Ping Marjorie: Stem and Leaf plots

In article ,
Donna Metler wrote:

I see nothing wrong with enrichment and extra concepts for students who have
mastered the basics. Where I see the problem is spending a huge amount of
time trying to get children who still don't have the concept of addition
down to add in base 8. And in my experience, teaching multi-base before
students have mastery of base 10 primarily convinces them NOT to trust their
common sense to tell them if an answer is logical. So, they see nothing
wrong with adding 10+10 and getting 1010. Because they know that 10+10 may
have a lot of different answers.

My children's school uses multiple base systems right from the start as
part of a foundation for a strong understanding of place value and the
base 10 system. It seems to work quite well for children of all levels
of ability. (I was working with 5- and 6-year-olds on an activity that
essentially taught base 4, though that wasn't explicitly stated. Not a
single child had any difficulty whatsoever with the activity, and there
was a pretty wide range of abilities in the group.) I don't think they
actually do operations in other bases until 5th or 6th grade, when they
should certainly be comfortable with basic operations in base 10, but
the math teacher specifically starts the youngest kids on "chip
trading" in bases *other* than 10 first, because it leads to a better
"aha" moment when they do try it in base 10 eventually, already very
comfortable with the concept.

So.... I don't see multiple bases as in any way comparable with stem and
leaf plots, which seem to me to be just one esoteric piece of knowledge
with little* interaction with other more useful things to understand.

--Robyn

* I say "little" and not "no" becasue when my son studied stem-and-leaf
plots in 4th grade (in a different school than the one discussed above)
they did tie it in with work on median, mean, mode, etc. which certainly
are more useful statistical concepts for an elementary-school child to
understand. But I don't think they substantially improved students'
mastery of the useful concepts (contrary to the use of multi-base
representation and arithemtic discussed above, which I think does
substantially improve students' comprehension of the base 10 system).


Same with Marjorie's stem and leaf plots. While there may be places they are
useful, is it really reasonable to limit instruction on something else in
order to include them? Are they so important that they should be given a
significant amount of time at the elementary level? We are currently
teaching much more advanced concepts at an earlier age than ever before,
without requiring demonstration of mastery of the previous skills (this is
the definition of a spiral curriculum, like Everyday Math or Connected
Math). The idea is that the child may not get addition the first, fourth,
or sixth time they see it, but may get it the 8th. For the child who masters
the concept easily, it's a waste of time. For the child who needs more time
and practice, its confusing.

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. And, except for
the very gifted, few children can get a concept really learned without a lot
of experimentation, exposure, and practice. Little bits here and there in a
rush to cover 100 topics in 180 days of school isn't going to make it.

Whew....off soapbox....
--
Penny Gaines
UK mum to three

In article ,
Donna Metler wrote:

"Clisby" wrote in message
...


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.

The requirement of having immediate real-world applications is a rather
short-sighted view of elementary math education. Presumably the goal
of elementary and middle-school math education is not *only* to teach
basics with real-world applications but also to prepare young minds for
higher-level mathematics of the high-school and college levels. This
isn't something you can effectively just start when they get to high
school. To do it right, the foundation must be laid from the start.

And, with the ubiquity of cheap calculators these days, I'm not convinced
that every child being able to compute a tip without a calculator is a
more laudable or important goal than preparing kids from an early age to
eventually be able to handle higher-level mathematics.

No, not everyone needs to know calculus, but society needs a certain
proportion of people who do, and do we really want to decide in
elementary school which children seem to have the aptitude and should
get the foundational math to allow them to succeed at the higher
levels, and which should get just the mechanical basics? (Smacks of
"tracking" to me).

So, that's the mathematician in me valuing the long-term view of
elementary math education... I'm sure others will find my priorities
strange.

--Robyn (mommy to Ryan 9/93 and Matthew 6/96 and Evan 3/01)