Arcadia 17,756 Report post Posted December 2, 2013 Does anyone have any thoughts on the British approach. As I understand it, Mechanics is integrated at the A-level in math. How beneficial is this for either math or physics majors? Mechanics is one of the options for Math and Further Math at O Level/GCSE and A Level exams. Statistics is one of the other option. The Mechanics portion gave me extra practice for my Physics A Level exams (whether or not you need it) The Statistics option is useful too as statistics was also tested in engineering math. I'm not sure how helpful it is for math or science majors. I went on to engineering. Share this post Link to post Share on other sites

bnbacademy 114 Report post Posted December 2, 2013 All of our sons are going into STEM majors. All will have calculus 1 in high school and two will have calculus 2. Faith Just curious... How did your sons get to calc 2? Did they take 2 math courses simultaneously? Share this post Link to post Share on other sites

FaithManor 30,770 Report post Posted December 2, 2013 8FilltheHeart, I agree and firmly believe that kids who arrive at college hoping to major in math or science having only completed Algebra 2, are not going to make it. First off, college trigonometry/ pre-calculus will be considered remedial for them. They will have to take that course first semester and pay top dollar to do so, but it won't count towards graduation for them as a math/science major. Yes, it might satisfy the math requirement for a music or art major, an English or History major, BUT NOT a science major. This will likely keep them out of other science pre-requisites the first semester. Second of all, people might be shocked to find out how many other pre-requisites not related to math the student might be prevented from taking. One of the trends in science majors is to house majors together, and gear the general education requirements towards the intended major instead of everyone taking gen ed from the same list of options. For example, many science majors will have "College Writing for Science Majors" which is very different from other college writing programs and is geared towards technical writing. DS will have an unusual college writing course as a comp sci major that will go through some basics for quicklyt, but then delve into skills needed to write software documentation for end users as well as business documents. It is not at all like the class that the Anthropology majors will take. So, if one is pre-empted from declaring his/her intended major due to needing to fulfill a remedial math requirement, one can then also be prevented from fulfilling other gen ed requirements as well. I always recommend to parents that when planning ahead for college/trade school, take a look at your child's strengths and weaknesses, natural talents and bents, etc. and then look at some college catalogs and trade school flow charts to see what possible paths your child might need to be on in order to complete a specific program in the traditional time frame. For dd, pre-calculus as a nursing major would have been remedial math and kept her out of the necessary chemistry rotation in order to get into clinicals and field study on time. When she decided to declare a chemistry/pre-med major, we were ever so glad we'd gotten her through a semester of calculus before she left for college and that was very valuable to her in keeping her 4.0 for her first semester of college which included college chemistry, biology, calculus 1, and a couple of very stout gen ed courses. Except for possibly humanities majors, I firmly believe that only completing algebra 2 could be a significant set-back and still, if one needs merit aid, then one has to consider what the other humanities majors may have accomplished. If they have approximately the same abilities and extra-curriculars and had that fourth year of math and science, well, all of the other things being fairly equal, the money goes to the one with the more competitive transcript. In terms of students who make it through pre-calc but not calc 1 and want to be STEM majors, I think the really motivated, determined, nose to the grindstone, resourceful students can still make it through the STEM Major. These are the students who will find out what tutoring is available, go see the professor during office hours, hang out with a study group, and put aside social life in order to get a good grade in calculus 1 and move on and keep up with the flow. But, those that are very interested in science or engineering, and maybe have an affinity for it, BUT expect that their college experience should include a not too taxing first semester, socializing, and NOT worrying about competing with other students for research positions or grades in courses where the professors use a curve, they may very well drop the major. If they drop before the deadline and classes aren't full, it might be possible to switch to something else, however for a lot of kids, dropping means getting behind and not graduating on time. It may also mean a loss of scholarships. So, I do believe some students will make it, however there will be more in that boat that do not. A lot will depend on just how devoted the student is to the dream of being an engineer, pharmacist, environmental researcher, etc. For the most part, if there aren't learning disabilities, given how competitive college admission's is and many middle class families need for some level of merit aid, I tend to recommend that the minimum for high school graduation for students going directly to universities and more competitive LAC's is pre-calculus not algebra 2 and even for those going into highly technical trades such as the electrical journeyman's program, alternative energy contracting, or two year ADN programs. Faith Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 2, 2013 Just curious... How did your sons get to calc 2? Did they take 2 math courses simultaneously? Some students start the high school math sequence in 7th grade. Both my kids did. I didn't rush them though. I made sure they were rock solid on basic math and rock solid in Algebra I. My dd is in public school now. Her math course in 10th grade is a precalc course. The school has multivariable calculus and linear algebra in alternating years for those students who finish calculus and still have one or two more years of high school left. It's not unusual. However, there are a lot of kids in dd's class who clearly have rushed through with no understanding. She comes home with stories of classmates who can't add fractions, and who can't algebraically manipulate formulas to move all variables to one side of an equation. Those kids may be aiming for STEM, but if they don't rebuild the foundation they won't make it. So, glad I taught my dc math without calculators and short cuts. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 2, 2013 Just curious... How did your sons get to calc 2? Did they take 2 math courses simultaneously? Kids that start alg in 8th grade can make it through cal 2 by 12th grade: 8th-alg1 9th-geo 10th-alg 2 11th-pre-cal 12th-2 semesters of college cal or AP cal BC (which will give credit for cal 1 and cal 2 with a score of a 5.) Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 2, 2013 Absolutely agree. I can't imagine what engineering dept would accept a student with only alg 2. Acceptance into the university and acceptance into a dept are 2 different things. Then add in getting into a specific major. W/in the engineering dept there are going to be levels of competitive acceptance. That is not necessarily true. Our students do not even have to declare their major immediately - they get admitted to the university, not a specific department. For those that think students should repeat cal at the university, do you believe that students that arrive only having completed pre-cal and place into cal are going to be at a disadvantage to students that repeat cal? Depends on your definition of disadvantage. Can a student successfully pass the calc 1 course at university without previous calculus at high school? Absolutely, even with an A. Will the student then be prepared for subsequent calculus courses at the university? Yes. Will the student develop the same deep insight as a student who intentionally repeats the course in order to delve deeper (not because he never understood, or forgot, all his high school calc)? No, he will not. But then, many students may not have this goal of thorough deep understanding, but merely the goal of a good grade. That's fine, too. I am just being honest when I say that I believe kids arriving with only alg 2 are at a serious disadvantage as a STEM major and are probably far less likely to complete a STEM degree. Again, the answer is "it depends". It depends on the reasons a student has only competed math through algebra 2. Very often, this is a sign of lacking aptitude, i.e. the student struggling in math, which would also mean the student is not suited for a STEM major. If, however, there are other reasons - illness, moves, substandard school - unrelated to the student's abilities, the student will only lose time, but can still be successful. We see students with high school precalculus still test into remedial college algebra. We see students with AP calculus quite often place into remedial trigonometry! Having taken a class is not the same thing as having mastered the material, and I would always err on the side of caution and go slower with a thorough understanding than faster just to have "calculus" on the transcript - and then have the student end up losing a year because he has to repeat college algebra and trig since he failed the placement test. Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 2, 2013 Just curious... How did your sons get to calc 2? Did they take 2 math courses simultaneously? My DD did: algebra 1 in 8th geometry in 9th algebra 2 and precalculus in 10th calc 1&2 in 11th multivariable calculus (=calc 3 ) 12th all courses at home. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 2, 2013 Again, the answer is "it depends". It depends on the reasons a student has only competed math through algebra 2. Very often, this is a sign of lacking aptitude, i.e. the student struggling in math, which would also mean the student is not suited for a STEM major. If, however, there are other reasons - illness, moves, substandard school - unrelated to the student's abilities, the student will only lose time, but can still be successful. Does your school keep stats that would indicate the number of students starting with pre-cal and graduating with degrees in engineering? The reason I am skeptical is b/c of just how many students change majors out of engineering (maybe this is different at your school since they don't declare when applying) and how many students even with solid math backgrounds aren't finishing their engineering degrees in 4 yrs. I'm not saying it isn't feasible, but I do think that it is far more unlikely. Share this post Link to post Share on other sites

Heigh Ho 8,312 Report post Posted December 2, 2013 For those that think students should repeat cal at the university, do you believe that students that arrive only having completed pre-cal and place into cal are going to be at a disadvantage to students that repeat cal? I am just being honest when I say that I believe kids arriving with only alg 2 are at a serious disadvantage as a STEM major and are probably far less likely to complete a STEM degree. Their disadvantage is going to be based on how strong their coursework was. Around here, high school pre-calc is remedial, for those that struggled in A2/Trig. Nonstrugglers take College Algebra and Trig, a semester each and that course is deeper in both topics than the year of high school pre-calc. The subsequent college course to pre-calc is a semester version of CA/Trig at the state schools, then one begins calculus in one's major. For a strong student, weak high school program, there is not going to be a disadvantage other than more time is required to fill in background knowledge. My son is in this position now; it's been a good start to take CA/Trig with people who really know how to teach it to visual spatial learners plus operate a math learning center as opposed to high school instructors who write off v-s learners and nonaccelerated students. There are some institutions that have generated statistics to show what the grad in five years odds are for a person arriving with an A2 background, split by SAT math score and math completed prior to enrollment. One has to keep in mind that some of these students are quite intelligent and will overcome their poor high school offerings given a chance..the odds are not zero for someone who has only completed A2. For the last state school I visited, the eng. prof giving the presentation was quite emphatic that high school physics was needed, but calc was not. He was aware of the issues in the various high schools, and prefers no calc over a poorly taught or shallow calc, and encouraged students who are in high schools where calc is not offered to still consider his program -- looking for learners & willing to work with them. The problem of no Regent's Physics ...the recommendation is a 3-2 transfer program for people in that situation; alternatively DE senior year if the high school doesn't have the needed courses (inthis area many high schools have no money for nonrequired classes, which includes R. Physics and all math after Algebra 2/Trig). When I was an engineering major, many of my fellow students entered with no calc. Their high schools simply didn't offer it. Not a problem, and not a disadvantage as they would learn it before they needed it for other coursework. Not ready for precalc though, would set them back a year. Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 2, 2013 Does your school keep stats that would indicate the number of students starting with pre-cal and graduating with degrees in engineering? The reason I am skeptical is b/c of just how many students change majors out of engineering (maybe this is different at your school since they don't declare when applying) and how many students even with solid math backgrounds aren't finishing their engineering degrees in 4 yrs. I'm not saying it isn't feasible, but I do think that it is far more unlikely. I am sure somebody is keeping stats, but I could not find any by a quick search. Most students are not finishing in 4 years anyway (4 year graduation rate is 27%), which does not necessarily mean that those are weak students; the best students take semesters off for coops and intenrships. Our university is untypical, since pretty much only students with a strong engineering and science interest are coming here, very few students choose this school specifically for a humanities major. So, even if they do not declare major, the default is pretty much "some kind of engineering" when they end up coming here. Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 2, 2013 When I was an engineering major, many of my fellow students entered with no calc. Their high schools simply didn't offer it. Not a problem, and not a disadvantage as they would learn it before they needed it for other coursework. Not ready for precalc though, would set them back a year. And I have encountered students whose pathetic rural high school did not even offer trigonometry! For those students, not having completed trig is not an indication of future lack of success. It will just cost them time. And money. Share this post Link to post Share on other sites

katilac 16,765 Report post Posted December 2, 2013 <snip> For dd, pre-calculus as a nursing major would have been remedial math and kept her out of the necessary chemistry rotation in order to get into clinicals and field study on time. When she decided to declare a chemistry/pre-med major, we were ever so glad we'd gotten her through a semester of calculus before she left for college and that was very valuable to her in keeping her 4.0 for her first semester of college which included college chemistry, biology, calculus 1, and a couple of very stout gen ed courses. <snip> Okay, this really shows how important it is to check the requirements/recommendations at the schools you are likely to be interested in. I would not have thought that nursing majors would need to be past pre-calc, and indeed a quick check of 2 of the nursing schools near show that neither of them require calculus or pre calculus in the program, much less before starting the program. One lists college algebra as a pre-req; the only thing I recognize as "math" in the actual program is Biometry/Statistics. Checking a few randomly (in various places), I haven't come across one that requires calculus yet. Statistics and variations thereof seem to be the most common - I am not seeing a lot of math courses, but I'm sure many of the 'nursing' course must include math. This is for a BSN - is that what your dd is going for? I confess that I am totally surprised that an RN degree would require calculus. Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 3, 2013 Yes, it is important to get a check of schools your are likely to be interested in. dd and I visited Virginia Tech last month. She has no idea what she wants to study, so we didn't look into specific departments, but the admissions officer did talk about what is expected on an application. He was addressing a group of about 200. He point blank said " if you are not taking the highest math course offered at your school, then you will not be admitted to the engineering department." To me the message is loud and clear that the vast majority of applicants will have calculus on their transcript. There are a few school districts in Virginia that have small populations and are remote so offering calculus might be difficult in those areas. My dd is in 10th. She requested to do these visits, even though most people seem to suggest waiting. It's been interesting to watch dd as she really pays attention to what the admissions officers say they are looking for. While most schools say a student must have taken algebra 2, these visits are mostly informally telling applicants that is the lowest of the applicant pool and those students mostly are not getting in. It really got me thinking that if you are visiting schools for the first time the spring of junior year, that is really too late to be finding out that the requirements to be considered an applicant with decent chance of admission are much steeper than the requirements listed on the university's website. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 3, 2013 I am sure somebody is keeping stats, but I could not find any by a quick search. I couldn't find any stats either. This link has some interesting demographic info on engineering grads: http://www.asee.org/papers-and-publications/publications/college-profiles/2011-profile-engineering-statistics.pdf Share this post Link to post Share on other sites

FaithManor 30,770 Report post Posted December 3, 2013 Just curious... How did your sons get to calc 2? Did they take 2 math courses simultaneously? [/quote The two boys who will have calc two in high school took algebra 1 in the 7th and geometry in 8th thereby beginning high school in algebra 2. We did not have to accelerate their learning in order to accomplish this. They are both big math enthusiasts and naturally talented in this subject, a trait they inherited from dh. I also credit Singapore Math in the younger grades for challenging their thinking and preparing for the concepts. Eldest boy did algebra 1 twice. Math is not as easy for him as for his other three siblings. But once he got the concepts cemented, he really took off. At first, I thought he would finish high school with precalculus. But he really matured the year that he started algebra two and he completed the course (Lial's) in one semester doing the odd problems and if he earned a 90% or better on the chapter review, I let him move on without doing the chapter exams opting instead for just a midterm and a final. He ended with a 94% and is maintaining a 95% in precalculus. Since we homeschool year around (235 days per yard on average) he will have a nice easy pace for calculus 1 which he will begin, if his current pace holds, in April. So the boys followed a more European or Asian path in math education including an introductory calculus course - trying to remember the name...Newton's Apple or something similar - that helped them discover the beauty and elegance of math. We are also an exceedingly science oriented house. So if a child wanted to attempt a chemistry, physics, or engineering project that required math they had not encountered yet, we didn't say "Maybe when you are older. You haven't had the math yet." Instead we figured that as soon as they could add, subtract, multiply, divide, and have even a rudimentary idea of working with fractions, we could hold their hands through the math. So they are kind of a fearless bunch. I think that the kids have probably benefited from our less American approach to teaching math and science. Faith Share this post Link to post Share on other sites

FaithManor 30,770 Report post Posted December 3, 2013 I do not like typing on my kindle. I have NO idea how my post ended up as a quotation of myself. Sigh... I need to take technology class! Share this post Link to post Share on other sites

FaithManor 30,770 Report post Posted December 3, 2013 Okay, this really shows how important it is to check the requirements/recommendations at the schools you are likely to be interested in. I would not have thought that nursing majors would need to be past pre-calc, and indeed a quick check of 2 of the nursing schools near show that neither of them require calculus or pre calculus in the program, much less before starting the program. One lists college algebra as a pre-req; the only thing I recognize as "math" in the actual program is Biometry/Statistics. Checking a few randomly (in various places), I haven't come across one that requires calculus yet. Statistics and variations thereof seem to be the most common - I am not seeing a lot of math courses, but I'm sure many of the 'nursing' course must include math. This is for a BSN - is that what your dd is going for? I confess that I am totally surprised that an RN degree would require calculus. I meant to say Pre-calc for nursing and calc for pre-pharma, chemistry etc. That said, college trig./pre-calc.was.considered remedial college mathematics for nursing majors at the better schools she looked into. There were also minimum ACT/SAT scores in order to qualify for the prenursing prerequisites. Organic chemistry, not for the feint of mathematical hearts, was one of the weeder classes for the top unis. They also hinted that the students getting the nursing scholarships were the ones taking the Guppy top math and science courses in high school. Dd applied primarily to universities in the top tier with nursing departments boasting 90-99% board passage rates hence the competition for merit money. As it was, she ended up choosing pre-med/chemistry. So I'm very glad we got that semester of calc one in and I wish we had known about Singapore math when she was younger so she could have begun algebra sooner. That said, I guess we didn't do to poorly with her. She is almost done withbuer chemistry degree and has a 4.0 at U of MI. and completed her EMT and Paramedic training as well. And yes that was a big mommy brag and I'm proud of her! Share this post Link to post Share on other sites

Gwen in VA 2,571 Report post Posted December 3, 2013 Our four kids have all graduated (except the senior who still has to take Calc 2 next semester) with math through Calculus 2. 8th grade -- Algebra 1 9th grade -- Geometry 10th grade -- Algebra 2 11th grade -- Precalculus 12th grade -- Calc I and Calc 2 at the local highly-ranked 4-year college I totally agree that having a strong background in algebra is THE key to success in math / science / engineering. I also strongly maintain that having calculus in high school is a huge advantage, so if possible it's good to have both a great algebra background AND calculus. It shouldn't be either / or. Share this post Link to post Share on other sites

Heigh Ho 8,312 Report post Posted December 3, 2013 And I have encountered students whose pathetic rural high school did not even offer trigonometry! For those students, not having completed trig is not an indication of future lack of success. It will just cost them time. And money. I looked at the money this way -- had I been able to find a similar home in a less rural district that offered math thru DiffEq & moved there, I would have paid an additional $12,000 in property taxes per year. That's a bit less than one semester of state college plus dorm here. So, not moving gave me plenty of savings to use to pay for supplemental texts, DE, and internet courses plus any needed extra classes in college. I am surprised though that your students' home districts weren't able to offer Trig via independent study or internet coursework. But then maybe it's too costly -- here the teachers get $4K/student for independent study courses so the super. has cancelled all i.s. The district does not pay for DE at all - the parents pick that cost up. I"ve met people here who have graduated their children after three years of high school so that they could get need based scholarships to pay for the fourth year's work/first year community college as there is no help for DE. Share this post Link to post Share on other sites

horsellian 356 Report post Posted December 3, 2013 Does anyone have any thoughts on the British approach. As I understand it, Mechanics is integrated at the A-level in math. How beneficial is this for either math or physics majors? Well I took A level a little while ago, but I've just looked, and it doesn't look like a whole lot has changed. If you are planning on reading maths at uni in the UK you would normally take 'double maths' or 2 A levels of maths - so you'd usually do about half an A level of mechanics, half an A level of stats and a whole A level of pure maths. Some future engineers or physicists will also take double maths. Otherwise, if you're only doing a single A level you can choose, depending on your future plans, to do half pure & half mechanics, or pure & stats, or half pure with a little bit of mechanics and a little bit of stats - this is the easiest option, and it's what I did, but it didn't hold be back particularly as I read Chemistry at a very good university. Share this post Link to post Share on other sites

mackkjackk11 0 Report post Posted December 3, 2013 hiii... Well this is quite useful site for particular forum.For your query, math has to be the key part to be played.Want an expert advice then have a look to... ATI RADEON HD 5670 â€“ SERIES GRAPHICS CARDS FROM AMD Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 3, 2013 reported Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 3, 2013 I totally agree that having a strong background in algebra is THE key to success in math / science / engineering. I also strongly maintain that having calculus in high school is a huge advantage, so if possible it's good to have both a great algebra background AND calculus. It shouldn't be either / or. I agree. Even if students don't make it through cal in high school, having at least 4 yrs of math alg 1 + should be the minimum goal for any student that wants to major in STEM. Many tech universities are going to have a 4 math requirement. I am not convinced that cal is an absolute goal for high school. But, I do think that pre-cal or advanced math or trig/college alg--a math beyond alg 2 leading toward being prepared for calculus--should be a high school objective. Since this is a homeschool board, limits are only imposed by 2 factors.....student ability or parental provider. If the reason for only going through alg 2 is the former, then whether or not the student is strong enough in math to manage a STEM major is not just being dismissive of the possibilities of success in college. It is a prudent question. If the reason is the latter, then a student might succeed, but the student may be at a disadvantage if their math background is weak due to it and will have to take the "boot strap" approach to filling in areas of weakness and gaps.....and be prepared for extra time. Share this post Link to post Share on other sites

Arcadia 17,756 Report post Posted December 3, 2013 This quote from the OECD report released today is interesting. I have not finish reading the report. Just thought it is relevant to this thread because of the understanding what you learn aspect. From PISA 2012 FOR THE UNITED STATES â€“ Â© OECD 2013 (bolded mine, link is a pdf) "Analyses of the items on which United States students performed relatively well indicate that the strengths in their mathematical competence lies in reading data directly from tables and diagrams; simple handling of data from tables and diagrams; and handling directly manageable formulae. In terms of weaknesses, the analysis suggests that U.S. students struggle with tasks requiring students to: use and apply the number Ï€; establish a mathematical model of a given real world situation; genuinely interpret real world aspects; and reason in a geometric context.An implication of the findings is that much more focus is needed on higher-order activities, such as those involved in mathematical modeling (understanding real-world situations, transferring them into mathematical models, and interpreting mathematical results), without neglecting the basic skills needed for these activities." ETA: Analysis of some of the questions start on page 67 of the 106 page pdf. ETA: In easier to read format with more details "Strengthsâ€¢ Reading data directly from tables and diagrams â€“ requiring students only to understand a short text and read single values directly from a representation provided such as a table or a bar diagramâ€¢ Simple handling of data from tables and diagrams â€“ requiring students to understand a short text, read two values from a given representation, and then perform some straightforward operation such as adding or comparing the valuesâ€¢ Handling directly manageable formulae â€“ requiring students to use a formula provided, e.g. inserting numbers for variables, and do some easy calculation. The formulae can be used directly, without any re-structuring. Weaknessesâ€¢ Use of the number Ï€ â€“ requiring students to make explicit use of the number Ï€ in a calculationâ€¢ Substantial mathematization of a real-world situation â€“ requiring students to establish a mathematical model of a given real-world situation in the form of a term or an equation with variables for geometric or physical quantities, before further actions (especially calculations) can take place. Students have to understand the situation and activate and apply the appropriate mathematical contentâ€¢ Genuine interpretation of real-world aspects â€“ requiring students to take a given real-world situation seriously and properly interpret aspects of itâ€¢ Reasoning in a geometric context â€“ requiring authentic reasoning in a planar or spatial geometric context by using geometric concepts and factsâ€¢ U.S. students have particular problems with mathematical literacy tasks where the students have to use the mathematics they have learned in a well-founded manner. Given that even in more demanding tasks some basic skills are nevertheless needed, an implication of the findings is that much more focus is needed on higher-order activities, such as those involving mathematical modeling (understanding real world situations, translating them into mathematical models, and interpreting mathematical results), without neglecting the basic skills needed for these activities" Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 3, 2013 This quote from the OECD report released today is interesting. I have not finish reading the report. Just thought it is relevant to this thread because of the understanding what you learn aspect. From PISA 2012 FOR THE UNITED STATES â€“ Â© OECD 2013 (bolded mine, link is a pdf) "Analyses of the items on which United States students performed relatively well indicate that the strengths in their mathematical competence lies in reading data directly from tables and diagrams; simple handling of data from tables and diagrams; and handling directly manageable formulae. In terms of weaknesses, the analysis suggests that U.S. students struggle with tasks requiring students to: use and apply the number Ï€; establish a mathematical model of a given real world situation; genuinely interpret real world aspects; and reason in a geometric context. An implication of the findings is that much more focus is needed on higher-order activities, such as those involved in mathematical modeling (understanding real-world situations, transferring them into mathematical models, and interpreting mathematical results), without neglecting the basic skills needed for these activities." Basically word problems. ;) The word problems are what I love about Foerster's and the weakness I see in a lot of other programs. Plug and chug or apply what you know. Share this post Link to post Share on other sites

anne1456 353 Report post Posted December 3, 2013 My oldest only got through Algebra II in high school. She was accepted everywhere she applied (mid-level schools) as either an environmental science or biology major without pre-calc. She received merit aid at every school she applied to, ranging from half to full tuition. The math was basically the one weakness in her application, but most students a have weakness somewhere. The results probably would have been different if she had been an engineering major, but not having pre-calc in high school is not a deal breaker for all STEM majors. For my daughter it made more sense to go thoroughly through algebra and geometry and make sure she really understood it rather than push her through pre-calc. It worked because she has been successful in pre-calc, calc and stats in college. And she is thrilled she will never have to take another math class. Share this post Link to post Share on other sites

Teachin'Mine 1,887 Report post Posted December 3, 2013 8, which plug and chug programs? Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 3, 2013 Basically word problems. ;) The word problems are what I love about Foerster's and the weakness I see in a lot of other programs. Plug and chug or apply what you know. But don't you know all those poor kids who are "really good at math, just not good at word problems"? (I can't count how often I have heard or read this, either from the kid, or from a parent, even on these boards) Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 3, 2013 8, which plug and chug programs? MUS for one. It focuses on the operational methods of algebra, but it is very weak in application and all the word problems follow a pattern. If you set up for one, the rest will be set up essentially the exact same way. It is why I use it as pre-alg bc it does help them build very basic alg skills. Foerster's, otoh, if a student doesn't understand the "what's" that they are doing, they will not be able to set up the problems. But don't you know all those poor kids who are "really good at math, just not good at word problems"? (I can't count how often I have heard or read this, either from the kid, or from a parent, even on these boards) Yep. :( Share this post Link to post Share on other sites

flyingiguana 3,071 Report post Posted December 3, 2013 Again, the answer is "it depends". It depends on the reasons a student has only competed math through algebra 2. Very often, this is a sign of lacking aptitude, i.e. the student struggling in math, which would also mean the student is not suited for a STEM major. If, however, there are other reasons - illness, moves, substandard school - unrelated to the student's abilities, the student will only lose time, but can still be successful. What I see going on in our dept is this -- we have a number of very bright students who did well in math and enter with calc 1 or 2 (or even calc 3). And they generally do fine. And then there are a number of other students who didn't get much math background. This can be for a variety of reasons -- goofing off in high school, getting into drugs, going to a school that didn't push kids on in math, having the school decide the student was just kind of dumb and shouldn't do much math (seeing this a lot with ESL students), or maybe even going to a school that didn't offer much math. These kids might just be shut out of a STEM major, except that some colleges do realize that lack of math doesn't necessarily mean the kid has no potential to do the math. They just need some help getting up to speed in the first year. And for some of these kids, they are HIGHLY motivated. And they do just fine, although they may have to work hard. The college can make a big difference in whether kids in this category can succeed in STEM or not. There may be a lot of colleges that just figure it's not their problem. But there are some schools who see that as their job. So they do it. Course, best case scenario is that no one ends up in this situation, but it does happen. It's nice to know there are colleges that can be successful in dealing with it. After graduation, there usually isn't a lot of difference between those kids who came in with calc 3 and those who might not have even had pre-calc -- not in terms of where they may go on to grad/professional school etc, or what jobs they get. There are some kids who come in with little math who really never do get it, despite everyone's best efforts. But, you know, that's ok too. It's just nice that there is a potential for a STEM major after screwing up high school for those who do have the untapped talent in that area. ETA -- I'm in a physics department. However, I've seen the same things happening in the biology and chem depts at this school. Some kids just need a little more time, or a little more confidence, or a math class that actually explains it for the first time. I just hate to write kids off who might be a little "math-slow" in high school. Share this post Link to post Share on other sites

flyingiguana 3,071 Report post Posted December 3, 2013 But don't you know all those poor kids who are "really good at math, just not good at word problems"? (I can't count how often I have heard or read this, either from the kid, or from a parent, even on these boards) Sat next to an engineer at a PTA meeting once. We both heard this line and cracked up. And pointed out that word problems were the whole REASON we found math interesting. Share this post Link to post Share on other sites

bugs 597 Report post Posted December 3, 2013 I did not read all the posts, but I'll give you a personal anecdote about high school math and college STEM. I did graduate high school in 1980 so things may have changed. In 9th grade I took Alg 1, then in 10th I took Geometry. I began loving math by this point so I signed up and took Alg 2 in the summer before my junior year. I wanted to take Calculus as a senior. As a junior my first semester was a trig class. My second semester was to be College Algebra but we moved to a different state. The only math class left that I could take at my new school was Analytical Geometry (I think that was the title). So I finished math at that school in my junior year. No math in my senior year - I was bummed. Anyway, I was accepted into an engineer school and I had to take math modules in areas I had forgotten over the year - but I took them concurrently with my Calc I class. Once I hit college the math was no longer "easy" for me, but I did okay. I did receive my engineering degree, however I was motivated (full ROTC scholarship). So in a nutshell: A student can be successful without taking Calculus in high school just not ideal. Share this post Link to post Share on other sites

Crimson Wife 19,603 Report post Posted December 3, 2013 But don't you know all those poor kids who are "really good at math, just not good at word problems"? (I can't count how often I have heard or read this, either from the kid, or from a parent, even on these boards) Strong math students can still struggle with word problems. A good home educator, however, will recognize this issue and look for textbooks & other resources that place relatively less emphasis on solving straightforward equations and more emphasis on solving tricky word problems. Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 4, 2013 Strong math students can still struggle with word problems. Well, math is "word problems". Anything else is simply computation, arithmetic. Being a "strong math student" means the student understands and is able to apply math concepts to, and make mathematical models for, real situations - in other words, can solve word problems. Being good at arithmetic is not the same thing as being strong in math. (Of course, even strong math students will be struggling with word problems of AoPS and competition level... but that was not what was originally meant, or what was measured in the study.) Share this post Link to post Share on other sites

FairProspects 2,569 Report post Posted December 4, 2013 Well, math is "word problems". Anything else is simply computation, arithmetic. Being a "strong math student" means the student understands and is able to apply math concepts to, and make mathematical models for, real situations - in other words, can solve word problems. Being good at arithmetic is not the same thing as being strong in math. (Of course, even strong math students will be struggling with word problems of AoPS and competition level... but that was not what was originally meant, or what was measured in the study. My dyslexic can rock the problem solving once he understands what the language is asking him to do. It has everything to do with the wordiness and nothing to do with his ability to think the problem through. My dyslexic can rock the problem solving once he understands what the language is asking him to do. He does struggle sometimes with word problems and it has everything to do with the wordiness, not the ability to think it through or to set up the equation. Obviously it is a work in progress but problem solving ability does NOT necessarily = good at word problems. Kids who struggle with word retrieval and vocabulary can indeed be very strong math students who have issues with these types of problems. Share this post Link to post Share on other sites

regentrude 77,356 Report post Posted December 4, 2013 My dyslexic can rock the problem solving once he understands what the language is asking him to do. He does struggle sometimes with word problems and it has everything to do with the wordiness, not the ability to think it through or to set up the equation. Obviously it is a work in progress but problem solving ability does NOT necessarily = good at word problems. Kids who struggle with word retrieval and vocabulary can indeed be very strong math students who have issues with these types of problems. OK, granted. I was not thinking of students with specific LDs. Sorry. Share this post Link to post Share on other sites

FairProspects 2,569 Report post Posted December 4, 2013 No problem. I just know I have posted about difficulties with word problems before and I didn't want you to think we were all lazy educators who only focus on computation. :D There actually is a legitimate disconnect for some math kids. We're working on it. I do realize the importance of word problems and problem solving for higher math. Share this post Link to post Share on other sites

Crimson Wife 19,603 Report post Posted December 4, 2013 Well, math is "word problems". Anything else is simply computation, arithmetic. Being a "strong math student" means the student understands and is able to apply math concepts to, and make mathematical models for, real situations - in other words, can solve word problems. Being good at arithmetic is not the same thing as being strong in math. (Of course, even strong math students will be struggling with word problems of AoPS and competition level... but that was not what was originally meant, or what was measured in the study.) Real world math absolutely comes in the form of word problems. But I personally have a hard time thinking of a student who can easily solve straightforward equations and always scores in the 99th percentile on standardized math tests as being bad at the subject. She's not math-intuitive the way her younger brother is, but I would say that in general she is a strong math student. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 4, 2013 Heigh Ho posted this link on the general board. I was very shocked by the numbers. It reminded me of the conversation here, so I thought I would post the link and one of the graphs. http://nces.ed.gov/fastfacts/display.asp?id=97 (ETA: the stats below are only based on students earning either a standard or honors diploma) I found this link which discusses the number of math credits required for a high school diploma by state: http://files.eric.ed.gov/fulltext/ED535222.pdf I was shocked by both. Obviously my impression of what students are achieving are very skewed. That only 16% of students are taking cal was actually very surprising and that significantly less than 50% are taking pre-cal was even more so. My reading this forum must REALLY skew my thoughts. Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 4, 2013 I was shocked by both. Obviously my impression of what students are achieving are very skewed. That only 16% of students are taking cal was actually very surprising and that significantly less than 50% are taking pre-cal was even more so. My reading this forum must REALLY skew my thoughts. The chart shows all students. Not students go on to post high school education. The chart certainly doesn't show anything about the specific group of students accepted into university level STEM programs. When evaluating what your student needs you need to look at what opportunity you and he want available and build your plan from there. In my house that meant long range planning back in K (I'm a little obsessive like that). I didn't know what my dc were going to do then (I still don't), but I knew I was going to make every effort to keep all the doors open for them to choose from. I live in a competitive area and the best state universities in my state, including liberal arts programs, are expecting to see calculus on the transcript, particularly from applicants in my part of the state (because they know it's readily available public, private and dual enrollment programs). It really helps to know something about the colleges you may be targeting. Keep in mind what they expect to see on a transcript is often more difficult than the "requirements" listed for the university in a college guide or listed on the school's website. That said, I would not continue to push a student through subjects simply to get them on the transcript. Build a strong foundation and only get through Algebra 2. If the student really wants to do engineering, she can take spend a year at cc getting more advanced math and physics. Or she can attend a university with an engineering program, but start as undeclared and spend her first year doing remedial math and then apply to the engineering dept. If the student really has a strong foundation in basics and is determined to go this route they will probably do fine. It will take an extra year of college, but it will work out. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 4, 2013 The chart shows all students. Not students go on to post high school education. The chart certainly doesn't show anything about the specific group of students accepted into university level STEM programs. When evaluating what your student needs you need to look at what opportunity you and he want available and build your plan from there. In my house that meant long range planning back in K (I'm a little obsessive like that). I didn't know what my dc were going to do then (I still don't), but I knew I was going to make every effort to keep all the doors open for them to choose from. I live in a competitive area and the best state universities in my state, including liberal arts programs, are expecting to see calculus on the transcript, particularly from applicants in my part of the state (because they know it's readily available public, private and dual enrollment programs). It really helps to know something about the colleges you may be targeting. Keep in mind what they expect to see on a transcript is often more difficult than the "requirements" listed for the university in a college guide or listed on the school's website. That said, I would not continue to push a student through subjects simply to get them on the transcript. Build a strong foundation and only get through Algebra 2. If the student really wants to do engineering, she can take spend a year at cc getting more advanced math and physics. Or she can attend a university with an engineering program, but start as undeclared and spend her first year doing remedial math and then apply to the engineering dept. If the student really has a strong foundation in basics and is determined to go this route they will probably do fine. It will take an extra year of college, but it will work out. Actually, it wasn't for all students. It was only for honors and standard diploma receivers. And, based on the % of high school grads going on to college, that is still a high percentage of students entering w/o pre-cal and cal. Directly to College (%) High School Graduates - 2008 First-Time Freshmen Directly from High School Enrolled Anywhere in the US - Fall 2008 Nation 63.3 http://www.higheredinfo.org/dbrowser/?level=nation&mode=data&state=0&submeasure=63 The numbers just really didn't fit what I thought was occurring in high schools. FWIW, in no way did I mean to suggest that aiming for alg 2 should be a goal or that that was a good choice for STEM students. It is obviously not a route I have taken with my own kids. ;) I guess I forget just how out of the norm they are. Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 4, 2013 Actually, it wasn't for all students. It was only for honors and standard diploma receivers. And, based on the % of high school grads going on to college, that is still a high percentage of students entering w/o pre-cal and cal. Directly to College (%) High School Graduates - 2008 First-Time Freshmen Directly from High School Enrolled Anywhere in the US - Fall 2008 Nation 63.3 http://www.higheredinfo.org/dbrowser/?level=nation&mode=data&state=0&submeasure=63 The numbers just really didn't fit what I thought was occurring in high schools. FWIW, in no way did I mean to suggest that aiming for alg 2 should be a goal or that that was a good choice for STEM students. It is obviously not a route I have taken with my own kids. ;) I guess I forget just how out of the norm they are. do you know what qualifies as an honors diploma? In my state you can get an "honors" diploma with just algebra 2, but that isn't going to make you a competitive applicant to most universities in my state. Share this post Link to post Share on other sites

8FillTheHeart 30,198 Report post Posted December 4, 2013 do you know what qualifies as an honors diploma? In my state you can get an "honors" diploma with just algebra 2, but that isn't going to make you a competitive applicant to most universities in my state. I would assume it is based on the individual states requirements when reporting the scores. My pt was that the stats were not for all students but actual graduates receiving standard/honor diplomas. I expected a majority to have taken at least pre-cal. FWIW, I have never once stated that it would make a student competitive nor advocating anything. I was simply posting that the stats don't match what I would have thought. All of my kids have had more than 4 math credits upon graduation. (some significantly more.) Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 4, 2013 I would assume it is based on the individual states requirements when reporting the scores. My pt was that the stats were not for all students but actual graduates receiving standard/honor diplomas. I expected a majority to have taken at least pre-cal. FWIW, I have never once stated that it would make a student competitive nor advocating anything. I was simply posting that the stats don't match what I would have thought. All of my kids have had more than 4 math credits upon graduation. (some significantly more.) i'm sorry I sound like I'm picking on you. It's just that the table really doesn't give much relevant info for someone to use it to help a student plan his studies. I'm picking on the table. Not you. You are nice. Share this post Link to post Share on other sites

Teachin'Mine 1,887 Report post Posted December 4, 2013 How on earth do we have any engineers, mathematicians, or scientists who graduated in 1990 or before then? One of the things the above chart show me is that while calculus is expected for some of the most competitive STEM programs, for years calculus was first studied in college, and that can work just fine now for all but the most selective schools. We should encourage our students to pursue their interests, academic or otherwise, and plan their courses according to their abilities at the time. There is definitely more than one way. JMO. Share this post Link to post Share on other sites

bettyandbob 17,679 Report post Posted December 4, 2013 How on earth do we have any engineers, mathematicians, or scientists who graduated in 1990 or before then? One of the things the above chart show me is that while calculus is expected for some of the most competitive STEM programs, for years calculus was first studied in college, and that can work just fine now for all but the most selective schools. We should encourage our students to pursue their interests, academic or otherwise, and plan their courses according to their abilities at the time. There is definitely more than one way. JMO. How much of the student population actually enters STEM programs? Not much Share this post Link to post Share on other sites

Teachin'Mine 1,887 Report post Posted December 4, 2013 Betty, maybe I would have made my point better if I went back another 10 or 20 years to 1970 or 1980 graduates. I'm sure an extremely small percentage, far smaller than the number of STEM majors, took calculus before college. I'd also bet that a fairly significant number of those students taking calculus in high school aren't taking it for a math heavy major, but to get requirements out of the way in high school. I would think that many pre-med students would be inclined to do this, or at least to make it easier for them to achieve an A grade in university. I'm not including pre-meds as STEM majors as they are usually excluded. Share this post Link to post Share on other sites

Crimson Wife 19,603 Report post Posted December 4, 2013 Isn't a "standard" diploma just any diploma other than the SPED one? General ed track students at my high school receive a standard diploma if they pass all the required courses and the state exit exam. It didn't mean they met the admissions prerequisites for the state's 4 year colleges. Even in my affluent suburban hometown, not every kid aspires to a 4 year college. I had a number of classmates who enlisted in the military, went to trade school, or just got some entry level job. Share this post Link to post Share on other sites