1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.
  2. Hi Guest, welcome to the TES Community!

    Connect with like-minded education professionals and have your say on the issues that matter to you.

    Don't forget to look at the how to guide.

    Dismiss Notice

Incorrect Past Practices can result from incorrect Pedagogical Reasoning

Discussion in 'Mathematics' started by karisshad17, Apr 8, 2019.

  1. karisshad17

    karisshad17 New commenter

    When teaching Equal Fractions, teachers, textbooks, curricula, teacher-training, student-learning, visual demonstrations...ALL, without exception draw upon an implausible assumption: i.e. when multiplying the numerator and denominator by the same number, it produces the "increase" in the the number of equal parts ( 3-fourths "increase" to 9 twelfths!). This is patently absurd and fails the test of all four levels of Mathematical reasoning:
    1. Visual Reasoning 2. Verbal Reasoning 3. Numerical Reasoning and 4. Pedagogical Reasoning.

    In order to demonstrate this, I have uploaded 2 videos on My Resources for downloading for free. In addition, the videos may also suggest that Primary-Middle Math CAN be taught without the use of spoken language. We use verbal mediation (without visual mediation) to convert printed words to sounds, then to meaning. Likewise, it can be proved (as I do in the videos) that we use "visual mediation" to convert visuals directly to meaning without any recourse to verbal mediation. I remain open to any comments, inputs. And also to correction, of course! :)
     
  2. moscowbore

    moscowbore Lead commenter

    Not sure if you are looking for an appraisal of your general philosophy or what.

    Are you proposing that teachers should use your resources to teach Mathematics?
     
  3. TCSC47

    TCSC47 Star commenter

    Hi Kari. Try posting this in the Maths subject area. We discuss issues and items relevant to education that have appeared in the news here.
     
  4. Teslasmate

    Teslasmate Occasional commenter

    Confused by this post, but 3/4 = 9/12. Just sayin'.
     
  5. karisshad17

    karisshad17 New commenter

    Pl watch BOTH videos....:)
     
  6. karisshad17

    karisshad17 New commenter

     
  7. karisshad17

    karisshad17 New commenter

    I am simply correcting a misunderstanding/mistake/oversight (or whatever you call it) that has been baked into prevailing practices for generations. Beyond that it is up to the practitioners. They can do whatever they wish. It's not for me say what, how, when or where. Not sure if reading/attributing/checking my intentions sheds any light on the problem itself i.e. the teaching of equal Fractions in classrooms.
     
  8. karisshad17

    karisshad17 New commenter

    I am simply correcting a misunderstanding/mistake/oversight (or whatever you call it) that has been baked into prevailing practices for generations. Beyond that it is up to the practitioners. They can do whatever they wish. It's not for me say what, how, when or where. Not sure if reading/attributing/checking my intentions sheds any light on the problem itself i.e. the teaching of equal Fractions in classrooms.
     
  9. Lalad

    Lalad Star commenter

    I have never taught that three-fourths "increase" to nine-twelfths, nor, as far as I know, do any of my colleagues.
     
  10. karisshad17

    karisshad17 New commenter

    If you show students that you "divide by half" in order to split wholes into smaller equal parts, (and show that division operation by half), before "flipping it to X 2" then that would be the correct thing to do. But if you begin by multiplying both the top and the bottom by 2 and say: "...so this way it breaks into 4 smaller parts....." then the choice of the multiplication operation to explain what you are doing, would (in the children's minds) suggest an "increase in number" from 2 (wholes) to 4 (parts). This is a logical and conceptual inconsistency. It doesn't square up. From what I have seen, this is the normal practice in schools. I am glad that you are an exception :)
     
  11. Doitforfree

    Doitforfree Star commenter

    I've never known anyone to teach fractions like that. Why would they? It would be nonsense. Maybe you saw one person doing that and assumed it was how all teachers do it.
     
    colpee likes this.
  12. colpee

    colpee Star commenter

    But that would be weird - who does that?
     
  13. colpee

    colpee Star commenter

    I don’t think they do. The concept of supporting a bit of a maths lesson with an animation is valid enough; plenty of such resources have been used for years. But merely because a certain support strategy appears to be successful with a certain level of student, hardly raises it to a pedagogical revolution in teaching;)

    Isn’t that what silent animations do?:confused:
     
  14. karisshad17

    karisshad17 New commenter

    Would help if you saw the videos. It would make the conversations and dialogues less opinionated and more focused on the actual math concepts within the context of what the video explains.
     
  15. karisshad17

    karisshad17 New commenter

    Yes, they do. Which is why I suggest that you watch the "silent animation on Math" that I uploaded. Things will become clearer re: what can be achieved and what not (and what could be achieved, but was not). What I was trying to say (and didn't make it clearer) is: "Primary Maths can be understood and learned (I shouldn't have used the word "taught"....my mistake) without a single word being spoken, via animations". I stand by this because it's being proven every day. It's like silent reading for comprehension (mainly for pleasure). However one still needs to be "taught" language to "test" what is understood, how much, how well. Whether a student can answer questions not just from the lines but from between and beyond the lines. Likewise, Maths. It can be understood and learned via certain genres of animations. However, it still needs to be taught to ensure that what has been understood and learned converts into solid bits of knowledge (or knowing) needed for problem-solving.
     
  16. karisshad17

    karisshad17 New commenter

    Nobody, it seems, judging by what you're saying. Nobody explains (or so it would seem) WHY the numerator and the denominator is multiplied by the same number. Everybody (it seems) simply multiplies without explaining anything, other than stating (perhaps?) :"...and so we get this new fraction which is equal to the other fraction because 1 out of 2 is the same as 2 out of 4". How? Why? Is that it? Do such implicit statements suggest pedagogical reasoning? Do such affirmative (mathematical) statements serve as the equivalent of numerical reasoning? No, to both.
    Secondly those who do try to explain the sameness of equal fractions do so by using a concept that is not taught till two-three years later (ratios).

    The equivalence of fractions and its differentiation from the equivalence of "ratios" is argued, demonstrated and explained visually, using animations, without a SINGLE spoken word, in the videos I uploaded. Do please see them if you get curious enough. :)
     
  17. colpee

    colpee Star commenter

    I posted after seeing the videos, which tbh seem pretty standard fare (albeit with irritating sound effects), which is great if they work for you - I just don’t think they are actually doing anything new.

    it seems’ explains a lot.
     
  18. karisshad17

    karisshad17 New commenter

    I assume, your response is "arguing" (in a sense) that equal fractions are indeed taught in classrooms by dividing the numerator and denominator by the same fraction (and I... "it seems"... am blissfully unaware of this common practice...). You are also implying that this is standard practice. Therefore, all text-books, worksheets, sample test-sheets, all curricular material should show the division of the numerator and denominator by a fraction before proceeding to multiply by an integer. Consequently, the videos I uploaded do not shed any light on any problem relating to prevailing practices regarding the teaching of Equal Fractions. Is this what you are really saying?
     
  19. karisshad17

    karisshad17 New commenter

    Also: for all who have seen the videos and are interested in this thread of discussion, I invite your mathematical arguments/reasoning offered in defense of the current prevailing practice. As far as I know and have seen, it is about "multiplying the top and bottom numerals" of a fraction by an integer to obtain equal fractions. And it is without any reference to the original division by a fraction. All other arguments sound quite extraneous to the actual issue on hand: Multiply by an integer or divide by a fraction first?
     
  20. adamcreen

    adamcreen Occasional commenter

    Karisshad has invented a solution to a problem that doesn't exist. More than that, we are required to teach division by fractions before we teach equivalent fractions. Uh huh. No way Jose.
     
    slstrong123 likes this.

Share This Page