Dotwithaperiod 15,213 Posted October 3, 2013 Report Share Posted October 3, 2013 http://www.popsci.com/science/article/2013-08/argument-against-algebra Â I know there are kids who will never "need" certain aspects of higher math, but this article makes me cringe. Link to post Share on other sites

Embassy 676 Posted October 3, 2013 Report Share Posted October 3, 2013 This says it all: Â Â Â So, math is like juggling, and should be reserved for that one weird enthusiastic kid in the class. And the rest of us could be spared the effort of trying to find an equation for tears shed per problem. Â Math should be reserved for the weird. :glare: Link to post Share on other sites

Embassy 676 Posted October 3, 2013 Report Share Posted October 3, 2013 This says it all: Â Â Â So, math is like juggling, and should be reserved for that one weird enthusiastic kid in the class. And the rest of us could be spared the effort of trying to find an equation for tears shed per problem. Â Math should be reserved for the weird. :glare: Link to post Share on other sites

Mom22ns 5,760 Posted October 3, 2013 Report Share Posted October 3, 2013 The problem with the article is that Algebra isn't only needed by the one weird kid in the class. It is needed in computer science. It is needed in engineering and all branches of science, even practical sciences like nursing. Geometry is needed by construction workers. Statistics is needed in science and business people. Â "Advanced Math" is needed by the majority, not the one weird kid. It is true that some will never use algebra again after high school. But it isn't true for a huge number of people and if they haven't learned it, their options are limited. Link to post Share on other sites

8FillTheHeart 34,585 Posted October 3, 2013 Report Share Posted October 3, 2013 Oh my....the comment section--synopsis of the ones that stuck out-- **this is in Popular Science magazine......seriously? **I hated history, literature, social studies.....get rid of the fluff **why should any subject be required. They waste the students time. Â Jeepers. Â Eta: I love this one about renaming Popular Science to "Inconsequential Twit Monthly." Link to post Share on other sites

Candid 735 Posted October 3, 2013 Report Share Posted October 3, 2013 I think the overall argument is dumb unless whoever is making wants to make it about all other subjects. I couldn't help notice that SWB commented on her facebook page favorably about it, but if you ask me algebra 2 is a lot more useful than literary analysis (which I love).Â Â Further from my experience listening to moms, it isn't algebra that makes people math phobic, they are that way long before they get to algebra. From my own experience I found math boring and tedious until I got to algebra so stopping early would have left me without any math skills. Instead I enjoyed math in high school and did statistics (as a social science major) fairly extensively in college.Â Link to post Share on other sites

regentrude 81,686 Posted October 3, 2013 Report Share Posted October 3, 2013 I have many thoughts about this one, but it is a waste of time to write them all. Let me just say one thing: Â Statements like Â The vast majority of the human race, and the vast majority of the college-educated human race never need any mathematics beyond arithmetic to survive successfully, can be applied to virtually everything: writing essays, knowing about the universe, speaking foreign languages, art and music... The majority of people will get by with a great deal of ignorance about a great deal of things. The question is whether we consider this a desirable goal. I don't. Link to post Share on other sites

KathyBC 2,304 Posted October 3, 2013 Report Share Posted October 3, 2013 He's on to something, IMO.Â Â Â Â Cornell University mathematician Steven Strogatz told Baker it alarmed him to see a large portion of students not just not learning in math classes, but actively suffering.We need less math for the average kid, Strogatz said, but more meaningful math. 'We spend a lot of time avalanching students with the answers to things that they wouldn't think of asking.' Baker's solution to the problem is this: We should, I think, create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus...Take students to see the mathematical sequoia, tell them how great it is, but don't force them to climb it until their arms go numb and they fall. If math were an elective, "American science and technology would be unharmed, and a lot of poisonous math hatred would go away instantly. Â Link to post Share on other sites

kiana 11,468 Posted October 3, 2013 Report Share Posted October 3, 2013 It depends. Â I don't think we should require Algebra 2 for just graduation from high school with a general diploma. Unfortunately, with the mad rush to make every single kid college-ready, general diplomas are going the way of the dinosaur. Â I see no issue with requiring it for a college-prep diploma. But I don't see any reason why someone who already knows that they want to be, say, a cosmetologist, needs to work through Algebra 2. If they change their mind at an adult age, there are developmental math classes at community colleges, which I doubt will be going away anytime soon. I do think that every kid who's able should try to pass the course, but someone who's already struggled through algebra with a C- and a load of hard work would probably be better off with a 'consumer math/review and application of algebra 1' course than marching on into further algebra. Â Allowing kids who have already identified themselves as not college-bound to opt out of algebra 2 will allow us to strengthen the course for the students who are more likely to need it. Link to post Share on other sites

regentrude 81,686 Posted October 3, 2013 Report Share Posted October 3, 2013 It depends. Â I don't think we should require Algebra 2 for just graduation from high school with a general diploma. Unfortunately, with the mad rush to make every single kid college-ready, general diplomas are going the way of the dinosaur. Â I see no issue with requiring it for a college-prep diploma. But I don't see any reason why someone who already knows that they want to be, say, a cosmetologist, needs to work through Algebra 2. If they change their mind at an adult age, there are developmental math classes at community colleges, which I doubt will be going away anytime soon. I do think that every kid who's able should try to pass the course, but someone who's already struggled through algebra with a C- and a load of hard work would probably be better off with a 'consumer math/review and application of algebra 1' course than marching on into further algebra. Â Allowing kids who have already identified themselves as not college-bound to opt out of algebra 2 will allow us to strengthen the course for the students who are more likely to need it. Â Actually, I would like to see a departure from the mandatory 12 years of school for non-college bound students altogether. in my home country, those students graduate with a diploma from high school after 10th grade and continue their education in vocational training or apprenticeship for another 2 or 3 years. Only college bound students do 11th and 12th grade. But those get a more rigorous education than here, irrespective of major. Link to post Share on other sites

WishboneDawn 3,816 Posted October 3, 2013 Report Share Posted October 3, 2013 The original article is about Algebra 2, not Algebra and that article should probably be read along with the Popular Science one. Â I don't have an issue with the idea. There`s little enough streaming and specialization in high school and demanding some kids take an Algebra 2 when they could be taking one more suited to their goals seems wasteful. Â Kiana also made the excellent point that by putting all kids in Algebra 2 the course trends to get have to cater to an average student with less interest and skill then it would otherwise. It's a recipe for mediocrity. Â Kids need a strong foundation in arithmetic. They need algebra. They need to be mathematically literate in order to be informed and thoughtful citizens. Everything before Algebra 2 can get them to that point if done well. Let Algebra 2 and beyond be more exclusive for the sake of those who really want and need it. Link to post Share on other sites

WishboneDawn 3,816 Posted October 3, 2013 Report Share Posted October 3, 2013 Actually, I would like to see a departure from the mandatory 12 years of school for non-college bound students altogether. in my home country, those students graduate with a diploma from high school after 10th grade and continue their education in vocational training or apprenticeship for another 2 or 3 years. Only college bound students do 11th and 12th grade. But those get a more rigorous education than here, irrespective of major. I think a lot of people here in NA think trades, vocational training, apprenticeships, etc. signal some sort of intellectual deficit and mean a less rigorous education. Any push for that might be seen as deciding there are kids who are not "smart enough" for college.Â My father left school in grade nine to support his family. He later joined the Canadian air force and became an aircraft engineer. His chosen trade gave him a deep understanding of math and physics. And he was a drop out who had a trade. Â As an aside, one of his friends is a retired physicist from McGill. With him, my dad can get in well over his head. It's fun to see. :D the friend is somewhat envious of Dad who, aside from years of working on planes and helicopters, is now rebuilding a fishing boat because there are many things he'll explain that Dad can't grasp in those terms but has an intuitive or practical understanding of. Making replacement plans to fit the curves and twists in an old boats hull for instance. They're respective understandings complement each other and it's neat to watch them in conversation. Link to post Share on other sites

Julie in MN 603 Posted October 3, 2013 Report Share Posted October 3, 2013 is true that some will never use algebra again after high school. But it isn't true for a huge number of people and if they haven't learned it, their options are limited. Â I actually think you use algebra when grocery shopping and deciding which size is cheapest, or when purchasing something and deciding whether you will have enough for your space or your recipe.Â No, you may not use the quadratic equation in particular, but you are creating equations.Â Algebra is helping you develop dexterity and accuracy.Â I'm a fan of algebra as a practical course for being a good consumer, if nothing else. Â Julie Link to post Share on other sites

Dicentra 3,853 Posted October 3, 2013 Report Share Posted October 3, 2013 I think a lot of people here in NA think trades, vocational training, apprenticeships, etc. signal some sort of intellectual deficit and mean a less rigorous education. Any push for that might be seen as deciding there are kids who are not "smart enough" for college. Â :iagree: Â And this is a truly unfortunate thing. Â I'm going to say this and it's probably not going to be popular but here I go... Â There are some people who are not intellectually cut out for university. Â (Ducking rotting vegetables and angry retorts...) Â I think we do young people an enormous disservice when we give them trite advice like "You can be anything you want to be!". Â I'm sorry - that just isn't true. Â Given my sturdy, peasant physique :D, I will never be a ballerina. Â Given my complete and utter lack of artistic ability, I will never be a professional artist or designer. Â I will never play hockey in the NHL. Â I will never be a poet. Â There are countless strengths that I wasn't born with and to live a contented, fulfilled life I need to recognize that and work with the strengths I WAS born with. Â Trades are an integral and valuable part of modern life. Â If hands-on skills and working with one's hands are strengths for a particular student, why on earth do we make that student feel like he/she should ignore that and try to push him/her into an academic arena that values a narrow kind of intellectual ability? Â Aren't we setting the student up for, if not failure, an extremely difficult struggle to attempt to conquer an area that doesn't AT ALL complement his/her natural strengths? Â It just doesn't make any sense to me. Â Don't get me wrong. Â I'm not one of those "all nature, all the way" folks. :) Â I do believe we can improve our skills and abilities in areas that are not our natural strengths. Â I'm sure if I took dance classes, I could learn to enjoy dancing as a recreational hobby. Â I could probably learn a few skills in art class in order to paint for enjoyment. Â But I still won't ever be a professional ballerina and NO ONE will ever pay me for a painting. :D Â I've learned to be OK with that. Â I have often heard that we shouldn't "crush the spirit" of students so we need to make sure we never tell them they can't do something. Â I don't think that it's "crushing the spirit" of a student to help the student recognize his/her strengths and weaknesses and to guide him/her towards a career that will tap into the strengths. Â But that's only my two cents. :) Â (Edited to fix all of the times I switched between using singular pronouns and plural ones and all of the instances of improper plural pronoun use. Â Apparently, writing is NOT one of my strengths. ;)) Link to post Share on other sites

kiana 11,468 Posted October 3, 2013 Report Share Posted October 3, 2013 Actually, I would like to see a departure from the mandatory 12 years of school for non-college bound students altogether. in my home country, those students graduate with a diploma from high school after 10th grade and continue their education in vocational training or apprenticeship for another 2 or 3 years. Only college bound students do 11th and 12th grade. But those get a more rigorous education than here, irrespective of major. I agree with this for sure, as long as a student who goes for a vocational program after 10th grade can go back to adult education later to complete the college-prep track, if they so choose. I know you have said that you can do this in Germany, and we should also allow this. Â Honestly, what I think I would do is have 'graduation' moved to after 10th grade with transcripts covering 8-10 grades. For their last two years, students could choose between going to the CC for a vocational associates, going to CC for a transfer associates, going directly to university if they are an accelerated student, going directly to work, or continuing at the high school in a 'life skills' program if they have serious special needs. Â This also allows us to give a significant carrot to students who are indifferent about working in school and just want to move on with their lives -- we can tell them 'If you pass the 10th grade graduation exam and all your mandatory courses, you can leave and go to work. Otherwise, you have to stay in school until you are 18.' Link to post Share on other sites

lewelma 17,011 Posted October 3, 2013 Report Share Posted October 3, 2013 I'm going to be dodging rotten eggs too. Â I have been a high school math teacher, and I know from experience that there is a significant portion of high school students who can not get through Algebra 1, let alone Algebra 2.Â And that it is a complete waste of time to try. Â First of all, let me define Algebra 1 so that we are on the same page - I am talking about using a book like Jacobs.Â I understand that recently Algebra 1 has been dumbed down in many states so that it can be taught in 8th grade, this is not the course I am talking about (because I have not taught it). Â I worked in a school which streamed the students into 4 streams, and I was teaching both the 2nd and 3rd stream (so not the lowest or highest).Â My lower stream class was taking algebra, and I remember being shocked that they could not do even basic problem solving. These kids were 15!Â Every morning I would put a word problem on the board that did not have any algebra in it just to keep them relating math to the real world.Â And at least half of the students would not know even where to start.Â Here is an example: Â You have an L shaped driveway that is of xxx dimensions and you wish to pave it with bricks.Â The bricks are xxx dimensions.Â How many bricks do you need to buy? Â No WAY could they do this problem or others like it, and I was teaching them quadratic equations!?!?!Â Â There is just a disconnect between the standard math curriculum and a large number of students.Â I would argue that 20% of kids will really struggle with Algebra 1, and a good 40% will struggle with algebra 2.Â It is not that these students do not need math instruction, they just don't need algebra.Â What I would argue that they do need is math that they will actually encounter in life.Â I am not talking about shopping and taxes, I am talking about problem solving and statistics.Â Students need to be able to understand the math that they see in the news - which is the statistics behind medical claims, environmental claims, polls, etc.Â And they can learn to interpret and understand this material with a minimum of algebra.Â Plus any algebra that would be required could be taught from the point of view of "you actually need to know this to be able to read this newspaper that I am holding."Â Â I think that requiring Algebra 2 for graduation is absolutely nuts.Â Â ---- ducking now ---- Â Ruth in NZ Link to post Share on other sites

AdventureMoms 612 Posted October 3, 2013 Report Share Posted October 3, 2013 Â I agree with this for sure, as long as a student who goes for a vocational program after 10th grade can go back to adult education later to complete the college-prep track, if they so choose. I know you have said that you can do this in Germany, and we should also allow this. Â Honestly, what I think I would do is have 'graduation' moved to after 10th grade with transcripts covering 8-10 grades. For their last two years, students could choose between going to the CC for a vocational associates, going to CC for a transfer associates, going directly to university if they are an accelerated student, going directly to work, or continuing at the high school in a 'life skills' program if they have serious special needs. Â This also allows us to give a significant carrot to students who are indifferent about working in school and just want to move on with their lives -- we can tell them 'If you pass the 10th grade graduation exam and all your mandatory courses, you can leave and go to work. Otherwise, you have to stay in school until you are 18.' Â I really like this. I have a brother, he is about 28 now. When he was around 9th or 10th grade, he wanted to go to a vocational program at my school. This led to a local diploma, not college-bound. My father was totally dead said against it, because he wanted his son to go to college, like my father never did. My mother pointed out that I three he was going, my brother was not going to make it through high school, let alone into college. He had no motivation, and was totally disinterested in school. He ended up in the vocational program, and did extremely well in it. They got him interested enough in school that he went on to get his associates degree from a trade school. If wanted to, he could have gone on in college from there. He still could, many four year schools would take him with an Associates degree. He really just needed something practical to focus on. By 15 or 16 years old he was just done with the standard school model. There were a lot of these people in my school, I think 11th and 12th grade classes could be more rigorous and better for the rest of us, if those who have no interest in being there can be given a different way to meet their goals. Link to post Share on other sites

Azalea 1,069 Posted October 4, 2013 Report Share Posted October 4, 2013 Ruth in NZ, just out of curiosity, where was the school you were teaching in?Â Link to post Share on other sites

Julie in MN 603 Posted October 4, 2013 Report Share Posted October 4, 2013 I'm going to be dodging rotten eggs too. Â I have been a high school math teacher, and I know from experience that there is a significant portion of high school students who can not get through Algebra 1, let alone Algebra 2.Â And that it is a complete waste of time to try. Â First of all, let me define Algebra 1 so that we are on the same page - I am talking about using a book like Jacobs.Â I understand that recently Algebra 1 has been dumbed down in many states so that it can be taught in 8th grade, this is not the course I am talking about (because I have not taught it). Â I worked in a school which streamed the students into 4 streams, and I was teaching both the 2nd and 3rd stream (so not the lowest or highest).Â My lower stream class was taking algebra, and I remember being shocked that they could not do even basic problem solving. These kids were 15!Â Every morning I would put a word problem on the board that did not have any algebra in it just to keep them relating math to the real world.Â And at least half of the students would not know even where to start.Â Here is an example: Â You have an L shaped driveway that is of xxx dimensions and you wish to pave it with bricks.Â The bricks are xxx dimensions.Â How many bricks do you need to buy? Â No WAY could they do this problem or others like it, and I was teaching them quadratic equations!?!?!Â Â There is just a disconnect between the standard math curriculum and a large number of students.Â I would argue that 20% of kids will really struggle with Algebra 1, and a good 40% will struggle with algebra 2.Â It is not that these students do not need math instruction, they just don't need algebra.Â What I would argue that they do need is math that they will actually encounter in life.Â I am not talking about shopping and taxes, I am talking about problem solving and statistics.Â Students need to be able to understand the math that they see in the news - which is the statistics behind medical claims, environmental claims, polls, etc.Â And they can learn to interpret and understand this material with a minimum of algebra.Â Plus any algebra that would be required could be taught from the point of view of "you actually need to know this to be able to read this newspaper that I am holding."Â Â I think that requiring Algebra 2 for graduation is absolutely nuts.Â Â ---- ducking now ---- Â Ruth in NZ Â Ruth, no tomatoes but does the fact that schools are failing to teach kids basic math necessarily mean that they are incapable of or not in need of any algebra skills?Â When I was a kumon tutor, we had lots of failing public school kids, and I agree that basic computation is fundamental.Â But we took them back to those basics and by cementing them, they were pretty much always able to move ahead.Â Â I just don't see how kids could read the newspaper if they were unable to plug unknowns into an equation, move it around with some dexterity, and come up with what they need to know -- which to me is "algebra."Â Statistics would be great, but can you truly understand the skewing of statistics by the media if you can't move equations around and see whether they are equivalent?Â I am forever frustrated by the success of vague marketing strategies that seem built on the assumption of poor mathematical education, by insuring the equation gets convoluted.Â But there I am about consumers again. :)Â I do think it applies to the news, too -- somehow it seems you must need algebraic thinking to figure out the other side, what they're not saying, and whether it all comes out to 50-50 or what.Â The assumption isn't so much that folks can't calculate but that they can't or don't easily put together a string of information to locate, and solve for, the unknown.Â This seems to be what you're frustrated with in your students.Â Don't you think that this kind of math understanding culminates in algebra, with solving for unknowns? I'm not necessarily a fan of Jacobs Algebra, and I don't think that means dumbing down is the only other alternative.Â My dd came out of public school in 10th grade after failing math (along with everything else) and it was more a matter of finding a math program that taught her well, rather than her inability to master algebra.Â The first programs I thought would help didn't, either.Â It's a complicated issue.Â It seems impossible for a classroom teacher to solve for such a large group.Â Â Sometimes I hate the whole algebra focus on the quadratic formula.Â But then I think having one focus is probably teaching a lot of different skills along the way.Â And when our math program explained some of the uses of the quadratic, it made it all the more palatable for us.Â And I don't have a better idea for an algebra focus that incorporates as many skills, anyway. Â I'm not a die-hard fan of algebra 2, but I know several people who failed algebra 1 miserably and aced algebra 2.Â In some ways, it's just a repeat and expansion, so maybe they just needed more time on the subject, or more maturity.Â Or it could be that a new teacher or new text explained it better for them.Â I still remain a die-hard fan of algebra 1 :)Â And if someone struggled with that, I'd hate to eliminate the possibility that Algebra 2 would be the key. Â Interesting conversation. Julie Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 Just one added comment about algebra 2: the exponential and logarithmic function are typically taught in algebra 2. Understanding the behavior of the exponential function is vital for understanding compound interest. And understanding compound interest is something everybody who borrows money, either as a mortgage or through a credit card balance, needs - so this is a real life application not restricted to STEM students! Â Maybe the financial crisis would not have been as bad if people had a better understanding of the underlying math. You can't have financial literacy without math, math beyond simple arithmetic. Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 My lower stream class was taking algebra, and I remember being shocked that they could not do even basic problem solving. These kids were 15!Â Every morning I would put a word problem on the board that did not have any algebra in it just to keep them relating math to the real world.Â And at least half of the students would not know even where to start.Â Here is an example:Â You have an L shaped driveway that is of xxx dimensions and you wish to pave it with bricks.Â The bricks are xxx dimensions.Â How many bricks do you need to buy? Â No WAY could they do this problem or others like it, and I was teaching them quadratic equations!?!?! To me, this does not prove that the students are intrinsically incapable of learning algebra, i.e. that their brains are not able to handle this. To me, this illustrates primarily that whatever math instruction they had prior to high school was seriously lacking and that they have never been taught critical thinking skills. Â Sure, there is a certain percentage of students with metal retardation or learning disabilities who can not ever learn math - my brother is one of them. But there is a much larger percentage of students who would do a lot better in math had they been taught from the very beginning by teachers who themselves are proficient in, and enthusiastic about, math. Â I find it much more likely that your student had a rotten math education than that you have only been seeing special needs students in your classes. Link to post Share on other sites

kiana 11,468 Posted October 4, 2013 Report Share Posted October 4, 2013 Maybe the financial crisis would not have been as bad if people had a better understanding of the underlying math. You can't have financial literacy without math, math beyond simple arithmetic. Â I think you are overestimating the average person's propensity for rational behaviour when they think they can get something for nothing :p Â We should spend a lot of time teaching "If it seems too good to be true, it probably is" Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 I think you are overestimating the average person's propensity for rational behaviour when they think they can get something for nothing :p Â We should spend a lot of time teaching "If it seems too good to be true, it probably is" That, of course, too. :001_smile: Â But I also genuinely think that many people do not have the slightest idea how compound interest works and how quickly a debt grows, and what difference a small change in interest rates makes. Imagining it graphed might help... some of them. Link to post Share on other sites

Dicentra 3,853 Posted October 4, 2013 Report Share Posted October 4, 2013 Do you (the general "you") think that we're talking about two (or more) different algebras here? Â Depending on where each one of us went to school, how long ago we went, and the curriculum that we're familiar with based on our homeschooling choices, our ideas of the concepts that would be included in algebra (either 1 or 2) will be different. Â Our ideas of how algebra is taught will be different as well. Â I find myself nodding and agreeing with lots of opinions in this thread - even when they seem to be on different sides of the discussion. :) Â I don't actually think that it's so much a matter of "Which math should a given student stop at?" but probably should be a question of "How do we best teach math to students with different end goals?". Â I've always looked at the teaching of math as being philosophically split into two camps - algorithmic and conceptual. Â For students that are going on to university, a conceptual (or "understanding-based") approach to math is vital. Â For students that will only use math in a practical sense in later life (everyday math - cooking, shopping, finances), maybe an algorithmic approach to math would be better. Â I've taught and tutored many students and, going back to my earlier post, some of their brains are simply not set up to understand math conceptually. Â You can see the look of relief on their faces when you take the conceptual explanation and simply turn it into an algorithm. Â I know math education (like every other educational field) has gone through swings of the pendulum over the years - schools taught all math algorithmically, then they went to conceptually, back to algorithmically, etc. Â I think, currently, the math education muckity-mucks have decided that conceptually is the best way to go. Â Based on my time both inside and outside the classroom, I just don't think that every child's brain is hard-wired to understand math conceptually. Â Teach conceptually first but then also teach the same concept algorithmically for those students who can't process the conceptual explanation. Â I'm not talking about only special needs students, here - there is a great number of neuro-typical students who are not hard-wired to understand math concepts. Â They can learn the algorithms and learn where to apply them but they'll never understand (or care!) how those algorithms were derived. Â I agree with previous posters who have said that if we had truly interested, proficient math teachers in the early elementary years, the number of students capable of understanding math conceptually at the high school algebra level would probably be increased. Â But I still don't think it would be all of them. Â And even if we had all those wonderful math teachers in the elementary system, I still think we need to approach high school algebra in the way I described above - each concept presented conceptually and then algorithmically. Â As to the "Where does a given student stop in math?" question, I think that's a difficult question to answer since there doesn't seem to be a firm consensus as to what is included in each level of math. Â What one of us might be thinking of as belonging in Algebra 2, another might be thinking belongs in Algebra 1 depending on where and when we went to school. Â One last point. :) Â Idealistically, of course I would love to have every student capable of understanding math conceptually. Â It would make the teaching of science vastly easier. ;) Â Realistically, I just don't think it will ever happen. Â When I teach moles, stoichiometry, limiting reagents, equilibrium calculations, and a host of other chem concepts that require math, I teach each concept conceptually and then algorithmically. Â It works. Â The students who can process and understand the conceptual explanations are probably the ones who are going to go on to STEM careers - they are working with their strengths. Â The ones who don't have natural strengths in understanding math conceptually are eternally grateful for the algorithms, can pass the class, and never take chemistry again. :D Â Just my additional two cents (for a running total of four cents :)). Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 Â For students that will only use math in a practical sense in later life (everyday math - cooking, shopping, finances), maybe an algorithmic approach to math would be better. Â I've taught and tutored many students and, going back to my earlier post, some of their brains are simply not set up to understand math conceptually. Â You can see the look of relief on their faces when you take the conceptual explanation and simply turn it into an algorithm. Â Â Â When I teach moles, stoichiometry, limiting reagents, equilibrium calculations, and a host of other chem concepts that require math, I teach each concept conceptually and then algorithmically. Â It works.Â Â Question: It has been my experience that people "forget" math. People who have been taught to memorize a specific algorithm will most likely not remember a longtime later what to do. Simple example: dividing by fractions. Many adults vaguely remember "there was something being flipped". Ouch. In contrast, something that has been understood once will never be really forgotten. With the students in your example, I'd be worried that the algorithmic procedure ("first I do this and then i do that" ) will not be retained in the long term -whereas conceptual understanding is virtually indestructible and can still be retrieved decades later. So, to extend the question: is there value in teaching students something they will have forgotten after one semester? What good does it do that they can do stoichiometry (or something else) precisely now, but won't retain the concept in the long term? Â I still wonder if we could not train children toÂ a better abstract critical thinking if we incorporated it differently in early education. All small children are curious and want to know why things are the way they are. It is only when they have made the experience that those questions will not be answered and will be seen as a nuisance, something that happens mainly in schools, but also some families, that kids develop the intellectual laziness of "just tell me the procedure so I can work the problem and get my points". I think this is learned behavior. Maybe if formal education did more to encourage children's curiosity and foster critical thinking, kids would still want to know "WHY?" when they are teens. Link to post Share on other sites

8FillTheHeart 34,585 Posted October 4, 2013 Report Share Posted October 4, 2013 I can understand the argument that not all students need alg2 or capable of achieving that level of mathematical competence......but I don't really accept the argument that it isn't necessary bc is irrelevant to everyone other than STEM majors. Independent tradesmen would be well-served understanding basic quadratic functions/relationships in terms of their business costs/profits. Â I think one area where math education fails is that math is taught simply as solving equations instead applied concepts. Link to post Share on other sites

Corraleno 32,203 Posted October 4, 2013 Report Share Posted October 4, 2013 I still wonder if we could not train children toÂ a better abstract critical thinking if we incorporated it differently in early education. All small children are curious and want to know why things are the way they are. It is only when they have made the experience that those questions will not be answered and will be seen as a nuisance, something that happens mainly in schools, but also some families, that kids develop the intellectual laziness of "just tell me the procedure so I can work the problem and get my points". I think this is learned behavior. Maybe if formal education did more to encourage children's curiosity and foster critical thinking, kids would still want to know "WHY?" when they are teens. Â :iagree:Â :iagree:Â :iagree:Â Â Jackie Link to post Share on other sites

WishboneDawn 3,816 Posted October 4, 2013 Report Share Posted October 4, 2013 I can understand the argument that not all students need alg2 or capable of achieving that level of mathematical competence......but I don't really accept the argument that it isn't necessary bc is irrelevant to everyone other than STEM majors. IndN-Gageependent tradesmen would be well-served understanding basic quadratic functions/relationships in terms of their business costs/profits. Â I think one area where math education fails is that math is taught simply as solving equations instead applied concepts. But it's not simply in running a business that math is important when it comes to trades. Whether you're laying brick or rebuilding an aircraft engine there's often some fairly demanding math involved. Many trades are not too far removed from engineering themselves. Â I'm thinking more on Dicentra`s last post with regards to what constitutes Alg 2. Heck, there was no such thing when and where I went to school as it was, and remains, integrated. Â Maybe we need a discussion that's centered on teaching kids what they need for their expected careers rather then if they need Alg 2? Is math for flexible then either/or Alg 2? Link to post Share on other sites

Laura Corin 38,870 Posted October 4, 2013 Report Share Posted October 4, 2013 I really like this. I have a brother, he is about 28 now. When he was around 9th or 10th grade, he wanted to go to a vocational program at my school. This led to a local diploma, not college-bound.Â Â My brother was similar but the pressure came from the school. Â He was great with his hands and quick at arithmetic. Â He would have made a good joiner or something. Â Instead, the school pushed him into academic subjects, I think because we were a middle class family, and he didn't do well. Â He dropped out of college (he was training to be a drama teacher) and has had bits and pieces of various jobs, none fulfilling, most minimum wage. Â I think my parents trusted the school.. Â L Link to post Share on other sites

lewelma 17,011 Posted October 4, 2013 Report Share Posted October 4, 2013 Ruth in NZ, just out of curiosity, where was the school you were teaching in?I taught math in NZ.Â Here math is integrated, so each year students increase their skills in geometry, algebra, and statistics.Â For many students the time spent reviewing the material each year is very helpful.Â This is why I was still teachingÂ the material traditionally taught in the USA during Algebra 1 to 15 year olds, because by that time they had already completed a course in geometry and basic statistics. Link to post Share on other sites

lewelma 17,011 Posted October 4, 2013 Report Share Posted October 4, 2013 Ruth, no tomatoes but does the fact that schools are failing to teach kids basic math necessarily mean that they are incapable of or not in need of any algebra skills?I definitely think that it is a failure of earlier schools. But I also think that there are a lot of kids that do not need traditional algebra. They might get through the class and know how to move this or that around, but it has absolutely NO meaning to them. They very quickly forget anything about algebra, it is just too abstract. Teach it to them as a part of using spreadsheets, or as a part of finance, or as a part of a 'statistics in the news' class. But for many students it MUST be applied to be retained. Â I just don't see how kids could read the newspaper if they were unable to plug unknowns into an equation, move it around with some dexterity, and come up with what they need to know -- which to me is "algebra."Â Statistics would be great, but can you truly understand the skewing of statistics by the media if you can't move equations around and see whether they are equivalent?I have thought long and hard about this 'statistics in the news' class that I would like to teach. I would spend 4 months teaching the kids to thinking statistically and probabilistically by teaching them non-parametric statistics. These stats can be done with no algebra and done on either a spreadsheet or by hand. You are just ranking and counting. Once my student understood the purpose of statistics and how to actually do nonparametric statistics, I would spend 5 months going over the basics of distributions, generally what you are testing for with means vs distributions, and how to *understand* and *interpret* (not do) parametric statistics. They need to have a large overview of the possibilities of statistics in order to understand a newspaper or the statistician at their job. A black box for the details is ok. Any algebraic manipulation that needed to be taught would be taught in context of a larger goal. This is key. Link to post Share on other sites

shawthorne44 6,320 Posted October 4, 2013 Report Share Posted October 4, 2013 Since when did Algebra become Advanced Math? Â Â educators say algebra is the major academic reason for dropping out Â This quote had me laughing and crying.Â In which planet is this true?Â Link to post Share on other sites

lewelma 17,011 Posted October 4, 2013 Report Share Posted October 4, 2013 I don't think that NZ has brilliant math education, however it is instructive to see how other countries do things. Â You must pass algebra 1 to attend college Â You do not have to pass the equilavent of USA algebra 1 to graduate from high school. All kids take 9th grade math which does have some basic algebra in it (it is an integrated math class). Â If you don't meet the entrance requirements for university after you finish high school, you can wait 2 years and enter university none competitively at age 20 on a provisional basis. At that point if you had not taken or passed algebra, you could take it as a part of your provisional requirements. Link to post Share on other sites

8FillTheHeart 34,585 Posted October 4, 2013 Report Share Posted October 4, 2013 But it's not simply in running a business that math is important when it comes to trades. Whether you're laying brick or rebuilding an aircraft engine there's often some fairly demanding math involved. Many trades are not too far removed from engineering themselves. Â I'm thinking more on Dicentra`s last post with regards to what constitutes Alg 2. Heck, there was no such thing when and where I went to school as it was, and remains, integrated. Â Maybe we need a discussion that's centered on teaching kids what they need for their expected careers rather then if they need Alg 2? Is math for flexible then either/or Alg 2? Â :iagree:Â I didn't mean to suggest just business costs, but it was simply one that leaped out in my mind.Â Â When people say that alg or alg 2Â are never used again in their life, I have to wonder if it is b/c they simply associate those terms with factoring equations and not real life situations.Â Â Â Sadly though, I am never surprised by how poor people's math skills are.Â Â We went to a Monte Carlo fundraiser at church and were playing black jack and the woman dealing at our table couldn't even add the cards to determine who was winner unless it was a 10/face card and one other card.Â Â It was beyond pathetic.Â Â Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 I don't think that NZ has brilliant education, however it is instructive to see how other countries do things. Â You must pass algebra 1 to attend college You do not have to pass the equilavent of USA algebra 1 to graduate from high school. All kids take 9th grade math which does have some basic algebra in it (it is an integrated math class). If you don't meet the entrance requirements for university after you finish high school, you can wait 2 years and enter university none competitively at age 20 on a provisional basis. At that point if you had not taken or passed algebra, you could take it as a part of your provisional requirements. Â In Germany, every university bound student must take calculus in high school, irrespective of planned major. Â Students on the non-college bound track cover: linear equations and systems of linear equations in 8th grade quadratic equations in 9th grade the exponential function and trigonometric functions in 10th grade. Geometry is taught interspersed, every year. Those students graduate after 10th grade with a non-college-bound high school diploma. And did not start school until first grade at age 6 or 7. Â I find it remarkable how different countries have so different expectations about student abilities: stuff that is considered "advanced" here in the US because students do not have the "maturity" is taught in the lowest track high school to kids of the same age back home. I think we are expecting far too little in this country. I wonder what we have to show for *13* years of schooling.... Link to post Share on other sites

lewelma 17,011 Posted October 4, 2013 Report Share Posted October 4, 2013 Absolutely fascinating, regentrude. Clearly Germany has better elementary and middle school math teachers than NZ, because by the time i got these students at age 15 there was no way i could teach them at that level. Link to post Share on other sites

lewelma 17,011 Posted October 4, 2013 Report Share Posted October 4, 2013 Regentrude, there must be a certain portion of the population with lower IQs (perhaps lower than 80) that cannot take these math classes. Statstically speaking, is it not about 15%? What happens to those students? Are they sent to other special schools? NZ mainstreams everyone, so perhaps I am seeing more students than what you would find in a traditional school in germany. Link to post Share on other sites

regentrude 81,686 Posted October 4, 2013 Report Share Posted October 4, 2013 Regentrude, there must be a certain portion of the population with lower IQs (perhaps lower than 80) that cannot take these math classes. Statstically speaking, is it not about 15%? What happens to those students? Are they sent to other special schools? NZ mainstreams everyone, so perhaps I am seeing more students than what you would find in a traditional school in germany. Â Students with extremely low IQs that are considered mentally retarded are not mainstreamed, but attend special schools. I have a mentally retarded brother who can not even learn his abc or count to ten - of course those kids are not expected to pass any math. Â And yes, even among those who attend regular schools, there are students who will fail math. A student who fails math has to have passing grades in the other subjects in order to pass 10th grade. But just because a certain small percentage may fail, the standards are not lowered to a level where everybody will pass: the students who are capable of passing are still expected to do so and taught at that level. This may be the biggest difference to the US system, where the bar is lowered until everybody passes, but capable students don't learn because nothing is expected of them. (Btw, I don't think the students who fail 9th grade math in Germany know any less math than students who pass 12th grade "basic math" in a US high school and basically sit through a regurgitation of elementary arithmetic every year until they are 18. ) Â Extremely low performing students have the opportunity to finish after 9th grade with a third kind of diploma (depending on state). in my state, they would be in the 10 grade school, but leave a grade earlier. Some states have three different kinds of schools; mine only has two. Link to post Share on other sites

Julie in MN 603 Posted October 4, 2013 Report Share Posted October 4, 2013 Â I have thought long and hard about this 'statistics in the news' class that I would like to teach. I would spend 4 months teaching the kids to thinking statistically and probabilistically by teaching them non-parametric statistics. These stats can be done with no algebra and done on either a spreadsheet or by hand. You are just ranking and counting. Once my student understood the purpose of statistics and how to actually do nonparametric statistics, I would spend 5 months going over the basics of distributions, generally what you are testing for with means vs distributions, and how to *understand* and *interpret* (not do) parametric statistics. They need to have a large overview of the possibilities of statistics in order to understand a newspaper or the statistician at their job. A black box for the details is ok. Any algebraic manipulation that needed to be taught would be taught in context of a larger goal. This is key. Â What a blessing you would be to help educate the next generation.Â Maybe you could write a homeschool curriculum?! Â Â Just one added comment about algebra 2: the exponential and logarithmic function are typically taught in algebra 2. Understanding the behavior of the exponential function is vital for understanding compound interest. And understanding compound interest is something everybody who borrows money, either as a mortgage or through a credit card balance, needs - so this is a real life application not restricted to STEM students! Â I always learn something new on homeschooling boards! Link to post Share on other sites

Teachin'Mine 1,887 Posted October 5, 2013 Report Share Posted October 5, 2013 Regentrude, as they differentiate for students depending on their abilities or test scores, I'm assuming it's determined by testing, what do they do for the students who are able to be more advanced than the majority of university bound students who are taking calculus?Â Â Do they have "gifted" education, or something similar under a different name? Link to post Share on other sites

regentrude 81,686 Posted October 5, 2013 Report Share Posted October 5, 2013 Regentrude, as they differentiate for students depending on their abilities or test scores, I'm assuming it's determined by testing, what do they do for the students who are able to be more advanced than the majority of university bound students who are taking calculus?Â Â Do they have "gifted" education, or something similar under a different name? Â No, there is no gifted education, except for very few boarding schools, and some magnet schools for students with special talents in math& science o languages or arts. The split into the two tracks happens in 5th grade based on grades and parental wish; it is about 50-50, so not a particularly strong selection. There is NO testing; we don't have standardized tests at all, and schools do not perform IQ tests as it is standard in the US. Â In 11th and 12th grade, students are required to select a certain number of subjects in which they are going to take advanced instruction while taking the remaining subjects at the regular level. A student with a strong math interest would be able to choose math as one of his advanced subjects. The regular math for all university bound students is differential calc in 11th, integral calc including transcendental functions in 12th, plus some statistics, vectors, and analytical geometry in both years. Students with advanced math study the same topics at a deeper level and add some multivariable calc and differential equations. In both classes there are some optional topics from which students can choose. Students take the courses designed for their grade; they do not choose language class x plus math course y plus science course z. Consequently, particularly strong students don't take "calculus" a year earlier than their classmates; they could only skip an entire grade across the board in all 12 subjects. I do not believe that grade skips in the last two years are possible, but they happen in elementary and middle grades. Link to post Share on other sites

lewelma 17,011 Posted October 5, 2013 Report Share Posted October 5, 2013 Regentrude, I am still a bit confounded as to where some of my students would go in the education system if they were in Germany. Â Like I said before, I taught the 2nd and 3rd streams out of 4.Â The lowest stream were students with intellectual disabilities and did not take standard classes, but were still in the school (I did not teach these students).Â Let me paint a picture for the lower stream of the two streams of 10th grade math that I taught.Â They were all considered capable of taking standard 10th grade math, which finishes up Algebra 1, Geometry, and basic statistics: Â Class #1 (24 students): 8 students were medicated for ADD/ADHD with varing success 1 student was a 'coke' baby and was 'normal' in intelligence but had some *extreme* behaviours 1 student tried to commit suicide the year I taught her 1 student was was a refuge from Africa, and clearly had some PTSD Â Class #2 (25 students) (this class was specially created to cluster these types of kids that had be kicked out of other schools): 3 students were so violent that they had personal body guards that attended my class everyday and protected the other students from their outbursts.Â I did observe 1 of these incidents when the student started throwing *desks* across the room 1 student was cutting himself, and was later murdered that year 2 students were clearly on drugs everyday 3 students had a homelife which not conducive to any study (I will not say more, but you can use your imagination and you won't be far off) 2 students where English was their second language, and they were not very proficient. 1 student was in foster care and was so much trouble that he kept loosing his foster family.Â Some days he would come to school and tell me that he had to go back to the social worker's office that night to find a place to sleep. Â So all 25 students were intellectually capable, but half in each class just did not have a chance to pass.Â These are clearly not typical classes in NZ, but they do represent the students that I am talking about.Â Most of them did have assigned social workers helping them, but I was still expected to teach them algebra, which to my mind was completely unrealistic and pointless (although I did try). Â Does Germany not have any students like this?Â If they do, where are they?Â Are they really passing linear algebra in 8th grade and trig by 10th?Â Are they just required to take these classes, and then fail them?Â Can students with the 3rd type of diploma (if available) get a job?Â If they can't pass quadratics can they still get the 3rd type of diploma? Â Sometimes life gets in the way of education.Â And IMHO, if these students cannot get that little piece of paper called a high school diploma without passing Algebra 1 (let alone Algebra 2), how do we expect them to get a half-way decent job?Â They are not going to be brain surgeons, they just need a high school diploma in America to get a job. Just a job.Â Â I will say again that there is a disconnect between the current math education and *certain* students.Â They *do* need math education, they just don't need Algebra. And by focusing all our efforts on Algebra, we lose the opportunity to teach them the math that they actually need to function in society and be a part of the voting public. Â I completely agree with you that the bar should not be lowered for most students. I just don't know how to help the students that I have taught if they have to reach a bar set impossibly high for them. Link to post Share on other sites

goldberry 30,774 Posted October 5, 2013 Report Share Posted October 5, 2013 Actually, I would like to see a departure from the mandatory 12 years of school for non-college bound students altogether. in my home country, those students graduate with a diploma from high school after 10th grade and continue their education in vocational training or apprenticeship for another 2 or 3 years. Only college bound students do 11th and 12th grade. But those get a more rigorous education than here, irrespective of major. Â I have been in favor of a system like this for a long time.Â I think it would work well for alot of people.Â Â Â Has it ever been tried in America?Â Link to post Share on other sites

Candid 735 Posted October 5, 2013 Report Share Posted October 5, 2013 In Germany, every university bound student must take calculus in high school, irrespective of planned major. Â Students on the non-college bound track cover: linear equations and systems of linear equations in 8th grade quadratic equations in 9th grade the exponential function and trigonometric functions in 10th grade. Geometry is taught interspersed, every year. Those students graduate after 10th grade with a non-college-bound high school diploma. And did not start school until first grade at age 6 or 7. Â I find it remarkable how different countries have so different expectations about student abilities: stuff that is considered "advanced" here in the US because students do not have the "maturity" is taught in the lowest track high school to kids of the same age back home. I think we are expecting far too little in this country. I wonder what we have to show for *13* years of schooling.... Â Having gone through the Singapore equivalent of what every student must do, I must say they have similar list for their noncollege bound students as well. The Singapore math folks say you can count what they do as an Algebra II course. They even dabble in a bit of calculus, and this all by tenth grade.Â Link to post Share on other sites

MIch elle 730 Posted October 5, 2013 Report Share Posted October 5, 2013 I have been in favor of a system like this for a long time.Â I think it would work well for alot of people.Â Â Â Has it ever been tried in America?Â Â It's done at the vocational/technical schools.Â http://worcestertechnicalhigh.com/ Â Link to post Share on other sites

DarlaS 528 Posted October 5, 2013 Report Share Posted October 5, 2013 My one "weird" kid who loves math just got his first job. As a programmer! He's 19 and the youngest the company employs. Â Not all of his younger siblings share his love for math, however. It does seem like most degrees any of them would be pursuing require at least Calc 1. I guess they'll be learning it anyway... Â I am very much in favor of skill specific "co-op" or vocational type programs. Much of what is done for careers should be learned by actually doing it. Link to post Share on other sites

kiana 11,468 Posted October 5, 2013 Report Share Posted October 5, 2013 I have been in favor of a system like this for a long time.Â I think it would work well for alot of people.Â Â Â Has it ever been tried in America?Â We used to have a much better vo-tech system and a lot more tracking. We also had a lot of classism/racism where students who should have been college-bound were stuffed into a vocational diploma or a lower track because 'you know how those people are'. This still goes on today in some corners of the country. Â I don't remember exactly where, but I remember reading someone's blog (she's somewhere in the south, teaching middle school) where she was ranting about how she had white students with a 15th percentile score on last year's end-of-grade test in the upper-track class and black students with a 70th percentile score on THE SAME end-of-grade test in the lower. Â This is asinine and wrong. Now, I think that halting the whole system of tracking because of this sort of idiotic behavior is throwing the baby out with the bathwater. But there were very good reasons why people pushed to move away from it. Link to post Share on other sites

DarlaS 528 Posted October 5, 2013 Report Share Posted October 5, 2013 We used to have a much better vo-tech system and a lot more tracking. We also had a lot of classism/racism where students who should have been college-bound were stuffed into a vocational diploma or a lower track because 'you know how those people are'. This still goes on today in some corners of the country. Â I don't remember exactly where, but I remember reading someone's blog (she's somewhere in the south, teaching middle school) where she was ranting about how she had white students with a 15th percentile score on last year's end-of-grade test in the upper-track class and black students with a 70th percentile score on THE SAME end-of-grade test in the lower. Â This is asinine and wrong. Now, I think that halting the whole system of tracking because of this sort of idiotic behavior is throwing the baby out with the bathwater. But there were very good reasons why people pushed to move away from it. It makes no sense to give tests and choose to ignore the results. o.O Â However, no one middle school aged or above should be placed in one track or other without it being at least partly their choice. Who says that a kid who struggles with math in 7th grade can't be an engineer someday? Maybe the kid who excels in math would rather be a journalist... Â That said, the numbers do reveal more about ability than personal bias (assuming the tests themselves are not somehow biased... which may be assuming a lot). Given a choice between the two (if they *must* put kids on one track or another) they really need to go with the numbers. Link to post Share on other sites

Teachin'Mine 1,887 Posted October 5, 2013 Report Share Posted October 5, 2013 Thank you Regentrude, it's interesting how differently each country handles education, and obviously differences within areas of the country as well. Link to post Share on other sites

regentrude 81,686 Posted October 5, 2013 Report Share Posted October 5, 2013 Does Germany not have any students like this?Â If they do, where are they?Â Are they really passing linear algebra in 8th grade and trig by 10th?Â Are they just required to take these classes, and then fail them?Â Can students with the 3rd type of diploma (if available) get a job?Â If they can't pass quadratics can they still get the 3rd type of diploma? Â Of course there are those students, too, mainly in large cities with a high immigrant population. Language issues are a big problem in those schools; there are second and third generation immigrant students who are not fluent in German because they socialize exclusively with students from the same background and their families are not encouraging German language learning. And of course there are also home life issues, drug abuse. Students who are severely disturbed, have issues with violence and PTSD, can attend special schools (Foerderschule fuer Erziehungshilfe). They would have very small classes, more personnel, counseling, behavioral training, but I am not personally familiar and can not give details. I do not know which portion of students with issues are attending those schools. The curriculum guidelines for those schools, however, are the same as for regular schools, and attending is usually temporary with the goal of returning to a main stream school. Â The other students attend the non-college bound school in states where there are two tracks, or the lowest tracking 9th grade school in states where there are three. The will spend a number of years reaching 9th grade, would typically repeat grades, and hopefully will receive the 9 year diploma ("Hauptschule"). As I said elsewhere: some will fail math, but they can still graduate if they pass in enough other subjects. Â Their job perspectives are not good. In Germany, you don't just go work somewhere, you have to train for pretty much any job through vocational training or apprenticeship, and that would be the normal path for students graduating from 9th and 10th grade. There are very few jobs that require no qualification whatsoever, much fewer than in the US (As I explained once in another post: you go to school to be a secretary, or to work in retail.). It is difficult to find an apprenticeship with a 9th grade diploma, and there are a lot of initiatives and special programs to get these young people into some kind of training. Students who dropped out of school without even completing the 9th grade diploma are a pretty hopeless case, with hardly any prospects. Some are just not employable and will fall through the cracks. Â ETA: Just to clarify: the point of my earlier post was solely that there are differences in what is considered developmentally appropriate in math for average students. I did not mean to imply that all German students magically can fulfill these requirements - but that what is expected and considered achievable for a student of a certain age seems to be a lot more than in the US. Link to post Share on other sites

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