Should Algebra Be Required At Community Colleges?

[PhotonSSBM]

The question in the OP is equivalent to, "Should the math requirements in college be lower than the college prep math requirements in most high schools?"

It is also equivalent to, "Just because many high schools are dumbing down math education, should colleges dumb it down also?"

In light of this, it is surprising to find so many shills for the further dumbing down of math education in the US. What next? Remove Algebra 1 and Algebra 2 from the high school college prep sequences? Remove algebra from the ACT because it is a barrier to student success? Stop worrying about all the math teachers passing students in high school algebra courses who are nowhere near proficient? Stop including so many problems that require real high school algebra skills in introductory physics courses?

What do you propose as a solution to the problem if not replacing intermediate algebra with something else to, as you suggested, work out the mind? Or do you believe these numbers for CC graduation/transfer rates to be sustainable/acceptable?

 

[Auto-Didact]

The question in the OP is equivalent to, "Should the math requirements in college be lower than the college prep math requirements in most high schools?"

It is also equivalent to, "Just because many high schools are dumbing down math education, should colleges dumb it down also?"

In light of this, it is surprising to find so many shills for the further dumbing down of math education in the US. What next? Remove Algebra 1 and Algebra 2 from the high school college prep sequences? Remove algebra from the ACT because it is a barrier to student success? Stop worrying about all the math teachers passing students in high school algebra courses who are nowhere near proficient? Stop including so many problems that require real high school algebra skills in introductory physics courses?

I feel again this is unnecessarily far too confrontational a view, focusing again largely on the luxury problem that without algebra one is handicapping students to properly be able to do our most beloved subject, instead of focusing on the larger societal problem, namely that there needs to be an alternative way of dealing with the situation that most people do not want or feel they need algebra in life per se, a position which the educational system acknowledges to some extent, but one which they seem to be incapable of meeting head on by adequately offering to teach other mathematical subjects instead.

It goes without saying but most people do not plan to nor enter into STEM, let alone specifically physics or mathematics. If one does not plan on entering into STEM or one of the practical sciences (mostly public servants such as health care and CSI) there is a case to be made that mastery of elementary algebra is not an essential skill in life. Empirical research has shown well and above that most people are actually capable of getting by fine in life without it. Hell, there are even a substantial amount of people who aren't able to read yet still are able to get by in life, sometimes even fully unnoticed by others (NB: contrary to popular opinion this requires some considerable reasoning skills).

Research has also shown that both mathematicians and non-mathematicians naturally tend to be more proficient at some particular mathematical field or point of view, instead of generally being 'mathematically strong or weak'. This is obvious really: having a knack for say tensor calculus says absolutely nothing about having an a priori knack for set theory as well. The fact that we act otherwise today is because we confound the entire question by artificially making it only possible for a select few to learn these skills and then stare ourselves blind on them.

The select few are of course those capable of passing the traditional teaching strategy, while anyone else regardless of their natural skills aren't even considered. The select few tend to be called mathematicians, but the point here to take away is exactly one need not be a mathematician to be able to do some mathematics, and the existence of physics as a separate field of study and of physicists with their own particular flavor of mathematics is the perfect example of this. There is therefore a case to be made that perhaps elementary algebra could perhaps be replaced with some other mathematical subject, and if deemed absolutely necessary down the road, be developed from the point of view of this other perspective or just learned later down the road, just as how we tend to teach these other subjects to a select few much later down the road.

This would first and foremost likely exacerbate any naturally occurring differences in different mathematical skill sets among children; one is for example no longer broadly labeled as 'mathematically weak' if one happens to be shown at the same time to be very skilled at say logic or graph theory. The chances that one has no mathematical strengths at all is of course a possibility albeit a somewhat unlikely one; this would most likely be indicative of a learning error, teaching error or perhaps both. Moreover, I severely doubt this would significantly decrease the number of applicants to STEM or mathematics specifically, and I'd even wager that it might actually increase the number of applicants to interdisciplinary fields with unexplored but strong mathematical overtones which are at the present moment still in their infancy stages.

This really is a behavioral hypothesis to be tested in practice of how things actually are, not merely philosophised about in regard to some ideal fantasy of how we would like things to be. Any further questions of the utility of teaching such widely varying skill sets to different people and the possible effects thereof on future science, mathematics and society remain open questions which can only be answered by carrying out large controlled educational trials and comparing different teaching strategies with respect to different goals. In any case, it should be patently clear that a 'one size fits all' approach is far from the optimal strategy to adhere to when teaching elementary mathematics, especially when the consequences of this are so dire for all levels of society.

 

[Dr. Courtney]

What do you propose as a solution to the problem if not replacing intermediate algebra with something else to, as you suggested, work out the mind? Or do you believe these numbers for CC graduation/transfer rates to be sustainable/acceptable?

Your errant assumption is that most of those who do not become proficient in algebra can't become proficient in algebra. Having taught high school algebra, college algebra, and algebra-based physics (high school and college), my observation is that most students willing to make an honest effort at the homework every day, CAN become proficient in algebra. I've seen this personally from high schools in the rural south to community college in the midwest. If you let student's claim they "can't" and provide alternate pathways, they won't. Take away the alternate pathways, and suddenly most are able to do it when they DECIDE to work hard enough.

And for those who either cannot or will not become proficient in the algebra that is universally required on college prep tracks in US high schools, their pathways should then be limited to education and career options that do not require college degrees. As soon as you get serious about saying, "Your college dreams are over unless you learn algebra" most students who truly aspire to college will learn algebra. The battle is one of the will, not of the abilities.

 

[PhotonSSBM]

Your errant assumption is that most of those who do not become proficient in algebra can't become proficient in algebra. Having taught high school algebra, college algebra, and algebra-based physics (high school and college), my observation is that most students willing to make an honest effort at the homework every day, CAN become proficient in algebra. I've seen this personally from high schools in the rural south to community college in the midwest. If you let student's claim they "can't" and provide alternate pathways, they won't. Take away the alternate pathways, and suddenly most are able to do it when they DECIDE to work hard enough.

And for those who either cannot or will not become proficient in the algebra that is universally required on college prep tracks in US high schools, their pathways should then be limited to education and career options that do not require college degrees. As soon as you get serious about saying, "Your college dreams are over unless you learn algebra" most students who truly aspire to college will learn algebra. The battle is one of the will, not of the abilities.

It's very good to hear that your experiences have led you to the conclusions in your first paragraph. Honestly, I was truly hoping that someone who taught at various levels of mathematics in the past would post here.

I do feel as though everything you said is true, and have for the course of the thread. My teaching experiences have led me to the same conclusions with respect to ability and willpower. But at the end of the day, I always go back to the numbers of my school and others that encouraged me to make this thread. So many fail, and so many give up, all because of math. We're already at a place where alternate pathways are non-existent. You have to learn algebra or drop out, and that drives the vast majority of CC students to failure (again, 72% for the school I tutored at).

Perhaps I'm giving these numbers more credit than they deserve. Maybe they are acceptable in some way. I'm just having a hard time rationalizing them and finding them acceptable. Which is one reason I made the thread. I can see that you do not believe there is a problem from the perspective of a student, but what would you say to a school with these issues. You've taught for decades. If California's CC system came to you and asked, "How do we fix this?" What would you tell them?

 

[Dr. Courtney]

If California's CC system came to you and asked, "How do we fix this?" What would you tell them?

Prosecute the high school teachers who pass these students in Algebra 1 and Algebra 2 for fraud and corruption. Put them in jail as the criminals they are: collecting their paychecks, not doing their job, and passing the students on to downstream situations where they will have a much harder time succeeding.

 

[Haelfix]

I just finished tutoring my fiance the entirety of middle school and high school math, which she hadn't practiced for a decade. As a student, bright as she may be, she was singularly unsuited for the subject and had all the usual red flags (fear of failure, predilection for putting of the hard work, desire to memorize instead of understanding etc). I of course would not let her do any of those things, and drilled her pretty harshly in the way that teachers refuse to do anymore in the US.

It wasn't pleasant for her, but in the end she just aced her university entrance exams and would have likely scored well on an advanced placement test for calculus. The whole exercise took 5 months, and about 2 hours a day.

The point is it really isn't that difficult, and I firmly believe that almost anyone can do it if they're instructed properly. We used to not allow students to get away with failure, and there is absolutely no reason why anything should have changed. Indeed if anything it's tremendously easier to learn new things in the Information Age . The only failure I can see is in the will of the instructors, and those administrators who contemplate ridiculous measures like the above.

 

[bhobba]

I live in Queensland Australia and thought I would give my perspective based on that.

We do it a bit differently here. Where I am is undergoing a bit of a change so I will describe how it was when I went through - it will be slightly different in future to bring us in line with the the other states of Australia.

First we start grade 1 at 5 - not 6 and finish grade 12 at 17 (the change underway is to start at 5.5 and finish at 17.5 ie increase it by 6 months).

We combine your algebra and geometry into one subject done over two years in grade 7 and 8 - but since we start a year earlier that would be your grade 6 and 7 in what you call middle school. We then do a combined algebra 2 and some pre-calculus in grade 9 and 10, but some private schools stop at grade 9 ie when you finish middle school. Also some of the better students are accelerated and finish then to start on calculus. This is to maximize year 11 and 12 results by doing it over 3 years instead of 2 while the better students do university math in year 12 ie at 16 years of age. In 11 and 12 we do a combined pre-calculus and calculus either as one subject (equivalent to you calculus AB) or as two subject equivalent to your BC plus a few extra things like beginning linear algebra, beginning Markov chins, some mechanics etc etc. Then at 17 they go to university, but since they have done what you in the US do in first year uni its only 3 year degrees here - we start with multi-variable calculus, differential equations etc first year. The best students do that in year 12 so they start on our second year math subjects when they go to uni at 17

So from our experience here we would say - what - middle school students do algebra here and calculus in the age group of your high school students. I, and I suspect most people here would be shaking their heads - you guys need a different more rigorous system - you should have well and truly finished with algebra by community college level - you should be doing calculus - and advanced calculus at that.

Now is calculus required to get a degree here? There is a big debate about that out here right now. It used to be required for most degrees because common subjects like Economics required it, but they have now dumbed it down so its now not necessary. Such a pity.

Guys over there in the US - wake up to yourself - finish algebra and geometry in your middle school and do pre-calculus and calculus at HS. Community college is not the place for it.

Thanks
Bill

 

[symbolipoint]

Should Algebra be required for A.A. Degree from Community Colleges?
Yes. AT LEAST through Intermediate Algebra.
Why? Basic finance, common citizen & consumer knowledge such as Richter Scale (a measure of earthquales), more assured understanding of linear interpolation, momentary cost-purchase budgeting, constant rates applications (which often form either linear equations or quadratic equations); too many other examples which other members may discuss.

 

[cristo]

Guys over there in the US - wake up to yourself - finish algebra and geometry in your middle school and do pre-calculus and calculus at HS. Community college is not the place for it.

I think it's important to keep in mind the mission statement of a community college. As opposed to a four year university, a community college aims to provide affordable education for anyone who seeks it. The student body is diverse, and does not only include students fresh out of high school, but also older students who perhaps dropped out of high school, or who the public school system failed. It includes parents, perhaps single parents who were unable to complete their schooling but are wanting to return to obtain an education. So to say to "wake up" is really missing the main point of a community college.

So the community college has a diverse student body, which can be essentially split into traditional and non-traditional students. The former are looking to get a jump on their four year degree at a lower price, while the latter are looking for education that they should have got at an earlier age, but for whatever reason life prevented that. Having both sets funneled through the same algebra sequence is, in my opinion, a problem. How to fix this problem is, of course, a non-trivial question.

 

[bhobba]

or who the public school system failed.

Yes - that's a big problem here as well.

We have a school taking an entirely different approach because of it with very good results:
https://tc.vic.edu.au/

Everyone is on an individual learning plan. You leave when you are ready and its total flexible learning. No university entrance - they have arrangements with universities that you go when they think you are ready - that may be 15 or 20 - it doesn't matter - it's when you are ready:
http://www.theage.com.au/victoria/school-dumps-cutthroat-vce-ranking-20160226-gn4gk0.html

Here in Aus HS starts grade 7 - some start university entrance type subjects right from the start and leave in 3-4 years. Others take longer thn the usual 6 years - while others never go, instead doing what's called TAFE (that's equivalent to your Community College) and prepare for trades, shop assistants etc - you know ordinary everyday jobs you don't need a university degree for but of course in some cases like being an electrician it won't hurt. My father was a qualified electrician and had an engineering degree (the reason why is a bit complex to do with silly regulations that have since gone away requiring to do any work on stuff with voltages greater than some voltage you need to be a qualified electrician - engineers were not considered qualified electricians)

They actually bypass grade 7 and go straight to grade 8. Most have no issues and when finished have done the equivalent of your geometry and algebra. From that point on they do what they feel like. You cannot progress from that grade (called it's foundation year) until you have passed it. Some are so good they skip it by passing subjects more advanced than grade 8 while some need 2 or 3 years to do it - but everyone must do it and pass it - it's not negotiable. You can't leave that school until you have mastered the basics and algebra, correctly, is considered a basic. Sure they may only rarely use it if they want to be say a pharmacy assistant, which they can study for there, but algebra teaches you sound thinking practices of breaking a problem into chunks you can write equations for as well as some pretty basic financial things they will surely use later eg understanding why if you take out long loans you end up paying much much more than short term ones.

To me its much more rational approach than trying to correct these deficiencies at what you call CC and we call TAFE - in fact TAFE is integrated into HS for those that want that path.

Thanks
Bill

 

[vela]

I live in Queensland Australia and thought I would give my perspective based on that.

I'm curious. A major part of the problem in the US is the public's attitude toward math. Here it's acceptable to fail, and people will often brag about their inability to do math. Do you face the same attitudes in Australia?

 

[bhobba]

I'm curious. A major part of the problem in the US is the public's attitude toward math. Here it's acceptable to fail, and people will often brag about their inability to do math. Do you face the same attitudes in Australia?

Most definitely not.

Everyone here knows its importance.

The only issue is taking advanced math in 11 and 12 ie calculus. That is falling dramatically because, as I said, common subjects even liberal arts students take, most notably economics, no longer requires calculus as a prerequisite. This means people tend to opt out - why - well its perceived as hard - but failing it when its compulsory in grades 1-10 is very frowned upon. They are trying to do something about it by giving bonus points in university entrance if you take it. Its not required, for example, in medicine, but unless you take it its doubtful without the bonus points you will have a high enough entrance score to get in.

That is for parents that actually care about education - as you probably know many don't regardless if its math, English, science or pretty much anything - that's a much bigger problem.

Thanks
Bill

 

[jfmcghee]

Prosecute the high school teachers who pass these students in Algebra 1 and Algebra 2 for fraud and corruption. Put them in jail as the criminals they are: collecting their paychecks, not doing their job, and passing the students on to downstream situations where they will have a much harder time succeeding.

It seems to me that this falls on the administration and government at least as much as on the negligent teachers. At my school it's not even up to the teachers if the student moves on, it's up to the score the student makes on the state required test. Of course then if the student doesn't pass they get endless opportunities to try again or even take a different, "equivalent" test, just so graduation rates stay acceptable. I'd lose my mind if I had to teach math. We lost half of our math department last year. It's no wonder lots of students go to post-secondary school with completely inadequate math preparation.

 

[Dr. Courtney]

It seems to me that this falls on the administration and government at least as much as on the negligent teachers. At my school it's not even up to the teachers if the student moves on, it's up to the score the student makes on the state required test. Of course then if the student doesn't pass they get endless opportunities to try again or even take a different, "equivalent" test, just so graduation rates stay acceptable. I'd lose my mind if I had to teach math. We lost half of our math department last year. It's no wonder lots of students go to post-secondary school with completely inadequate math preparation.

Then the power to fail students needs to be given back to the teachers, so that specific individuals can be held accountable if students are passed who are not proficient in the material.

 

[jfmcghee]

The teachers unions would sure try to stop that from happening. I still don't have a contract for the last school year because our bargaining unit can't do it's job, but if something like holding individual teachers accountable were to be proposed you can be sure they'd find a way to crush it. They also don't want to reward individual teachers for doing a good job, it has to be for everybody. I think this whole "let's treat everyone the same, let's not punish or reward anybody"- from the students all the way up speaks directly to the problem of the OP. The solution is simply to change the culture of the U.S. No big deal...

 

[bhobba]

Then the power to fail students needs to be given back to the teachers, so that specific individuals can be held accountable if students are passed who are not proficient in the material.

Without doubt - it should never reach the stage where you have to do algebra at CC - that should have been done at a much lower grade.

The school I mentioned I like the approach of has its foundation year. You MUST pass it even if it takes 3 or more goes before you progress to what they call their flexible learning environment and you can study whatever you like. They have the equivalent of CC (here in Aus called TAFE) at or close to the school and you can do that strand if you like or prepare yourself for university entrance - which as I pointed out is different - you go when your HS teachers think you are ready not based on what you call SAT etc or what we call ATAR. Universities are waking up that its a crock - success depends on factors like good study habits, ability to to individual research and self motivation rather than test scores - your HS teachers are the best judge of that and completing a year long research assignment in your chosen university field by yourself then being graded on it.

Thanks
Bill

 

[bhobba]

but if something like holding individual teachers accountable were to be proposed you can be sure they'd find a way to crush it.

I have mentioned it in similar threads before but Professor Hattie of the University Of Melbourne has researched exhaustively what works in education:
http://www.abc.net.au/tv/programs/revolution-school/#/divca4470761

He turned a school around from the bottom 10% to the top 25% as detailed in the documentary associated with the link above.

Its so simple - all he did was sit in on teachers lessons without warning and give them feedback. That's all that's needed. But of course teachers will have to change their ways. They deserve a big pay-rise for it - anyone would hate being under constant scrutiny like that so deserve to be compensated for it,

But the chances of teachers unions allowing it is zero. They would love, and in fact deserve, the big pay rise, but not what they would have to do to get it. Teachers unions in Australia have refused to pilot test the model further - instead they want what's called Gonsky over here to reduce class sizes etc - the usual stuff that Professor Hattie has shown has zero efffect on outcomes. How do they get away with it - the public is totally ignorant of the facts about education and simply say - spend more money:
http://www.abc.net.au/tv/programs/revolution-school/Summary_Survey_And_Research.pdf

Politicians are only too happy to cater to it to get reelected, so we end up with really bad waste in education spending - after all they want to get elected - not tell the electorate the truth.

We have met the enemy and he is us - Pogo.

Thanks
Bill

 

[thejosh]

The truth is we live in a world that is extremely competitive and quite frankly the reason math is such a requirement is often that the challenge that maths provides sifts out the best people for the job, ask yourself these questions:
1.If everyone could get a degree, would anyone value it?
2.Why do academic requirements keep steadily rising?
3.Why is it that universities accept a handful of the TOP scholars?
Once you answer some of these questions you'll begin to realize that the reason some of these carrier barriers are there is for the very purpose of insuring the best of the best are the ones that make it through.
Not a very nice thought is it?
I know it isn't but the truth is the truth.

 

[olivermsun]

The truth is we live in a world that is extremely competitive and quite frankly the reason math is such a requirement is often that the challenge that maths provides sifts out the best people for the job, ask yourself these questions:

How do maths sift out the "best" people for the job? By grades? Testing? There's a lot more to being good at a job (or in life) than grades or test scores in math.

1.If everyone could get a degree, would anyone value it?

That's like asking why individuals have value even though everyone is an individual. Or arguing that food would no longer be valued if everyone had enough to eat.

 

[symbolipoint]

The truth is we live in a world that is extremely competitive and quite frankly the reason math is such a requirement is often that the challenge that maths provides sifts out the best people for the job, ask yourself these questions:
1.If everyone could get a degree, would anyone value it?
2.Why do academic requirements keep steadily rising?
3.Why is it that universities accept a handful of the TOP scholars?
Once you answer some of these questions you'll begin to realize that the reason some of these carrier barriers are there is for the very purpose of insuring the best of the best are the ones that make it through.
Not a very nice thought is it?
I know it isn't but the truth is the truth.

Point #1: Good implication.

Point #2: Maybe some standards are rising. Are they really all rising? Or just some of them?

Point #3: Wrong assumption or presumption. Anyone who is qualified and has secured the funding can be accepted to a university; maybe not all possible universities, but somewhere, at least some state or local one. One way to ensure qualification is to start in low-gear at a community college, rev-up a bit, and transfer to chosen university.

 

[thejosh]

@olivermsun I'm sorry if that's what you think but I strongly beg to differ, we may say things like this but I would like you to list Universities that accept students without any mathematical qualification, there is little or no colleges and Universities that would do that, with this in mind @symbolipoint I am sorry I was not as clear as I should have been. What I was trying to put out is that Universities are inclined to accept the best students/scholars they can get their hands on, that is if the level of education they provide is high quality, and one of the main ways they can do this is by requiring a high achievment in one or more difficult subjects such as -yes you guessed it- maths.
As for standards rising a good and solid example is this- we know more than we did 10 years ago-right?
Therefore we cannot limit our requirements to what they knew 10 years ago-right?
Consider a doctor, even though he is a doctor already he should continually learn new things concerning the medical world in case let's say a new strain of pathogens breaks through, new diseases emerge with new cures and implications, disease epidemics such as, of late, ebola.
Now imagine our doctors refused to learn saying they already know enough or they do not need to learn more,
what would happen if multiple pathogens developed resistance to "old" cures?
MANY people would die.
We are forever becoming more knowledgeable therefore we cannot afford to leave old standards untouched.
​

 

[olivermsun]

@olivermsun I'm sorry if that's what you think but I strongly beg to differ, we may say things like this but I would like you to list Universities that accept students without any mathematical qualification, there is little or no colleges and Universities that would do that, with this in mind

What parts of my reply, specifically, do you differ on? I don't recall saying anything about Universities accepting students without any mathematical qualification.

As for standards rising a good and solid example is this- we know more than we did 10 years ago-right?
Therefore we cannot limit our requirements to what they knew 10 years ago-right?
...
We are forever becoming more knowledgeable therefore we cannot afford to leave old standards untouched.

It's true that we are accumulating ever more knowledge, it's doubtful that much of the undergraduate or even early graduate curriculum, especially in maths, has much to do with new stuff that has been discovered in the last 10 years.

Furthermore, testing for area-specific knowledge of stuff that has been discovered in the last 10 years isn't probably not the best way to identify the "top" candidates for, e.g., a given job. Even at a research level it's most often about the ability to learn new stuff or apply very basic stuff in novel ways.

 

[thejosh]

There's a lot more to being good at a job (or in life) than grades or test scores in math.

Wrong, maths replicates life itself by incorporating problems that need solutions, diverse and absolete numbers of solutions to the same question, perseverence in answering difficult tasks discoveries and let downs, for a person to do maths requires discipline and focus, no oliversun why do you think maths is so hard?A person who is capable of conquering maths is equipped with many of the traits required to do other difficult tasks and is able to execute job tasks with high standards.Why do you think having mathematical genius on your cv immediately sets you aside from the rest?Why do you think maths' students are in such high demand?

Even at a research level it's most often about the ability to learn new stuff or apply very basic stuff in novel ways.

And what better way than to see if a student is capable of learning one of the hardest subjects on Earth and who is able to apply simple maths rules to solve complex questions?
And if what you say about the last 10 years not being important even in undergraduate than you are implying that the exams are-by your implications- the same level of difficulty.I would like you to please verify this and I am pretty sure this cannot be true.
You being a scientist knows that without maths much of what we learn would've simply been impossible to have discovered in the first place.
NOTE I am not trying to tear anyone down but we must realize the importance of maths before we opt to eradicate it which, I might add is highly unlikely due to the high esteem maths has acquired.
Yes, maths is difficult, yes many people struggle with it, yes it may not seem important to some students but the reason it is there is because of this:
Nothing worth doing is ever easy and maths is not an exception.
Consider this; maths is one of the only subjects required globally at o level and for most Universities even A level, so if you want an established education insure maths is your friend and do not fight it back.

 

[symbolipoint]

thejosh,
The importance of "intermediate algebra" requirement is not just for its difficulty to ensure smart people get their associates degree from a c.c. Students should be informed and well-studied enough to be aware how and where algebra has an impact. I gave my points on this and then suggested that other members on this board & topic could add to this.

 

[Joseph M. Zias]

Consider too an alternative. How about a course in problem solving. At one community college I worked at they adopted a course "Problem Solving" using the text
"Crossing the River With Dogs". It was actually fun to teach and did indeed teach logical thinking. I think math has been used as a vehicle in teaching logical (analytical) thinking to those who really won't actually use math in their day-to-day work. One problem that creeps up all too often is that some students have a very difficult time with the symbology. Some people who have math type problems to solve can do so with calculators designed for those problems. For example, private pilots can buy an E-6B calculator that is programed to solve almost all of the problems needed for flight planning.
By-the-way, anyone remember the old text "It's a Man Made World" - talk about logical thinking.

 

[Apple_Mango]

How does memorizing the quadratic equation improve critically thinking skills and problem solving? A lot of people say learning Algebra 1 helps with critically thinking skills and problem solving so I'm curious to know their reasoning how does memorizing the quadratic equation does this? How does learning the quadratic equation help an English teacher?

 

[symbolipoint]

How does memorizing the quadratic equation improve critically thinking skills and problem solving? A lot of people say learning Algebra 1 helps with critically thinking skills and problem solving so I'm curious to know their reasoning how does memorizing the quadratic equation does this? How does learning the quadratic equation help an English teacher?

MOST of this is already explained; but unsure how to say as "help an English teacher".

The "English Teacher" is either (two simplest possibilities) English teacher NOW, or an unestablished maybe-future English teacher. Another possibility is the English teacher in transition from having a S.T.E.M. degree and some years of career experience in either science or engineering work, who will have had AT LEAST College Algebra & Trigonometry plus some Calculus and associated course credit. The unestablished maybe-future English teacher will at least need to earn acceptable credit in Intermediate Algebra. As said, already been discussed, and more examples have been requested.

 

[Dr. Courtney]

How does memorizing the quadratic equation improve critically thinking skills and problem solving? A lot of people say learning Algebra 1 helps with critically thinking skills and problem solving so I'm curious to know their reasoning how does memorizing the quadratic equation does this? How does learning the quadratic equation help an English teacher?

The quadratic equation is only one of several methods commonly taught to solve quadratics. (Others are factoring, completing the square, and graphing.) Better algebra 1 courses don't stop at questions like: Use the quadratic formula to solve 5x^2 - 3x +2 = 0. They include a variety of word problems where the student needs to solve a variety of problems that require choosing variables to represent physical quantities, setting up equations correctly, then choosing an appropriate method to solve them. Real problem solving always includes learning to make the right choices about which tools to use.

One could also ask, "What possible use does an engineer or Physicist have for reading Romeo and Juliet?" The truth is, "None." Physicists and engineers can have fine careers without ever reading that specific play. But reading and literature are build very important skills for every profession, and English teachers need to choose specific works of literature to build those skills.

Just as a Physicist or engineer could function fine had other literature been chosen (and Romeo and Juliet been excluded), English teachers could function fine had the quadratic formula been left out of the math class. Just as other works of literature could build the needed reading skills, other math techniques and exercises can build the needed problem solving skills.

But the biggest reason the English teacher needs to pass Algebra is because they need to know and internalize that educational standards matter. Even if no one upheld the math standards in their high school, they need to develop an internal commitment that ALL the educational standards should be upheld (in all courses) in the schools they teach in. Giving students a pass on a topic, because one does not see how that specific student will use it later is the heart of grade inflation and educational decline. Since I don't want Physicists and engineers given a pass on Romeo and Juliet (if reading it is assigned by an English teacher), I also don't want English teachers given a pass on the quadratic equation (if that is a part of their math curriculum).

 

[bhobba]

How does memorizing the quadratic equation improve critically thinking skills and problem solving?

Mathematics is about concepts - not memorization. Sure its advantageous remembering the result, but of vastly greater importance is understanding how it was arrived at. Completing the square is a general method of problem solving in math. Exposure to seeing how simple observations and concepts leads to powerful results is something every educated person should understand. That's the key - not the actual result - even though it by itself has numerous applications. For example its used to find eigenvalues which which has some important applications to, for example, populations:
http://math.harvard.edu/archive/21b_summer_05/supplements/popgrowth.pdf

Learning how to think is always valuable and why here in Australia quadratic equations was done when I was 13 - ie in your middle school. We then knew in trying to solve some problem or understand something seemingly innocuous observations are a powerful weapon.

Thanks
Bill

 

[bhobba]

Just as a Physicist or engineer could function fine had other literature been chosen (and Romeo and Juliet been excluded), English teachers could function fine had the quadratic formula been left out of the math class. Just as other works of literature could build the needed reading skills, other math techniques and exercises can build the needed problem solving skills.

Well let's not get too pedantic about this. I failed senior English, detested Shakespeare, in fact its a pet hate of mine people are forced to endure it after grade 10. I had long discussions with people that thought it was important as an example of good English - my opinion is bollocks. We need to be able to understand what we read and write clearly, critically and intelligently, which is NOT literary deconstruction - that's something else again. A valid area of study - sure - but not necessary.

Like algebra we need exposure to it - I am all for that - but it - well actually made me mad that you pretty well have to study Shakespeare in grade 12 and not calculus to go to university. Years ago most did calculus in grade 11 and 12 and were prepared for a much deeper understanding of concepts in subjects like economics pretty much everyone did (IMHO correctly) - but that has gone by the wayside. Yet in our day to day life its much more important than literary works. And no I don't think you should be forced to study calculus - but there is a double standard going on here that rarely gets talked about.

Thanks
Bill