<p>“Algebra should beging in 5th grade and geometry, trig. should start in 6th, all taught as separate subject.”</p>
<p>My sixth grader doesn’t need to be studying trigonometry. Why? How does this relate to her life as an 11 year old? </p>
<p>Again, it isn’t for everyone and that’s fine.</p>
<p>BCEagle, I was always tremendously interested in unschooling. That was basically the approach I took with my older son’s early interest in math. I just threw stuff at him and let him follow what interested him. He read a lot of stuff about math that was theoretically too hard, but he found very interesting. He learned about Pascal’s triangle, Fibonacci numbers, surreal numbers and game theory all while still in elementary school.</p>
<p>“My sixth grader doesn’t need to be studying trigonometry. Why? How does this relate to her life as an 11 year old?”
-It does not relate to me either in my close to retirement age. English literature or any lit. for that matter does not relate either. The same goes for chemistry, physics, phys. ed, spelling (all done by computer automatically), art, music, history, geography, andy social science (which is for most part I personally disagree anyway)…I am very sorry if I missed any other subject, but frankly no academic subject relates to my life, neither to the life of 11 y o, period. Have I wasted my life going to school until my fifth decade? I have hard time believing that. Did I waste my time studying trig., nope. Any math will develop additional analytical skills. Choosing Electrical Engineering major is not possible without trig. Starting learning trig. at college is huge waste of time and money.<br>
I know, maybe we should have only dances in school since they related very well to 11 y o girls. I do not think girls will mind.<br>
And again, there is nothing that is difficult in trig, none, zero, zilch. We are not talking about PhD in Math, we are talking about k - 12. If we want to fall more and more behind in educating our kids, yes, we should teach less and less in k -12, let them have fun, they are just kiddies, they do not need any trig., I agree. However, I would not let my kids escape it, no way…all were bored with math anyway, kids, grandkids, it was very sad to see how they felt about such an exciting subject, the one that should be challenging, not boring.</p>
<p>^^Good post Miami…imagine the happy kiddies at those middle school dances! They might also like art because doodling flowers and butterflies is so much more fun than algebra!</p>
<p>“My sixth grader doesn’t need to be studying trigonometry. Why? How does this relate to her life as an 11 year old?”</p>
<p>Trigonometry is one principal basis for the production of spatial and numerical reasoning abilities. It is also the convention by which more advanced logical reasoning can be accessed. Since you didn’t appear to know this, the absence of your knowledge is the rationale for promoting the acquisition of this knowledge in your child. I hope it doesn’t find root in that “I got by without it, and so will she” mentality.</p>
<p>“It” relates to her life as an 11 year old because she will eventually be a 15 year old and then a 20 year old, and so forth. Unless you plan to curtail her full mental development, and if you intend to have your child advance to college and professional life, she needs this kind of knowledge, as cognitive tools, just as much as she would need a fork to eat spaghetti with, or an automobile to get to work with. Why not rephrase the question:</p>
<p>“My sixth grader doesn’t need to be exposed to standard knowledge or technology. Why? How does this relate to her life as an 11 year old?”</p>
<p>The nature of your question is its own answer.</p>
<p>I’m talking about an 11 year old. If she starts with Algebra in 8th grade that’s fine. I strongly disagree that literature, history, and social studies do not relate to her everyday life. They do! So many ideas, current events, stories, etc, they do relate to the world she lives in. So we read, we discuss, we travel. Trigonometry not so much. That’s for high school. My kid is not a math genius. That’s wonderful for the kids who are inspired by mathematical ideas. But it’s not necessary for everyone. These are children who need to explore childhood. Standards should be fluid.</p>
<p>X posted with polar bear</p>
<p>For an 11 year old? Really? Im not saying she should never take trig, I’m saying she doesn’t need it at 11, and she isn’t going to be impeded in her life if she is not exposed to it in sixth grade. This is just silly.</p>
<p>“Since you didn’t appear to know this, the absence of your knowledge is the rationale for promoting the acquisition of this knowledge in your child”
Did you really just write this, Polar?</p>
<br>
<br>
<p>Here’s a fairly extreme example of unschooling that’s fairly well
known in unschooling circles:</p>
<p>[What</a> Makes Kids Love Math: Community and Playfulness | GeekDad | Wired.com](<a href=“http://www.wired.com/geekdad/2008/10/what-makes-kids/]What”>What Makes Kids Love Math: Community and Playfulness | WIRED)</p>
<p>One of my coworkers used a similar approach with excellent results.</p>
<p>Redpoint, let me engage you in a sort of philosophical discourse. You may note that trigonometry is not “just the math” but also the development of a kind of thinking. It is really a kind of cognitive technology. </p>
<p>So, like you said, what does a 5th or 6th grader need this for? </p>
<p>A related question seems to be: Does any child need to be sure that what they are told is real? </p>
<p>And how does a child become an independent thinker, with the ability to develop her own method for testing the reality of what her culture presents to her? </p>
<p>One way is to understand at an early age that math is a way of thinking, and “trigonometry” is only a kind of tool. Perhaps in certain school cultures, the methods of certain maths are overcomplexified, but to actually understand what one school of math is for, and what it can do, she will know that it is not for “math geniuses”; it is only another kind of cognitive method for gauging things, seeing reality, and for, eventually, regulating the environment. </p>
<p>So, if she acquires this tool early on, she will gauge things, judge them, and understand them from a different perspective, and have a different view of space and time. It will not stunt her natural development. It will make her more perceptive, and in a way, more powerful because she can control her environment and her reality.</p>
<p>
I think this is nonsense. It’s essentially the same argument that people made when I argued that cursive writing should no longer be taught. I can accept that an 11-year-old may eventually need to know trigonometry, depending on what field of endeavor she pursues, and that it’s a bad idea to cut off options early. But I think it’s silly to suggest that you need to know trigonometry in order to “control your environment and your reality.” Trigonometry is just one of many tools–I don’t think it has any special power.
I do think that algebra is more basic, though.</p>
<p>
</p>
<p>One thing that also needs to be brought up regarding Japanese and German education is that in both societies, it is commonly accepted that not everyone is college material and that it’s not the failing of the teachers, schools, or system if most students do not go on to higher education.</p>
<p>From their equivalent of 8th grade onward, students are tracked into college prep(Gymnasium for Germany, academic high schools in Japan), polytechnics/skilled trade schools*, apprenticeships, or find an unskilled job of some sort. </p>
<p>Moreover, speaking of the Japanese education system, it’s not a system which allows for second chances if one screws up even in elementary/middle school. It is also a society which tends to assume by default that the student is responsible for any shortcomings or failure to achieve unless proven otherwise. </p>
<p>Knew one older Japanese undergrad back in the late '90s who wouldn’t have had an opportunity for a college education because he was involved in one schoolyard fight in 7th grade and as a result, was refused further education. He had to come to the states to finish junior high, high school, and college. By the time he was given a second chance at an education, he already spent several years in the workforce doing various unskilled odd/factory jobs. </p>
<ul>
<li>Incidentally, not learning algebra or other “non-essential” subjects usually taught in high school or select junior high schools could also shut one out/get one kicked out of these polytechnic/skilled trade schools…let alone admission to college.</li>
</ul>
<p>Math is indeed too simple in the lower grades. I would wait until at least sophomore/junior year until instruction of calculus because it takes a certain level of maturity, but perhaps we need to start with a simple form of algebra earlier and keep building off of it from there until calculus. Many people coming into calculus do not have a solid enough of a foundation in algebra, geometry, and trig to truly understand the rigor of the course (delta-epsilon definition of a limit, etc). Now, a counter argument would be that not everyone needs to learn rigorous calculus, but my belief is that calculus is like the list of classic books that everybody should read. Everybody should know it because it really elucidates the beautiful simplicity of mathematics once one understands it.</p>
<p>I think our math curricula should be structured differently. Look at Japan; they have students learning basic calculus at the end of sophomore year - and that’s not even considered an advanced level. The reason is that they return to earlier concepts all the time to make a much more fluid curriculum structure; that way, students don’t forget everything they’ve learned and subsequently don’t need a whole lot of reviewing. When I went there and shadowed my host student (a sophomore), they covered advanced algebra, trigonometry, and logarithms in the same class period, and the kids were able to keep up. I swear, there’s so much wasted time here, and I don’t think American kids are stupid or that it’s their fault for not being more advanced. It’s just that, when they have to spend three years in algebra only to forget the more advanced topics by the time pre-calc starts, we can’t really expect them to compare to the East Asian kids.</p>
<p>I don’t get it- why is trig too hard for a middle schooler? </p>
<p>I don’t get why people have this misconception that math is hard. It’s not, especially if taught right. Trigonometry is nothing especially difficult. It’s just a way of relating parts of triangles to each other. </p>
<p>I think the problem is that we think that it’s too damned hard and set kids back. If trig in grade 7-8 was the norm, as it could be (I took Algebra 1 H in grade 7) and it was taught properly, I doubt that people would have a problem with it.</p>
<p>The problem is threefold.
<p>^Yes, we spend too much time re-teaching math to kids. For instance, in my elementary thru middle school years, the first half of the school year was spent re-teaching everything from last year that the kids forgot over the summer. Only the last half was spent teaching new material. This system is flawed.
I agree with ecouter11 that there is nothing inherently difficult about mathematics. Math is logical. Trigonometry involves nothing more than algebraic manipulations. Geometry only builds off of algebra. If we start educating earlier and stop re-educating, then kids will be able to learn at a new pace. Kids can adjust to this pace, as nothing earth-shattering is taught.
However, I do believe Calculus should be only taught at the post-freshman high school level. It involves a deeper set of critical thinking and reasoning skills that haven’t fully developed in the prefrontal cortex of younger children. In fact, I’ve heard it said that most people don’t even begin to truly understand Calculus (and not just “plug-and-chug”) until a year after they learn it. Calculus, by virtue of its relatively new material, should be taught when the kids are more mature. Until then, schools need to educate children more comprehensively in mathematics so that they have a strong foundation for Calculus, in which complete mastery of algebra and trigonometry are expected.</p>
<p>I think development of basic math skills is by far the most important thing. It’s terrible when you just get pushed through school, not really understanding stuff and then are forced to perform tasks that require a strong understanding of the prerequisite skills.</p>
<p>Ever since I was 6 or 7, my parents would buy me workbooks for various subjects, such as Reading Comprehension, Writing (sadly not grammar- that would’ve been very useful!), and mathematics.</p>
<p>Since there was literally no work throughout elementary school, my parents would give me small <em>assignments</em> from these workbooks. Through this, I could not only practice math, but challenge myself beyond the curriculum and learn. When I was 6, I taught myself the multiplication tables, just because I thought it was cool. When I was 8, I really wanted to learn algebra and so I moved on to a new workbook. </p>
<p>It was basically an accelerated Singapore math method and it worked very well for me and some of my friends. </p>
<p>Math is definitely not too hard or impossible! We just need to be ready to make some major changes to get things to work.</p>
<p>@ptontiger, I agree with you. Calculus certainly requires more mathematical maturity. You need to visualize, translate english into math, and really think about things a bit differently. I actually tried learning calculus myself when I was a little bit younger and it didn’t work out too well. I had a hard time understanding the connections.</p>
<p>I think this was also partially due to an incomplete understanding of concepts from Algebra 2 H/Trig (Really PreCalc at my old school). I can say that it was partially due to my mediocre work ethic frosh year but also due to the strange practices of my teacher. We rarely did real practice problems that reviewed the concepts and more than half the class was very unhappy with their marks (and these math kids ranging from moderately to very talented too, mind you). </p>
<p>It’s such a mess. :-/</p>
<p>
</p>
<p>This should not be a significant issue. Reaching calculus by sophomore year in high school is three grade levels ahead of the normal case (taking calculus as a college freshman), so only the very top students in math will be taking it then. Anyone reaching calculus earlier than that is probably an extreme outlier prodigy in math for whom normal assumptions about math ability and maturity probably do not apply.</p>
<p>On the other hand, if parents and schools are pushing students further ahead in math than they are actually ready, then that leads to various problems, which may be why so many school districts have mandatory slow-pacing of calculus (AB one year, rest of BC the next year).</p>
<p>@ucbalumnus - I definitely see the point in your argument that pushing students past their intellectual ability would invariably damage their learning. But who is to decide when the children are ready? The children? If someone had asked the eighth grade me if I wanted to take trigonometry, I’d have said a resounding “No!” But was I well developed enough in my mathematical skills that I could have? Yes. What children want and what they are capable of are different things. If we don’t push them out of their comfort zone just a little bit, then we are rather underestimating their ability.
So who else can decide? Administrators? Teachers? These may also underestimate the child’s ability due to various factors. For instance, the child may not be trying as hard as he or she can, creating the perception that he or she “cannot” learn the material instead of the reality that he or she “doesn’t really want to.” Recall the distinct “classes” of children at school? The ones who study, the ones who party, the ones who don’t care, etc. So where do we draw the line where we can definitively say “This child is ready”?
All I’m saying is that we need to quicken the pace of learning so that half the year is not spent on relearning the previous year. Also, since trigonometry, geometry, and precalculus material are all based upon algebraic manipulations, it follows that algebra is key. Algebra does not involve any earth-shattering concepts all that different from sixth grade math. Children have the capacity to learn it and therefore have the capacity to learn the subjects arising from it. This is different from Calculus, where completely new concepts are introduced. That is why a slow pace is necessary. Who but mature students can comprehend the delta-epsilon definition of a limit? Who but mature students can solve a transcendental function? Who but mature students can truly understand the meaning and applications of a derivative? The very concepts that make up Calculus are new - it’s like learning a whole new language.
I apologize for the incessant rambling and my tone was not meant to be adversarial in any way.</p>
<p>
</p>
<p>True, but that probably only makes a practical difference when students are on the normal sequence or possibly one year ahead. Yes, these students are the majority of high school students, but they do not seem to be what this sub-discussion is about.</p>
<p>The (uncommon) students who are two years ahead or more (i.e. the top math students and the super prodigies in math) are more likely to enthusiastically take whatever the next math course is until they have taken all of the available courses in their high schools and local community colleges. In other words, these students can be allowed to take the math courses at their own (advanced) pace without any need to “push” (and “pushing” them even further ahead has diminishing returns anyway, due to the limitations of courses offered at the local community college).</p>