It’s been back-to-school time for everybody in our domiciliary (hence an alibi for the ablaze posting). We started classes at the academy today, and aftermost anniversary the 4.5-year old went aback to preschool full-time and the 6.5-year old started aboriginal grade. (The 1.5-year old is agitation the bounded daycare.) One of the bigger changes for the kids is for our first-grader, Lucy, aback she has absolute appointment for the aboriginal time. It’s not much; the apprehension is about 20 account a night, Monday through Thursday. Some of that appointment is math, which I was absolute aflame about — but again that action angry to active attention aback I abstruse my daughter’s chic was application enVisionMATH.

I wrote this column on enVisionMATH about three years ago, basically bedlam it off the blogosphere for its happy-clappy, careless accepting of unproven digital nativist frameworks and for activity way over the top with smartboards. Little did I apperceive that my own baby would be in the average of it aloof three years later. So, in an accomplishment to action what she’s accomplishing (for me, for her, and for anybody abroad who cares), this is the aboriginal of what adeptness be abounding posts about the specifics of enVisionMATH, as beheld by a ancestor whose kid happens to be acquirements from that curriculum, and who additionally happens to be a mathematician and algebraic teacher.

I’ll alpha with the worksheet Lucy brought home this evening, alleged “Making 8″:

I’ve never had a kid in aboriginal brand before, nor can I bethink how I did this actuality in aboriginal grade, nor accept I afresh formed with a kid in aboriginal grade. So I’m activity to allotment my thoughts, but apprehend I accept no advertence for what’s “normal” apprenticeship for 6-year olds and what’s not.

This worksheet is absolutely about subtraction, although it never comes out and says so. The aboriginal two contest are attempting to body a faculty about addition by accepting kids to anticipate about how genitalia fit calm to anatomy a accurate quantity. enVisionMATH appears to be absolutely big on accepting kids to admit numbers visually rather than by counting. I’ll charge to blog about this in a after post, but Lucy’s had some added contest that, for example, accent the adeptness to admit this:

…as the cardinal 6, aloof by attractive at it and after counting the dots, about to the point of cogent kids that they shouldn’t be counting annihilation but rather alignment things into patterns. Again, that’s for addition post.

So, aback to the worksheet, kids are declared to attending at the aboriginal accumulating of balloons and, alive that there are eight of them, see — and alone “see” — that 8 splits into 2 additional 6, and again 4 additional 4. I did a few added of these with Lucy application bill (no balloons on hand, sadly). Bigger claiming here: Keeping Lucy from aloof counting the atramentous balloons and again counting the white balloons. And the alone acumen this was a claiming was because, as a algebraic person, I knew what the worksheet was accepting at: acquainted quantities through beheld patterns rather than counting, so the accepted aphorism is for kids not to calculation the balloons. But added parents apparently didn’t apperceive this, and their kids aloof counted. I don’t anticipate this is necessarily wrong, but it doesn’t necessarily advice in the aing sections either.

The aing area is rather startlingly labelled “Algebra”. Remember: This is a worksheet for a aboriginal brand class. Why we are bringing up the chat “algebra” at this point is anybody’s guess. I doubtable this is added to accomplish parents, academy boards, and accreditors blessed than it is to alpha accepting kids to feel adequate with the chat “algebra”. But anyway, as you can see, the two problems are aloof the aboriginal two problems in reverse.

Lucy had a adamantine time with this. Aboriginal of all, she didn’t accept what “the whole” meant. This is not the aboriginal time Lucy’s struggled not with the algebraic but with almost abstruse cant in her algebraic lessons. Aftermost anniversary she had a worksheet area she was to align three integers “in adjustment from greatest to least” and “from atomic to greatest” and we had to booty a moment to amount out what all of that meant. Maybe added people’s kids don’t attempt with that, but on the added duke it’s been absolute that Lucy is account at a third or fourth brand akin appropriate now, so I admiration if it’s aloof her.

We had to assignment these out application manipulatives. We started with fingers because that’s the aboriginal affair I anticipation of. So, I said, if the accomplished is 8:

…and one allotment is 3:

…then what was the added part?

Lucy was able to get the acknowledgment of “5″ with no problem. But… I don’t anticipate she got it the appropriate way. Because aback we abashed to the aing botheration and the “one part” was 1, for her, the added allotment was still 5! This was because aback I captivated up one feel on my larboard duke this time, there were of advance bristles fingers on the appropriate hand. I approved captivation up eight and fluctuant one feel instead of putting the “one part” on one hand, but that aloof abashed her. So, we went aback to bill and congenital a “balloon diagram” like in the aboriginal two problems, and she got them aloof accomplished (and after counting).

I don’t anticipate contest 3 and 4 are bad problems necessarily, but I do anticipate they came in actuality way too early. Conceivably I’m missing the ambience of the absolute classroom alternation amid Lucy and her teacher, but it would assume like a bigger abstraction to do as abounding contest like 1 and 2 as accessible afore affective on to the “algebra”. After all, if you stick to absolute integers, there are alone seven means to ample in the blanks __ __ = 8. (And accomplishing all seven adeptness advice kids ascertain the capricious acreage aboriginal on, which seems like a abundant added important affair to accompany up than “algebra” in aboriginal grade.)

And then, it’s not bright to me that accomplishing “algebra” is a bigger abstraction actuality than aloof accomplishing erect subtraction. What’s to be acquired by adage “the accomplished is 8; one allotment is 3; the added allotment is ____” against “What is 8 bare 3?” Again, maybe I’m out of touch, but addition is a axiological accomplishment that algebra builds upon; accomplishing algebra afore addition seems a little backwards to say the least. A kid who is adequate with addition will be able to do these whole/part problems in a breeze by application subtraction. A kid accomplishing these “algebra” problems basically has to ad-lib addition in adjustment to do them, or abroad draw pictures of balloons and alpha counting. It feels like the chic is aggravating to be carefully nontraditional here, aloof for the account of accomplishing things abnormally rather than because it works better.

Then we appear to the “Journal” question, which is absolute sophisticated: “The accomplished is 8. One allotment is 8. What is the added part?” Actuality we ability austere abstraction: You can’t draw balloons like in contest 1 and 2, and in actuality resorting to concrete backdrop is tricky.As Derek Bruff mentioned in a cheep about this beforehand this evening, the use of the chat “part” in affiliation with the abundance 0 is already array of questionable. What does it alike beggarly to say the “part” is 0? What “part”? I don’t see a “part”. The accustomed way of interpreting what a “part” is, is as a agglomeration of objects. If there are no altar present, again there absolutely isn’t a “part”.

We had to resort to cerebration not about altar but containers that authority the objects. I took two books sitting nearby. I took my eight bill and said: The accomplished is 8. One allotment is 2 — and put 2 bill on one of the books. What is the added part? — and put the actual bill on the added book. Lucy got the appropriate acknowledgment quickly, and she did so by attractive aback at exercise 1 with the balloons and acquainted it was the aforementioned botheration with altered objects, which I anticipation was appealing smart. I’ll accomplish an algebraist out of her yet! Again I again with one allotment actuality 1. Again I did it with one allotment actuality 6; again 7. Again I said, “The accomplished is 8; one allotment is eight.” — putting all eight bill on one book. “What’s the added part?” — assuming her my abandoned easily and an abandoned book. “Zero,” she said appropriate away.

For her, and maybe not aloof her, “zero” represents not a admeasurement of a allotment but a accompaniment of blank of a alembic — or conceivably the admeasurement of a set. It’s how abundant you see aback annihilation is there. To map the “zero” abstraction assimilate a abstraction of “part” that presupposes article is there aloof doesn’t accomplish sense. If this sounds like the New Math, I anticipate we’re barking up the appropriate tree.

The “Tell how you know” was abnormally boxy because it involves accepting Lucy to allocution about what she did, alike admitting she’s accomplishing it at a array of belly level, and again spell the words she needs to use — which is the added blazon of appointment she has. I got her to say out loud what she was thinking, and again I had her say it aback to me and again helped her spell the words.

So we fabricated it through the worksheet, but there are a lot of questions in my apperception about the pedagogical architecture of this stuff. And how in the apple does this array of affair assignment in a domiciliary area the parents don’t accept the time, patience, interest, fluency, or abundance akin in mathematics to sit bottomward and assignment all this out with the kid?

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