Hw-Procedures-2010

Hw-Procedures-2010 - G.
González
 A.
Poetzel
 
...

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Unformatted text preview: G.
González
 A.
Poetzel
 
 
 
 
 Problems
on
Explaining
Procedures
 
 Do
one
problem
in
algebra
and
one
problem
in
geometry
for
homework.

Read
and
 think
about
all
of
the
problems.
 1. Susi
Wan
is
teaching
the
procedure
for
bisecting
a
segment
to
her
geometry
class.

 She
says:

“If
you
have
a
segment
AB,
put
the
tip
of
the
compass
on
A,
fix
the
radius
 of
the
compass
so
that
it
has
the
length
of
segment
AB,
and
then
trace
a
circle
with
 center
on
A.

Don’t
change
the
radius
and
trace
a
circle
with
center
on
B.

When
you
 join
the
intersection
points
of
the
two
circles
you
have
the
perpendicular
bisector.”


 a. Discuss
whether
Susi
is
promoting
“flexibility”
when
performing
a
procedure.
 b. If
you
think
that
there
are
things
that
she
should
say
differently,
script
a
 different
explanation.

If
you
think
that
her
explanation
is
fine,
identify
her
 teaching
actions
according
to
the
rubric
of
explaining
procedures.
 c. Make
a
diagram
that
you
might
expect
students
to
have
as
a
result
of
this
new
 explanation.
 d. One
of
Susi’s
students
raises
her
hand
and
says,
“How
do
we
know
for
sure
if
 it
really
is
the
perpendicular
bisector?”.

Script
a
response
to
this
question
 that
can
help
students
to
know
how
to
justify
the
procedure.
 
 
 2. Ron
Schwatz
is
teaching
a
lesson
on
solving
linear
equations
to
his
algebra
class
and
 he
says:

“Make
sure
that
you
align
all
the
equal
signs
as
you
solve
the
equation.

 Also,
if
you
add
something
to
the
right
side
make
sure
that
you
add
the
same
thing
to
 the
left
side.

The
same
applies
when
you
subtract
something
to
one
side.

You
 should
do
the
same
to
the
other
side
to
keep
the
equation
balanced.

I
want
to
see
 zeros
in
the
next
line
when
you
get
rid
of
a
term.

At
the
end,
the
x
always
goes
in
the
 left
side
because
you
are
saying
‘my
x
equals
whatever.’”
 a. What
kind
of
work
do
you
expect
Ron’s
students
to
do
when
they
solve
 equations?
 b. What
are
plausible
reasons
for
Ron’s
emphasis
in
steps
when
performing
the
 procedure?
 c. How
could
Ron
promote
“flexibility”
when
performing
a
procedure?
 d. How
could
Ron
modify
his
explanation
so
that
he
would
teach
students
the
 justification
for
the
procedure?
 e. How
could
Ron
teach
students
to
have
means
of
control?
 f. Script
a
few
lines
about
what
should
Ron
say
to
teach
students
about
means
 of
control.
 
 
 
 
 
 
 G.
González
 A.
Poetzel
 
 
 
 3. Miguel
Feliciano
is
teaching
his
algebra
students
how
to
make
a
table
and
a
graph
of
 a
quadratic
function.


 a. Select
the
first
two
examples
that
he
can
use.

Explain
your
choice
of
 examples
(what
criteria
helped
you
to
choose
these
examples?).
 b. Identify
notation
that
Miguel
should
teach
students
to
use.
 c. Script
a
few
lines
to
describe
what
he
should
say
to
lead
students
to
make
 decisions
about
what
points
would
give
them
enough
information
to
draw
 the
graph.
 d. If
Miguel
wanted
to
hold
his
students
accountable
for
performing
and
 understanding
this
procedure,
what
might
he
do
next
inhis
lesson?

Justify
 your
choice
of
actions
using
the
rubric
for
explaining
a
procedure.
 
 
 
 
 4. Lisa
Carr
is
teaching
her
geometry
students
how
to
calculate
the
area
of
a
regular
 polygon
given
the
length
of
one
of
its
sides.
 a. Identify
mathematical
terms
that
she
should
include
in
her
explanation.
 b. Choose
two
examples
that
she
could
present
to
students.

Explain
what
the
 unique
features
are
for
each
one
of
the
examples
and
what
elements
the
two
 examples
have
in
common.
 c. Script
a
few
lines
that
she
could
say
to
her
students
to
summarize
the
 procedure
by
comparing
the
two
examples.
 d. Create
a
new
problem
on
which
students
should
be
able
to
work
on
their
 own
and
that
could
be
useful
for
Lisa
to
assess
their
understanding
of
the
 procedure
for
calculating
areas
of
regular
polygons.
 
 ...
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