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Higher Level Math Courses on Transcript Don't Correlate to Math Ability


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Algebra II and the Declining Significance of Coursetaking

 

A friend whose kids were/are on the AP track at a local (good) high school shared this.  They've been rather disenchanted with the stress and treadmill feeling their kids have had in high school.  Their oldest just headed off to a strong Midwestern college for engineering.

 

The gist of the article is that having higher level math courses on the transcript doesn't imply that the student is capable at that level (or foundational levels) of math.  A significant number of students who completed Algebra II with good grades test into remedial math in college.

 

 

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This is not encouraging. I suspect though that the problems really begin in elementary school as I have read that a MAJORITY of elementary school teachers self-report that they dislike and/or consider themselves week in math. Deficits in foundational instruction and learning naturally lead to weaker comprehension and application ability as students progress into high school mathematics.

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This is not encouraging. I suspect though that the problems really begin in elementary school as I have read that a MAJORITY of elementary school teachers self-report that they dislike and/or consider themselves week in math. Deficits in foundational instruction and learning naturally lead to weaker comprehension and application ability as students progress into high school mathematics.

 

Well, not only that, but then we pass students who haven't learned a reasonable amount of the course material into the next course.

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Thanks for the link Sebastian.

 

In my mind it is just further evidence that the solutions to the problems with our educational system continually compound them and don't actually improve anything. The pushing down of what is consider appropriate levels of education to lower ages has not improved upper levels. Earlier ages for higher level academics is not the answer and yet it is what is being done almost universally.....just like the college for everyone POV.

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Therefore I believe the problem isn't just that the kids don't score well it's that they don't retain the information.

I think they don't retain it because they never really mastered it. In Daniel Willingham's book "Why Students Don't Like School," there is an interesting graph. It shows that students that take calculus and do well it still do well on algebra tests even decades later. Students that take lesser levels of math have much less retention of algebra even a year or two later than the calculus students have 30-50 years later! (If I remember correctly, they did try to control for the possibility that the good math students took calculus and the poor ones didn't. If I remember, I will look it up in the book and come back and post about it later.)

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Earlier ages for higher level academics is not the answer and yet it is what is being done almost universally.....just like the college for everyone POV.

Although more American students might be taking algebra in middle school than in the past, does the rest of the world really consider age 13 "too early" for average students? For example, in the US it is considered "normal" to not be "ready" to understand geometric proofs until 10th grade or later. But I believe Regentrude said they were taught in 6th grade where she grew up. Are average German students considered incapable of algebra at age 13?

 

If it turns out that much of the world teaches average students algebra in middle school, then I think the real problem we have is terrible math teaching in elementary school, not that algebra before age 14 is unrealisic.

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Although more American students might be taking algebra in middle school than in the past, does the rest of the world really consider age 13 "too early" for average students? For example, in the US it is considered "normal" to not be "ready" to understand geometric proofs until 10th grade or later. But I believe Regentrude said they were taught in 6th grade where she grew up. Are average German students considered incapable of algebra at age 13?

 

If it turns out that much of the world teaches average students algebra in middle school, then I think the real problem we have is terrible math teaching in elementary school, not that algebra before age 14 is unrealisic.

 

You misunderstand my post.   I think it starts off in K and is compounded yr by yr.   For example, expecting 2nd graders to write a page on a topic instead of focusing on proper sentence construction.   Expecting 2nd graders to be doing multiplication vs. solidifying addition and subtraction.   There is a push to have Kers doing what used to be considered 1st grade, etc.  Then there is a continued race forward every yr.   What you witness is a collapse in middle and high school b/c the foundation was actually hollow and not solid.

 

Obviously I don't believe that all kids are incapable of doing those things early (my own kids do multiplication in 2nd ;) ), but when you are talking about general ed for the populace at large, it is why I think you see the graph in the article.

 

If instead there was a focus on moving slower and steady at the beginning instead of trying to use middle school as place to remediate and then leap forward, the slow and steady would win the race b/c the earlier skills would be understood and the upper skills would not be compounded into the mix of unmastered skills.

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I think they don't retain it because they never really mastered it.

 

This, exactly. It is not possible to "forget" algebra once you have understood it conceptually. Students who "forget" have memorized algorithms and drilled procedures, but never really understood what they are doing.

 

Some skills should be automatic like bicycling or swimming: rearranging equations, combining terms, isolating variables.

Other specific details may slip from memory: it is entirely normal that a student may not remember the quadratic formula if he has not used it in a while - but a student who understood where it was coming from can easily derive it by factoring.

It is also completely normal not to be able to remember trigonometric identities if they are not used  - but again, a student who understood trigonometry can simply derive them from Euler's formula.

 

Students who "forgot" algebra because they had geometry and precalc never actually mastered algebra. THAT is the problem.

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As far as the original article, I wonder which is the cause and which is the effect. Did unprepared students join the courses, causing them to be watered down? Or were the courses watered down first, thus allowing more unprepared students in?

Both.

If the quality of a school is measured by how many students are taking upper level courses, schools have a strong incentive to push unprepared students into courses with higher sounding names and then consequently to water down those courses as not to fail all of them. The reward structure is wrong. A school should not be judged by the percentage of its students enrolled in AP classes - if anything, it should be the percentage of students getting a 5 on the exam  (and to be hones, I would not even find it sensible to measure the overall quality of a school by anything related to AP)

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If instead there was a focus on moving slower and steady at the beginning instead of trying to use middle school as place to remediate and then leap forward, the slow and steady would win the race b/c the earlier skills would be understood and the upper skills would not be compounded into the mix of unmastered skills.

Multiplication is started at 3rd grade here even though teachers might teach earlier. 

 

The "impression" I get from being in the states is that middle school is basically just the school system waiting out the teenager fog. Public school honors science courses are not that hard either.  So we (general)  basically have a "wasted" three years and plenty of bullying and truancy going on.

I'm sure Asian teenagers get all hormonal too but math and science are ramped up from around 5th grade and just gets harder from there.

 

How to solve this issue, I don't know.  My local school district board members are too busy campaigning and politicking.

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The "impression" I get from being in the states is that middle school is basically just the school system waiting out the teenager fog. Public school honors science courses are not that hard either.  So we (general)  basically have a "wasted" three years and plenty of bullying and truancy going on.

I'm sure Asian teenagers get all hormonal too but math and science are ramped up from around 5th grade and just gets harder from there.

 

You put very succinctly what I have been feeling as well (and experienced first hand when my kids suffered through a useless year of middle school). There is NO reason why, when arithmetic with positive integers has been taught in elementary, it should take 3 or 4 years to teach arithmetic with fractions and negative numbers to get students ready for "algebra" in 8th or 9th grade.

German teens, too, get hormonal, but like Arcadia reports from Asia, they are still taught math.

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Multiplication is started at 3rd grade here even though teachers might teach earlier. 

 

The "impression" I get from being in the states is that middle school is basically just the school system waiting out the teenager fog. Public school honors science courses are not that hard either.  So we (general)  basically have a "wasted" three years and plenty of bullying and truancy going on.

I'm sure Asian teenagers get all hormonal too but math and science are ramped up from around 5th grade and just gets harder from there.

 

How to solve this issue, I don't know.  My local school district board members are too busy campaigning and politicking.

 

I don't know if it is holding or if it is remediating.  (fwiw, I have never witnessed teenage fog in any of my kids.   Go figure.)   Either way, there is a definite disconnect.     I have been asked by a mom to tutor her ps-ed sr in alg 2 (which based on what is being learned looks far more like alg 1).   Her dd doesn't understand fractions, decimals, percentages, rules of exponents.   There is so missing that is elementary or pre-alg level skills that it is obvious that she was just continually advanced w/o actually understanding anything other than  the most rudimentary +/-/*// skills.     I have to wonder if she is an isolated example or typical of the struggling high school math student.

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Other specific details may slip from memory: it is entirely normal that a student may not remember the quadratic formula if he has not used it in a while - but a student who understood where it was coming from can easily derive it by factoring.

It is also completely normal not to be able to remember trigonometric identities if they are not used  - but again, a student who understood trigonometry can simply derive them from Euler's formula.

 

 

[bolding mine]

 

You make an interesting point. I was listening to a bunch of kids coming out of a math team practice when one boy was lamenting that he'd have so much to memorize. One of the other kids gave him a funny look and said something like, "No, you don't. Just derive them when you need them." 

 

In light of this thread, I'd be really interested to compare the middle-school math educations of Kid A and Kid B.

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You misunderstand my post.   I think it starts off in K and is compounded yr by yr.   For example, expecting 2nd graders to write a page on a topic instead of focusing on proper sentence construction.   Expecting 2nd graders to be doing multiplication vs. solidifying addition and subtraction.   There is a push to have Kers doing what used to be considered 1st grade, etc.  Then there is a continued race forward every yr.   What you witness is a collapse in middle and high school b/c the foundation was actually hollow and not solid.

 

Obviously I don't believe that all kids are incapable of doing those things early (my own kids do multiplication in 2nd ;) ), but when you are talking about general ed for the populace at large, it is why I think you see the graph in the article.

 

If instead there was a focus on moving slower and steady at the beginning instead of trying to use middle school as place to remediate and then leap forward, the slow and steady would win the race b/c the earlier skills would be understood and the upper skills would not be compounded into the mix of unmastered skills.

 

Eight, years ago I asked my childrens second grade teacher about the changes she had seen in 30 years of teaching. She was quick to respond that she was teaching third grade to second graders, who weren't ready to be third graders.

 

Our local newspaper recently published an article on how the Common Core would affect our state and individual grade levels. I am fine with requiring third graders instead of fourth graders to memorize their multiplication facts. Back in the Dark Ages, we memorized them in third grade so I know it can be done. On the other hand,  the idea of having first graders pull from multiple sources to write a report is frankly, ludicrous. I know a few high schoolers that have problems with that skill.

 

To me, much of the Common Core standards that I have read equate to teaching the butterfly to a kid who can barely keep his head in the water and dog paddle.

 

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. I have to wonder if she is an isolated example or typical of the struggling high school math student.

From what I see teaching at the cc, she's typical.

I showed students last week why we have the rules we have for decimal arithmetic. (Because they're fractions!) They'd never seen it or had it explained. Sad.

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From what I see teaching at the cc, she's typical.

I showed students last week why we have the rules we have for decimal arithmetic. (Because they're fractions!) They'd never seen it or had it explained. Sad.

That might explain my local community colleges low graduation rate. The two local community colleges with much better graduation rates attract the more stem oriented kids (as in less likely to take remedial math).

 

ETA:

Looking at the statistics for one of top performing local community college, the remedial math rate went up over a five year period.

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I had a friend (chemistry) have a student say she couldn't read an analog clock.

 

I have had a number of students who don't know how many states there are. This was about 13 years ago when I saw it was an issue and gave it as a bonus question on tests to get some data. One calculus student tried to argue with me about the answer. (Sigh)

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Oh, and don't get me started on elementary math. In my county 3rd grade teachers have 20+ kids for a 45min class for 145 days (after testing days, field days, etc.) and they are expected to cover 25 state mandated grade level expectations. They must cover those. In order to cover them all they must move on even if half the class doesn't understand what was covered. Then, teachers are pressured to pass students who have no business moving to the next grade. By the time those kids hit what is supposed to be Alg2, it is a miracle if any of them mastered basic computation with whole numbers. :/

 

Mandy

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From what I see teaching at the cc, she's typical.

I showed students last week why we have the rules we have for decimal arithmetic. (Because they're fractions!) They'd never seen it or had it explained. Sad.

Looking at the statistics for one of top performing local community college, the remedial math rate went up over a five year period.

I had a friend (chemistry) have a student say she couldn't read an analog clock.

I have had a number of students who don't know how many states there are. This was about 13 years ago when I saw it was an issue and gave it as a bonus question on tests to get some data. One calculus student tried to argue with me about the answer. (Sigh)

The math tutor I have used for years teaches Alg2 at a local ps. He gives some placement tests of his own at the beginning of the school year. This year not a single student passed the test over the four operations with fractions. How is he going to teach those kids Alg2?

Mandy

May I say that all of these posts depress me? How is it that we live in this country and have so many students that are literally not being educated? How do students reach alg 2 or higher w/o really understanding elementary math skills?

 

I am continuously thankful for being able to educate my own kids at their pace and that advancement is strictly based on their mastery and no one else's determination.

 

And, no, I do not believe common core or any other standardized testing will fix the problem. It is just a band-aid giving the illusion of fixing the problem by masking it once again under "new" goals.

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In my state, a student now MUST start algebra in 9th, regardless of personal readiness or prior preparation. Students who need more help are given a math lab in their schedule. Pre-algebra is not offered at all anymore. I can't imagine that EVERY SINGLE ninth grader is ready and prepared for algebra. So, in my mind, there must be some modifications being made to the curriculum.

 

On top of this, our pre-high school district changed to Math in Focus last year and the transition was not at all smooth for teachers or students, and I've wondered how that will affect the preparation for algebra for those students in middle school who spent the last year very confused. Not that Math In Focus is a bad program at all, but it was the timing of the switch into a much more rigorous program for all kids that I've been concerned about. I saw in fifth grade how the teachers cut out material on tests because it was impossible for the students to master it. It could only be worse in middle school. And how will that affect them going into high school math?

 

Also in our state now, all students must complete science through chemistry. I also can't believe that EVERY SINGLE student is able to do chemistry. 

 

Maybe I sound like an academic wimp but I think changes like these which require all students to follow the same academic path lead to watering down. 

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And, no, I do not believe common core or any other standardized testing will fix the problem. It is just a band-aid giving the illusion of fixing the problem by masking it once again under "new" goals.

No. One thing that would START to fix the flippin' problem is if we stopped equating equality of outcomes with equality of opportunity.

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Also in our state now, all students must complete science through chemistry. I also can't believe that EVERY SINGLE student is able to do chemistry. 

 

Maybe I sound like an academic wimp but I think changes like these which require all students to follow the same academic path lead to watering down. 

 

I agree.  When I was in high school, we had an academic track diploma and a vocational track diploma.  Algebra II and chemistry were available for the college-bound students in their junior year, but they were not required for graduation or for college admission.  Students who didn't take them had time to take more English, music, or foreign language courses to better prepare them for their college studies in those fields which suited them better.  Now that everyone has to take algebra II and chemistry, of course the material is being watered down.  The classes are filled with students who would never even have taken them 30 years ago!  The same thing is happening with Algebra I.  If everyone has to take Algebra I in 9th, either all of the kids who would have taken consumer math 30 years ago will  fail or the teacher will significantly reduce expectations so they won't.  Hence, the upsurge of "honors" level courses to accommodate the students who are ready for the subject at the level it was taught before. 

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Yes, this sort of thing is why we quietly continue to homeschool even though the majority of our friends in the immediate area who came up through the years homeschooling now have their kids in local high schools or at the community college.  And I say quietly because they are adamant about their decisions, but I know too much.  

 

Teaching at the local community college for almost 15 years now has taught me how poorly even the top graduates are prepared for college.  It really is appalling.  They advertise AP classes, but the scores don't show college-prep quality (a few 3's and the rest are 1's and 2's).  One kid I know took AP Latin with all "A's" and got a "1" on the actual exam.  He said that the teacher ordered the wrong book and kept teaching from it all year because she didn't want to admit her mistake.  And I know from firsthand experience that the community college is not necessarily the best place for homeschooled students in the last years of high school.  It is a very *adult* environment with a culture of failure in the first-year classes.  Less than 1/4 of those who are admitted actually graduate.

 

A friend of ours in another district is the math department head at a large high school.  She teaches all of the kids who have failed algebra before or have other issues who put them behind like jail time, homelessness, etc.  And the pressure on her to get them through algebra at any cost is intense.  She told me one time that she only assigns about 100 problems a semester as homework (i.e. 90 days of class) because "they wouldn't do them anyway."  How can you learn algebra without practice?

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I agree!  I had a chance to talk with my ds's friends' moms while waiting to pick him up from Scouts last week. They were all talking about how their kids are suddenly struggling in school.  I suspect that the root of the problem is that their children don't understand fractions, decimals, percents, ratios, and simple algebraic expressions.  Local teachers here blow through these topics as they try once last time to get the kids to memorize their basic math facts before they get shoved into algebra.  No one in the district is willing to flunk half of a class.....

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Algebra II and the Declining Significance of Coursetaking

 

A friend whose kids were/are on the AP track at a local (good) high school shared this.  They've been rather disenchanted with the stress and treadmill feeling their kids have had in high school.  Their oldest just headed off to a strong Midwestern college for engineering.

 

The gist of the article is that having higher level math courses on the transcript doesn't imply that the student is capable at that level (or foundational levels) of math.  A significant number of students who completed Algebra II with good grades test into remedial math in college.

 

I didn't read the article yet, and this is just one example.... but Diamond tested into a developmental math class at community college (She had FABULOUS scores for her English test- just not a mathy gal) Anyway, her class is about half mid-aged adults returnign to school, a few clearly not hard-working 18yos needing "13th grade" and several kids who passed AP Calc but had completely forgotten basic math!

 

My friend teaches math at a major city university, and he always has several students in his classes who took/passed AP Calc, but completely bomb his classes.

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I think the problem is compounded in that these students take advanced math courses, receive high grades, and then think they are "good at math."  I had a college junior in my office this week who told me, "I am great in math. It has always been my best subject."  She could not solve X = 100(2 + .03)and she had no idea of what a sigma sign meant. Somehow she had made an A in calculus!

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I thin one big problem is the compartmentalization of math in this country. "Algebra 1" and "geometry" are neatly packaged sets of material that is taught without any relation to "other" math. I had one student tell me she chose my calculus based physics class because she "was good at calculus but bad at algebra", and thus did not want to take the (easier) algebra based course. :banghead:

 

This packaging seems to be a US idiosynchracy; elsewhere in the world, students are taught "math".

Back home, students cover triangle congruency and geometric proofs in 6th grade, linear equations in 7th, geometric similarity maybe in 8th, quadratic equations and parabolas in 9th... it is all MATH. It is never suggested that there are certain "subjects" in math that can be filed away once completed; the entire discipline is treated as one organic fabric. I believe that makes a big difference to perception and also to the way it is taught.

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I thin one big problem is the compartmentalization of math in this country. "Algebra 1" and "geometry" are neatly packaged sets of material that is taught without any relation to "other" math. I had one student tell me she chose my calculus based physics class because she "was good at calculus but bad at algebra", and thus did not want to take the (easier) algebra based course. :banghead:

 

This packaging seems to be a US idiosynchracy; elsewhere in the world, students are taught "math".

Back home, students cover triangle congruency and geometric proofs in 6th grade, linear equations in 7th, geometric similarity maybe in 8th, quadratic equations and parabolas in 9th... it is all MATH. It is never suggested that there are certain "subjects" in math that can be filed away once completed; the entire discipline is treated as one organic fabric. I believe that makes a big difference to perception and also to the way it is taught.

 

One of the things I did appreciate about our choice to use Saxon for math when my ds came home from public schools was that geometry was incorporated throughout the levels. When ds took geometry last year, he was comfortable with and prepared to move into the subject. What then bothered him was the lack of review or use of his algebra skills. Compartmentalization can be problematic even for decent math students. Skills grow stronger with continuous practice and exposure. Our system doesn't allow for that.

 

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Teaching at the local community college for almost 15 years now has taught me how poorly even the top graduates are prepared for college.  It really is appalling.  They advertise AP classes, but the scores don't show college-prep quality (a few 3's and the rest are 1's and 2's).  One kid I know took AP Latin with all "A's" and got a "1" on the actual exam.  He said that the teacher ordered the wrong book and kept teaching from it all year because she didn't want to admit her mistake.  And I know from firsthand experience that the community college is not necessarily the best place for homeschooled students in the last years of high school.  It is a very *adult* environment with a culture of failure in the first-year classes.

 

This whole thread is depressing, but I did want to give a shout out for my community college. My second son took two semesters of math a the community college. The first was titled Pre-Calc Alg and the second was titled Pre-Calc Trig. The private college he ended up attending required that all freshman take math placement tests. He took the basic placement test and based on scores had the option to take more. When he took the trig placement test, he blew it out of the water. The college asked him both by e-mail and snail mail if he was absolutely certain that he didn't want to take the calculus placement test. He had not taken calculus so he declined, but the math he has taken he knows. I definitely attribute some of that to the instruction at the community college. (Both my big boys also had an incredible, enthusiastic US history prof at the cc. I hope she is still teaching when my youngest is in high school!)

 

Although I do have to add that I didn't let my sons move on in math without having mastered a course. Now that my last child is repeating Alg2 all of my boys have taken Alg2 twice. I attributed it to dyslexia with my oldest. Then, I attributed it to teenage brain fog with my second. With my third I have just decided that my boys, who have all been different ages when they first took Alg2, have some sort of mental block against retention of this course. They did fine while taking it, but at the end of the year a quick retention check indicated that they had no business moving on. My oldest son took a year of Advanced Math/ PreCalc with a tutor before taking college Alg at the community college, and my second son also took a year of Advanced Math/ PreCalc with a tutor before taking pre-calc at the community college. Second ds had no idea that others did it differently, but he is so very sure of himself that if he did I am sure he would wonder why the system would move students to the next course who hadn't truly mastered (not just passed) the material and why in the world that student would want to move on. He thought Discrete Math was super easy his first semester at college.

 

I am glad I homeschool, so that my sons have the ability to take a course for 2 years before receiving credit without the system bullying them on to the next level or peers making them feel bad. (and I do plan to enroll my youngest in classes at our community college where I expect him to take full advantage of having a live instructor and a study lab. :leaving: It was a good fit for us.) 

Mandy

 

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