Are Recent Students All Google Crazy?

[mpresic3]

At least three times in the last month, I have had colleagues/new-hires express a shocking reliance on google to understand and perform relatively easy calculations. I could understand if the math involved was not in their line. I would not ask my doctor or nurse to do the calculation, but engineering and math/ physical science graduates should know some of these things. (BTW, I would like to think the doctor and nurse have some idea what a normal body temperature and blood pressure might be. Doctors and nurses have some numeric literacy)

1. In demonstrating a calculation, I asked (really off hand) if the new-hire could take the determinant of the 3x3 matrix. I almost expected the new-hire (engineer) to be indignant at even the suggestion that the person did not know this. Instead, this person told me: I don't know the formula off-hand but I can google it. (I was not really looking for the equation, but knowledge of the process, and I amost thought the person was kidding me)

2. At a recent conference, Schuler oscillations in inertial guidance was discussed. There are textbooks all over the floor that address this. There are knowlegeable people that can discuss this. Instead, the new-hire googled the concept, and received the most, (I will say it) idiotic treatment of Schuler oscillations I ever saw, in a paper which, was several levels more advanced than the person could find just by asking, or reading textbooks.

3. In helping a HS senior on an incline plane problem, the first thing he wanted to do was see what google said about it. His high school teacher told him, please don't do this. You will never learn if you just try to parrot the solution that you may be able to find on google.

4. I was told that MATLAB was wrong in the matrix multiply operation because it did not multiply two same size matrices component by component. (This was about 20 years ago though, so it was not an example from recent history)

I find that most physical science students nowdays have no idea:

The distance from the Earth to the Sun
The distance from the Earth to the Moon
Roughly how long it takes the Moon to revolve around the Earth.
Roughly the radius of the Earth.
The population of the US to the nearest order of magnitude. I have heard figures ranging from 1 million to 1 billion.

Some defenders have told me that with Google, you don't have to know those things and they are unimportant.Maybe I am misrembering, but I seem to recall that before GOOGLE, students were more capable and could manipulate facts and figures better than today. I just saw the movie Apollo 13 on TV. I think it would be awkward if the mission controllers (also engineers/scientists) said: Wait a minute, let me look up how long it takes the moon to revolve around the Earth, or how big is the Moon? How far away are they?

Anyway thanks for listening to this rant, but I really hope it conveys a point. I hope colleges and high schools see some value in stressing at least some values and concepts in science and math need to be on the fingertips, and will develop lessons accordingly. Has anyone else encountered this problem / development

 

[phinds]

OK, not a math student, but still ...

I was at a Lowes when the guy in front of me had a flat-bed cart with 12 potted flowers in 4 rows of 3. The young lady behind the cashier started counting them and the guy said, "Uh ... it's 4 rows of 3". She just gave him a totally blank look and started counting all over again.

 

[BillTre]

OK, not a math student, but still ...

I was at a Lowes when the guy in front of me had a flat-bed card with 12 flowers in 4 rows of 3. The young lady behind the cashier started counting them and the guy said, "Uh ... it's 4 rows of 3". She just gave him a totally blank look and started counting all over again.

They walk among us.

 

[Bystander]

They walk among us.

Indeed.

 

[PeroK]

At least three times in the last month, I have had colleagues/new-hires express a shocking reliance on google to understand and perform relatively easy calculations. I could understand if the math involved was not in their line. I would not ask my doctor or nurse to do the calculation, but engineering and math/ physical science graduates should know some of these things. (BTW, I would like to think the doctor and nurse have some idea what a normal body temperature and blood pressure might be. Doctors and nurses have some numeric literacy)

1. In demonstrating a calculation, I asked (really off hand) if the new-hire could take the determinant of the 3x3 matrix. I almost expected the new-hire (engineer) to be indignant at even the suggestion that the person did not know this. Instead, this person told me: I don't know the formula off-hand but I can google it. (I was not really looking for the equation, but knowledge of the process, and I amost thought the person was kidding me)

2. At a recent conference, Schuler oscillations in inertial guidance was discussed. There are textbooks all over the floor that address this. There are knowlegeable people that can discuss this. Instead, the new-hire googled the concept, and received the most, (I will say it) idiotic treatment of Schuler oscillations I ever saw, in a paper which, was several levels more advanced than the person could find just by asking, or reading textbooks.

3. In helping a HS senior on an incline plane problem, the first thing he wanted to do was see what google said about it. His high school teacher told him, please don't do this. You will never learn if you just try to parrot the solution that you may be able to find on google.

4. I was told that MATLAB was wrong in the matrix multiply operation because it did not multiply two same size matrices component by component. (This was about 20 years ago though, so it was not an example from recent history)

I find that most physical science students nowdays have no idea:

The distance from the Earth to the Sun
The distance from the Earth to the Moon
Roughly how long it takes the Moon to revolve around the Earth.
Roughly the radius of the Earth.
The population of the US to the nearest order of magnitude. I have heard figures ranging from 1 million to 1 billion.

Some defenders have told me that with Google, you don't have to know those things and they are unimportant.Maybe I am misrembering, but I seem to recall that before GOOGLE, students were more capable and could manipulate facts and figures better than today. I just saw the movie Apollo 13 on TV. I think it would be awkward if the mission controllers (also engineers/scientists) said: Wait a minute, let me look up how long it takes the moon to revolve around the Earth, or how big is the Moon? How far away are they?

Anyway thanks for listening to this rant, but I really hope it conveys a point. I hope colleges and high schools see some value in stressing at least some values and concepts in science and math need to be on the fingertips, and will develop lessons accordingly. Has anyone else encountered this problem / development

There's no doubt that some facts and figures are largely irrelevant to understanding a subject. If, however, someone has very little grasp of basic facts- like population of the US - then, IMO, they are susceptible to serious misinformation. And you can start to see how conspiracy theories that are patently ludicrous can take hold without the obvious disconnect with reality being noticed.

 

[Hornbein]

The trouble with not having a set of basic facts is that then you don't know what questions to ask. Then what good is having all the knowledge of the world for the asking?

The trouble with not knowing basic methods is that your subconscious can't go to work on a problem.

 

[Vanadium 50]

I am more concerned with the opposite effect - people come here and ask us something (or use as an incorrect premise for their question) something that could have been learned or rectified in seconds by asking Google.

More Google, not less.

 

[mpresic3]

That might be OK for some rather sophisticated concepts, but I expect a graduate aerospace engineer would not have to google multiplying 3x3 matrices, or taking the determinant of these matrices. When I go to the bagel shop, I don't expect the cashiers to google "simple addition and subtraction"

I expect graduated physicists to know the rolling (without slipping) condition that relates the angular velocity of a point on the rim to the speed of the wheel, without googling, or the relation of voltage to current in an ideal resistor.

In another thread about a year ago, the poster posted that they were going to teach a course in engineering mathematics for the first time. They asked which topics should be included:

How about teaching matrix operations. The play a vital role in circuit analysis, as well as other engineering areas. After a few well designed problem sets in circuits, the student would surely get enough practice in matrix determinants (assuming they did not find the answer in google, and just write it down.)

 

[Hornbein]

When I go to the bagel shop, I don't expect the cashiers to google "simple addition and subtraction"

They use a calculator.

 

[Hornbein]

One day in Santa Cruz I was at a grocery store. The young ladies at the cash register had the final price of something and were trying to figure out the before-tax price. One said, "I can't remember how to do this. I wish there were a mathematician here!" Stepping forward said I, "I'm a mathematician." Grasping the pencil, the equation was solved, and the damsels relieved of distress.

 

[DaveE]

I don't have a problem with using references when you need them. We all do it, all the time.

But, there is a problem with not learning the basic material. You will forever be stuck at that level, googling determinants and such. This will become a large impediment to learning more advanced Linear Algebra, or quickly solving your linear systems. You will never be able to work with gradients or laplacians if you are always googling "what's a derivative?".

It indicates to me that they simply don't value or haven't practiced those skills enough to memorize them yet. If they don't know the approximate population of the US, it's because they never cared to really think about it. I was forced to memorize lots of stuff that I long ago forgot because that material wasn't useful to me. OTOH, I have inadvertently memorized another bunch of stuff just because I used it a lot.

My experience hiring EE's, from decades ago, before google was in everyone's pocket, was that most of the candidates that applied simply didn't know the material they needed to solve real world problems. That wasn't google's fault.

 

[BillTre]

One day in Santa Cruz I was at a grocery store. The young ladies at the cash register had the final price of something and were trying to figure out the before-tax price. One said, "I can't remember how to do this. I wish there were a mathematician here!" Stepping forward said I, "I'm a mathematician." Grasping the pencil, the equation was solved, and the damsels relieved of distress.

Giving mathematicians a good name!

 

[vela]

1. In demonstrating a calculation, I asked (really off hand) if the new-hire could take the determinant of the 3x3 matrix. I almost expected the new-hire (engineer) to be indignant at even the suggestion that the person did not know this. Instead, this person told me: I don't know the formula off-hand but I can google it. (I was not really looking for the equation, but knowledge of the process, and I amost thought the person was kidding me)

This anecdote reminds me of a story making the rounds when I entered grad school, that one of the professors had failed a third of his undergrad quantum mechanics class the previous year. We asked him about it, and the story turned out to be true. Apparently, in every example he did in lecture and on all of the homework problems where a matrix had to be diagonalized, the characteristic polynomial could be factored by hand. On the final, however, they couldn't. Many of the students didn't remember the quadratic formula, so they couldn't get started on the problems and ended up failing the course.

 

[DaveE]

Many of the students didn't remember the quadratic formula

Or apparently how to "complete the square" and derive that formula, which isn't that hard for a physics grad student IMO. Granted it takes a bit more time, but memorizing formulas isn't the only way, sometimes actually understanding the subject works too. Concepts and methods are more important than memorized formulas IMO. IRL, you can google the formulas.

This is a great example of why timed exams are problematic. That's not the way scientists and engineers work once they graduate. It sounds like that might not have been the best test design.

 

[DaveE]

OK, another, peripherally related story. When I was an undergrad, my roommate was a physics/astronomy major. He had a test in an upper level astronomy class that required him to derive a formula and solve for some wind speeds on Venus. He did the derivation perfectly, but made an arithmetic error at the end and got the wrong answer, by a lot, something like 1/2 the speed of light. When he got the test back he got no credit for that question, when he complained to the prof, the reply was something like "IRL, results matter, checking your work matters. Welcome to real life. If you had just written a comment that indicated that you knew you were way off, I would have given you full credit."

There is more to knowledge than formulas.

 

[PeroK]

OK, another, peripherally related story. When I was an undergrad, my roommate was a physics/astronomy major. He had a test in an upper level astronomy class that required him to derive a formula and solve for some wind speeds on Venus. He did the derivation perfectly, but made an arithmetic error at the end and got the wrong answer, by a lot, something like 1/2 the speed of light. When he got the test back he got no credit for that question, when he complained to the prof, the reply was something like "IRL, results matter, checking your work matters. Welcome to real life. If you had just written a comment that indicated that you knew you were way off, I would have given you full credit."

There is more to knowledge than formulas.

Or, it goes to show how important it is to memorise the speed of light. Why is a wind speed of $10^8 m/s$ absurd, unless you've memorised typical wind speeds?

In a way, that goes back to the original point. If a student has no idea whether the speed of light is $300 m/s$ or $3000 m/s$ or whatever, then nonsensical answers don't seem nonsensical.

 

[mpresic3]

Some of these replies scare me. I do not like to fail people, but 1/3 of the undergraduate quantum mechanics class cannot solve an algebraic quadratic equation. These equations are common in the ninth grade mathematics exam in the state of NY. Did they learn nothing in math for 6 years?

Googling formulas can sometimes be impossible anyway. Suppose in the quantum mechanics example, the student obtained a cubic characteristic polynomial, and it was not clear what any of the numerical roots were, for example the roots were not rational numbers.

Have you ever seen the formula for the cubic equation in terms of the coefficients of the cubic polynomial? The algebraic processor in MATLAB can display it; it goes on for pages, and the coefficients in the terms are completely mysterious. Nevertheless, with numerical coefficients, there is a process to solve the cubic equation without the "formula". Many physicists and mathematicians have solved general cubic equations like this in (the mercifully few cases )where it becomes necessary, through a process outlined in Schaum's outline.
(I will say using this process in the timed test situation would be over the top)

I am not at all a fan of timed tests. I like homework, where I can dawdle and drink coffee while doing a physics problem, but the solution of a quadratic equation should be second nature to these students.

 

[vela]

Or apparently how to "complete the square" and derive that formula, which isn't that hard for a physics grad student IMO. Granted it takes a bit more time, but memorizing formulas isn't the only way, sometimes actually understanding the subject works too. Concepts and methods are more important than memorized formulas IMO. IRL, you can google the formulas.

These were undergrads, not graduate students. Regardless, the quadratic formula is something you learn in high school algebra, and being physics majors, they likely used it fairly often in the previous three years. I don't think it's unreasonable to expect the students to have known something so basic.

It's a false dichotomy to pit understanding concepts and methods against memorization. Both are important, and they complement one another.

This is a great example of why timed exams are problematic. That's not the way scientists and engineers work once they graduate. It sounds like that might not have been the best test design.

Physics majors in their senior year didn't know the quadratic formula, so the test was flawed? You must have some pretty low expectations.

 

[Vanadium 50]

Since we're telling "get off my lawn you kids!" stories, a student complained to the engineering professor "but it was only a sign error!"

The reply was "Make a sign error, build the bridge upside down and people and cars fall off. No credit."

 

[DaveE]

Physics majors in their senior year didn't know the quadratic formula, so the test was flawed? You must have some pretty low expectations.

No, that's not it. I dislike tests under pressure where failing one part of a problem eliminates their chance successfully show what they do know. I dislike tests that are sequential problems, where failing a bit early is much more expensive than failing part of it later. Of course, I don't have any information about the class or test. Maybe they all should have failed regardless. If they were failed solely for not knowing that formula, I'm OK with that. But if they were failed because not knowing that formula caused them to be unable to solve other parts of the test that they otherwise knew, then I think it might be a poor test design.

For example, instead of:
1) For a given matrix A, find the eigenvalues and eigenvectors.

I would prefer:
1a) For a given matrix A, find the eigenvalues.
1b) For a given matrix B and it's eigenvalues λ_k, find the eigenvectors.

Still, I agree, the quadratic formula is pretty simple, and should be expected knowledge, for this class.

 

[Hornbein]

This is a great example of why timed exams are problematic. That's not the way scientists and engineers work once they graduate. It sounds like that might not have been the best test design.

As someone once told me, "you get a nice curve that way.". I thought that was the tail wagging the dog.

I have learned in my 70 years that logic plays a rather limited role in human affairs. Tradition and conformity are far more weighty. Statistics is taught much like it was 50 years ago.

 

[Astronuc]

Or, it goes to show how important it is to memorise the speed of light. Why is a wind speed of 10⁸ m/s absurd, unless you've memorised typical wind speeds?

Good question. However, would one not expect someone in STEM to recognize 10⁸ m/s would be relativistic for matter, possibly in an exceptional system.

Speed of light, 299 792 458 m/s ~ 3 x 10⁸ m/s, so 1 x 10⁸ m/s = 0.33 c.

I tried to find an example of relativistic stellar winds, but only quickly found an example of 2.5 x 10⁶ m/s, which is roughly 0.008 c.

Among the bright X-ray sources in the sky a significant number consists of a compact object accreting from the wind of such massive stars. These winds are fast, with typical terminal velocities up to 2500 km/s

Ref: https://www.issibern.ch/teams/stellarwindxray/

On the other hand, we find ultrahigh energy photons in the TeV, PeV range, and possible sources are relativistic electrons, protons or other charged particles interacting with one another, or in one example I found, the decay of relativistic neutral pions, π⁰ -> 2γ as a source of PeV photons. I imagine the annihilation of a relativistic positron-electron pair could also result in a pair of TeV or PeV gammas.

If a university-level STEM student is calculating wind speeds in a planetary atmosphere and/or speed of sound in said atmosphere, wouldn't one expect the student to have an idea of an appropriate speed (or order of magnitude), given the context?

OK, another, peripherally related story. When I was an undergrad, my roommate was a physics/astronomy major. He had a test in an upper level astronomy class that required him to derive a formula and solve for some wind speeds on Venus. He did the derivation perfectly, but made an arithmetic error at the end and got the wrong answer, by a lot, something like 1/2 the speed of light. When he got the test back he got no credit for that question,

Grading and giving all or nothing vs partial credit is a separate issue. It was an issue when I was grading undergrad homework and tests 40+ years ago.

More recently, I reviewsd a set of technical reports in which one table had a column of values for which the units were given as moles. There were three separate but related reports, which were authored by at least two different authors, one with several decades of professional experience and the other with at least a decade of professional experinece. Looking at the values and the context, the values or the units were not consistent, i.e., the amount of material was orders of magnitude off. Instead of moles, it should have been milli-moles, or mole fraction, instead of moles. Not only did experienced STEM staff make a signficant mistake, but the independent (peer) reviewers, and at least two levels of management, missed that mistake, which was repeated in at least 3 reports, which reflected similar experimental work over about 5 to 6 years!

Correct equations/derivations are important as are the numbers. Otherwise, in applied science/engineering, catastrophic failure may occur, and folks may be injured or killed as a result.

 

[jrmichler]

When he got the test back he got no credit for that question, when he complained to the prof, the reply was something like "IRL, results matter, checking your work matters. Welcome to real life. If you had just written a comment that indicated that you knew you were way off, I would have given you full credit."

When I was a grad student teaching assistant in the early 1990's, I assigned a design problem for the gears and bearings class. The assignment:
Design a brake disk for the Mini Baja
Speed 45 MPH
Gross weight 500 lbs
It needs to make one stop from full speed
Use materials from your textbook

Almost half of the assignments came up with brake disks 2 to 4 inches thick by 22 to 30 inches diameter. Half of those had a note that they realized the answer was way off, but they ran out of time. Those got a 98%, the ones without a note got 50%.

I did not have to wait long before two students showed up in my office asking about my grading policies. So I discussed cross checking, including looking at the brake disks on the row of parked motorcycles in front of the ME building. One student looked me and said "But you didn't tell us to use common sense".

 

[berkeman]

Almost half of the assignments came up with brake disks 2 to 4 inches thick by 22 to 30 inches diameter.

 

[gleem]

We should remind students that bad things can happen in real life if one does not pay attention to details, for example, the Mars Climate Orbiter (1999) failure when engineers used the incorrect units for the orbit calculations.

 

[AlexB23]

Good question. However, would one not expect someone in STEM to recognize 10⁸ m/s would be relativistic for matter, possibly in an exceptional system.

Speed of light, 299 792 458 m/s ~ 3 x 10⁸ m/s, so 1 x 10⁸ m/s = 0.33 c.

I tried to find an example of relativistic stellar winds, but only quickly found an example of 2.5 x 10⁶ m/s, which is roughly 0.008 c.

Ref: https://www.issibern.ch/teams/stellarwindxray/

On the other hand, we find ultrahigh energy photons in the TeV, PeV range, and possible sources are relativistic electrons, protons or other charged particles interacting with one another, or in one example I found, the decay of relativistic neutral pions, π⁰ -> 2γ as a source of PeV photons. I imagine the annihilation of a relativistic positron-electron pair could also result in a pair of TeV or PeV gammas.

If a university-level STEM student is calculating wind speeds in a planetary atmosphere and/or speed of sound in said atmosphere, wouldn't one expect the student to have an idea of an appropriate speed (or order of magnitude), given the context?


Grading and giving all or nothing vs partial credit is a separate issue. It was an issue when I was grading undergrad homework and tests 40+ years ago.

More recently, I reviewsd a set of technical reports in which one table had a column of values for which the units were given as moles. There were three separate but related reports, which were authored by at least two different authors, one with several decades of professional experience and the other with at least a decade of professional experinece. Looking at the values and the context, the values or the units were not consistent, i.e., the amount of material was orders of magnitude off. Instead of moles, it should have been milli-moles, or mole fraction, instead of moles. Not only did experienced STEM staff make a signficant mistake, but the independent (peer) reviewers, and at least two levels of management, missed that mistake, which was repeated in at least 3 reports, which reflected similar experimental work over about 5 to 6 years!

Correct equations/derivations are important as are the numbers. Otherwise, in applied science/engineering, catastrophic failure may occur, and folks may be injured or killed as a result.

First off, it is cool that you used multiquote. More importantly, when people rely on computers for doing calculations entirely for them, errors are bound to happen.

For instance, an airplane was fueled with imperial instead of metric, leading to the plane only having 45% of the fuel required to make the journey. This aircraft went down in history as the Gimli Glider. No lives were lost, as the pilot flew the plane on an unpowered glide to an airport.

Source:
https://www.cbc.ca/archives/when-a-metric-mix-up-led-to-the-gimli-glider-emergency-1.4754039