1. OldSchoolSkill says

    As an old bastard, I attest that modern math teaching dramatically reduced understanding & increased incomprehensibility. Our kids had trouble with math until my wife (also an engineer) sat down with them every night & practiced from old text books.

    Kids today are not stupid. They get bored and distracted easily, especially in large classes with dreary teachers and their “modern” methods.

    Math is simple; but only when presented well.
    Those who control schools do not want educated citizens.

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  3. socratus1 says

    Simple Mathematics

    It began in 1907 when Minkowski tried to understand
    SRT using 4D space
    Nobody knows what Minkowski negative space really is.
    Trying to understand it, Kaluza in 1921 created 5D space
    Nobody knows what it is too
    If we don’t know what 1+1 = 2
    how can we know what 5 + 4 = 9 ?

    And if we don’t know what is 4-D
    how can we understand 10-D, 11-D ?

    Israel Sadovnik Socratus

  4. sleeper2345 says

    Hard to generalize from an N of 1. However, most students do this anyway and think they are doing algebra.

  5. tjhombs says

    …and there we go with the insults.

    In any case, asking, “Paper or Plastic?” seems to have worked out well for this dropout:

    ofrf (dot) org (slash) pressroom (slash) organic_news_clips (slash) 050214_forbes_wholefoods (dot) pdf

  6. tjhombs says

    “Little Intelligence” does not mean lack of understanding.

    Intelligence: Skilled use of reason.

    You said my example could simply be done on the calculator, which would be using “little intelligence.”

    Your definition of rote is only one of many.

    Rote: Mechanical
    Mechanical: Automatic
    Automatic: Spontaneous
    Spontaneous: Mechanical, Without Deliberation

    Rote = Spontaneous, and without deliberation

  7. sleeper2345 says

    I couldn’t agree more. Have your son learn everything by rote. Good luck! Have him repeat “paper or plastic.” There are many jobs available.

  8. tjhombs says

    The wikipedia article you reference includes these notes:

    “Progressive reforms such as Outcomes-based education which have put an emphasis on eliminating rote learning in favor of deep understanding have produced a storm of controversy as a generation of students are failing new math assessments which were aimed at increasing math performance.”

  9. tjhombs says

    You tell me to change terminology, and then get mad when I do. My definitions came from Merriam-Webster – they are not mine.

    I am communicating my ideas, and I have explicitly stated that I am a proponent of rote RECALL, not rote LEARNING. Understanding is just as important as being able to effectively and quickly use what is known.

    You are continuing to argue against me for things we agree on. Discussing this any further is pointless.

  10. sleeper2345 says

    Webster Dictionary definition of rote: the use of memory usually with little intelligence. Note that you are not communicating your ideas.

  11. sleeper2345 says

    Create your own new definitions if you wish. However, this will not facilitate communication. Wikipedia: Rote learning is a learning technique which avoids understanding of a subject and instead focuses on memorization. The major practice involved in rote learning is learning by repetition. The idea is that one will be able to quickly recall the meaning of the material the more one repeats it.

  12. tjhombs says

    You disagreed with my earlier change in terminology, but I will present it again, with additions for your sake:

    Know: Innate Cognition (A mental process originating from within.) The idea becomes a part of yourself – you no longer think about it. It just IS.

    Rote: Rapid
    Recall: Experiential Memory
    Fact: Experience

    Rapid memories of experiences. More = Faster.

    BTW: I never said “facts” in my use of rote recall. You are making assumptions again. Ideas are important too.

  13. sleeper2345 says

    You keep referring to memorizing and recalling rote facts. Your rhetoric infers that you are focusing on facts devoid of meaning. This is that rote recall insinuates: that there is no connection to meaning. I suggest a change of terminology so that you can better relay information.

  14. tjhombs says

    We agree again. Why are we arguing?

    Once the idea is understood, repeat it enough times so that you don’t have to think about it anymore. You will then know it, and can use it to think about something else.

  15. sleeper2345 says

    You can’t just memorize facts without understanding what they mean. For example, many college students think that 3/4 is the same as 6/8 because you double 3/4 to arrive at 6/8. Without this understanding they can’t perform other operations. They have to understand what things mean, not just memorize meaningless information.

  16. tjhombs says

    “No, students should recall it quickly…more to be learned…” – Why are you arguing then? We agree.

    “You’re all for rote recall.” – When did I say that that was my only concern? You are making false assumptions. I said this because people here are arguing it is not necessary. I disagree.

    “…can be done by a calculator.” False assumptions again – no calculators for tests. Try again.

    “What is hard…’ Agree again – what is easy should be memorized and not waste time.

  17. sleeper2345 says

    Are you reading anything that I’m typing? No, students should recall it quickly (once they know what it means). However, there is much more to be learned than just these basic facts. You’re all for rote recall, but this is the least of our worries. What you’re describing can be done by a calculator. What is hard is what needs to be done by the human mind.

  18. tjhombs says

    So, if my son can finish a math test in half a day, with reasonable accuracy, because he understand the material, but he fails the test in class because he doesn’t know the sum of 3+8, your contention is that I should not drill him the addition problems, thereby allowing him to complete the test on time. Very interesting.

  19. sleeper2345 says

    Sure they should apply it quickly. Right now most students can’t because they have learned by memorizing meaningless facts that they don’t understand. For example, they can say that (x-1)(x+1) = x^2 -1 but they don’t believe that it is true. They can’t apply it to numbers. Your focus on rote recall is misguided.

  20. tjhombs says

    Having the ability to apply something is not the same as being able to apply it in a testable timeframe.

    But in any case, what is your point? Why are you are arguing against being able to use the information quickly and efficiently? I don’t believe I ever said that the should not understand the information (by your definition), that they should not be able to apply the rules, or realize what they mean.

    I believe I have argued the opposite – they should be able to apply them – QUICKLY.

  21. sleeper2345 says

    My definition of understanding: Able to apply mathematical ideas and know why these ideas are valid. Your definition lacks such knowledge. We’re loaded with college students who have memorized facts. They can show that two fractions are the same (e.g., 1/2 = 2/4) but they don’t know why or when this information can be applied. They’ve learned the rules, they just don’t know when to use them or why.

  22. tjhombs says

    Understanding is not the same as knowing.

    Understand: Accepting as fact.

    Know: To have innate congition (originating from the mind, rather than from experience).

    How that knowledge is achieved is not as important as the fact that it is achieved.

    My question about rules applies to Teachless’ assertion that learning vocabulary is unimportant, but learning the rules is. You cannot learn the rules unless you learn the vocabulary that describes the rules.

  23. sleeper2345 says

    How does some obtain quick recall? We know that this occurs through developing a deeper understanding. What does your question (about new rules) mean? What are you trying to say?

  24. tjhombs says

    I am “4” exactly the opposite: I am for rote recall. That is, you should not have to think about simple things. For example, when you work with algebra, you should be thinking about how algebra works, not how addition or subtraction works.

    How do you learn new rules without using the words that describe the rules?