Common Core math for pilots

Henning

Henning

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iHenning
There appears to be a lot of confusion as to what Common Core math is all about. It just struck me how to explain it in a way that pilots will understand. Every pilot uses Common Core math and were taught it in ground school. When you learned how to interpolate in a performance chart to get a result by measuring a visual value, you were using Common Core. That is what Common Core is about, teaching math by providing a foundation of visual interpolation skills, rather than to leave that for later learning.

I posted this here and not in Spin Zone because the intent is to help confused parents who are pilots and perhaps help them with understanding their children's homework, not to raise political discussion. Please do not turn this into any kind of ethical debate.
 
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I'll play (but then I have errands so this will be a drive-by):

I think it's an apple and orange thing.

CC math instruction in elementary school tries to teach the "why", and ground school tries to teach the "how".

Why does x*y=z? and draw a picture to show it.

How do you find z when you have x and y? Use the given table or chart to show it.
 
How did they ever put a man on the moon, build the SR-71, develop the atomic bomb, build super computers, etc. without common core math? Didn't those guys know that they had inadequate math skills back then? :D
 
Most of the politically motivated common core complaints I see surround math problems where the intent was to teach techniques for estimation and the kid gave a precise answer and got marked down for it.

I really think if they're going to go that route they need to change the question format... preferably by asking real world problems orally and asking for an oral response with no calculator or pencil... OR making it multiple choice and making the student select the closest reasonable answer. Some kids... and I was one... who are really good at mental math at a young age are going to get confused by instructions that say to estimate on a math problem that they can solve in their head almost as fast as they read it.
 
Common core math question for pilots:

"What are the minimums on this approach? Why do you get that answer?"

Old answer: 200 ft AGL and 1/2sm visibility

Common Core answer: 0/0 because I feel like it!

Oh wait, that was also the freight dog answer.
 
Common Core math question.

How many socks am I wearing.
 
Interpolation is a skill on it's own. The example given in the other thread is not an example of interpolation. I'm still struggling to appreciate the significance or the method, can't figure out what it shows. The shown method will not help you with algebra, "flip multiplying" will and as you get into more advanced math you understand why flipping works.
 
Drawing a diagram to show the relationship of one number to another (one grid has 6 boxes, one grid has 12) might visually represent quantities and let you "see" some manipulation at work.

A performance chart shows the data, recorded through various tests, and lets you find an answer using the formula provided in a graphc format.

takeoffChart.jpg
 
A real,Common Core math question:

Show how to get 10 when adding 8 + 5.

If the student says 8 + 5 = 13 not 10, it is counted Wrong. 8 + 2 = 10, then add the other 3 to get the final,answer of 13. This is the Approved Common Core Math Answer.

We, as a country, are doomed!
 
Matthew said:
I'll play (but then I have errands so this will be a drive-by):

I think it's an apple and orange thing.

CC math instruction in elementary school tries to teach the "why", and ground school tries to teach the "how". Ground school is about "why" as well.

Why does x*y=z? and draw a picture to show it.

How do you find z when you have x and y? Use the given table or chart to show it.
Click to expand...

You just confused the issue. The difference between CC and traditional arithmetic is in how you understand the relationships between numbers. Traditionally you learn it through rote memorization of specific relationships, CC learn it through visualization of the relationships.
 
SkyDog58 said:
How did they ever put a man on the moon, build the SR-71, develop the atomic bomb, build super computers, etc. without common core math? Didn't those guys know that they had inadequate math skills back then? :D
Click to expand...

Actually, they did, slide rules work under the principles that Common Core uses to their most complex degree. Traditional arithmetic quits functioning well as complexity increases, and visual principles become more efficient and complex. The SR-71 was built using slide rules. Maybe that's why so many people have trouble understanding their E-6B and wind angle mechanical computers.

We'll know in a decade if we made a mistake with it.
 
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cowman said:
Most of the politically motivated common core complaints I see surround math problems where the intent was to teach techniques for estimation and the kid gave a precise answer and got marked down for it.

I really think if they're going to go that route they need to change the question format... preferably by asking real world problems orally and asking for an oral response with no calculator or pencil... OR making it multiple choice and making the student select the closest reasonable answer. Some kids... and I was one... who are really good at mental math at a young age are going to get confused by instructions that say to estimate on a math problem that they can solve in their head almost as fast as they read it.
Click to expand...

The complainers should actually understand what it is they are complaining about as well. The reason to teach estimation is because regardless how brilliant you are, you will face problems that are so complex, that to solve them sufficiently to act on in the time frame you have until you need an answer will require estimation, approximation, and interpolation, to complete. And it also teaches you about margins of error by allowing you to see how much exists. Estimation is a survival skill.
 
Henning said:
The complainers should actually understand what it is they are complaining about as well. The reason to teach estimation is because regardless how brilliant you are, you will face problems that are so complex, that to solve them sufficiently to act on in the time frame you have until you need an answer will require estimation, approximation, and interpolation, to complete. And it also teaches you about margins of error by allowing you to see how much exists. Estimation is a survival skill.
Click to expand...

Soo.... Basically, you are advocating compete bull****?
 
Here's an example of Common Core math applied to my PP Checkride. Cruising along and the DPE declares, "It's solid IFR ahead, we're diverting to XXXX, take me there." I pull out my chart, find XXXX, turn for it based on the mountains I see, spread my forefinger and pinky between two lines of latitude which in that plane represents 30' latitude, 30 nm, 20 minutes, and 2 gallons of gas per span. I knew how much time in fuel I had left, so I walked my fingers up the chart from present position and told him with 20 seconds of the diversion and no tools, "I don't have the fuel to take you there, but I can get to the other side of the pass and get us to YYYY." He looked at me and asked, "How did you do tha so fast?" That was when he went into instructor mode and the ride was passed.

I wish they taught Common Core back when I was in school, I had to figure visual math out for myself.
 
But CC would have failed you because you did it wrong. You (probably) weren't taught that trick by your CFI, and I don't remember any FAA training materials that say anything about the distance between each 30' latitude (maybe there are, I don't remember), so it would be a bust. You used the tools available to you, you came up with the right answer, but you didn't do it the "right" way.
 
Matthew said:
But CC would have failed you because you did it wrong. You (probably) weren't taught that trick by your CFI, and I don't remember any FAA training materials that say anything about the distance between each 30' latitude (maybe there are, I don't remember), so it would be a bust. You used the tools available to you, you came up with the right answer, but you didn't do it the "right" way.
Click to expand...

The chart says it right on the side on the scale. Perhaps you should study your chart a little more closely.

The kid failed the estimation problem providing the calculated question because the problem was about estimating. He didn't read and comprehend the question, so he got it wrong.
 
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Matthew said:
Perhaps I should. CC failed me...
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I note you didn't address the fallacy in the propaganda you read and are spreading.

Latitudes are marked at the edges of the chart, but I can see your point is to spread more political BS than actually help people understand the concept, so I'll disengage now.
 
I don't have a sectional handy for reference. I know latitudes are printed, I didn't remember a reference scale for distance other than the scale along the bottom. I'll have to dig out a chart to see where the distance per latitude mark is.

My point wasn't any "political propaganda", since this is a non-political thread, my point was that CC math programs reward students for using the "method" more than for calculsting the correct answer. In your example, the DPE didn't know how you did the math, so it wasn't the way he expected. CC tests would have graded you down for that.
 
This reminds me of the calculus thread where I gave some rules of thumb and someone replied that the person with the calculus project should try to prove the rules of thumb mathematically. I don't think it takes calculus to prove those rules of thumb, but I have not been curious enough to figure it out because the rules just work.
 
Henning said:
There appears to be a lot of confusion as to what Common Core math is all about. It just struck me how to explain it in a way that pilots will understand. Every pilot uses Common Core math and were taught it in ground school. When you learned how to interpolate in a performance chart to get a result by measuring a visual value, you were using Common Core. That is what Common Core is about, teaching math by providing a foundation of visual interpolation skills, rather than to leave that for later learning.

I posted this here and not in Spin Zone because the intent is to help confused parents who are pilots and perhaps help them with understanding their children's homework, not to raise political discussion. Please do not turn this into any kind of ethical debate.
Click to expand...

I think you are not understanding the issue with common core.(you don't have kids bringing this crap home everyday so it's understandable)

We as parents know what it is and what it's about. THERE IS NO SECRET.

The MAJOR issue is teachers are not teaching it correctly.

Also how common core is used as a one size fits all type of learning, which is a big mistake.

Majority of our kids "get" math and it comes easy to them. The ones that have a problem, common core will help.
 
There are a lot of issues with Common Core, but there can be no debate about the fact that it IS NOT focused on precision, even in the Language Arts.

Good, experienced teachers know what works and how to teach kids so that they get it. Common Core does nothing to help, and in fact creates complexity in areas that don't need to be complex.

The big issue with Common Core is that there IS NOT agreement among academics on what the results will be, but it is being crammed down the throats of students and teachers anyway. It's a grand experiment, changing what we know works well to something where the results are unknown. The reason kids here are "behind" is because the public education system is focused on everything but academics. Common Core isn't going to fix that problem, but it could sure make it worse.


JKG
 
Everskyward said:
This reminds me of the calculus thread where I gave some rules of thumb and someone replied that the person with the calculus project should try to prove the rules of thumb mathematically. I don't think it takes calculus to prove those rules of thumb, but I have not been curious enough to figure it out because the rules just work.
Click to expand...

I'm pretty sure that was the project, to model the flight path mathematically or maybe even control input effects on the flight path. I'm thinking the second question, basically asking for other influences, is another lesson showing that while the model may function for the assignment, in reality there things are never as simple as they seem and accounting for additional conditions make the mathematical model exponentially more complex.

Engineers love to model complex things as a way to understand them and as a way to find problems with designs before they are implemented.
 
JGoodish said:
There are a lot of issues with Common Core, but there can be no debate about the fact that it IS NOT focused on precision, even in the Language Arts.

Good, experienced teachers know what works and how to teach kids so that they get it. Common Core does nothing to help, and in fact creates complexity in areas that don't need to be complex.

The big issue with Common Core is that there IS NOT agreement among academics on what the results will be, but it is being crammed down the throats of students and teachers anyway. It's a grand experiment, changing what we know works well to something where the results are unknown. The reason kids here are "behind" is because the public education system is focused on everything but academics. Common Core isn't going to fix that problem, but it could sure make it worse.


JKG
Click to expand...

Administrators: This is common core....now teach it!!

Teachers: Wait...what???

Administrators: Teach it or get the fuuuuuuuck out!!!

Teachers: Wait....what???

And you see the conundrum.

No voice from the trenches where the opinion SHOULD come from.

When I say it's not being taught correctly....I'm not sure it's teacher fault as much as ciriculum fault and their trying to get up to speed with a reasonable integration.
 
Matthew said:
I don't have a sectional handy for reference. I know latitudes are printed, I didn't remember a reference scale for distance other than the scale along the bottom. I'll have to dig out a chart to see where the distance per latitude mark is.

My point wasn't any "political propaganda", since this is a non-political thread, my point was that CC math programs reward students for using the "method" more than for calculsting the correct answer. In your example, the DPE didn't know how you did the math, so it wasn't the way he expected. CC tests would have graded you down for that.
Click to expand...

Look, you're just regurgitating bull****. The kid got it wrong because he didn't follow instructions, the problem was one of estimating, not calculating, therefore the answer he derived was incorrect. The failure was ADD, not CC. The argument is a manifestation of the combination of ignorance and stupidity by people who hate change because they have to maybe learn something new.
 
Mathematics is a universal language that cannot be bastardized.

I'm too old to know anything about common core, but to me, math is one of the only pure things in this world. Cohesive, unequivocal, and absolute.

When and if we ever make contact with an alien race, math will most likely be our interpreter.
 
Fun thread.
The actual problem was lost in the scrum, though (not unusual for this bunch :D )

The real problem is that the person who wrote that question of performing multiplication by repeated addition does not understand the Law of Commutation and the kids do.
Look here for those who have been out out school too long:
https://www.mathsisfun.com/associative-commutative-distributive.html

Now the issue was they had to show how they get 5 times 3 through repeated addition.
The test writer wanted them to add five sets of "3" together.
The kids being smarter than he/she added three sets of "5" (quicker and easier)
The Law of Commutation says either way is correct - and the KIDS knew this.
So, they got marked Wrong for the order in which they did the additions.
If the test writer had known mathematical symbols he/she could have forced the order of operation.
He/she didn't and so half the kids did it the easier way (the smarter half of the class)
It was the idiot 'adults' who failed, not the kids.
And as far as New Math, my children went through that disaster. My kids did just fine because I made them do their homework (in front of me ) twice. Once the New Math way and once the correct way - correct in the old readin/writin/rithmatic and gazintas sense.
And as far as 'estimation' that osme are sneering at - if you don't have a sense of what the magnitude of the answer should be then you will accept anything the calculator grinds out - and that is the point of Hennings comment.
I still advocate that children should initially be taught mathematics first using tables of logarithms and a slide rule.
Why?
Well, not because I am a curmudgeon - rather because it gives them the ability to at least look the powers of the numbers about to be manipulated by the calculator and by adding and subtracting the powers in their head, know almost instantly that the result will be in the 10^4 range (for example). If the calculator spits back and answer in the 10^5 or 10^7 range then you know immediately there is a problem :dunno:
99% of the kids coming out of high school today cannot do that - and that is a real shame-on-us who are the adults in the room.
 
PaulS said:
I'm pretty sure that was the project, to model the flight path mathematically or maybe even control input effects on the flight path. I'm thinking the second question, basically asking for other influences, is another lesson showing that while the model may function for the assignment, in reality there things are never as simple as they seem and accounting for additional conditions make the mathematical model exponentially more complex.

Engineers love to model complex things as a way to understand them and as a way to find problems with designs before they are implemented.
Click to expand...
Even though it may not be as simple as a rule of thumb, in a practical sense, that kind of accuracy is not necessary when figuring out when to start a descent or what rate of descent to use. I find some people like to calculate things out to decimal places when the instruments they are using to fly with, and their ability to fly that accurately don't match up with the accuracy of the math.
 
Henning said:
Look, you're just regurgitating bull****. The kid got it wrong because he didn't follow instructions, the problem was one of estimating, not calculating, therefore the answer he derived was incorrect. The failure was ADD, not CC. The argument is a manifestation of the combination of ignorance and stupidity by people who hate change because they have to maybe learn something new.
Click to expand...

Alright, I'll reset. But calling something CC is going to bring all its baggage along with it.

Ground school does teach us to use visual aids and shortcuts, rules-of-thumb, and other techniques so we can visualize a math problem. An E6B for WCA is a great example. You can use all these tools to come up with an answer. But does it teach math (this is the tie-in to CC)? I grew up in the era where calculators were first coming out and the argument then was over if they should be allowed in school. Now schools teach how to use calculators - middle schoolers are given particular models they are expected to buy (mine were). I can use an E6B to get a WCA and see it drawn out, but it doesn't teach me the math behind the vectors.

The original assumption was that ground school teaches CC. If the definition is using something visual to come up with an answer, then that's probably true. If the definition is only to use something visual to come up with an answer, then it's probably false.
 
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So, a student is presented a drawing of a right triangle with the two sides marked 3" & 4" and the hypotenuse marked as "X". The student is told that the triangle is drawn to actual size. Laying on the table is a ruler. The student is asked to solve for X. In order to be correct, does the student:

a) Measure X to be 5" using the ruler.
b) Use the Pythagorean theorem to mathematically arrive at 5"
c) Estimate that it is 5" by deciding that the difference between the two sides of 3" & 4 " appears to be the same as the difference between 4" & X.
d) Recall that his carpenter father always uses 3-4-5 right triangles when building things so decides that X must be 5.

Or does it really matter which method he uses as long as he gets the correct answer?
 
New math, common core math, if you don't invent new ways to do math every few years there's no reason to write new math books and make million$ on our tax dollars.
 
Common Core math is just relational mathematics. It's all about teaching mental math. That said, I think punishing students who get the correct answer using a different method is absurd.

Just like when I got in trouble for doing calculations in my head and not showing my work long-division style. Different side of the same coin. I never once memorized a multiplication table...
 
SkyDog58 said:
So, a student is presented a drawing of a right triangle with the two sides marked 3" & 4" and the hypotenuse marked as "X". The student is told that the triangle is drawn to actual size. Laying on the table is a ruler. The student is asked to solve for X. In order to be correct, does the student:

a) Measure X to be 5" using the ruler.
b) Use the Pythagorean theorem to mathematically arrive at 5"
c) Estimate that it is 5" by deciding that the difference between the two sides of 3" & 4 " appears to be the same as the difference between 4" & X.
d) Recall that his carpenter father always uses 3-4-5 right triangles when building things so decides that X must be 5.

Or does it really matter which method he uses as long as he gets the correct answer?
Click to expand...

No, and frequently is doesn't even matter if the answer is correct either.

As a father who just had to go through this with a son who used to love math, I know exactly what Common Core is about. They teach many, many different ways to calculate an answer and let the student choose which one to use. For example, to add 26 and 56, there are about 9 strategies to apply, none of which is the way we learned how to do it. (6+6=12, carry the 1, 2+5+1=8, the answer is 82).

It sounds great. The student will not learn just one strategy, they will have all 9 to give them more power! My son loved math, he loved the precision of it. He loved it so much that in kindergarten he discovered a "Math Blaster" computer game which taught him how to solve GCD and LCM problems before he started 1st grade. Despite the fact that he knew all this, he was forced to learn and apply each of the different strategies for each of the different types of math problems. Not so he could learn how to get the right answer, which he already knew after looking at the problem for 2 seconds....it was so that he could prove that he knew the different ways of solving the problem.

Tedious does not begin to describe it. Spending 13 weeks learning the different ways how to add two 2 digit numbers together was horrible for him and it never got better. Now part of that is because the school system teaches so that 90% of all students are "successful", which means they teach to an IQ of 70. That IQ is clinically classified as an idiot. It is wasting a lot of effort and even more enthusiasm on things that do nothing to advance a student's knowledge of math.

In aviation terms - What is the authorized DH/DA or MDA? What are all the different ways you can get the DH/DA or MDA? Know the rules for how to calculate it by ALL different strategies while flying. Reference to FAA and Jeppeson approach plates are not to be used directly, nor is FAR 91.175. You can't just learn the way that works for you, you also have to learn the ways that don't.
 
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