Math Forum Discussions

GS Chandy

Posts: 4,348
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05

Re: Topic 5 - The Beginning of the End
Posted: Oct 9, 2012 7:25 PM

Plain Text

Robert Hansen (RH) posted Oct 8, 2012 8:54 AM (GSC's remarks follow):
>
> So here is the beginning of the end for many
> students.
>
> In enVision (Grade 4 Florida Version), topic 5 is 16
> pages about multiplication and here is what is
> covered.
>
> 1. Expanded algorithm using partial products.
> 2. Standard algorithm (like we do it).
> 3. two, three and four digit numbers by one digit.
> 4. Algebra (Compare 2 * 90 to 89 + 89)
> 5. Solving compound problems (algebraish).
> 6. Estimating and checking.
> 7. Extra or missing information.
> 8. Using a calculator.
>
> This year I have been backing off a bit and letting
> my son take more responsibility for his work and this
> weekend I asked him what they did in class Friday. He
> said "We started topic 5, it was multiplication but
> he was having a problem with some of it." I asked him
> to explain to me what the problem was and he said
> that the teacher was showing them how to multiply 3
> times 15 and he didn't understand. It was different
> than how we had done it."
>
> I know what you are thinking, something like
> grid-multiplying, but it wasn't that, enVision is
> pretty traditional in method. It was just
> multiplication using partial products, what they call
> the "expanded algorithm", but it was being taught
> with pictures and the pictures are just not that
> helpful. I am of the opinion that if you add a visual
> to a lesson it should help the student to see the
> original point, not add yet a second point to figure
> out. I also don't think he was paying attention as
> well as he should have.
>
> So today we opened up topic 5 for a little help. The
> topic begins with the idea of multiplying a one digit
> number by a two digit number using partial products
> and rather than stick with a clear description of the
> steps, it uses pictures of unit cubes (grouped in
> tens and ones) that do not do a very good job at all
> in representing a sequence of STEPS. I have attached
> the 2 pages that start this topic and at the top
> there is a brief description of what is happening.
>
> I've complained before that this book avoids
> descriptive prose. It is written like a comic book
> that jumps from one situation to another. But my
> point in this post isn't the lack of prose, it is how
> many situations (as listed above) it has managed to
> stuff into 16 pages. This is just one topic out of
> 14. These kids will have witnessed many things in
> this class. They will master none of them, except of
> course, unless they have someone making sure that
> they do.
>
> The problem obviously has to do with using topic
> lists to define a math curriculum. Too much focus on
> the trees and not enough on the forest. But the
> problem also has to do with injecting later topics
> into the same space where you are supposed to be
> developing earlier topics. In the third page I
> attached, they compare the expanded algorithm to the
> standard algorithm. Where do they teach the standard
> algorithm? Right there! Do you not see the comic book
> panel containing the standard algorithm at the top of
> the page? Now, I know that no 4th grade book can
> replace a teacher explaining these algorithms at the
> board but that doesn't mean it should avoid
> explanations altogether.
>
> When I first started reading this section and it said
> "Compare the Expanded Algorithm to the Standard
> Algorithm", I asked my son "What's the standard
> algorithm?" and he said "I guess they mean the way we
> do it." I replied, "But where does it say that?"
> There is nothing but that brief mention on the
> following page (page 95). Can you imagine what a
> typical parent goes through? I have been studying
> curriculums for how long?
>
> All of us (I assume) have read an advanced math text
> at some time.There are two ways to read an advanced
> math text. The first way is to breeze through it and
> when you finish you will know "of" the topics in the
> text. The second way is to work every problem offered
> by the text and when you finish you will "know" the
> topics in the text. This book is written with the
> first way in mind. Unfortunately, the topics are
> fundamentally important and practical. After
> following this series for 3+ years, I am convinced
> that much was lost when we abandoned the systematic
> approach to teaching arithmetic. I am also convinced
> that this plays into the very poor results in
> algebra.
>
> Bob Hansen
>
This is NOT a comment about "enVision (Grade 4 Florida Version)".

I entirely agree with you when you claim:

> "I am convinced that much was lost
> when we abandoned the systematic
> approach to teaching arithmetic."

I only doubt - based on most of your interactions with me over the years - that you know anything about the "systematic approach" that you seem to applaud. Hence this question:

"What, in your opinion, constitutes this wonderful 'systematic approach to teaching arithmetic' that you now seem to applaud?"

GSC
(Still Shoveling Away!" - with apologies if due to Barry Garelick for any tedium caused; and with the humble suggestion that the SIMPLE way to avoid tedium is to refrain from opening any message purported to originate from GSC)

Message was edited by: GS Chandy