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)