Students failing their first course of Algebra

[symbolipoint]

This article sounds or reads like the same old problem: http://news.yahoo.com/algebra-unnecessary-stumbling-block-us-schools-170616735.html

Why should that be? Students fail algebra 1 either because of lack of effort, lack of motivation, or, if for any student the course is difficult, the need for just more time or repetition of the course.

Contrary to how some students found, algebra 1 was both difficult AND helpful. Took it ONE TIME to pass it, but repeated study ( as occurred upon continuing to other algebra courses), some of it on my own, was what helpted me to understand some of the more difficult parts of the course.

My belief about Algebra 1 is that you do not need to be smart - you just need to work hard; and the results will happen (successful results).

 

[Simon Bridge]

It appears to be more complicated than that .., as an educator I have seen students work really hard and still not get it.
If you really want to understand the situation, I strongly urge you to teach/tutor failing or at-risk students. Lots of them.

 

[micromass]

"One out of 5 young Americans does not graduate from high school. This is one of the worst records in the developed world.

This is very bad. Especially considering that compared to the rest of the developed world, the mathematics american high school students see is very easy and watered down.
And now they want to make things even easier and water things down even more? How does that make sense?
Why doesn't the US look at the other countries in the developed world and see why they can handle difficult math and americans can't?

 

[Andy Resnick]

I think the larger issue is not being explicitly discussed, which is something like: Should there be a minimum level of demonstrated proficiency-based content required to obtain a high school diploma? The same question could be posed for any academic credential.

Naively, the reflexive answer is "yes", and discussions typically devolve into details about minimal content- and often ignore the reality that in the US, there is no central authority to set content. In addition, there is rarely a discussion about the consequences of potentially returning to a time when many people do not have a high-school diploma. Maybe this was not a problem when most people without formal education lived on farms, but that's no longer the case.

Functionally, what does a high-school diploma mean? Is it a terminal degree or not? Does the concept of K-12 need to be changed to K-14 or K-16? Could community college now be thought of as the final two years of high school?

And as Simon points out, what, if any, societal obligations to we have towards 'at-risk' kids? The reflexive answer "not my problem!" is not productive.

 

[jtbell]

there is rarely a discussion about the consequences of potentially returning to a time when many people do not have a high-school diploma. Maybe this was not a problem when most people without formal education lived on farms

Or worked in factories, steel mills, etc., in jobs which have been mechanized out of existence or moved out of the country.

 

[Astronuc]

Could community college now be thought of as the final two years of high school?

In a failed educational system.

Why should that be? Students fail algebra 1 either because of lack of effort, lack of motivation, . . .

My belief about Algebra 1 is that you do not need to be smart - you just need to work hard; and the results will happen (successful results).

Sometimes kids are distracted - by homelessness, by poverty in which they lack proper nutrition, or in the worst case, they either witness domestic violence (spouse assaulting or battering spouse) or are a victim of violence or sexual abuse, or have to deal with one or both parents who are drug addicts or alcoholics.

When I was in junior high and high school, some of my classmates came from troubled homes, and in some cases, some had no permanent home. One of my classmates carried a gun for protection. He'd stash it near school and pick it up on the way home in the afternoon.

About 40 years later, my wife is a teaching assistant and helps students experiencing much the same set of problems. She told me of one child who came to school distressed after seeing his father assault his mother. It's difficult to focus on academics when one's world is in chaos.

The OP seems related to this thread:
https://www.physicsforums.com/threads/the-math-myth-and-other-stem-delusions.859826/

 

[OrangeDog]

This article made me sick. One of the reasons I want to get my PhD is so I can help reform the education system in the US. This quote in particular drove me nuts:

This is where their hopes and aspirations go to die," Klipple said. "They're in college to try to make a better life for themselves, and they're stopped by mathematics.

Newflash: if you aren't willing to work hard, aren't talented enough, or lucky enough (the one thing you cannot control), then your hopes and dreams are useless. We should not be lowering the standards because a large fraction of students cannot make the cut. We should be evaluating why this is the case first, then taking action. The problem is that education in America has become a business run by morons who probably couldn't do algebra to save their lives. More generally, algebra is used EVERYWHERE. I can't see how one could get ahead in life without it. Need to tip your waiter or bartender? Figure out how much material you will need to install a fence. Balance a grocery budge? All basic algebra. How can the US education system get so poor and pathetic, that they think cutting algebra might be a good option? Sometimes I wonder if it is intentional.

 

[Astronuc]

I've always wondered how well school administrators, school board members, government executives and legislators would do on the 'standardized tests' that high school students must take. My guess is 'not well'.The teaching or learning of mathematics has to go back to first grade at the latest, where children learn counting, which relates to addition, subtraction and multiplication. Numeracy should be second nature at some point.

 

[vela]

My belief about Algebra 1 is that you do not need to be smart - you just need to work hard; and the results will happen (successful results).

Some of this has to do with attitudes in the US toward math. It's acceptable to be openly innumerate in US society. You're told from birth that math is difficult and that a lot of people don't understand it. These beliefs are perpetuated, often intentionally, by parents, teachers, and popular culture. It's like you have permission to fail, unlike with reading or writing.

There's also the idea that being good at math is something you're born with. If you struggle with basic math, it's simply because you, like most everyone else, don't have the inborn talent to do math; it's not because you didn't put in the effort to learn the subject. If students do put in effort but don't make much headway, well at least they gave it a shot. There's no sense throwing good money after bad, so to speak; they just don't have the ability to do math, so any more time spent will be wasted effort.

Then there's also the fact that some people just don't have the skills yet to learn effectively. (It was a revelation to one professor when he realized his students didn't know how to use their textbook, so now he spends some time at the beginning of the semester going over how the book is organized, the features it has to help students learn, etc.) Students may therefore end up spending a lot of time not making much progress. It's no surprise they get frustrated and give up.

 

[Kevin McHugh]

First of all, you do not need algebra to graduate high school. Two years of general math will suffice. The kids who are failing Algebra, are doing it in college. So, if they cannot make the grade, then vocational programs may be the better choice.

 

[Isaac0427]

Yes, let's get rid of algebra 1. And then you can't have algebra 2 without algebra 1, right? There's precalc without algebra 2, and no calc without precalc. Let's just get rid of all the math that is viewed as hard by society and cause people's GPA to stumble. I mean, who needs logarithms, derivatives and integrals. Definitely not the chemists who make medicine that much of our population relies on. Definitely not the engineers and physicists who design new inventions such as satellites, TVs, phones and cars that many of us can't imagine life without. Oh, and they are definitely not useful at all for providing electricity and energy, things our modern civilization could not exist without.

"You might say only a certain percentage of kids will go on to use algebra, but we don't know which kids those are,"

Exactly! Let's not give some people a useless lesson because that is not more important than medicine, technology and energy.

Please, help me understand why they think this is a good idea.

 

[symbolipoint]

First of all, you do not need algebra to graduate high school. Two years of general math will suffice. The kids who are failing Algebra, are doing it in college. So, if they cannot make the grade, then vocational programs may be the better choice.

The first part is just plain false. Algebra IS a high school graduation requirement. --------at least in some states. Maybe most states. Maybe there is still a state which does not require it?

 

[ShayanJ]

Algebra is introduced in high school? Isn't that late?
Maybe that's the reason students have so much problem with it!

 

[PeroK]

Some of this has to do with attitudes in the US toward math. It's acceptable to be openly innumerate in US society. You're told from birth that math is difficult and that a lot of people don't understand it. These beliefs are perpetuated, often intentionally, by parents, teachers, and popular culture. It's like you have permission to fail, unlike with reading or writing.

It's actually worse than that. It is practically unacceptable (in the UK) to be openly numerate. No one interviewed on television would dare to admit any interest or aptitude at maths (except maths educators who are brought on to discuss this sort of issue). The presenters and any unwitting guests will all immediately distance themselves from mathematics and declare "I was hopeless at maths at school".

 

[ShayanJ]

This thread reminded me of this:

My cousin, at that time, who was three years older, was in high school and was having considerable difficulty with his algebra and had a tutor come, and I was allowed to sit in a corner while (LAUGHS) the tutor would try to teach my cousin algebra, problems like 2x plus something. I said to mycousin then, "What're you trying to do?" You know, I hear him talking about x. He says, "What do you know—2x + 7 is equal to 15," he says "and you're trying to find out what x is." I says, "You mean 4." He says, "Yeah, but you did it with arithmetic, you have to do it by algebra," and that's why my cousin was never able to do algebra, because he didn't understand how he was supposed to do it. There was no way. I learned algebra fortunately by not going to school and knowing the whole idea was to find out what x was and it didn't make any difference how you did it-there's no such thing as, you know, you do it by arithmetic, you do it by algebra—that was a false thing that they had invented in school so that the children who have to study algebra can all pass it. They had invented a set of rules which if you followed them without thinking could produce the answer: subtract 7 from both sides, if you have a multiplier divide both sides by the multiplier and so on, and a series of steps by which you could get the answer if you didn't understand what you were trying to do.

Maybe this is relevant!

 

[symbolipoint]

Algebra is introduced in high school? Isn't that late?
Maybe that's the reason students have so much problem with it!

Hard to know if introducing it in high school is late or not late. Some students are not ready and need remediation up to grade 9 (first year high school). Some students are better and are introduced in grade 7 or 8. Remediation for basic Arithmetic and then a "pre-algebra" course were what prepared me to start Algebra 1 in my first year of high school. As I learned some Algebra, I also improved very much in basic Arithmetic and in my sense of Numbers. Still the situation would have gone nowhere if I did not put in the effort to learn.

 

[ShayanJ]

Hard to know if introducing it in high school is late or not late. Some students are not ready and need remediation up to grade 9 (first year high school). Some students are better and are introduced in grade 7 or 8. Remediation for basic Arithmetic and then a "pre-algebra" course were what prepared me to start Algebra 1 in my first year of high school. As I learned some Algebra, I also improved very much in basic Arithmetic and in my sense of Numbers. Still the situation would have gone nowhere if I did not put in the effort to learn.

I'm not familiar with US educational system and how they teach algebra, but the way you people talk about it, makes me think its like a university course, one course named algebra with its own book which is tought only in one grade, either in high school or one or two years earlier, and its just expected that the students know it afterwards. Is it true?

 

[Mark44]

I'm not familiar with US educational system and how they teach algebra, but the way you people talk about it, makes me think its like a university course, one course named algebra with its own book which is tought only in one grade, either in high school or one or two years earlier, and its just expected that the students know it afterwards. Is it true?

When I was in high school, back in the early 60s, the schools started with Algebra in 9th grade (which for me was junior high school), Geometry in 10th grade, Algebra/Trig in 11th grade, and Calculus in 12th grade. These classes were for college-bound students; not all students took these classes. As I recall, each subject had its own book -- I don't think we used the same book for 9th grade algebra as for 11th grade Alg/Trig, but I'm not sure of that.

 

[micromass]

When I was in high school, back in the early 60s, the schools started with Algebra in 9th grade (which for me was junior high school), Geometry in 10th grade, Algebra/Trig in 11th grade, and Calculus in 12th grade. These classes were for college-bound students; not all students took these classes. As I recall, each subject had its own book -- I don't think we used the same book for 9th grade algebra as for 11th grade Alg/Trig, but I'm not sure of that.

I think this is a very bad system. Here in Belgium, we start seeing algebra and geometry simultaneously from the start of 7th grade. Every year, we just expand our knowledge on algebra and geometry (including trig) until we get to calculus in the 11th and 12th grade. Other special topics like probability theory, statistics, combinatorics are treated occasionally. I believe this kind of continuous exposure is far better than spending an entire year on some topic.

 

[symbolipoint]

I think this is a very bad system. Here in Belgium, we start seeing algebra and geometry simultaneously from the start of 7th grade. Every year, we just expand our knowledge on algebra and geometry (including trig) until we get to calculus in the 11th and 12th grade. Other special topics like probability theory, statistics, combinatorics are treated occasionally. I believe this kind of continuous exposure is far better than spending an entire year on some topic.

How well does that work for everybody?

When I was in high school, back in the early 60s, the schools started with Algebra in 9th grade (which for me was junior high school), Geometry in 10th grade, Algebra/Trig in 11th grade, and Calculus in 12th grade. These classes were for college-bound students; not all students took these classes. As I recall, each subject had its own book -- I don't think we used the same book for 9th grade algebra as for 11th grade Alg/Trig, but I'm not sure of that.

That WAS a good sequence of well-put-together courses. The way the courses were concentrated ensured that the concepts were very sharply focused. Integrating among different topics , although a bit complicated, is usually not very difficult to accomplish. This lack of difficulty about integrating among topics is mostly because many courses along this sequence of Math ARE CUMULATIVE, but this is not the only reason (and I will let the education specialists explain it further).

 

[Andy Resnick]

In a failed educational system.

That's not entirely fair. As you wrote:

It's difficult to focus on academics when one's world is in chaos.

There's plenty wrong with education in the US, don't get me wrong. From my perspective, there are too many competing interests.

 

[Andy Resnick]

I think this is a very bad system. Here in Belgium, we start seeing algebra and geometry simultaneously from the start of 7th grade. Every year, we just expand our knowledge on algebra and geometry (including trig) until we get to calculus in the 11th and 12th grade. Other special topics like probability theory, statistics, combinatorics are treated occasionally. I believe this kind of continuous exposure is far better than spending an entire year on some topic.

But the US systems doesn't work like that. In the US, each state can decide what subjects it wants taught (or not taught, as the case for evolution in Texas). Each district within a state is given responsibility to meet state requirements but not given funding to support the effort- operating funds have to be generated by taxes raised in the district. Some districts are populated by rich people who consent to give their schools their tax dollars. Others are populated by poor people who have little money and thus do not provide tax revenue to their school district. Some districts do better than others on state competency exams- I'm sure you can guess which ones. Some students receive inferior educational opportunities compared to others- I'm sure you can guess which ones.

It's the american way...

 

[ShayanJ]

I think this is a very bad system. Here in Belgium, we start seeing algebra and geometry simultaneously from the start of 7th grade. Every year, we just expand our knowledge on algebra and geometry (including trig) until we get to calculus in the 11th and 12th grade. Other special topics like probability theory, statistics, combinatorics are treated occasionally. I believe this kind of continuous exposure is far better than spending an entire year on some topic.

Yeah, its almost the same in Iran too. In 7th grade, there is a little chapter in the math book which introduces algebra, only the notion that you can represent numbers with variables starting with using apples and pears instead of letters and then a bit about simplifying algebraic expressions. Then the next year, a bit more and at the junior high school, it becomes more serious with the introduction of functions, algebraic identities, rational expressions and other stuff. This is really important to let the kid "grow up" with the stuff, so to speak.

How well does that work for everybody?

The point is, using this system, algebra is not a big deal and just blends in with the other math. If someone is good with other things, they'll be good with algebra too. I mean, this is really reasonable as even von Neumann says: you should get used to math!

 

[Kevin McHugh]

The first part is just plain false. Algebra IS a high school graduation requirement. --------at least in some states. Maybe most states. Maybe there is still a state which does not require it?

grade.ts.
Thanks for that. I had not realized the standards had changed. It looks as most states changed the requirements around 2011 -2013.

 

[micromass]

This is really important to let the kid "grow up" with the stuff, so to speak.

Exactly. In the Belgian system (and I assume the Iranian system too), the students are really slowly introduced to the various mathematics. In the 7th grade, we solve various very easy equations. So by the time we are in 8th grade, most of us are already very comfortable with what an equation is. Likewise, factoring and the special forms like $(a+b)^2 = a^2 + 2ab + b^2$ are introduced gradually so our students are very comfortable with these things. The abstraction is being raised very slowly. The same with geometry, it's really spread out to make the students comfortable. It is also constantly reinforced.

In the US (as I understand), everything is crammed into one year. This doesn't leave enough time to really get used to stuff. Furthermore, you run the risk of forgetting what you've learned in algebra since you don't use it in geometry.

I'm not saying our system is perfect. There are a lot of flaws. But I prefer this gradual system where we grow up with math, than one where everything is piled on top of each other. I really conjecture that this might have to do something with the inadequacy of most american students.

 

[vela]

Exactly. In the Belgian system (and I assume the Iranian system too), the students are really slowly introduced to the various mathematics. In the 7th grade, we solve various very easy equations. So by the time we are in 8th grade, most of us are already very comfortable with what an equation is. Likewise, factoring and the special forms like $(a+b)^2 = a^2 + 2ab + b^2$ are introduced gradually so our students are very comfortable with these things. The abstraction is being raised very slowly. The same with geometry, it's really spread out to make the students comfortable. It is also constantly reinforced.

In the US (as I understand), everything is crammed into one year. This doesn't leave enough time to really get used to stuff. Furthermore, you run the risk of forgetting what you've learned in algebra since you don't use it in geometry.

A few years ago, I worked with a few kids in elementary school and junior high, and your description of the Belgian system sounds identical to what the kids here in the US experience, at least with algebra. It's not like they never see an equation or a variable before stepping into Algebra I. I don't think it's actually changed that much, topic-wise, since I was back in school.

 

[Isaac0427]

Exactly. In the Belgian system (and I assume the Iranian system too), the students are really slowly introduced to the various mathematics. In the 7th grade, we solve various very easy equations. So by the time we are in 8th grade, most of us are already very comfortable with what an equation is. Likewise, factoring and the special forms like $(a+b)^2 = a^2 + 2ab + b^2$ are introduced gradually so our students are very comfortable with these things. The abstraction is being raised very slowly. The same with geometry, it's really spread out to make the students comfortable. It is also constantly reinforced.

In the US (as I understand), everything is crammed into one year. This doesn't leave enough time to really get used to stuff. Furthermore, you run the risk of forgetting what you've learned in algebra since you don't use it in geometry.

I'm not saying our system is perfect. There are a lot of flaws. But I prefer this gradual system where we grow up with math, than one where everything is piled on top of each other. I really conjecture that this might have to do something with the inadequacy of most american students.

My school's (I am in the USA) system is:
K-8: General math
9: Algebra 1
10: Geometry
11: Algebra 2
12: Usually precalc but you can take stats

We learned to solve equations like 13+x=5 in 6th grade and then 3x-7=14 in 7th grade.

I enjoy the structure, as I skipped 10th grade math completely, and I'm very glad I did that. If somebody already has knowledge in geometry, they should be able to skip it (with passing the midterm final exams, of course). I got an average of 90% on the geometry midterm and final, so they let me go straight to algebra 2.

I will say however, the concern about forgetting algebra during geometry is very valid. I didn't get that problem, but many people in my class did.

 

[PeroK]

so they let me go straight to algebra 2.

Straight to algebra 2? I thought they let you go straight to Quantum Mechanics!

 

[jtbell]

When I was in high school, back in the early 60s, the schools started with Algebra in 9th grade (which for me was junior high school), Geometry in 10th grade, Algebra/Trig in 11th grade, and Calculus in 12th grade. These classes were for college-bound students; not all students took these classes. As I recall, each subject had its own book -- I don't think we used the same book for 9th grade algebra as for 11th grade Alg/Trig, but I'm not sure of that.

In my old school system, in Ohio in the late 1960s, the normal college-prep sequence was:

9th grade: Algebra I
10th grade: Algebra II
11th grade: Geometry
12th grade: Trigonometry & Analytic Geometry (now usually called Precalculus, I think)

Most students didn't start calculus until the first year of college/university.

I was in the "accelerated" sequence which shifted these courses one year earlier, and added calculus in 12th grade. Both sequences had two years of algebra.

I don't know how they do it nowadays.

 

[Astronuc]

K-8: General math
9: Algebra 1
10: Geometry
11: Algebra 2
12: Usually precalc but you can take stats

My school system (in the late 1960s/early 1970s) had a similar schedule, but it varied among the schools in the same municipal district.

We did general math in 8th grade, in which we were introduced to more developed set theory, introductory algebra and word problems. I think some trig could have been introduced here. Starting with 9th grade, I did honors or major works classes in math and science, starting with Algebra 1 in 9th grade. Our junior high school included 7th, 8th and 9th grade. I went to one high school for 10th grade, then switched to a different high school for 11th and 12th grade.

In 10th grade, I did Geometry and Trigonometry. The normal program did Geometry over the entire year, with maybe some trigonometry at the end. I was in an honors program that accomplished the Geometry program in one semester, then did a full course in Trigonometry the second semester. During the summer, I did course work in calculus and physics, which was part of a program for high school students offered by a local university (I think earlier, I did matrix algebra, but I don't remember the year). Had I stayed at the first high school, I would have completed only up to Analytical Geometry (pre-calculus), since that's the most advanced course they offered.

When I changed high schools, I found out that I could take Calculus in my senior year. The program at the second high school did Algebra II with Trigonometry, and some Analytical Geometry. Then the senior year did Analytical Geometry and Calculus. The high school was perhaps the most advanced in the district with respect to academics. Even with that, I felt there was a deficiency, since I felt we could have done more with matrix/linear algebra, and more theoretical treatments.

When I did my 4-year academic plan in the latter part of 8th grade, I signed up for all the math and science (chemistry and physics) courses I could. One of the counselors thought I was overdoing it (and seemed to discourage me in this respect), and my peers thought I was just showing off. I simply wanted to take advantage of the opportunity to do as much as I could as early as possible, since I expected to go to university to study mathematics, physics and chemistry.

So, I'm now wondering with respect to the OP, does the question about algebra pertain to all students, or those in STEM, or those who pursue course work in the humanities (arts and letters)? I ask this because, algebra is absolutely necessary for those in STEM. I use algebra almost every day since it is a basic part of science and engineering. This week I used it to review some work on the calculation of stresses in tubing, and previously, I've used it in describing various material properties (I also have to use statistics in data analysis), which is part of design and performance analysis of systems and components, as well as in design of experiments. The work I do also involves integral calculus, and solving ODEs, PDEs and systems of ODEs and PDEs, which can often be nonlinear. Various codes that I use or review involve finite difference or finite element methods.

 

[Astronuc]

That's not entirely fair. As you wrote:

There's plenty wrong with education in the US, don't get me wrong. From my perspective, there are too many competing interests.

I think my assessment is fair, although I agree that there are many competing interests. With regard to the second point and the statement "It's difficult to focus on academics when one's world is in chaos," I was reflecting on other reasons why students might perform poorly in school, but those reasons may apply to something like 10 to 20% of typical schools, but might represent higher percentages in schools in areas with greater poverty. My comments are based on personal observation going back 50 years.

Reflecting on 50 years, I don't see much improvement or advancement in academics, and if anything, there seems to be a decline.

I have always wondered why I did so well and others seem to struggle with varying degrees. I often assisted peers with assignments.

 

[symbolipoint]

So, I'm now wondering with respect to the OP, does the question about algebra pertain to all students, or those in STEM, or those who pursue course work in the humanities (arts and letters)? I ask this because, algebra is absolutely necessary for those in STEM. I use algebra almost every day since it is a basic part of science and engineering. This week I used it to review some work on the calculation of stresses in tubing, and previously, I've used it in describing various material properties (I also have to use statistics in data analysis), which is part of design and performance analysis of systems and components, as well as in design of experiments. The work I do also involves integral calculus, and solving ODEs, PDEs and systems of ODEs and PDEs, which can often be nonlinear. Various codes that I use or review involve finite difference or finite element methods.

The question is about Algebra for all students.

 

[Isaac0427]

When I did my 4-year academic plan in the latter part of 8th grade, I signed up for all the math and science (chemistry and physics) courses I could. One of the counselors thought I was overdoing it (and seemed to discourage me in this respect), and my peers thought I was just showing off. I simply wanted to take advantage of the opportunity to do as much as I could as early as possible, since I expected to go to university to study mathematics, physics and chemistry.

We just scheduled for high school a few days ago, and I have had pretty much the exact same experience (although I was able to convince my counselor I was doing the right things for me).

But I digress. While I am a little bias with being a physics and math supernerd, I feel like there is hardly anything more useful than algebra, not only because it is necessary for the survival of our society (see my original post), but it shows up everywhere. While I have many things against the low standards of common core (and I don't wish to open up a discussion about this), it does do something extremely well; it gives examples of when you will need the math. I am still surprised that there are professionals who don't understand the importance of algebra.

 

[Astronuc]

But I digress. While I am a little bias with being a physics and math supernerd, I feel like there is hardly anything more useful than algebra, not only because it is necessary for the survival of our society (see my original post), but it shows up everywhere. While I have many things against the low standards of common core (and I don't wish to open up a discussion about this), it does do something extremely well; it gives examples of when you will need the math. I am still surprised that there are professionals who don't understand the importance of algebra.

I too believe that algebra is a basic necessity in life. Perhaps it's a matter of perception. Arithmetic and numeracy are basic necessities, but one can only apply that so far. I think it is important to know some algebra. It can apply to consumer mathematics, e.g., financing in terms of budgets, household expenses, mortgages, financing an automobile purchase. It can also apply to practical skills, e.g., plumbing, carpentry or electrical work where one might have to purchase various supplies for a project as an example. One might need to purchase so many pieces of lumber (2x4's or 4x4's) and fasteners (nails and/or screws), or so many sections/lengths of pipes and fittings, or so many lengths of wire and connectors/switches, etc.

 

[Andy Resnick]

<snip>Reflecting on 50 years, I don't see much improvement or advancement in academics, and if anything, there seems to be a decline.

Aha! I've solved the mystery- the original source of this quote is Astronuc! :)

I have always wondered why I did so well and others seem to struggle with varying degrees. I often assisted peers with assignments.

Again, if you think that a high-school diploma should only be awarded through mastering Astronuc-approved content, you should at least offer a thought regarding those students who, for whatever reason, can't 'get it'. Should they be kept in school until they pass?

I'll also brag that my prediction (paragraph 2, post #4) came true on this thread.

 

[Astronuc]

Again, if you think that a high-school diploma should only be awarded through mastering Astronuc-approved content, you should at least offer a thought regarding those students who, for whatever reason, can't 'get it'. Should they be kept in school until they pass?

I don't believe I have indicated any idea that students should 'be kept in school until they pass', nor have I suggested a specific curriculum to be mastered.

I have reflected on why little or no advancement in broader public education. Clearly there are plenty of kids who get it - maybe 5% or so, and a few percent who do extraordinarily well, e.g., math/science fairs/Olympiads.

As for those who don't seem to get it, then the obvious question is, "How can we improve the teaching of the particular subject (and precursors/prerequisites) so more kids 'get it'?" Or how can we make dry or abstract subjects, less dry or less abstract, i.e., more relevant. I certainly recognize that it is difficult to address all of the issues, such as distractions involving one's peers or situations outside the classroom.

 

[mpresic]

I too came from a school where in general: 9th grade: Algebra, 10: Geometry 11: Algebra 2 and Trigonometry. 12: Solid Geometry, assorted topics, or for the best students 12: Calculus. With one exception. The best students in 6th grade were selected out for a high level integrated program and these students even had access to a time-shared computer terminal (and this was in the 1960's and early 1970's). I wasn't in the chosen group.

One reason for the compartmentalization is that when the students go to college, it is easier for the academic advisors to assess, the student has algebra 1 and geometry (for example), than to say, the student has 2/3 geometry, 2/3 algebra, 2/3 trigonometry or some such. Likewise in a science curriculum, it is a lot easier to say the student comes with biology and chemistry, no physics, than 2/3 biology, 2/3 chemistry and 2/3 physics.

Now the interesting thing about the group of kids chosen early for math aptitude is this. I had a friend in the special group and he helped me study for a MAA exam. He told me while studying, his program treated geometry rather lightly. He knew he was at a disadvantage in the exam, and sure enough, the top 5 scores were all obtained from the lower group. That should suggest the folly of selecting kids for special programs too early.

I found in teaching physics in college that geometry is important, and many students need to be better at it. I have read ideas from young students to take geometry in summer school, or advance without geometry to get to something advanced and I entreat you, "Don't do this". Better you learn the basics thoroughly.

 

[Astronuc]

One reason for the compartmentalization is that when the students go to college, it is easier for the academic advisors to assess, the student has algebra 1 and geometry (for example), than to say, the student has 2/3 geometry, 2/3 algebra, 2/3 trigonometry or some such. Likewise in a science curriculum, it is a lot easier to say the student comes with biology and chemistry, no physics, than 2/3 biology, 2/3 chemistry and 2/3 physics.

Please explain 2/3's in a subject.

 

[mpresic]

This is what I am saying. If I see a student transcript and I see (s)he took mathematics up to but not including the 11th grade. In the old way, I could reasonably believe the grades are in algebra 1, and geometry. These course listings also appear in his transcript. On the other hand suppose I see two courses; Integrated high school mathematics I and II (of a three year math sequence) in secondary school. Can I assume (s)he has been exposed to synthetic division, (an 11th grade algebra 2 topic, the old way) or not. Can (s)he multiply complex numbers (I believe this is an eleventh grade topic the old way) or not. I know his grades are good for his 2/3 of a three year sequence, but I do not know how much of the algebra I, how much of the geometry, or how much of the algebra 2 he or she knows.

 

[symbolipoint]

This is what I am saying. If I see a student transcript and I see (s)he took mathematics up to but not including the 11th grade. In the old way, I could reasonably believe the grades are in algebra 1, and geometry. These course listings also appear in his transcript. On the other hand suppose I see two courses; Integrated high school mathematics I and II (of a three year math sequence) in secondary school. Can I assume (s)he has been exposed to synthetic division, (an 11th grade algebra 2 topic, the old way) or not. Can (s)he multiply complex numbers (I believe this is an eleventh grade topic the old way) or not. I know his grades are good for his 2/3 of a three year sequence, but I do not know how much of the algebra I, how much of the geometry, or how much of the algebra 2 he or she knows.

Your basic concept of a fraction of a course is very understandable. Clear enough. Someone who passes a "pre-algebra" course may be understood as having maybe 1/2 of Algebra 1. Someone who takes one semester of Geometry in high school but not the second semester, but has a Mathematical Analysis Plus Trigonometry course might be understood as having something between 1/2 and 2/3 of a course of Geometry. He might not necessarily be seen as having a full 100% course on Trigonometry, but that depends on actual content passed and the way the institutions view the course taken.

 

[ProfuselyQuarky]

Yes, let's get rid of algebra 1. And then you can't have algebra 2 without algebra 1, right? There's precalc without algebra 2, and no calc without precalc. Let's just get rid of all the math that is viewed as hard by society and cause people's GPA to stumble. I mean, who needs logarithms, derivatives and integrals

Well said! I entirely agree with you. This is an interesting thread. The math structure in schools I’ve been to is the same as listed in earlier posts (although, @jtbell, we have to generally geometry before algebra 2). However, I’m in 10th grade and my high school is really lax and flexible with all of that. You can meet ninth graders taking calculus and seniors taking algebra 2 . . . you’ve got the smart and the motivated and the equivalent opposites of these students. I was able to finish two years of math in the same time it would take a normal-paced student half a year. My goal is to be done with all calculus before junior year ends and then take either high school statistics or a college level math course come 12th grade. Anyway, there is no reason why any form of algebra to abolished. It should remain standard. That’s like asking a child to learn multiplication without learning addition.

I do believe, however, that pre-algebra was not necessary, for myself at least, and that there were hardly any new concepts learned in geometry, aside from learning to complete proofs.

 

[ProfuselyQuarky]

To add to that, I am constantly disappointed that my school is increasingly adding courses reflecting the “arts” such as drama and film and music instead of paying more attention the sciences.

(but that’s a bit off topic)

 

[Isaac0427]

I entirely agree with you.

You agree with my sarcasm, right?

I do believe, however, that pre-algebra was not necessary, for myself at least, and that there were hardly any new concepts learned in geometry, aside from learning to complete proofs.

You sound exactly like me!

Math classes I skipped:
Kindergarten math
Pre-algebra (8th grade)
Geometry

Well, I would have skipped 7th instead of 8th but they didn't let me take the test. I wouldn't be allowed to skip both and if I skipped 7th and went right to 8th, I would have been just as bored in 8th as in 7th (for some reason, I felt like other than Pythagorean theorem and y=mx+b, which were covered in 8th grade, the two taught the same exact things, as their final exams closely resembled each other).

 

[ProfuselyQuarky]

You agree with my sarcasm, right?

Of course with your sarcasm. Is there anyone in a physics forums that would say that integrals are not important? Or that we should get rid of math?

Well, I would have skipped 7th instead of 8th but they didn't let me take the test. I wouldn't be allowed to skip both and if I skipped 7th and went right to 8th, I would have been just as bored in 8th as in 7th (for some reason, I felt like other than Pythagorean theorem and y=mx+b, which were covered in 8th grade, the two taught the same exact things).

I understand the "being bored" part. All the math I took seventh grade to ninth grade felt like forced review. This became a slight issue. For example, in 7th grade, the first lesson on trig ratios only taught sine, cosine, and tangent. Can you imagine how confused I was to not hear anyone say anything about secant, cosecant, and cotangent? Instead of letting students who aren't interested in math do whatever they want (i.e. skip algebra), schools should give that same freedom to students who actually want to learn.

Kindergarten math

What's that even supposed to be? My parents tell me that my pre-K teachers constantly commented that I didn't pay attention. Maybe that was because I had had enough of counting straws and adding apples

My conclusion: schools systems are at least partly corrupt which is why self-study is a necessity to anyone who cares.

 

[micromass]

I understand the "being bored" part. All the math I took seventh grade to ninth grade felt like forced review. This became a slight issue. For example, in 7th grade, the first lesson on trig ratios only taught sine, cosine, and tangent. Can you imagine how confused I was to not hear anyone say anything about secant, cosecant, and cotangent? Instead of letting students who aren't interested in math do whatever they want (i.e. skip algebra), schools should give that same freedom to students who actually want to learn.

To be fair, nobody uses secant and cosecant nowadays anymore. They also could have mentioned the versine

 

[ProfuselyQuarky]

To be fair, nobody uses secant and cosecant nowadays anymore. They also could have mentioned the versine

Yeah, sure, but teaching three without the others is still incomplete, nonetheless. I use those trig ratios, though. It still gives you the right answers and the word cosecant sounds lovely in my mouth: cooooosecant

 

[micromass]

Yeah, sure, but teaching three without the others is still complete, nonetheless. I use those trig ratios, though. It still gives you the right answers and the word cosecant sounds lovely in my mouth: cooooosecant

Did they at least mention what tangent and cotangent have to do with tangent lines?

 

[ProfuselyQuarky]

Did they at least mention what tangent and cotangent have to do with tangent lines?

Nope. The words "tangent lines" did not even appear in the textbook. I learned that on my own during the summer between middle school and high school. I learned it officially in geometry.

 

[micromass]

Nope. The words "tangent lines" did not even appear in the textbook. I learned that on my own during the summer between middle school and high school. I learned it officially in geometry.

Sigh... And then they wonder why students hate math...

 

[ProfuselyQuarky]

Sigh... And then they wonder why students hate math...

Yes, it's not entirely students' fault. Lucky for me, my current school is independent study! I stay home almost everyday with the Internet and parents who love science and math as much as I do!

(No matter how amazing the class is, however, sometimes there is just no desire to learn. That's why you can now download video games onto graphing calculators. Who needs cell phones now? These guys are con artists!)