
697 posts, read 1,861,894 times
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Quote:
Originally Posted by coldwynn View Post

This is an issue with many variables: textbooks that are written this way, standardized tests, how gradeschools prep for higher learning, current teachers who have been taught this way and therefore tend to teach this way, the socio-polical climate . . . but what's to be done???
Keep in mind, I am no scientist, but I do have a daughter who, since the age of 3 wanted to be a neonatal specialist and research scientist.

Kids are given a problem to solve with an already known outcome. They are either right or wrong according to someone else's conclusions, so their focus is on getting it right to satisfy an already set answer. What if, from the beginning of their science education in school, they were given the tools (in all areas of science and physics), to find their own problems (or a set problem) and outcomes. When children start out with the mindset of having to work thinking inside the proverbial box, they never get OUTside of said box, but if they went into it EXPECTED to think outside, their minds can use it's own creativity with no expectations of a set answer.

So, if a teacher presents an idea to students that has no solution, or an insufficient solution, there are no expectations of finding a particular answer. The expectations would be to find a better, more workable solution. The process would be to learn to find an answer as opposed to learning an already established process.

They would learn to find their own answers instead of someone else's.

Younger children have remarkable minds, and the key is to get them thinking at an early age. They are also the risk takers and are in their glory experimenting with different ideas. There are no inhibitions, so they are not afraid to fail and start over until they are satisfied.

IMO

P.S. Children naturally THINK science. They are TAUGHT to APPLY science.

Last edited by 925mine; 09-26-2008 at 07:55 AM..
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Old 09-26-2008, 07:52 AM
 
57,213 posts, read 45,324,916 times
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I'm not a scientist but I do use math to solve problems. Frankly, what you describe needs a measure of creativity and that's not a common skill but it can be taught\learned. I wonder how many of the creative students get lower grades and then the robots with straight A's get hired and the employers complain about canned thinking.

I always struggled with this in school, I was always trying to LEARN and UNDERSTAND what was going on which made learning slower for me but once it was in there I had it down and could apply it in outside of that specific scenario. Others in my class would cram it in their brain, ace the test and a few weeks later have to re-cram it in their brain for the final and then forget it again. To each their own.
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Old 09-26-2008, 10:23 AM
 
130 posts, read 414,234 times
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Quote:
Originally Posted by Mathguy View Post
I'm not a scientist but I do use math to solve problems. Frankly, what you describe needs a measure of creativity and that's not a common skill but it can be taught\learned. I wonder how many of the creative students get lower grades and then the robots with straight A's get hired and the employers complain about canned thinking.

I always struggled with this in school, I was always trying to LEARN and UNDERSTAND what was going on which made learning slower for me but once it was in there I had it down and could apply it in outside of that specific scenario. Others in my class would cram it in their brain, ace the test and a few weeks later have to re-cram it in their brain for the final and then forget it again. To each their own.
Me too!! I still do this, in grad school .

Back in college, I was sitting in my Calc 2 class when the lightbulb went on and I said "oh, THAT's what we were doing in Calc 1!" I stuck with trying to grasp the "why" because I wanted to know. Grasping the "why" sometimes made it incredibly difficult to do well on a poorly designed multiple choice test, because I could then apply that to multiple scenarios. (Some (many?) teachers/profs don't know a lot about good test design.)

What I always found most interesting about science is what happens during a paradigm shift--we have knowledge and evidence, and think things work a certain way, then we gain a sufficient amount of evidence that doesn't fit that model so we have to come up with a new way of explaining things. We tend to think science is "proven" when really it is the best explanation we have at the time given what we know--(and what we know is largely dependent on our "observation tool" and what we choose to measure)--that is subject to change. Being exposed to that gave me the freedom to question things--not always a popular trait I might add!

Last edited by SomeThings; 09-26-2008 at 10:24 AM.. Reason: spelling :)
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Old 09-26-2008, 12:14 PM
 
Location: Pennsylvania
5,726 posts, read 10,460,219 times
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Quote:
Originally Posted by 925mine View Post
Keep in mind, I am no scientist, but I do have a daughter who, since the age of 3 wanted to be a neonatal specialist and research scientist.

Kids are given a problem to solve with an already known outcome. They are either right or wrong according to someone else's conclusions, so their focus is on getting it right to satisfy an already set answer. What if, from the beginning of their science education in school, they were given the tools (in all areas of science and physics), to find their own problems (or a set problem) and outcomes. When children start out with the mindset of having to work thinking inside the proverbial box, they never get OUTside of said box, but if they went into it EXPECTED to think outside, their minds can use it's own creativity with no expectations of a set answer.

So, if a teacher presents an idea to students that has no solution, or an insufficient solution, there are no expectations of finding a particular answer. The expectations would be to find a better, more workable solution. The process would be to learn to find an answer as opposed to learning an already established process.

They would learn to find their own answers instead of someone else's.

Younger children have remarkable minds, and the key is to get them thinking at an early age. They are also the risk takers and are in their glory experimenting with different ideas. There are no inhibitions, so they are not afraid to fail and start over until they are satisfied.

IMO

P.S. Children naturally THINK science. They are TAUGHT to APPLY science.
I like what you say here, and I think it applies to subjects besides science as well. You're promoting a process of divergent thinking that results in a student constructing understanding as opposed to a convergent 'scavenger hunt' where students have to apply clues to complete a task.

So why doesn't it happen more often? Assessment . . . it's much easier to assess performance on convergent tasks than on divergent tasks. It's my opinion, though, that the ability to think divergently has more value in the adult world than the ability to think convergently.
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Old 09-26-2008, 12:45 PM
 
890 posts, read 1,305,788 times
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Coldwynn,

1) Physics and chemistry aren't classified as natural sciences, they're classified as physical sciences, just FYI.

2) Deductive reasoning vs. scientific process (what I think you meant when you wrote 'inductive') = natural philosophy vs. true science. Science is a process and the process involves observing, formulation of a hypothesis, then testing for proof, whereas deductive reasoning is 'proof' by argument. Ancient Greeks (Aristotle, etc) laid down much of the foundation for the sciences of today by deductive reasoning, sometimes they were right, sometimes they were way off.

For example, Aristotle came up with the idea that the earth was not flat because of the shape of the earth during a lunar eclipse, plus the fact that he saw the tops of the sails of ships before seeing the whole ship (if the earth was flat, he would see the whole ship. He was correct in that the earth wasn't flat, but he also believed that all matter was made from the 4 basic elements of air, earth, fire, and water. When a man named Democritus came up with the idea that all matter was made up of atoms, he was almost laughed out of Alexandria.

3) Regarding this: "In this sense they are being asked to apply already known knowledge to specific problem sets. This is deductive reasoning. We're teaching them to go from the general (the fundamental knowledge) to something specific (the problem to be analyzed)."

a. That's not deductive reasoning, that's applied analysis
b. Teaching them to apply general knowledge to specific problems isn't necessarily a bad thing. It reinforces the knowledge and integrates concepts with problem solving techniques, which is what you were saying that it doesn't do (not sure if you see what I mean by this, but if I understand you correctly, your example contradicts what you are speaking out against)

4) I would argue that teaching students to solve problems is a good thing, provided they understand why. I think proper problem solving structure develops logical thinking ability. I also think that the structure of proper problem solving develops discipline in thought (not just the ability to think logically).

5) Consistent with #4, I agree that teaching the students how to blindly solve problems independent of the concepts is not good. It shows a lack of the ability to communicate knowledge to your students. I teach physics, and put concepts first in all aspects of teaching (visual, auditory, and kinesthetic). I believe that it's up to the teacher to make sure that doesn't happen, and I certainly don't! During my questioning my favorite question is 'why?'!

6) Do you know about inquiry based learning? I employ a few inquiry based activities but concentrate more on other methods. I find that inquiry based activities are good once in a while because there are plenty of things that the students can 'discover' on their own without it relying on previous knowledge, and there are plenty of opportunities where students can apply proper scientific processes in the classroom setting where the processes of observation, testing and experimenting are alive and well.

7) A good teacher will teach them how to 'think' science, and that science is a natural process, and will help to develop that vs. making them blindly apply concepts or problem solving steps. There are some bad teachers out there, sure, but there are plenty who are doing what they should. I think it should be treated on a teacher-by-teacher basis, not stereotyped as a culture of science educators teaching a 'dead' curriculum.


Just my $.02

Last edited by NJmmadude; 09-26-2008 at 01:04 PM..
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Old 09-26-2008, 01:42 PM
 
697 posts, read 1,861,894 times
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Quote:
Originally Posted by maf763 View Post
I like what you say here, and I think it applies to subjects besides science as well. You're promoting a process of divergent thinking that results in a student constructing understanding as opposed to a convergent 'scavenger hunt' where students have to apply clues to complete a task.

So why doesn't it happen more often? Assessment . . . it's much easier to assess performance on convergent tasks than on divergent tasks. It's my opinion, though, that the ability to think divergently has more value in the adult world than the ability to think convergently.
I agree. That's why I homeschool.
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Old 09-26-2008, 02:18 PM
 
148 posts, read 585,638 times
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I think a lot has to do with how science/maths is introduced and taught in the elementry and middle school. I live in one of the "best" county and volunteer at the local public school and am appalled at the attitude of teachers towards science/maths and how they shut the kids up (or label them as trouble makers) when they ask curious science questions. IMO, The weak science/maths curriculum, disinterested and mostly unqualified teachers are the reason why kids are not motivated to develop a passion towards science at an early age. The high school students is another story..I come across so many who cannot apply concepts they learnt in junior classes to a high school problem, esp. in Maths where the knowlege tends to be cumulative.
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