Other Does it matter if I forget the formulas?

[Apple_Mango]

I forget the formulas I learned after a few weeks. I was wondering if it matters if I forget the formulas. Should I really have drilled the formulas into my head and remember how to do every single one?

 

[Mark44]

I forget the formulas I learned after a few weeks.

Then you didn't really "learn" them.

I was wondering if it matters if I forget the formulas. Should I really have drilled the formulas into my head and remember how to do every single one?

For some formulas, it really matters. For example, the distance formula and quadratic formula should be memorized.
It would help if you tell us what formulas you're talking about.

 

[symbolipoint]

One learns which formulas must be memorized and which may later be searched for in reference materials.

 

[Vanadium 50]

Then you didn't really "learn" them.

This.

In previous messages, you've discussed trying to whip through the material and skipping courses. Mark is right; if you can't remember them weeks later, you didn't really learn them.

 

[symbolipoint]

I forget the formulas I learned after a few weeks. I was wondering if it matters if I forget the formulas. Should I really have drilled the formulas into my head and remember how to do every single one?

Which formulas do you not remember? Do you need them for your work from one course to another? Those you do, you need to remember as well as to understand.

 

[Dr. Courtney]

At some point, many formulas can be derived from other more fundamental formulas, definitions, and principles. But usually, students don't have the time or mastery to do that yet when the formulas are needed (as on an exam). For example, all the kinematic equations follow from the definitions of velocity and acceleration and the assumption of constant acceleration. But the quickest way to derive the formulas requires Calculus, and most students find it easier to memorize them than to re-derive them under time pressure.

There is also an important difference between more fundamental formulas that apply in a wide range of circumstances and more specific formulas that only apply in a narrow range of circumstances. For example, the kinematic equations apply whenever the acceleration is constant. They are often used as a starting point in solving projectile motion and other kinematic problems. In contrast, the range formula is an intermediate result that applies to give the range of a projectile whose final height is the same as the starting height. It is more of the answer to a problem than the starting point. There is much less need to memorize less fundamental formulas like the range formula.

I often see students trying to memorize formulas for solutions to Atwood machines in various configurations. This is silly, because the odds of remembering the right formula for a wide variety of configurations is slim. The needed formula is Newton's second law and possibly the kinematic equations.

 

[Tio Barnabe]

No.

The most important thing is to learn the theory. Once you learn it, you should be able to derive the equations, or "formulas", from the theory. That doesn't work, however, for the cases where the equations are empirical or follow up from postulates/principles.

 

[Apple_Mango]

Perhaps I should had specified more details in my post.

A few weeks after I did my first exam, I find myself not remembering some of the formulas I did from my first exam. I think I can remember the formulas again if I had the formula sheet. I was wondering if it matters if I forget the formulas I did from my first exam? For instance, I don't remember slope formula. Is there really a point in remembering the formulas if I can use the formula sheet to refresh my memory?I find it mind boggling to remember every single math formula.

 

[Apple_Mango]

At some point, many formulas can be derived from other more fundamental formulas, definitions, and principles. But usually, students don't have the time or mastery to do that yet when the formulas are needed (as on an exam). For example, all the kinematic equations follow from the definitions of velocity and acceleration and the assumption of constant acceleration. But the quickest way to derive the formulas requires Calculus, and most students find it easier to memorize them than to re-derive them under time pressure.

There is also an important difference between more fundamental formulas that apply in a wide range of circumstances and more specific formulas that only apply in a narrow range of circumstances. For example, the kinematic equations apply whenever the acceleration is constant. They are often used as a starting point in solving projectile motion and other kinematic problems. In contrast, the range formula is an intermediate result that applies to give the range of a projectile whose final height is the same as the starting height. It is more of the answer to a problem than the starting point. There is much less need to memorize less fundamental formulas like the range formula.

I often see students trying to memorize formulas for solutions to Atwood machines in various configurations. This is silly, because the odds of remembering the right formula for a wide variety of configurations is slim. The needed formula is Newton's second law and possibly the kinematic equations.

I do not understand what you're saying. I am just in Algebra 1. I don't understand those terms you're telling me.

 

[gleem]

Just to clarify your OP what course are you referring to and could you give examples of equations that you are forgetting.

 

[Dr. Courtney]

I do not understand what you're saying. I am just in Algebra 1. I don't understand those terms you're telling me.

Reader's Digest version: If you cannot derive it, then you should memorize it.

 

[Vanadium 50]

For instance, I don't remember slope formula.

Yes, that is a problem.

 

[symbolipoint]

Perhaps I should had specified more details in my post.

A few weeks after I did my first exam, I find myself not remembering some of the formulas I did from my first exam. I think I can remember the formulas again if I had the formula sheet. I was wondering if it matters if I forget the formulas I did from my first exam? For instance, I don't remember slope formula. Is there really a point in remembering the formulas if I can use the formula sheet to refresh my memory?I find it mind boggling to remember every single math formula.

I do not understand what you're saying. I am just in Algebra 1. I don't understand those terms you're telling me.

You need to both understand AND memorize certain formulas. Educators put certain formulas onto formula-sheets for test-taking purposes, especially if rederiving them will be too time-consuming. Some formulas you MUST memorize for Algebra 1 are slope of a line, slope-intercept equation of a line, standard form equation of a line, factorization for quadratic trinomial, factorization for difference of two squares; possibly a few others. You may need to know how to work your way through constant-rates formulas of the form k=y/x which may be applied in the form, y=kx.; handling the units of measure often hints at how to arrange the variables.

Later, in such courses as College Algebra, Trigonometry, Calculuses 1,2,3,4, any Physicses or Engineerings, you still must keep memorized those same things, AND MORE.

 

[I like Serena]

Yes, that is a problem.

I consider blindly memorizing formulas to be generally useless. Better look them up if that's all we do.
Understanding where they come from (make a drawing!), and practicing with them is how we learn them.
As a side effect we may actually be able to write down such a formula without looking it up, or deriving it again, which is nice since it means we can use them quicker and easier.

Then again, I guess we're talking about teaching methods here?
As a teaching method we can start with blindly memorizing, and to try to get to understanding later.
Either way, it means that the memorization is just an intermediate step.
If we forget after a couple of weeks, we can just memorize it again, and again, until understanding dawns one way or another through practice.
Then there won't be a need to memorize it again.

 

[symbolipoint]

I consider blindly memorizing formulas to be generally useless. Better look them up if that's all we do.
Understanding where they come from (make a drawing!), and practicing with them is how we learn them.
As a side effect we may actually be able to write down such a formula without looking it up, or deriving it again, which is nice since it means we can use them quicker and easier.

Then again, I guess we're talking about teaching methods here?
As a teaching method we can start with blindly memorizing, and to try to get to understanding later.
Either way, it means that the memorization is just an intermediate step.
If we forget after a couple of weeks, we can just memorize it again, and again, until understanding dawns one way or another through practice.
Then there won't be a need to memorize it again.

The discussion seems to be both teaching and studying/learning. Formula understanding must go along with memorization, especially at the level of Algebra 1 (as Apple_Mango gives for his current course).

Blindly memorizing, I would suggest NOT to do. The necessary formula needs to be taught, including derivation if can be done. A definition can just be explained and then expressed, and re-explained.

 

[Mark44]

A few weeks after I did my first exam, I find myself not remembering some of the formulas I did from my first exam. I think I can remember the formulas again if I had the formula sheet.

That's not "remembering the formulas" if you have the sheet of formulas in front of you.

For instance, I don't remember slope formula.

For the class you're in, that's a problem. Graphs of straight lines are the simplest kinds of graphs. If you are given two points on a line, you should be able to find the slope of the line, without having to look at a sheet of formulas.

 

[symbolipoint]

I forget the formulas I learned after a few weeks. I was wondering if it matters if I forget the formulas. Should I really have drilled the formulas into my head and remember how to do every single one?

Does it matter if you forget the formulas?
In short, YES.

Picture yourself in a real-world working situation.
You need to know the density of a liquid. You find that at 80 degrees F, it is 1.01 grams per ml. You cool the liquid to 55 degree F and it is 1.13 grams per ml. You NEED to know its density at 68 degrees F. What can YOU do?

• Make a graph on paper and plot (55, 1.13) and (80, 1.01); and draw the line through the two points; and now, read the coordinate for 68 degrees F.
• Use the two data points to form and simplify a linear equation for density as a function of temperature; and use this to compute what you need (like, x=68; find y).
• Use simple linear interpolation to find what is y , having (55, 1.13), (68, y), (80, 1.01).

Most of that is what someone who learned Algebra 1 can do.

 

[Vanadium 50]

blindly memorizing formulas

I never advocated blindly memorizing anything. But if you are taking algebra and can't find the slope of a line without a sheet in front of you, it's hard to argue you really learned the material.

 

[Dadface]

"Never memorise something that you can look up" ......... Einstein

However that is not necessarily good advice for a student. It's important to understand the equation and to know their limitations, if any. Also you need to be competent at applying the equations so practise using them.

It can be an advantage if you memorise the equations, particularly when it comes to exams. My advice is to make a list of every single equation you need for a particular course. You may find that the list of equations is not very long. Make sure that you understand every equation. Next, write your equations up neatly and stick your list(s) on one or more walls somewhere, for example on a bathroom wall. You can now take a quick look at the equations every time you visit the rooms.

 

[Apple_Mango]

I never advocated blindly memorizing anything. But if you are algebra and can't find the slope of a line without a sheet in front of you, it's hard to argue you really learned the material.

I disagree. If one didn't learn the material, then one wouldn't be able to do solve the equation in the first place.

 

[gleem]

If you know the meaning of slope then you do not need to remember a formula.

 

[gmax137]

If you know the meaning of slope then you do not need to remember a formula.

Right - that's why I was taught, "slope is rise over run." This you must memorize, since it could just as well be "run over rise." It is a convention. Say it out loud over & over. When you read "slope" in the test question, you hear your voice saying it: "rise over run."

By the time you get to calculus etc. you no longer have to even think about it.

 

[donpacino]

I disagree. If one didn't learn the material, then one wouldn't be able to do solve the equation in the first place.

This isn't true. Following an example in a textbook is a very easy way to solve many problems, but not actually know how to do it.

 

[Vanadium 50]

I disagree.

I see. So you're not really looking for advice. You're looking for validation.

 

[Mark44]

I never advocated blindly memorizing anything. But if you are taking algebra and can't find the slope of a line without a sheet in front of you, it's hard to argue you really learned the material.

I disagree. If one didn't learn the material, then one wouldn't be able to do solve the equation in the first place.

It seems that the problem isn't to solve an equation, but rather, to graph the equation or determine its slope.

I think I can remember the formulas again if I had the formula sheet.

As has already been said, if you need a formula sheet to remember how to calculate the slope of a straight line, then you didn't really learn this concept.

 

[symbolipoint]

"Never memorise something that you can look up" ......... Einstein

However that is not necessarily good advice for a student. It's important to understand the equation and to know their limitations, if any. Also you need to be competent at applying the equations so practise using them.

It can be an advantage if you memorise the equations, particularly when it comes to exams. My advice is to make a list of every single equation you need for a particular course. You may find that the list of equations is not very long. Make sure that you understand every equation. Next, write your equations up neatly and stick your list(s) on one or more walls somewhere, for example on a bathroom wall. You can now take a quick look at the equations every time you visit the rooms.

Nice point! The list of equations to memorize from Algebra 1 is fairly small. The list of equations to memorize from Algebra 2, maybe larger, but still relatively small. Some of them can be derived again if needed, but then also easier to look for them in a listing - either in your book, or , wherever.

 

[Apple_Mango]

It seems that the problem isn't to solve an equation, but rather, to graph the equation or determine its slope.

As has already been said, if you need a formula sheet to remember how to calculate the slope of a straight line, then you didn't really learn this concept.

I see. I am incorrect.

 

[I like Serena]

I never advocated blindly memorizing anything. But if you are taking algebra and can't find the slope of a line without a sheet in front of you, it's hard to argue you really learned the material.

I see. So you're not really looking for advice. You're looking for validation.

To be honest, the reason I quoted your post is because I dislike its message. Your follow-up post is more of the same.
Here we have an OP that is uncertain about whether forgetting memorized formulas might be a problem in the future.
And the response is basically that there is 'something wrong with the OP' and that he 'didn't learn what he was supposed to'.
How does that help?
I believe it's the wrong message to send to any OP.
It's destructive and doesn't add anything. The OP already knows that it may be a problem that he's forgetting memorized formulas.
The real question is what that means, and how the OP might deal with it.

 

[Mark44]

I see. So you're not really looking for advice. You're looking for validation.

Here we have an OP that is uncertain about whether forgetting memorized formulas might be a problem in the future.

There's some posting history by the OP, @I like Serena, that you might be unaware of, in which both V50 and I have participated. Several of the threads appear at first glance to be asking for advice, but if you read farther in the thread, they seem to be more about asking for validation. The OP started two threads (one of which was deleted by a mod) in which he opined that there should not be homework assigned in high school math classes, and that all work assignments should be done during class time. The reasoning behind this opinion was that when high school students get home, they play video games or otherwise socialize instead of doing the assigned work.

 

[Vanadium 50]

I dislike its message

Of course you do. "You didn't learn the material" is not something anyone likes to hear. People don't like to say it either. But the alternative, telling someone that they did learn the material when they didn't is worse. I maintain that if you need a formula sheet to determine the slope of a line, you haven't learned the material. Saying you have may temporarily boost your self-esteem, but doesn't help you learn.

 

[FactChecker]

Most of mathematics is extremely cumulative. Practically every formula you see in algebra, trig, and calculus will be used over and over in combinations in later classes. If you don't have them by memory, you will never survive. That being said, you should not confuse formulas that you need to know from memory with exercises that are example uses of the formulas. You do not need to know the latter by memory.

 

[Apple_Mango]

There's some posting history by the OP, @I like Serena, that you might be unaware of, in which both V50 and I have participated. Several of the threads appear at first glance to be asking for advice, but if you read farther in the thread, they seem to be more about asking for validation. The OP started two threads (one of which was deleted by a mod) in which he opined that there should not be homework assigned in high school math classes, and that all work assignments should be done during class time. The reasoning behind this opinion was that when high school students get home, they play video games or otherwise socialize instead of doing the assigned work.

I was the one who told the mod to delete one of my thread. The thread was essentially a repeat of my homework thread. I didn't realize the fact that my deleted thread was a repeat of my homework thread so I told a mod to delete it. Quite frankly, I don't see why it's bad to ban math homework in high-school. Maybe if people were forced to do their math homework in class, maybe people will get to get to cal 1 by the time they get to their last year of high-school.

 

[Apple_Mango]

Most of mathematics is extremely cumulative. Practically everything formula you see in algebra, trig, and calculus will be used over and over in combinations in later classes. If you don't have them by memory, you will never survive. That being said, you should not confuse formulas that you need to know from memory with exercises that are example uses of the formulas. You do not need to know the latter by memory.

Yes, I started to notice this in my Algebra one class I had half an hour ago.

 

[symbolipoint]

...Quite frankly, I don't see why it's bad to ban math homework in high-school. Maybe if people were forced to do their math homework in class, maybe people will get to get to cal 1 by the time they get to their last year of high-school.

Very poor sense!

 

[Apple_Mango]

Very poor sense!

How about this. When they get to college, they'll be off on their own and then math homework will be assigned.

 

[symbolipoint]

How about this. When they get to college, they'll be off on their own and then math homework will be assigned.

Also poor sense. This subtopic detracts from the main idea of the topic about "does it matter forgetting formulas".

 

[I like Serena]

There's some posting history by the OP, @I like Serena, that you might be unaware of, in which both V50 and I have participated. Several of the threads appear at first glance to be asking for advice, but if you read farther in the thread, they seem to be more about asking for validation. The OP started two threads (one of which was deleted by a mod) in which he opined that there should not be homework assigned in high school math classes, and that all work assignments should be done during class time. The reasoning behind this opinion was that when high school students get home, they play video games or otherwise socialize instead of doing the assigned work.

Of course you do. "You didn't learn the material" is not something anyone likes to hear. People don't like to say it either. But the alternative, telling someone that they did learn the material when they didn't is worse. I maintain that if you need a formula sheet to determine the slope of a line, you haven't learned the material. Saying you have may temporarily boost your self-esteem, but doesn't help you learn.

I've been a private tutor for a long time now, and the one thing I've learned is to never ever "put down" a student - no matter his or her attitude.
Or more accurately, to convince those students that regardless of all the teachers that have "put them down", that they shouldn't let it get to them - and that is hard!
As I see it, teaching students confidence in themselves (and perhaps a sense of purpose) is what ultimately makes them recover and finally succeed. It has much more impact than any knowledge or experience with the material at hand that I can pass on to them. We talk about it, and they appreciate my knowledge and experience, but once they get into it, it becomes irrelevant and they do everything themselves as they should. (I still have to teach them how to deal with fractions and such though. ;))

So forgive me for reacting to comments that I consider pretty close to "putting down" and that are actually against PF rules:

'snide remarks or phrases that appear to be an attempt to "put down" another member; and other indirect attacks on a member's character or motives.'​

 

[Moayd Shagaf]

Most Formulas is that you need to Understand It and explain it, there a very little equation that you must remember, but I think if you memorize the basic equation, then you can derive all other equations.

 

[I like Serena]

Most Formulas is that you need to Understand It and explain it, there a very little equation that you must remember, but I think if you memorize the basic equation, then you can derive all other equations.

Just make a drawing, and most formulas will fall into place.

 

[Apple_Mango]

Yes, this is helpful. thanks. I am done with this thread.

 

[Dr. Courtney]

Yes, this is helpful. thanks. I am done with this thread.

Perhaps. But I doubt you are done with polemics seeking to validate your unwillingness to master the tasks put before you.

I had great success in school, because (at least for the purposes and duration of a course), I didn't question whether the professor's way of teaching and assessing learning was the best. I treated that question as "above my pay grade" and simply worked as hard as I could to master the material set before me - according to how the prof was teaching and assessing. After the semester, I often reflected about what I liked and didn't like. But my view was shortsighted and more about my comfort than my learning, because I didn't know what academic and professional challenges lay ahead. But my professors did. Much later I realized the wisdom in the approach of my professors, because I realized how meeting their requirements had developed in me the abilities to succeed in graduate school and the working world. My goal when I became a teacher was at least to do for my students what my professors had done for me - impart learning with true value.

One valuable way to look at college coursework is that you will take (approximately) 40 classes and have 40 different bosses. Just as in the working world you will have to please a boss, your job in a college course is to please each professor as the boss for your work in their class. Stop thinking about whether what they ask of you is right or reasonable. Figure out how to please them and do it.

If you can learn to please the 40 bosses you'll have in college, you'll be well prepared to figure out and please the bosses you'll have in the working world.

 

[Vanadium 50]

So forgive me for reacting to comments that I consider pretty close to "putting down"

I don't see "you didn't learn the material" is "putting down". I would go a step further and say that telling a student that they have mastered the material when they have not interferes with their learning process, both short term and long term. Short term because they move on before they have mastered the material, and long term since knowledge is cumulative and they are starting on a shaky foundation.

 

[Mark44]

"You didn't learn the material" is not something anyone likes to hear. People don't like to say it either. But the alternative, telling someone that they did learn the material when they didn't is worse.

I've been a private tutor for a long time now, and the one thing I've learned is to never ever "put down" a student - no matter his or her attitude.
Or more accurately, to convince those students that regardless of all the teachers that have "put them down", that they shouldn't let it get to them - and that is hard!
As I see it, teaching students confidence in themselves (and perhaps a sense of purpose) is what ultimately makes them recover and finally succeed.

I don't see V50's comment as a putdown, but, rather, a realistic appraisal of this situation.

This is post #43 in what should have been a very short thread, something like the following:

Q: Does it matter if I forget the formulas?
A: It depends on which formulas you're talking about. Can you be more specific?
Q: Does it matter if I forget the formula for the slope of a line after two weeks?
A: Yes, very much. That's a formula that you should memorize.
---- End of thread​

Instead, we have an OP who is under the impression that having a sheet with formulas on it is the same as knowing those formulas. I'm all for promoting students' self-confidence, but that confidence has to be based on actual achievements, or it's meaningless; e.g., giving everyone on a team an award for "pariticipation.".

 

[vela]

I disagree. If one didn't learn the material, then one wouldn't be able to do solve the equation in the first place.

There are different levels of understanding, and they require different levels of mastery.

It's easy enough to teach students a recipe for finding the slope of a line: identify two points, plug the numbers into the right place in the formula, and calculate the result. Students can do this without any understanding of what the numbers mean and what the slope represents. This would rank as the lowest level of understanding. This kind of knowledge is the most fragile since if you forget the recipe or formula, you're screwed.

The next level up of understanding requires that students know and can explain what the numbers represent. They can explain why a horizontal line has 0 slope; they know why a line of slope 2 is steeper than a line of slope 1; they understand what the sign of the slope represents; and so on. If you have at least this level of understanding of slope, you don't really need to memorize a formula anymore. Knowing how to calculate the slope becomes "obvious" from one's understanding of the concept.

In all likelihood, you are expected to reach at least this second level of understanding of slope in Algebra I. It may have simply been an unfortunate choice of example on your part, but what people in the thread are saying is slope is such a basic concept that if you truly can't remember how to calculate the slope of a line, you very likely didn't reach the level of understanding of the concept that you needed to.

That said, learning isn't a linear process. The first time you learn about a concept, it's not unusual to still have some gaps in your knowledge. You may forget certain details and have to relearn them. It's often during this relearning process that you achieve higher levels of understanding. You're not starting from ground zero, and some aspects you may have only memorized earlier now start to make sense the second time around so you no longer have to rely only on memorization.

The trick is to achieve an acceptable level of understanding on the first go-around. You don't want it to be so superficial that you can't remember the material a week or two later, but it's typically not a disaster if you don't achieve 100% mastery either. You can fill in the holes as you go.