RWW Taylor wrote:
> With regard to her teacher education class at Orange Coast College, Karen
> writes:
>
> ..........................They are not allowed ANY calculator on their first
> exam...... and many cannot do a problem like:
> 3(2/5) + 1 1/2. I always get them on this. They think the first is 3
> AND 2/5. Who taught them their arithmetic?
>
> What you are "getting" your students on is misunderstanding of a notational
> convention. This is important, but is it mathematics? And why wouldn't this
> same misunderstanding (and other, more serious, ones) show up if you let the
> students use a calculator?
Chill a bit. This is a wicked bit of notational trapestry which is perfectly
fair game - I'm amused, and I know that the inconsistency of the mixed number
notation with the convention of multiplying adjacent expressions is often
confusing to students; it's "note"worthy.
Also, re Old Pro's comments:
> Now, I'm beginning to change my mind. In high school, I feel that approximately 50% (or even more of students), the average student
> just cannot do <adding fractions> sans calculators. Why, I don't know; maybe lack of proper foods, maybe air pollution that somehow is affecting
> the young ones.
>
> So..now I'm insisting that students get calculators so that they will be able to do the above calculations.
>
I think I'm beginning to experience the same "long-time teacher" syndrome:
you think, "Hey? Haven't I been teaching this stuff for a long time now!?; So
how come they don't get it yet!! How stoooopid can they be!!!"
<End exasperated voice of panic and adopt small, humble, naive child's falsetto>
Well - I know they're not the same people, they haven't been in my class
before - and, this is my *big chance* to make the whole business about
multiples, least common multiples, greatest common divisors, the division
algorithm, the Euclidean algorithm - *come alive*: I guess I'm just the farmer
who doesn't follow crop to market; I hang behind pulling weeds and mixing
seeds...but someday, maybe I too can go to market...
Finally, I'd like to see the student who can factor 510x^2 - 829xy -
1122y^2 but can't add 1/2+3/5 - as someone suggested.
Geoff Hagopian
Palm Desert, CA
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RWW Taylor wrote:
With regard to her teacher education class at Orange Coast College, Karen writes:Chill a bit. This is a wicked bit of notational trapestry which is perfectly fair game - I'm amused, and I know that the inconsistency of the mixed number notation with the convention of multiplying adjacent expressions is often confusing to students; it's "note"worthy...........................They are not allowed ANY calculator on their first exam...... and many cannot do a problem like:
3(2/5) + 1 1/2. I always get them on this. They think the first is 3 AND 2/5. Who taught them their arithmetic?What you are "getting" your students on is misunderstanding of a notational convention. This is important, but is it mathematics? And why wouldn't this same misunderstanding (and other, more serious, ones) show up if you let the students use a calculator?
Also, re Old Pro's comments:
I think I'm beginning to experience the same "long-time teacher" syndrome: you think, "Hey? Haven't I been teaching this stuff for a long time now!?; So how come they don't get it yet!! How stoooopid can they be!!!"Now, I'm beginning to change my mind. In high school, I feel that approximately 50% (or even more of students), the average student just cannot do <adding fractions> sans calculators. Why, I don't know; maybe lack of proper foods, maybe air pollution that somehow is affecting the young ones. So..now I'm insisting that students get calculators so that they will be able to do the above calculations.
<End exasperated voice of panic and adopt small, humble, naive child's falsetto>
Well - I know they're not the same people, they haven't been in my class before - and, this is my *big chance* to make the whole business about multiples, least common multiples, greatest common divisors, the division algorithm, the Euclidean algorithm - *come alive*: I guess I'm just the farmer who doesn't follow crop to market; I hang behind pulling weeds and mixing seeds...but someday, maybe I too can go to market...
Finally, I'd like to see the student who can factor 510x^2 - 829xy - 1122y^2 but can't add 1/2+3/5 - as someone suggested.
Geoff Hagopian
Palm Desert, CA
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