# Math Myths

Discussion in 'General Education' started by mmswm, Oct 20, 2008.

1. ### mmswmModerator

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Oct 20, 2008

I've been hearing a lot recently about difficulties with either learning or teaching Mathematics. Some of the things I've been hearing really bug me: things like "I'm just no good at math", or "Math is just not my thing". I hear this from students and teachers alike (and not just here...at work as well). Would you admit to not being able to read? To me, hearing these things is just like hearing somebody say "I'm just not good at reading" or "reading just isn't my thing". I'm not talking about advanced mathematics, but basic arithmetic. Anyway, I decided to share something that might help people out with their students' (or their own) attitudes and views about mathematics. This is reproduced with permission of the author.

Myths and Misperceptions in Mathematics

Math is impossible to understand unless you have a “math brain”
This is not true. While it is true that some people like math more than others, anybody can at least become proficient at math. Classroom math is just a formalization of things we do in everyday life. Some examples: planning a trip (distance formula, lines, solving for an unknown), grocery shopping (basic arithmetic, decimals, and percentages), shopping sales (addition, percentages), household budget (systems of equations), and cooking (fractions).

I’m just dumb when it comes to math. Many people have themselves convinced they’re just “math idiots”. This is one of the most damaging things a student can think. Unfortunately, the power of the mind is amazing, and if you tell yourself that you’re never going to learn something, you probably won’t.

Once you fall behind, you can never catch up. While it may not be easy to catch up if you fall behind, with a little work and a lot of time, you CAN catch up. Learning math is like learning to play a sport. You have to practice it. If you fall behind, you just have to devote more time to practicing the material you haven’t yet learned, and then learn the new material.

Men are naturally better at math than women.
We hear a lot about how men are better than women at math and math related subjects. There is some factual basis to this myth in that men do tend to do better in logic based subjects; however, much of this can be attributed to societal expectation. It hasn’t been too long since it was considered a waste of time to teach women math. Girls were taught basic arithmetic and that was it. Boys, however, were expected to learn math and for the most part they did. Unfortunately today, both boys and girls struggle with math, but for different reasons. Girls are taught that they have to fight nature to learn math and boys believe that they don’t really need it, so both genders don’t do as well as they could. Obviously, girls can and do learn math. There are many great female mathematicians both presently and in the past. The only thing that these women did differently is that they refused to believe what society was telling them.

Math isn’t really that useful in everyday life.
As discussed above, math is used frequently in everyday life. You can’t get through a single day (unless you sleep the whole day) without using a fair amount of math. Recently I gave a class an assignment to pay attention to when they used math in the course of their day. They had to keep a “math journal” for one day. The journals were very enlightening to them. They found math in places they expected, such as the gas pump and the grocery store, and also in places that they never expected, such as deciding whether or not they had time to go out with friends or if they could get home to watch a favorite TV show.

3. ### TeacherGroupieModerator

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Oct 20, 2008

Brava, mm! Thanks for sharing this!

4. ### ShebaCompanion

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Busting all those myths still doesn't overcome one simple fact: math is terribly, terribly boring (to around half the population). I had four different math teachers at secondary school. Did they all fail to make math remotely interesting or was the problem with me? I really don't see what is the point in forcing students with no interest, and perhaps very little aptitude, to study math beyond about grade 8 or 9. Once students are numerate, can do basic arithmetic, have a basic understanding of geometry, and can think abstractly with numbers math should be treated like foreign-language learning - something for those who have a specific interest and aptitude.

And for students with little interest, all those hours wasted in secondary school classrooms amounts to virtually nothing. I cannot remember a single thing I learned in grade 11 math (I didn't have to take it in grade 12, thank God); yet, when I wrote the GRE, I finished in the 66th percentile on the math component. About half the people taking the GRE are science or engineering majors. That means I beat at least 32%, probably more, of science and engineering majors on a test of basic arithmetic, algebra, and geometry, despite not having had a math lesson in ten years. Studying advanced-level math when there's no need to use it is rather like advanced language lessons when there's no opportunity to practice it: a waste of time learning things that will quickly be forgotten.

5. ### CeyberRookie

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Oct 20, 2008

As a math teacher and engineer, I have to disagree

Mathematics can be interesting! You have to get the right teacher though. Math needs to be taught properly, with lots of student involvement, a ton of manipulatives, and lots of real life applications. To teach math properly requires good inservice, or learning properly in your B. Ed. classes.

In regards to how it shouldn't be required, I again have to disagree. Mathematical thinking is logical thinking, it's noticing patterns in our lives, and it should be just as required as English or History or any of the arts.

Finally, why close doors? Far too many university courses require math, at some level. Many require it as an entrance, but some more require it to function properly within the course. Why cut off advertising, management, economics, all of the sciences, teaching, law, medicine, etc from students when they don't really know how they feel about math?

Bad teaching is one thing, but assuming math is boring or not important is incorrect. If you watch a good teacher teach math, you will enjoy yourself, and if you learn math long enough, you pick up the logical and critical thinking strategies that you wouldn't otherwise have.

6. ### ShebaCompanion

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Oct 21, 2008

You know, what's ironic about the 'let's make it more interactive and interesting' argument is that for subjects I disliked, those were often the teachers I liked the least. I would much rather just have some old fuddy-duddy who droned on at the front and let me tune out.

I agree with you about the relationship math and logic, and one of the most interesting and useful classes I ever took at uni was Introduction to Logic in the philosophy department. I think that statistics can also be quite useful.

As for math being just as important as English, there are no calculators and computers that can help you with input and output when it comes to writing. If I have to process statistics for a study I can just give the data to someone who's good at it to do an ANOVA and tell me what it means. And merely having an idea of what it means and how it works probably already puts me ahead of some of my schoolmates who did sit through twelfth-grade mat. It's not going to affect my abilities as an English teacher very much because it's a set of skills I'll rarely use. On the other hand, if you can't write grammatically, your marks on education courses will be dramatically lower, you won’t get into graduate school, and your better students will question your intellect. Unlike English, math is only a fundamentally necessary skill to a certain basic level.

7. ### TeacherGroupieModerator

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Oct 21, 2008

I've heard math majors make the exact opposite of this claim, Sheba - that reading and writing anything but math was useless and boring and there was no reason why they should have to endure classes about Shakespeare or Homer. And I've heard similar claims of uselessness about history, and about science, and about any other domain you care to name.

In no case does the claim hold water.

The teacher who really reaches all students isn't the one who slices and dices knowledge into this compartment or that and then declares one domain or another not worth pursuing, but rather the teacher who can connect not only with the strengths of the students who share his strengths but also with the strengths of the students whose strengths diverge from his.

If certain high school math classes are alienating all but all handful of students who are mathematically talented, then, yes, the teachers of those classes have something to answer for. And the same is true of English classes and science classes and history classes and, again, any other domain you care to name.

8. ### AliceaccMultitudinous

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Are you saying that, as of age 14, students are capable of deciding what's important for them to know?

You say that you finished in the 66th percentile. Knowing what that means, and the implications of it, are important! So we need to know statistics. Otherwise, when people manipulate statistics to make a point or sell a product, we won't recognize the problem. One obvious example: you state that math is boring for about half that population. A student who hadn't studied statistics might tend to take that as an actualy statistic, simply because you're a teacher. Hopefully a student who had studied his math would realize that what sounds like statistical data is sometimes a person's opinion-- a totally different matter.

Algebra teaches problem solving. True, the odds are that most people will never have to solve a problem which starts with "Two trains leave Chicago, traveling in opposite directions...." But, properly taught, the ability to solve that problem will enable kids, and the adults they'll become, to organize information in order to solve other problems they'll encounter along the way.

Geometry teaches logic. Properly taught, it teaches kids the ability to start with seemingly disjoint information, and form them into a logical argument. Are you saying that the ability to recognize a false arguement isn't a skill we need?

Trig is the study of the real world. It teaches more problem solving, but this time related to the shapes in the world around us.

And don't let the calulator myth fool you. A calculator can only give you the answer to the problem that's put in. A person who doesn't know which buttons to push is lost. Watch any group of kids taking the math section of the SATs. The kids who do well are those who spend most of their time on problem solving. Those who jump to press the calculator keys for each problem are the ones who are in trouble.

ANY class that's poorly taught is a problem, not because of its subject matter, but because of poor teaching. (Oh, oh. We're back to the subject of mediocrity in American schools.)

If kids complain that history is about "old dead guys" then the history teacher has failed to make history come alive for his kids.

If kids can't see beyond the boredom of grammar and spelling and vocab to where they're important tools for effective communication with others , then the English teacher has something to answer for.

If kids can't see why they should learn a foreign language in our increasingly smaller planet, then the language teacher hasn't explained things fully.

Every example you gave about the importance of English dealt with college. What about the big picture?? Learning English, like math and so many other subjects, makes us better educated adults, capable of functioning in the real world. It prepares us for life beyond the classroom. It stretches our brain and our imagination and what we think we're capable of doing. The problems of the 21st century are not going to be solved by a society which focuses only on what it needs for college, or on what a 14 year old deems "interesting."

It's not education for the sake of college, but education of the sake of living as intelligent educated adults.

9. ### 3SonsEnthusiast

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Oct 21, 2008

That's not what it means. The science and engineering majors do not finish with an average in the 50th percentile, and you know nothing of their distribution even if they did. I'd also dispute the validity of the GRE as a math test (I taught GRE test-prep, and there's a lot of non-math strategies you can use to get a good score).

When teaching SAT test-prep we had a little quip: A calculator helps you get the wrong answer faster.

Most of the time, I think catching up is a matter of really mastering the basics that everyone else never really mastered the first time. The ones who struggle in trig do so because their algebra was just enough to get by in the class. Those kids then have a harder time when (if) they go on to calculus, when if they'd just spent more time on algebra they would have much shorter learning curves for the next subjects.

10. ### Luv2LearnCompanion

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Oct 21, 2008

Alice,

As always :clap::clap::clap::clap::clap::clap: you come up with some very vital points.

All, I can say, Sheba, is if this is the attitude you put forward to your students, you need to change it. Okay, maybe to say that math isn't a favorite of yours is okay, but that isn't something I would express in front of students.

One of the reasons I love math ( and btw, I'm still battling calculus), is that it is like a puzzle, a mystery.

Kris

11. ### mmswmModerator

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Oct 21, 2008

What I find ironic is that Sheba's posts prove my point completely. The sentiments expressed are exactly the type that caused me to post to begin with.

Thank you TG, Ceyber, and Alice. I was planning on responding point by point, but you three seem to have done a more thourough job than I could have done.

Luv2learn, you also expressed one of my biggest pet peeves. If teachers show these types of attitudes, then what hope do we have for their students?

12. ### TeacherGroupieModerator

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Oct 21, 2008

Teachers who despise some area of knowledge are the stuff of my nightmares - and the reason I spend so much time on the Examinations for Teachers subforum.

13. ### mmswmModerator

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I don't like chemistry...I REALLY don't like chemistry. I cried my way through two years of it (gen and organic...and I still got A's all 4 terms). While my students are aware of the fact that I'm not to fond of it, they're also VERY aware of how important I think the subject is. I guess that's why certain attitudes get to me. Even though there are subjects I don't like, I don't react by calling the subject useless or boring. I tell my students that while everybody has their interests, and some subjects won't be as fun as others, that doesn't mean that they shouldn't know about the subject and be competent in it's basics.

14. ### MrsCMultitudinous

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Oct 21, 2008

We have a couple of teachers in our school whose "distaste" for math is so intense that they have negotiated with another teacher to teach their math for them on a "swap". They are very upfront with their students, "I hate math so Mr. B is going to teach math to you this year". One of the biggest struggles I have had every year has been to change the attitude of students (and the staff I work with) towards math.

I was never a huge fan of math in high school. I did fairly well because I was able to memorize formulas and procedures, but I never really understood why they worked. Once I began teaching math I grew to really enjoy it because I finally understood the "why" of many of the concepts. It is now my favourite subject to teach.

15. ### mmswmModerator

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MrsC...That's the kind of thing I try to avoid (the other teachers attitudes). I don't want my students leaving my class with the idea that chemisry (or any other subject) is worthless or something to be despised just because I don't like it. The subject comes up when students say they don't like something, or I see a bad attitude coming on. They get the whole lecture about the importance of a strong foundation and blah blah blah. Many of them are actually shocked when I admit to my dislike of chemistry, as I use examples from the subject on a fairly regular basis. I guess what I'm trying ot get across to them is that everything is important, regardless of your tastes.

I'm really glad to hear you're finally enjoying math. The biggest mistakes teachers make are trying to teach math in a vaccuum, with no connection to real life, or without any clues to the hows and whys. Sometimes it's impossible to fully explain why something works with the level of knowledge a particular group has, but most of the time it's not. In those rare cases, I tell my students to press the "I believe" button, and to come back to me when they've learned XYZ and I'll fully explain it to them

16. ### TeacherGroupieModerator

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And when the teacher's made the connections and supplied the how and why where it can be supplied, then the "I believe" button is a lot easier to push because it hasn't been overused.

17. ### AliceaccMultitudinous

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Oct 21, 2008

By the age of 3, it was fairly obvious that my youngest daughter needed some help with speech.( Some of you may remember this rant from 2 years ago-- sorry!)

I had her tested at our local elementary school. She did well on all measures except articulation where she scored in the 19th percentile. While they bent the rules and gave Kira services, technically she didn't qualify since she was above the 17th percentile.

I called to thank the director of Special Ed, and to ask how on earth the 19th percentile in articulation was deemed "acceptable." He started to explain how it was within "normal" bounds, being within one standard deviation from the mean.

Anyone without a working knowledge of what that means would have accepted the explanation. Upon hearing that I was a math teacher and still wasn't satisfied with the answer, I got the real truth: that budgetary concerns were the deciding factor. A parent whose son or daughter placed in the 19th percentile and who didn't get services might be satisfied with the explanation of how it eas "acceptable" and not worry, when worry is indeed warrented.

At age 14, I could never have imagined that I would care about normal distributions, or that that information might make a difference to anyone I loved.

Adults get to make the decisions because adults hopefully have their eye on the big picture. We know that life can take some unexpected paths, and that a liberal arts education is in the best interest of the kids we teach. That's why kids take math and foreign language and history and chemistry, even if "half" the kids taking them think they're "boring."

18. ### ShebaCompanion

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That's exactly what it means. I said 'at least'. That is to assume that if half the test-takers were science and engineering majors I must have done better than at least 32% of them. This is because even if such majors made up the 50th to 99th percentiles, I still beat at least 32% of them. However, I added 'probably more' because such majors likely weren't all in the top half.

And I can figure that out rather easily using the logic I learned at university and in life combined with the mathematical skills I had learned by grade 6.

19. ### mmswmModerator

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I'm going to hijack my own thread for a minute...

Sheba, I don't know where you got your statistics, but you need to recheck your sources. Going directly to the GRE website, Only 38% of test takers in 2005-6 were life science, physical science, or engineering majors. Your posts prove over and over again why I started this thread to begin with. You are so convinced you are right, when in fact you couldn't be farther from the truth. I feel sorry for the students you teach. They are having doors slammed shut based on the attitude of a teacher, and that's a real shame.

20. ### ShebaCompanion

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If such students have reached a point where they can read academic papers and understand them, write grammatically, and write papers that use proper references and quotations, I'd say that they shouldn't have to endure 'English' classes about someone who wrote in highly unusual Elizabethan / Jacobean English or ancient Greek if they hate it. However, such a person is much more likely to look and feel like an idiot later on because he has no idea what Homeric epic means than I am because I don't know what a noninvertable matrix is.

21. ### ShebaCompanion

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OK, if that was the case in 2000-1 then I can only claim that only claim to have done better than 8%, I suppose. But I would be fairly certain that at least 50% of test-takers had done some university level calculus, physics, or algebra. The point is that it's very possible for some people to do just as well or better than many people who have studied advanced-level mathematics on a practical test.

BTW, you'll be happy to know that one way I teach English numbers to EFL students is by doing math quizes in English.

22. ### ShebaCompanion

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I think the world needs mathematicians, engineers, physicists, and the like, and that people with such interests and aptitudes should be encouraged to pursue them.

I also think that ecclesiastical and literary history are very worth-while fields and teach us so much about where we've come from. However, they're not something I'd want to force uninterested teenagers to study. The same goes for advanced mathematics.

23. ### HMMCohort

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Do you have statistics to back up your opinion?

plus you still need to work on your math it's not 8%.

24. ### ShebaCompanion

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Oh yes, I guess it's at least 0.10526315789%. I suppose that's why people like me need people like you and calculators.

As for stats, according to Google 'Homeric epic' gets 33,200 hits. 'Homeric' gets 995,000. 'noninvertible matrix' gets 389. And 'noninvertible' gets 63,600. I'd say I'm statistically pretty safe on that one.

25. ### HMMCohort

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Type 'sex' into google...what is your point. What people look up online has no bearing on the opinion you stated.

26. ### ShebaCompanion

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You don't think the Internet provides at least some guage of what people who use English and have Internet access discuss?

27. ### mmswmModerator

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When I originally posted this thread, my intent was to help teachers who had problem students, or even to help teachers who have a little bit of anxiety themselves. I simply wanted to share a way of looking at things that might help bridge those gaps. I had the idea that this thread might get a lot of views, but not a lot of replies. I never expected that it would turn into what it has. The original post is an excerpt from a highly successful program who's aim is to help underprepared college students with a history of failure in college preparatory mathematics. I was hoping that people would be able to some or all of it to help their own students. The turn the thread has taken has become a source of grief for me. I thank all of you who have responded positively. I hope those of you who have read but not responded have gotten something useful from it. With that, I think I will leave this thread alone.

28. ### ShebaCompanion

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And in the case of elementary school students I'd say you're absolutely right. Sorry for torpedoing your thread with a much deeper question of why cumulative subjects should be forced on students who have already acquired the skills (in my and some other people's opinion) in that field necessary to function in careers not dirrectly related to them.

29. ### HMMCohort

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And how do these kids know that is not directly related to them. You barely scratch the surface of any subject in HS. We shouldn't pidgin hole students.

30. ### ShebaCompanion

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How do they know that drama and stage presence are not directly related to their futures? How many people are inhibited in their jobs simply because they can't make an engaging public presentation? Personally I think that drama was one of the most useful classes I ever took at school.

How do they know that taking PE won't be the tipping point that improves their metabolism and sets them off to a much healthier life?

How do they know that French won't be the subject that gives them a career edge when their company needs to send an employee to be their man in France?

How do they know that home economics won't give them the tools to find a simple job if they marry a foreigner and end up moving to another country?

How do they know that drafting won't give them a basis for a job as head of a building site?

I could go on and on listing the potential perils of not teaching every subject that could be taught in school, but I'm sure you get the idea. Unless students are going to be at school 24 hours a day studying everything that may conceivably be important to them some things need to be cut out or made elective. Secondary school mathematics and sciences would be better left as electives, imho.

31. ### HMMCohort

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Really, to be quite honest, by the time a student is in the 9th grade they have learned very little science and math (compared to what is out there). Therefore the student can't make an informed decision on what they will need to know to be successful in the future. That is why there are guidelines on what they should take. Most people think that english/math/science are all important.

Talk about feeling dumb ... only
'Four out of Five Americans Know Earth Revolves Around Sun'

I think a person is much more likely to look and feel like an idiot later on because he had no idea that the Earth Revolves Around the Sun than a person that didn't know what a Homeric epic means.

32. ### smalltowngalMultitudinous

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That is why it is up to the teacher of these students to have student dig deeper into cumulative subjects and connect the subject to something meaningful in their lives. I think it was mmswm that asks students in her class what kind of car they would like to drive, and then using math, have to figure out what their car payment would be with different rates applied to it. As far as your Homeric epic example, a teacher could very well connect The Odyessy to the journey that students take in life and the challenges that they have had to face and overcome to get where they are today.

33. ### smalltowngalMultitudinous

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Oct 22, 2008

Are you serious!?

34. ### cheeryteacherEnthusiast

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That's why there's room in a high school schedule for ELECTIVE classes. Students can explore their interests in elective classes. BTW, my sister has changed her college major 4 times. Some of her choices were math heavy, some were science heavy. My 21 year old sister still has no clue what she wants to do so why should a 14 year old get to decide that they don't need math and science? They don't know what their career is going to be yet. And I'm sorry, but math and science courses are quite difficult for many people. Some enjoy the challenge and some don't. Given the choice how many 14 year olds will choose to take home ec and PE over math and science? Too many students who don't know where there futures are headed and should not be in charge of making that discission.

35. ### smalltowngalMultitudinous

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Good point, cheery! In my HS, you had to take public speaking in some form or another (and it was required in college as well). PE was a requirement from elementary all the way to HS. Many decided to enter into athletics to play sports than do PE. Home Ec was not a requirement, but those that took it still needed that basic understanding of math: recipes, measuring fabric for sewing, etc. We were also required to take at least 2 years of a foreign language, unfortunately we were only offered Spanish. And it doesn't matter if a student knows they are going to college or they know they aren't, basic understanding of math and how it relates to life is fundamental in them being successful in the real world.

36. ### robinskyRookie

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I'm usually just a lurker or an asker of questions in these forums, but for this thread I feel compelled to respond. I've been a middle school math teacher for, oh, almost two months now, but I still think I have something pertinent to add to this discussion!

I think when you study math you're not only learning the specific skill involved, such as writing a linear equation form a graph or formulating a geometric proof. You're learning to think abstractly. That is extremely difficult for some people, and it is easier for others, but it is an important skill in life, and an important quality for informed citizens of a society to have. I don't think any other field requires as much in the way of abstract thinking as math does, and I can practically feel my students' brains stretching as they try to think in this new way. most of the math required for day-to-day living is the math you learn in elementary school, and is not very abstract. And even those skills are sorely lacking (I have a few anecdotes about sale prices in stores that I tell my students...) It's only in middle and high school that the math becomes so separated from a physical reality.

My school district only requires a certain number of years of math in high school. You could take your 4 years and end up in Algebra 2, or you can end up in Calculus. Whatever level a student is at, his or her brain is learning to think in a new way, and not just learning new information. I think that this is what makes math essentially different from those other disciplines mentioned in previous posts.

Whew, long post! Now I'd better get back to work prepping for tomorrow!

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I have to disagree with you. I am a math teacher and while you don't see the point, their are obviously plenty of engineers, scientist, etc. who will disagree with you as well. If we just stop teaching math past 8th grade then who will do all of these jobs? There are plenty of people who thinks math is fun and not a waste of time.

38. ### ShebaCompanion

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Maybe 14 years old is a bit young for students to start making such decisions related to academic fields, but I think North America could really learn something from the British system. In the UK, students are required to take a wider range of subjects to complete their GCSEs / O-levels (grade 10), and after that specialise in just a few subjects for their A-levels (grade 12). The amount of time they spend in the classroom during their last two years of school is much less than most countries.

Now, in the last decade standards in the UK have really been 'dumbed down' to try to get more students into university, with the result that these days a university degree from the UK doesn't really mean that much. However, you can be sure that anyone who graduated university in the UK prior to 1990 can demonstrate a very sound knowledge of several fields and has the ability to express him/herself quite accurately in either written or spoken English. It's also quite hard to think of a country that has produced such a disproportion of the world's top academics. And in the case of academics in social sciences and humanities, almost none had a formal mathematics lesson after age 15-16.

39. ### xmasqueenRookie

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Oct 22, 2008

Well since I teach math, obviously love math and I love science as well....the two correlate and usually my students who are good in math do well in science also. But I can't tell you how many times I've heard a parent say in front of their child, "I hated math when I was in school and I was really bad in math, I guess he/she just takes after me. Attitude in the classroom is everything. We are doing a bookstudy at school and since I'm sick right now and full of drugs the title will not come to me...but it's about this same thing. If you aren't enthusiastic about teaching it then your kids will sense that and take up the cause. I did not like teaching social studies....well except for map skills....but my students never knew it. I tried to put as much enthusiasm into those lessons as I did into the others that I love.

40. ### cheeryteacherEnthusiast

Joined:
Jun 24, 2006
Messages:
2,237
9

Oct 23, 2008

And why would we want to follow a system that you admit has dumbed down their standards????

We hear all of the time that Americans (and in the UK also) are losing math and science related jobs to people from different countries that put an emphasis on math and science education. If we make math and science electives after 9th grade that problem will only get worse. We live in a society where kids already think that they are entitled to good grades and if it doesn't come easy then it's not worth trying. Why perpetuate that standard by telling them that since advanced math and science courses are hard and boring you don't have to take them??? What would our society gain from making advanced math and science electives???

41. ### ShebaCompanion

Joined:
Sep 22, 2008
Messages:
185
0

Oct 23, 2008

I happen to teach in one of those countries that puts 'an emphasis on math and science'. Many, many students do not get into university programmes where they could thrive in a liberal arts field because their high school math and / or science marks aren't up to par. Many students with top marks get into American universities only to drop out or fail because they have no idea how to write a research paper. I'll spare you the details of the unbelievably crappy lives students live when they're forced to study all subjects all the way through high school all day long if they want to have any hope of getting into a good university.

Another problem with forcing students to study all subjects is that those with poor attitudes or little aptitude for them lower the level for those who are really interested in them. This is why I think that the British system is much more realistic. The fact that standards in the UK have been significantly lowered recently to process more students into university is beside the point. Having a system in which students can enter university based on the A-levels of a few subjects in which they have the most aptitude is a much better way both to assess them and to prepare them. If it's not producing enough future professionals with math and science skills it likely indicates that there is a problem with how math is taught up to fifth form (grade 10), not generating enough interest for more students to pursue it subsequently. Wasting more time, money, and resources forcing students to study it up to age 18 would be very unlikely to change that situation. Indeed, whether all students should even stay at school until their late teens is an issue that should be questioned, but that’s another debate.