<p>@mehozak- I think b@rlum is currently earning a PhD in math at Stanford. So it’s likely he (or she) has read a high level math paper and may have written some as well.</p>
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<p>One issue, though is that a credential is only as good as its curriculum requirements and how well the holder learned them. If a given high school diploma’s requirements are watered down, that diploma will often be perceived as worth less and its holder regarded accordingly by college admissions, vocational schools, and employers. </p>
<p>For instance, one reason why the US military has a limited quota on taking high school grads with only a GED as opposed to those with a regular high school diploma is partially due to the diluted curriculum of the GED program<em>…as well as their own experiences that more GED holders have issues finishing basic training, vocational training, and successfully serving out their first enlistment without academic and/or disciplinary issues.</em>* </p>
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<li>From my going over a few review tests to tutor a friend’s sibling in the late '90s, the math is only covered up to the 10th grade level at the time.<br></li>
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<p>** According to friends who served in the military…including a few former drill sergeants in Army/Marine boot camp. They actually prefer a GED holder get some community college credits to be regarded as the equivalent of a graduate with a regular high school diploma.</p>
<p>Wow. So, when faced with a challenge, we … run away. (My main impression after reading the article).</p>
<p>For me, algebra is the capstone of arithmetic. Poor arithmetic skills leads directly to trouble with algebra.</p>
<p>Here in NJ, I see high school students who don’t know what 7x9 is from memory. (Perhaps worse, they can’t logically determine the answer by adding nine 7’s. Why? They don’t connect multiplying with addition.) These students have used calculators extensively from early in elementary school. (Only very recently, a non-calculator section was added to the NJ state 4th grade math exams.) Coincidence? I’m not sure; amazingly enough, little (or no) research is available about the effects of calculator use in K-6.</p>
<p>Why are students having so much trouble with algebra now and not, say, 20 years ago? The article is mute on the historical perspective.</p>
<p>Finally, when did real-world use become the key factor in whether a subject should be taught? (The influence of this sentiment is apparent in modern high school math textbooks by an overabundance of “application” problems.) Should we bother teaching Shakespeare, or U.S. history?</p>
<p>I just found out that our state is adopting a new Common Core curriculum adopted now by 45 states. It will cost our local district millions in new textbooks. I shudder to think what’s in them.</p>
<p>I used Common Core books and they were absolutely horrific. They rarely include any solved examples and the practice questions are sparse and focus more on developing new skills from the core of the unit than actually revising the key ones. All of that, coupled with poor teaching = a sad year in math.</p>
<p>I feel sorry for you.</p>
<p>I don’t think the Common Core curriculum is so terrible, but it’s too bad they’ve come up with terrible textbooks. As far as I can tell any standard sequence of math books would cover the material - even the hated NYS Math A - Math B books.</p>
<p>@fignewton-
I think some kids have always struggled with Algebra. In fact, IIRC when I went to HS 30 years ago most kids didn’t take Algebra until 9th grade and relatively few took calc in HS (this is not just my recollection, there is data somewhere on this). These days I think CA requires some algebra in middle school.
Of course nobody suggested dropping it because it was hard for some kids.</p>
<p>If you’re not passing algebra, you shouldn’t receive any high school degree. No point in diluting the value of the degree by watering down the requirements. Basic math is absolutely essential to life: I tutor high school students who struggle to figure out how much is a 20% discount on original $120 purchase. How are you going to do grocery shopping or even survive without algebra?</p>
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<p>But the sophomore level course may vary greatly from one school to another. The question of this thread is if today’s math courses are too easy or too hard. I think they can be easier as long as students really understand the material. No high school student should have trouble understanding what 20% discount is.</p>
<p>I have two K-8 curriculum sets. One is from the 1960s and one is from the early 1990s. I have a bunch of Singapore Math sets too.</p>
<p>I should post a few problems from the third and fourth grade Singapore Math books. I would guess that your typical high-school (not typical CC) student would have trouble with many of the problems.</p>
<p>I followed the textbook trends for K-12 and really didn’t like where they were going around 1994-1995.</p>
<p>Our state came up with standards a long time ago which meant that every district would have to use Everyday Math. I ran into a huge number of complaints with it on our local town forum. There were schools that were using it successfully by supplementing it but that was done by individual teachers at those schools on their own time. The schools where teachers didn’t supplement didn’t do well. The publisher of Everyday Math apparently got in early on the standards development for the state and guided the standards to their product.</p>
<p>Singapore Math texts are pretty cheap BTW. They depend on the teacher knowing their stuff.</p>
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<p>A while back, my mom got possession of a math book one of her relatives had used in the 1910s or so. It was actually one of the best math books I’ve ever seen. The book was aimed at students whose career was going to be farming, but still expected mathematical literacy you’d want out of most high schoolers today. There were questions on compounding interest on your mortgage, how many man hours would it take to build a road made of dirt vs asphalt if you needed to have a different grade for each one, what sort of time-vs-money you’d expect if you’d need to maintain the non-paved road more, etc. There was determining inflation based off of year to year costs of Thanksgiving dinners. My dad actually wound up doing a “problem of the day” out of the book for his HS-level class, and it was actually pretty well received.</p>
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<p>Kind of like the McGuffey Readers for math. The McGuffey Readers were effective. They have errors and other things that wouldn’t be acceptable today but a lot of things in their meta-approach we found effective.</p>
<p>While I think that algebra is important, as well as other math which gets short shrift in the drive to get everyone “calculus ready”, I also think it is valid to examine individual parts of what is taught to determine whether they remain necessary. We no longer teach the algorithm for finding square roots of numbers by hand, or how to use logarithm tables, find cologarithms, antilogs, or use logs to find trig functions.</p>
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<p>I bought a copy of the CRC Handbook of Math tables when I was in high-school as it had a lot of interesting stuff for math-oriented kids. I have showed my kids this book in the past including the tables and how they are used. I’ve also showed them a slide-rule and explained how it worked.</p>
<p>My guess on finding square roots by hand is that they probably read it in some of the ancient textbooks that we used.</p>
<p>In 12 years x 200 hours, kids can’t learn algebra. What are they doing with all that time? There’s no time at all for math fun?</p>
<p>Other odd things that don’t make sense seem to be creeping into US math curricula in K-12. One common one, based on what is reported on these forums, is “pushing” students into more advanced math (two or more years ahead of grade level) and then slowing them down when they reach calculus (forcing them to take calculus over two years instead of one, which a student who is “naturally” good and motivated enough to be two years ahead of grade level in math should be able to handle).</p>
<p>Great post at #106 by barium.</p>
<p>I will also add that trigonometry when properly presented is easy to comprehend since aspects of the motic animal include innate understanding of how to change attitudes in space.</p>
<p>In my bold opinion, the math issue is a perfect storm of a few different factors:</p>
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<li><p>Teachers that can’t or won’t teach either because they do not know the material as well as they should or because of attitude with ‘I have an MS in Math and make $48k a year teaching AP Calc when I should be working as a COBOL programmer for XYZ Life Insurance making $80k’.</p></li>
<li><p>Too much reliance on tests and too little reliance on homework. The end result is that students get trivial homeworks and when tests come they have never seen the stuff. I’d rather mess up a homework and use office hours or what not to understand what I messed up rather than wait for the test. It’s like practicing for a marathon running a mile at a time and expecting to last the full 20something. Not gonna happen.</p></li>
<li><p>Teacher aversion to grading homework and administering quizzes.Who wants to grade 30 homeworks per day plus 30 quizzes a week (online takes care of this)</p></li>
<li><p>Horrible textbooks and supplementary materials.There is no excuse for having 100 different Geometry book and all of them being horrible - bunnies and puppies don’t make a textbook better.</p></li>
<li><p>Student attitudes - why should I study this? (self explanatory)</p></li>
<li><p>Not taking advantage of technology (online homeworks, quizzes, etc) or calculators or software</p></li>
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<p>Or homework that is voluminous but does not include a range of types of problems or more difficult problems, so that it provides a lot of practice on easier problems for the C students, but is boring and repetitive busywork for the B and A students.</p>
<p>Exactly - DD1 took Geometry in 9th grade and I made sure she solved each and every one of the homework, practice tests, unit reviews, and so on of the puppies-n-kittens textbook. Nearly all the problems were trivial (i.e. busy-work) and there were problem types that were not discussed or covered at all, about 50% by my estimate. </p>
<p>For extra frustration, the school does not allow the students to take home graded exams since exams are re-used. I had to bring it up to the school board to get DD1’s tests back for review…</p>
<p>Add the huge gaps between classes in my laundry list while we’re at it. There’s big gap between 7th and 8th (Algebra) grade math, and 8th to 9th (Geometry). Kids are not prepared at all for Geometry in K-7 and then they have to learn everything in a short amount of time…</p>
<p>Euclidean geometry only simply involves applying algebraic concepts to shapes. And even then you’re only dealing with two-dimensional space. I agree that children aren’t adequately prepared for geometry. Not because it’s not right time to teach it, but because the algebra isn’t sufficiently rigorous to prepare the students for geometry.</p>