Ping Marjorie: Stem and Leaf plots

Donna Metler wrote:
"Clisby" wrote in message
...


Donna Metler wrote:


Almost always, if something seems irrational, it's because someone (who
probably hasn't been near a child in years) decided that it was a good

thing

for kids to know, Which is why multibase appears every now and then in

math

books (although, with the possible exception of binary, it isn't used

much).


Why just binary? I can't think of any obvious application for binary
except computer science/programming, and in that case octal and
hexadecimal would be important also.

I agree with Dorothy - working with bases reinforces understanding of
place value: that is, in the decimal system, the "places" are
10**0, 10**1, 10**2, etc. In base 8, it's 8**0, 8**1, 8**2, etc. In
base 4, it's 4**0, 4**1, 4**2, etc. (I'm using '**' to indicate that
the next number is an exponent.)


Yes, and at the high school or college level, it would be reasonable to
teach it. But to force multi-base (and many of the other topics covered in
the elementary curricula) on young children who do not yet have the concept
of basic operations, let alone exponents, is confusing, at best. And any
time spent on various bases is time not spent on something which may have
more general and real-world applications.



I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade (that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything about
base-2 once I got out of college.

Clisby

In article , Clisby says...




I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade (that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything about
base-2 once I got out of college.

Clisby


I got it in 6th grade in 1966. That was the heyday of 'New Math'.

I did enjoy it and retain the basic concept and how it relates to our base-10
system.

Banty

On 1 Nov 2003, Banty wrote:

In article , Clisby says...




I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade (that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything about
base-2 once I got out of college.

Clisby


I got it in 6th grade in 1966. That was the heyday of 'New Math'.

I did enjoy it and retain the basic concept and how it relates to our base-10
system.

Banty

For me it was 5th grade, 1965. And I loved it, was totally fascinated.
Haven't used it since to speak of but I could if I had to - or so I
believe.

In article , Joni
Rathbun says...


On 1 Nov 2003, Banty wrote:

In article , Clisby says...




I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade (that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything about
base-2 once I got out of college.

Clisby


I got it in 6th grade in 1966. That was the heyday of 'New Math'.

I did enjoy it and retain the basic concept and how it relates to our base-10
system.

Banty

For me it was 5th grade, 1965. And I loved it, was totally fascinated.
Haven't used it since to speak of but I could if I had to - or so I
believe.




And in those days the mathematician (really!) and comedian, Tom Lehrer, wrote a
little song about it:

http://www.lyricsdir.com/t/tom-lehrer/new-math.php

Banty

"Banty" wrote in message
...
In article ,
Joni
Rathbun says...


On 1 Nov 2003, Banty wrote:

In article , Clisby says...




I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade
(that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything
about
base-2 once I got out of college.

Clisby


I got it in 6th grade in 1966. That was the heyday of 'New Math'.

I did enjoy it and retain the basic concept and how it relates to our
base-10
system.

Banty

For me it was 5th grade, 1965. And I loved it, was totally fascinated.
Haven't used it since to speak of but I could if I had to - or so I
believe.




And in those days the mathematician (really!) and comedian, Tom Lehrer,
wrote a
little song about it:

http://www.lyricsdir.com/t/tom-lehrer/new-math.php

Banty

I've used this one the last several years (since we adopted a curriculum
which has a close resemblence to the new math) in the workshops I do for
teachers-and it never fails to get a chuckle, or more!

I use quite a few Lehrer songs in my music integration program, and recently
found this gem while browsing the web. Especially good for middle or high
school chemistry students.

http://www.privatehand.com/flash/elements.html

In article ,
"Donna Metler" wrote:

If children don't master basic operations, in the simplest forms, at a
conceptual level in basic math in elementary school, algebra (which is
required for high school graduation, and is essential to most math and
science classes) will seem a cryptic foreign language, and nothing will make
sense. At best, they'll master it mechanically and by rote.

Anecdote alert...

I still don't feel I understand the basic operations very well. I can DO
them, but not very reliably -- I've learnt them by rote, just not very well!
However... I have never had any trouble with other mathematical concepts, and
in particular have always loved algebra. Once they allowed calculators, I was
up and running confidently, to the extent of doing 3 Unit Maths for the HSC
and scoring 137 out of a possible 150 in it.

After listening to Tom Lehrer's New Math, DH and I got talking, and it appears
that he was actually taught New Math. After some discussion it became clear
that I was taught ******* Son of New Math -- they missed out the bit about it
being important to "understand what you're doing, rather than to get the right
answer"! At 33, I finally understand that borrowing and carrying stuff!

--
Chookie -- Sydney, Australia
(Replace "foulspambegone" with "optushome" to reply)

"Jeez; if only those Ancient Greek storytellers had known about the astonishing
creature that is the *Usenet hydra*: you cut off one head, and *a stupider one*
grows back..." -- MJ, cam.misc

Banty wrote:
In article , Clisby says...



I wasn't arguing in favor of teaching it in 5th grade - I think the
concepts of bases and exponents were introduced to me in 7th grade (that
would have been about 1966). I did wonder why you singled out binary
- as a computer programmer, understanding base-8 and base-16 are
important to me every day, but I've rarely needed to know anything about
base-2 once I got out of college.

Clisby



I got it in 6th grade in 1966. That was the heyday of 'New Math'.

I did enjoy it and retain the basic concept and how it relates to our base-10
system.

Banty



Yes, I remember hearing later about "new math" and realizing I must have
had it in 7th grade - but I never found anything in 7th-grade math
confusing, so maybe it was taught well at my school. I started algebra
in 8th grade, so 7th was my last year of a general math course.

Clisby

Donna Metler wrote in :


"Penny Gaines" wrote in message
...
Donna Metler wrote in :

Almost always, if something seems irrational, it's because someone (who
probably hasn't been near a child in years) decided that it was a good
thing
for kids to know, Which is why multibase appears every now and then in
math books (although, with the possible exception of binary, it isn't
used
much).

What about pounds and ounces? They are a variety of multibase system.
[snip]

In my experience, the end result of piling a lot of various things into
math classes at the early level is that very basic skills are never
thoroughly mastered. The number of people who can't figure a tip without a
calcuator is rather appalling, for example. Same with a task like running
into a store with a $20 bill, and knowing how much you can buy, including
the sales tax. Mental math and estimation is often barely touched on, in
favor of touching on a dozen other topics.
[snip]

I get your point now: I was taught New Maths at school (as opposed to
Chookie's ******* Son of New Maths), and was mathematically inclined anyway,
so I didn't have a problem.

FWIW, I'd have to think hard how much I could spend with the $20 bill: over
here, the equivalent of sales tax is always added to the price shown in
the supermarket.

--
Penny Gaines
UK mum to three

Penny Gaines wrote:


FWIW, I'd have to think hard how much I could spend with the $20 bill: over
here, the equivalent of sales tax is always added to the price shown in
the supermarket.


Same in the US, but I do think it's great mental
exercise ;-) Even younger kids can do it if you phrase
it in terms of X cents extra per dollar, though it's more
difficult here since then went from 4 percent to 5.4 percent ;-)

Best wishes,
Ericka

In article ,
Ericka Kammerer wrote:

Penny Gaines wrote:


FWIW, I'd have to think hard how much I could spend with the $20 bill: over
here, the equivalent of sales tax is always added to the price shown in
the supermarket.


Same in the US, but I do think it's great mental
exercise ;-) Even younger kids can do it if you phrase
it in terms of X cents extra per dollar, though it's more
difficult here since then went from 4 percent to 5.4 percent ;-)

Best wishes,
Ericka



And here it will vary from city to city, but I'm pretty sure that right
now in THIS city it's 8.25% -- and I have a hard time keeping track of
what is and is not taxed.

meh
--
Children won't care how much you know until they know how much you care