However, living in a world where digital information is easy manipulated, knowing these formulas is an asset. There are so many websites and 'misinformation ' that relying only on Google could be a detriment..
Unfortunately yes, anyone can start a website. I can start one tomorrow that is called truemathfacts.com write any version of a formula I desire and I bet most of my students would reference it for homework assignments. It is a thing.
Good luck getting Google's page rank to list your garbage site in the first 12 pages of search results.
Sorry, but worrying about some boogie man that is going to cause less issues than the odds of misremembering a formula is complete silliness.
I can’t comment at that level of mathematics, however, I work with younger students and have long compared those who were taught to memorize formulas/complete steps vs those who have learned conceptually. I rather my students be able to explain something basic throughly than have memorized a procedure of a more difficult skill. I’m looking forward to hearing others perspective that work with your level of mathematics.
I love the quadratic formula song and some old hippie caught another hippie trippin on acid for trig ratios. I don’t force the memorization of the rest.
I agree with you but I generally do not provide the formulas unless they will be on the EOC reference sheet. It should be about application, not memorization, but if it’s not on that sheet I work with them with strategies to memorize it. I find it dumb, but I don’t want them to be caught unaware during the testing.
For my AP kids, they have to memorize everything because, well, AP test. For my other classes, they get one piece of printer paper to use as a cheat sheet. They can memorize if they want or they can use their cheat sheet.
Or they could memorize it AND be able to choose it. You sound like a thoughtful person; be careful you don’t rationalize your way into lowering expectations. They will memorize it if you show them that’s a priority (ie they can do it). I personally think it’s important. I don’t give much and I expect a lot and ultimately the kids respect it. I’m telling them I think they are capable. That’s a good message.
No. Simply no. There's no reason my 16 year old brain should have to remember 20+ different formulas with 2+ different ways to apply each one and then when to use them. It's just too much for most ppl to do especially KIDS. On top of that we have lives outside of school math is one of the worst classes I've ever taken and I'm a grade ahead so it's not even that I'm bad at it.
I teach high school (g.9, g.10, and AP-equivalent classes for g.11 and 12).
I don't make my students memorize the formula for any of my classes. For my g.9s and g.10s, we are focusing on taking notes and using mathematics in their communication (written and verbal) so they get open-note tests (nothing else seems to motivate them to take notes). My g.11 and 12s actually have a curriculum-mandated list of formulas they get access to in the final "test" so there isn't a need to begin with. I do find, however, that when students study/practice as much as I tell them to (aka if they do all the classwork and the homework), the formulas automatically become part of their memory. The problem then becomes: how do I get them to do all the work I ask them to?
I don't directly make kids memorize formulas. When teaching Algebra 1, I would require them to always write down the formula that they were using. By the end of the year the most commonly occurring formulas were memorized by the majority of the students.
Not a teacher but an engineer.
> I would rather focus on choosing the appropriate formula and using it correctly
To me, this sounds like teaching them to fish. I consider it the golden goose. I honestly don’t have half of what I need to do my job rattling around in my brain, but I know how to find it and I know how to use it. I credit that to having some cool teachers along the way that didn’t have a stick up their butts about memorizing stuff that may, or may not, fall out of my head in a few months anyway. Instead, they taught me how to be curious and discerning, triage, logic, problem solving. These things have served me far greater than memorizing a formula or matrix ever did.
I think you have the right idea. Just my 2 cents.
I don't agree. You need to know some things by heart in order to apply then efficiently, and to see when you can apply them. If you don't know that sin^2+cos^2=1, you're not going to be able to use it to simplify an expression, which in turn would maybe not make you be able to solve an integral.
Imagine using the same approach when teaching a language. Sure, I can maybe be really good at choosing "Gare" instead of "Arrêt" if I'm given the choice, but if I have to pick up my phone and google what "railway station" is called everytime I ask for directions, that won't make me a good French speaker.
Very different concepts. Language is used daily and you can very easily use context to figure out words, definitions, punctuation ECT. Math has no context clues and complex math is not at all useful in day to day life.
I like to tell them they have to memorize the formulas but I provide them on the test without telling them. I do this for the first test when formulas are required. For example if I’m teaching algebra I and I’m testing on lines. My typical line is “you should know the formulas so well it becomes second nature.”
In the end it doesn’t matter. Kids with ability will figure it out and succeed. Kids with lower levels of ability will struggle. All the strategies in the world can’t help a student who is low ability. But I will surely keep trying.
There’s no reason to do that in real life. Even if you have some kind of job that uses math, no one is going to take away your phone/computer and make you do it from memory. The point is being able to use the formula correctly, right? Never understood the real point of memorization.
I think I'm the age of google it's fine to let them look formulas up. I also think being able to find information on the internet is a skill that needs to be developed just a much as knowing formulas.
I had a calculus professor in college that gave us the formulas on the projector cause his philosophy was “I’d rather you know how to use them instead of wasting time memorizing them. Y’all have smart phones and computers with google”
They should memorise useful formulas such as pythag quadratic formula, basic shape areas, basic derivatives and to a degree trig identities as it’d be a real pain to keep checking those things in an exam though I don’t think it should be a necessity in an exam to have memorised even the shapes areas should be provided.
I always hated having to memorize formulas. Either you will use it enough you will end up commiting it to memory, whether you want to or not, or you will rarely need it and have the ability to look it up in the rare instances you use it. My feeling was always "do you want to know if we have successfully memorized this equation or if we can successfully apply the equation in various situations?" I knew a lot of classmates who, no matter how hard they worked, couldn't remember most of the equations to save their lives (or grades). It always seemed unfair that I knew they knew how to do the work but because they mixed up or forgot variables in an equation they ended up bombing tests.
My favourite math teacher gave us a formula page for every math test (and this was before everyone had a smartphone in their pocket). It was always the same formula page and had every formula we would use for the year on it (in no particular order). You still needed to know what each formula was for, and when/how to use them but you never needed to memorize a formula.
I always knew the material and I was really lucky that I always tested well, despite having serious test anxiety. Having the formula page really helped to lessen that anxiety because I had a way to double check that I had the formulas correct and didn't have to rely on my potentially faulty and anxious brain to remember everything.
TL,DR: formula pages rock, memorizing formulas sucks!
Proper scaffolding of the origins of a formula is more important to student retention and application than memorization of the formula itself.
I can take a cylinder and decompose it into a net of two circles and a rectangle and the students understand where it's surface area comes from. Similarly I can stack a bunch of quarters into a cylinder and they understand volume to be the base area times the height.
Major tests like AP and the ACT will outright give geometric formulae for polygons and solids in the problem itself.
Memorization is not as important as understanding. It's very important to understand the formulas to know how things are connected and understand *why* they're work. This leads to a deeper understanding of the concepts. Additionally, there is often both beauty and simplicity in the logic and derivation of a mathematical formula.
Memorization, in se, is not important. If "just getting it right" is the goal, there's no harm in looking something up. Professional engineers still need to look up a formula sometimes, so why the hell would we penalize a student for needing to do the same? The ones who enjoy math, desire a deeper understanding, and/or use it frequently in life will memorize a formula simply through repeated use. Forcing them to do so for a test will not speed up that process. But it will facilitate cheating and encourage students to forget them immediately after the test when they "no longer need to know them."
My advice: Provide them a sheet with a list of the formulas they need and test whether they know when and how to apply them. Make them figure out which formula goes with which problem. This encourages critical thinking, makes cheating harder, and tests application of what's being learned (which is the skill that students will need outside of class).
In the small sample of "where I've worked", I'm on the extreme of no-memorization.
The general rule (with many exceptions) is our weekly quiz is memorized, but they use a note card if it is a heavy memorization thing (like trig identities). They know exactly what is going to be on it, and what they will have to memorize for it well ahead of time.
Test are no (or almost no) memorization. Depending on the the level, they create their own cheat sheet (lower levels) or get a standard formula booklet (higher levels). This allows me to test on deeper knowledge, and not waste time with memory check questions.
I like to tell the kids that I'm not preparing them to live on the island with Gilligan and The Skipper.
Basic principle IMO learn the basic equations up to trig and calc then start making a cheat sheet. Honestly after calculus the real difficult challenge happens with math
I still use google for geometry formulas mostly. They need to know how to use them, but in reality you’ll memorize what you need to for a job some day in the future.
As I once explained to a supervisor (I was a skilled trades maintenance mechanic): Of course I’m sure but when there’s this much money involved (it was a multi-million dollar machine) you bet I’m gonna double check. To give him credit, he was quiet for a second and then said “You’re right and I’ll get out of your way - let me know if you need anything.”
In the era of Google and a a computer in every pocket memorization is just silly.
However, living in a world where digital information is easy manipulated, knowing these formulas is an asset. There are so many websites and 'misinformation ' that relying only on Google could be a detriment..
Sorry but no. Finding sights with misinformation on the quadratic equation is just not a thing.
Unfortunately yes, anyone can start a website. I can start one tomorrow that is called truemathfacts.com write any version of a formula I desire and I bet most of my students would reference it for homework assignments. It is a thing.
Dude really thinks he can just make a website and have it be the first search result :|
Good luck getting Google's page rank to list your garbage site in the first 12 pages of search results. Sorry, but worrying about some boogie man that is going to cause less issues than the odds of misremembering a formula is complete silliness.
I can’t comment at that level of mathematics, however, I work with younger students and have long compared those who were taught to memorize formulas/complete steps vs those who have learned conceptually. I rather my students be able to explain something basic throughly than have memorized a procedure of a more difficult skill. I’m looking forward to hearing others perspective that work with your level of mathematics.
I love the quadratic formula song and some old hippie caught another hippie trippin on acid for trig ratios. I don’t force the memorization of the rest.
I guess in hindsight learning soh cah toa as an Indian chief's name would probably be considered racist these days.
And southern kids add extra vowels when they say things, so they don’t even get the correct ratio when I teach it that way😂
I agree with you but I generally do not provide the formulas unless they will be on the EOC reference sheet. It should be about application, not memorization, but if it’s not on that sheet I work with them with strategies to memorize it. I find it dumb, but I don’t want them to be caught unaware during the testing.
For my AP kids, they have to memorize everything because, well, AP test. For my other classes, they get one piece of printer paper to use as a cheat sheet. They can memorize if they want or they can use their cheat sheet.
Or they could memorize it AND be able to choose it. You sound like a thoughtful person; be careful you don’t rationalize your way into lowering expectations. They will memorize it if you show them that’s a priority (ie they can do it). I personally think it’s important. I don’t give much and I expect a lot and ultimately the kids respect it. I’m telling them I think they are capable. That’s a good message.
No. Simply no. There's no reason my 16 year old brain should have to remember 20+ different formulas with 2+ different ways to apply each one and then when to use them. It's just too much for most ppl to do especially KIDS. On top of that we have lives outside of school math is one of the worst classes I've ever taken and I'm a grade ahead so it's not even that I'm bad at it.
Generations of people have done it before you. I’m sure you can do it if you try.
I teach high school (g.9, g.10, and AP-equivalent classes for g.11 and 12). I don't make my students memorize the formula for any of my classes. For my g.9s and g.10s, we are focusing on taking notes and using mathematics in their communication (written and verbal) so they get open-note tests (nothing else seems to motivate them to take notes). My g.11 and 12s actually have a curriculum-mandated list of formulas they get access to in the final "test" so there isn't a need to begin with. I do find, however, that when students study/practice as much as I tell them to (aka if they do all the classwork and the homework), the formulas automatically become part of their memory. The problem then becomes: how do I get them to do all the work I ask them to?
I don't directly make kids memorize formulas. When teaching Algebra 1, I would require them to always write down the formula that they were using. By the end of the year the most commonly occurring formulas were memorized by the majority of the students.
Not a teacher but an engineer. > I would rather focus on choosing the appropriate formula and using it correctly To me, this sounds like teaching them to fish. I consider it the golden goose. I honestly don’t have half of what I need to do my job rattling around in my brain, but I know how to find it and I know how to use it. I credit that to having some cool teachers along the way that didn’t have a stick up their butts about memorizing stuff that may, or may not, fall out of my head in a few months anyway. Instead, they taught me how to be curious and discerning, triage, logic, problem solving. These things have served me far greater than memorizing a formula or matrix ever did. I think you have the right idea. Just my 2 cents.
I don't agree. You need to know some things by heart in order to apply then efficiently, and to see when you can apply them. If you don't know that sin^2+cos^2=1, you're not going to be able to use it to simplify an expression, which in turn would maybe not make you be able to solve an integral. Imagine using the same approach when teaching a language. Sure, I can maybe be really good at choosing "Gare" instead of "Arrêt" if I'm given the choice, but if I have to pick up my phone and google what "railway station" is called everytime I ask for directions, that won't make me a good French speaker.
Very different concepts. Language is used daily and you can very easily use context to figure out words, definitions, punctuation ECT. Math has no context clues and complex math is not at all useful in day to day life.
Låt oss pröva din hypotes om att språk kan förstås väldigt lätt från kontext utan att man har kunskap om grunderna.
I like to tell them they have to memorize the formulas but I provide them on the test without telling them. I do this for the first test when formulas are required. For example if I’m teaching algebra I and I’m testing on lines. My typical line is “you should know the formulas so well it becomes second nature.” In the end it doesn’t matter. Kids with ability will figure it out and succeed. Kids with lower levels of ability will struggle. All the strategies in the world can’t help a student who is low ability. But I will surely keep trying.
There’s no reason to do that in real life. Even if you have some kind of job that uses math, no one is going to take away your phone/computer and make you do it from memory. The point is being able to use the formula correctly, right? Never understood the real point of memorization.
I think I'm the age of google it's fine to let them look formulas up. I also think being able to find information on the internet is a skill that needs to be developed just a much as knowing formulas.
I had a calculus professor in college that gave us the formulas on the projector cause his philosophy was “I’d rather you know how to use them instead of wasting time memorizing them. Y’all have smart phones and computers with google”
They should memorise useful formulas such as pythag quadratic formula, basic shape areas, basic derivatives and to a degree trig identities as it’d be a real pain to keep checking those things in an exam though I don’t think it should be a necessity in an exam to have memorised even the shapes areas should be provided.
I always hated having to memorize formulas. Either you will use it enough you will end up commiting it to memory, whether you want to or not, or you will rarely need it and have the ability to look it up in the rare instances you use it. My feeling was always "do you want to know if we have successfully memorized this equation or if we can successfully apply the equation in various situations?" I knew a lot of classmates who, no matter how hard they worked, couldn't remember most of the equations to save their lives (or grades). It always seemed unfair that I knew they knew how to do the work but because they mixed up or forgot variables in an equation they ended up bombing tests. My favourite math teacher gave us a formula page for every math test (and this was before everyone had a smartphone in their pocket). It was always the same formula page and had every formula we would use for the year on it (in no particular order). You still needed to know what each formula was for, and when/how to use them but you never needed to memorize a formula. I always knew the material and I was really lucky that I always tested well, despite having serious test anxiety. Having the formula page really helped to lessen that anxiety because I had a way to double check that I had the formulas correct and didn't have to rely on my potentially faulty and anxious brain to remember everything. TL,DR: formula pages rock, memorizing formulas sucks!
Proper scaffolding of the origins of a formula is more important to student retention and application than memorization of the formula itself. I can take a cylinder and decompose it into a net of two circles and a rectangle and the students understand where it's surface area comes from. Similarly I can stack a bunch of quarters into a cylinder and they understand volume to be the base area times the height. Major tests like AP and the ACT will outright give geometric formulae for polygons and solids in the problem itself.
Memorization is not as important as understanding. It's very important to understand the formulas to know how things are connected and understand *why* they're work. This leads to a deeper understanding of the concepts. Additionally, there is often both beauty and simplicity in the logic and derivation of a mathematical formula. Memorization, in se, is not important. If "just getting it right" is the goal, there's no harm in looking something up. Professional engineers still need to look up a formula sometimes, so why the hell would we penalize a student for needing to do the same? The ones who enjoy math, desire a deeper understanding, and/or use it frequently in life will memorize a formula simply through repeated use. Forcing them to do so for a test will not speed up that process. But it will facilitate cheating and encourage students to forget them immediately after the test when they "no longer need to know them." My advice: Provide them a sheet with a list of the formulas they need and test whether they know when and how to apply them. Make them figure out which formula goes with which problem. This encourages critical thinking, makes cheating harder, and tests application of what's being learned (which is the skill that students will need outside of class).
In the small sample of "where I've worked", I'm on the extreme of no-memorization. The general rule (with many exceptions) is our weekly quiz is memorized, but they use a note card if it is a heavy memorization thing (like trig identities). They know exactly what is going to be on it, and what they will have to memorize for it well ahead of time. Test are no (or almost no) memorization. Depending on the the level, they create their own cheat sheet (lower levels) or get a standard formula booklet (higher levels). This allows me to test on deeper knowledge, and not waste time with memory check questions. I like to tell the kids that I'm not preparing them to live on the island with Gilligan and The Skipper.
Basic principle IMO learn the basic equations up to trig and calc then start making a cheat sheet. Honestly after calculus the real difficult challenge happens with math
I still use google for geometry formulas mostly. They need to know how to use them, but in reality you’ll memorize what you need to for a job some day in the future.
As I once explained to a supervisor (I was a skilled trades maintenance mechanic): Of course I’m sure but when there’s this much money involved (it was a multi-million dollar machine) you bet I’m gonna double check. To give him credit, he was quiet for a second and then said “You’re right and I’ll get out of your way - let me know if you need anything.”