Less math in elementary school??

Discussion in 'General Education' started by TeacherGroupie, Apr 8, 2010.

  1. TeacherGroupie

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  3. Peachyness

    Peachyness Virtuoso

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    VERY interesting article. I read a long time ago about a study. They had two groups of kindergartners. One group received the normal mathematics (I believe they were focuing on math, if not, it was science. Sorry, I read this study a long while ago) instruction. The other group didn't. By the time both groups were in fourth grade, the other group insisted that they also start to learn math (or science). So, they began the program and the students not only picked up on the concepts quickly, they surpassed the other group!

    So, I think we need to do a lot more research and study, but perhaps some of the subjects can wait to be introduced.


    ETA: this stuck out to me
    I see this big time with my sixth graders. They have absolutely NO ability to think about WHY they are doing something. They don't care to learn the whys and the hows. They are dispassionate/uninterested about math (and just thinking), it is sad.
     
  4. Grover

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    It's aggravating that this kind of knowledge has been around since 1929 but policy continues to drive us toward more and more academics at earlier and earlier stages. Students of child development know, and have known for ages, that this is at best a waste of time and is generally actually damaging.

    There are programs of math education that are actually very effective with young children, but the ones I know of are thoroughly discovery based and involve very little 'teaching'.
     
  5. Aliceacc

    Aliceacc Multitudinous

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    Can you guess my reaction?
     
  6. MathNrd

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    I think it has more to do with how math is taught then when it is taught. I wonder how great our greatest mathematicians would have been if all they did was drill and no problem solving.
    I also agree with the statement that many elementary teachers pass their math phobia on to their students. Although, I do not blame them. It is how they were taught as students and I do not see teacher education or professional development addressing the issue.
     
  7. 3Sons

    3Sons Enthusiast

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    I find it a bit hard to trust a study done by someone not trained as a scientist in 1929 with a particular point to prove. I also find it quite unbelievable that the researcher mentioned later would have interviewed 50 elementary teachers and not found one that could calculate the area of a rectangle.

    It may be that some subjects can be learned later, but I don't think this article is very convincing on that point alone. I find it a bit more compelling that certain educational systems (Waldorf) or countries (Finland) don't introduce reading until comparitively late (like second-third grade).

    The exercise in recitation is interesting. I've read a pamphlet designed for Japanese intra-company transferees who were sending their kids to American public school, and one of the things it made pretty substantial mention of -- an appreciative glimpse at what they consider a stunning American innovation in education.

    Show and Tell.

    My kids' schooling goes even further in this regard, or perhaps I just notice it better now than when I was a kid. Every book report is accompanied by an in-class presentation. They must do four or five of these per year (they seem to do a book report every month or two).
     
  8. TeacherGroupie

    TeacherGroupie Moderator

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  9. KinderCowgirl

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    I'm also not sure in 1929 the kids were taught the levels of math that they are today. I mean most kids didn't go through 13 years of schooling like they do now-I can't imagine they learned things like calculus and trig back then. So maybe it was easier for the kids with less foundation in math to pick up the concepts because the math was just plain easier.

    I know every year I have to teach more and more to my Kinders. Instead of spending the time we should on number sense and one-to-one correspondence we're expected to teach them more abstract concepts like time, money and place value. I don't know if less math is the answer, but certainly more emphasis on hands-on experiences with the basic concepts would be nice.
     
  10. TeacherGroupie

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    Trig was certainly available in high school subject when my dad was growing up. I think what happened in the 1920s is that some kids learned a great deal of math and everyone else didn't - girls, notably, were Not To Worry Their Pretty Little Heads About It. (My sister vividly recalls asking why something in math worked and being blown off; that would've been in the sixties.)

    That there is real fear of math among many teachers is undeniable: the scores on teachers' basic-skills tests reflect it. Whether the solution to this is to ban math from the classroom for children who ARE cognitively ready for it is, I think, a very different question.
     
  11. Marci07

    Marci07 Devotee

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    I agree that less math should be taught at the early grades and the curriculum should focus on making sure students master adding and subtracting before introducing more concepts.
     
  12. Aliceacc

    Aliceacc Multitudinous

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    Sorry, TG, my mouth is still real sore from 2 hours at the dentist today. ( I hadn't been there since before all the other medical stuff popped up. Let's just say it wasn't pretty.)

    Not in the mood to handle something like this.
     
  13. obsteve

    obsteve Rookie

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    I think the author needs to do some contemporary research, in actual schools, before holding forth about teachers and teaching (he has done none).

    I have been posting on his blog for some time now, arguing against his pronouncements. You might like to check out some of his other articles. The comments he makes on this topic, that stood out as fabrications to me, were:

    "Nothing [in maths teaching] has worked."
    "Most of [the teachers] are math phobic"
    "No matter what textbooks or worksheets or lesson plans the higher-ups devise for them, the teachers teach math by rote,"
    "they just pray that no smart-alec student asks them a question such as "Why do we do it that way?" or "What good is this?"
    "The students, of course, pick up on their teachers' fear, and they learn not to ask or even to think about such questions. They learn to be dumb."
    "a math-schooled mind is a chloroformed mind."

    Thanks for flagging it up TeacherGroupie. I think what the man and his followers need is some genuine insight into real math teaching by real math teachers.

    I would be delighted if one or two people here could provide some real life accounts of Math in school.
     
  14. TeacherGroupie

    TeacherGroupie Moderator

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    Huge hugs, Alice.
     
  15. Aliceacc

    Aliceacc Multitudinous

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    The dentist just called to check in on me... what a sweetie!!!

    Thanks TG.

    Sorry for the hijack.
     
  16. TeacherGroupie

    TeacherGroupie Moderator

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    That's one fine dentist, Alice.

    So what about these claims, people?
     
  17. Genmai

    Genmai Companion

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    I'm a middle school math teacher at a urban public school, and I completely agree that the teachers at the elementary level absolutely fear and don't understand math beyond basic arithmetic. It is a real shame. Just this week, my mentor told me that most teachers "skip" an important topic because they don't understand it. I learned this in high school, and it is now taught in middle school!

    Overall, the people who really understand math don't become teachers. They mainly work in the private sector in medical, scientific, engineering or financial services areas. I'm told that I have good content knowledge which is funny because I'm not better than many of my peers from school, most of whom have vastly better math ability and knowledge than me and many of whom have gone off to Wall Street.

    There is a reason why engineering, accounting and statistics people earn much more money than others in the private sector - there is a greater demand for their skills and knowledge and the pay is commensurate with the demand. Unfortunately, the concept of paying more for people with rarer more highly sought skills is nonexistent in our woefully outdated education system. All else equal, why would any math person want to work as a math teacher when she can work as an accountant or actuary, earn many times more money and work under much less stressful conditions?

    Does this mean we shouldn't teach math in elementary? I think this approach is absurd as well. Because our world is becoming increasingly more technical, a solid foundation in math and sciences is critical. As Obama said, we need more people who can invent and build things. This means engineers. Unfortunately, I can't offer any viable solution that doesn't involve more money for better teachers in general and for math and science teachers specifically. Because education is the first area to get underfunded and cut (like in NJ right now), money is a real problem. Without real incentives, however, we will continue to be mired a system where many of the K-6 teacher live in abject terror of higher math and science...

    :2cents:
     
  18. Grover

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    It's an interesting paper and I haven't quite finished it, but it seems to ignore the importance of, um, 'importance' in fixing memory. That is, things of high emotional value, either positive or negative, tend to get fixed in long-term memory much more rapidly and securely than those things to which the learner is emotionally indifferent. One of the points of a properly constructivist approach is that involves, er, involving the learner emotionally.
    Also, the constructivist approach demands that the learner have a strongly contextualized learning experience. Something else that we know about memory formation is that it is in essence a process of pattern creation- memories are themselves neural connections, and the process of recall is the process of activating- connecting- these connections in relevant ways. The power of an appropriate constructivist approach is that it is rich in connectivity because it is rich in context.
    I would agree that entirely unguided learning is often slow and, depending on the subject matter and the characteristics of the learner, likely to lead to compounded errors and frustration. I don't think any proper constructivist from Dewey onward would consider this approach sound. 'Minimal' guidance is a vague notion, and I'm not confident that practicing constructivists would see their practice in the definition offered, with perhaps the exception of A.S. Neil.
    I am also not sure that it's legitimate to dismiss 'sense memory' from the discussion. If we look at both emotional and contextual elements of memory and learning, we see aspects of sense memory, and this is true also of Fernald-style multi-sensory reinforcement schemes, which are certainly well proven to work.

    The paper also asserts that working memory is not available for 'learning' if it is engaged in 'searching', which references the idea of inquiry based learning as a process of 'searching a problem space' for solutions. I would suggest that this is at best an extremely weak description of inquiry-based learning, let alone constructivism. The discussion presents learning as being a matter of acquiring a pre-determined end, which by definition makes constructivism 'fail'. However, if learning involves mastering the learning process, which is the constructivist aim, the entire 'search' is not just a learning experience but the experienced to be learned.

    In short, the authors take on a straw-man constructivism, and naturally win. Unfortunately, their citations reflect a serious misapprehension of the nature of constructivism. If they were to restrict their title to a critique of unguided discovery, I believe serious constructivists would entirely agree with it. As it is, the paper reads as a political hack job.
     
  19. TeacherGroupie

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    It's important not to err with straw men in either direction, I think. Funny how easy it is - on both sides - to dismiss what we don't agree with as "a hack job".
     
  20. Grover

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    TG, you're the one who is being dismissive. I made a detailed critique based on the authors' own words and a long immersion in constructivist theory and practice. While their arguments may be a devastating critique of something, that something is not constructivism.
     
  21. TeacherGroupie

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    Genmai, you've stated, "I completely agree that the teachers at the elementary level absolutely fear and don't understand math beyond basic arithmetic." That's a pretty broad statement; do you know this from what you've been told by mentors, or have you observed it?

    Everyone else: do you think this is true? If so, what should we do? Get rid of the teachers, get rid of the math, or what?
     
  22. Grover

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    TG- I see some teachers with a good grasp of math and quite a few that fear it and have a weak grasp of it. It almost doesn't matter, though, because I mostly see them teaching packaged math curricula that are most often poorly designed and seem to suggest that the publishers have little understanding of math or child development. It's difficult to see how even a good teacher with good math understanding can be effective when they are required to teach 'straight from the book' and the book is poorly designed.
     
  23. TeacherGroupie

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    Grover, yours is indeed a detailed and, by and large, thoughtful critique that cites a great many points about which you find the writers of the article misguided at best. It is therefore all the more regrettable that you cannot or will not see how the force of your argument is vitiated rather than reinforced by a gibe such as yours.

    Such a style of argument often springs from one of three sources: (a) the writer feels obliged not merely to rebut the opposing position but to contemn and disparage the opponent; (b) the writer mistrusts the capacity of an audience to comprehend the argument unless it is underlined for them; (c) the writer simply never outgrew a penchant for sophomoric digs.

    Extending courtesy in argument is not, however, an admission of defeat; neither is calling for courtesy in argument a personal attack.
     
  24. TeacherGroupie

    TeacherGroupie Moderator

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    The blog, as obsteve kindly quotes it above, asserts that it wouldn't much matter what the curriculum: the teachers would still teach badly. That's a different claim. Though I quite agree that badly written curricula exist and that they don't help whatsoever.
     
  25. KinderCowgirl

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    We have incredible math teachers on our campus. They have a great understanding of the concepts. One of them will talk math until the cows come home if you will let them, his kids leave him to go to middle school with a terrific understanding inside-and-out. I also think it's quite a generalization to say elementary teachers don't understand advanced math.

    We are teaching area and fractions right now-just to give you an example of how the expectations have changed-in Kindergarten. :eek:
     
  26. Grover

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    What you call a 'gibe' I would call a characterization, and it is made on the basis of the political climate of education. I think we have all noticed that the drive for standards and a more authoritarian approach to education has come largely from politicians, not educators. While it's possible to find someone to write a paper promoting almost any idea in fine academic style, it's not necessary to take them all as serious investigations. When the premises of a paper involve seriously mis-characterizing that which is to be critiques, it's either truly deplorable scholarship, of the kind for which I would reprimand even my elementary students, or political hatchet work. If you think it's more polite to believe that the authors have no clue as to what constructivism is, have not bothered to read Dewey, Piaget or Vygotsky, and are simply misinformed, than to believe they are intellectually dishonest, I cannot dispute you- it's merely a matter of taste. The evidence supports either view equally well.

    I share the sentiment that extending courtesy in an argument is a generally beneficial thing. I don't recall you calling for this, however, rather you dismissed what you now refer to as a detailed and, by and large, thoughtful critique as being itself dismissive.

    I am, by the way, perfectly willing to accept the diagnoses of ignorance and/or stupidity when the circumstances point clearly in that direction. I am reminded of a college paper on Apartheid that I graded in which the author used the terms 'African' and 'Afrikaaner' as synonyms throughout.
     
  27. hp123

    hp123 Comrade

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    I think children need exposure to math at a very young age. What concerns me is the way it is taught in the young grades. I think children need to learn it through more hands-on experiences, and have more time to absorb concepts.

    I also feel that reading instruction should start at a younger age. This comes from my background in Montessori.

    I really feel like we expect children to take in alot of information in a short amount of time.

    My daughter (6), really struggles with Math. We do alot of extra work at home so she can keep up. It seems that me main emphasis in primary is literacy (at least instruction). She does well with that, but struggles with Math. They don't recieve Math instruction everyday, which is really hard for her.
     
  28. TeacherGroupie

    TeacherGroupie Moderator

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    Humpty Dumpty redefined terms, too, when it suited him.

    Nowhere did your discussion reference either politics or hack jobs until that last bit at the end: your conclusion, as I assume you're aware, thus fails to follow from the premises you stated.
     
  29. Grover

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    Ah, well, when I write a doctoral dissertation on the subject I'll be sure to provide more background. I made the unfortunate assumption that I was having a conversation with educators who might be expected to have some awareness of the context in which their profession operates. I confess to being misled in part by the lively discussions going on on these boards regarding merit pay, tenure, budget cuts, loss of positions and so on.

    So, if you would like me to take you through the steps, they are these: There is a major push on the government level to make standards the end all and be all of our educational system. In this environment, when I see a publication that attacks constructivism by misrepresenting it's nature, I think it's a reasonable conclusion that the attack is part of that drive.
    I'm not sure why you are so attached to this paper- are you one of the authors? If you believe it is worth defending, then defend it. Please start by showing how the characterization of 'unguided learning' or 'minimally guided' learning applies to constructivism. Perhaps a good entry point would be to show how Vygotsky's Zone of Proximal Development equates to 'searching' an overly complex 'solution space' and creating 'cognitive overload'.

    I do not, btw, hold you personally accountable for the views represented in the paper (unless you are, indeed, one of the authors), but if you would like to champion them I'd appreciate you actually addressing them. Your current approach borders on ad hominem.
     
  30. TeacherGroupie

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    This, however, Grover, is a different argument - from which the claim that the article is "a political hack job" still doesn't follow logically, since it requires rather strong assumptions about the authors' intentions for which the evidence on the page is insufficient.

    Now that you've told me what I think about this article, I'm curious: do you generally believe the worst of people who happen not to agree with you in all points, or are you simply having a bad day?
     
  31. Grover

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    I told you, I'll accept either explanation regarding the authors. I'm not sure that thinking they are hacks is worse than thinking they are incompetent readers. I agree that there is no proof in the article itself that would stand the legal test of intent, but then we aren't in court. I'm giving an opinion, I've supported the opinion, and you continue to deflect. Since you don't really seem to have any interest in the actual content of the article I have lost interest in discussing it with you. It's not clear to me why you posted it at all.
     
  32. TeacherGroupie

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    Decrying an article's authors as necessarily either hacks or incompetent does tend to have a chilling effect on discussion, yes - or at any rate not to conduce to discourse that's constructive.
     
  33. obsteve

    obsteve Rookie

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    In general I agree with a lot of the author's principles. Child-centric learning, personally tailored education, freedom of choice on content etc.

    Where I strongly disagree with the author is that I see these practices happening in education already.

    I also think that the author is particularly poisonous with regards to teaching in general. He is fond of repeating phrases such as "school is prison" and "coersive teaching", which I think is unfair. It certainly is not my experience of education, but I am finding it quite hard to argue any of his points, seeing how little I know of US education.

    You might be interested to look at some of his other articles on his site
     
  34. TeacherGroupie

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    I noticed that tone as well, obsteve. Such language closes more doors than it opens, to be sure.
     
  35. webmistress

    webmistress Devotee

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    WOW. No I don't think it's true. Are there some horrible elem. teachers? Indeed.

    Genmai,
    When did elementary Math teachers become so fearful and bad at Math? Would you say every single one of your elementary teachers were bad and fearful of Math? Please don't group us all together.

    I performed extremely well in High school and College Math (mostly A's, Math Honor Society), even took it on the doctoral level and passed the classes. (not great scores, but I made it through) :haha:

    I'm just getting so sick of everyone pounding on us. Yes there are some horrible elementary teachers out there, but they're also some horrible engineers and scientists.....and doctors too (don't know why we're always compared in a negative light to other fields so much,as if they are so much greater)
     

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