Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Connected Mathematics Project 3 Preparing for the Transition:
Supporting Teachers to Successfully Implement CMP3
Professional DevelopmentParticiPant Workbook
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.2
For Professional Development resources and programs, visit www.pearsonpd.com.
Pearson School achievement Servicesconnected Mathematics Project 3Preparing for the transition: Supporting teachers to Successfully implement cMP3Participant Workbook
Pearson provides these materials for the expressed purpose of training district and school personnel on the effective implementation of Pearson products within classrooms, and other professional development topics. these materials may not be used for any other purpose, and may not be reproduced, distributed, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without Pearson’s express written permission.
Excel® is a trademark of the Microsoft group of companies.
Published by Pearson School achievement Services, a division of Pearson, inc.1900 E. Lake ave., Glenview, iL 60025
© 2013 Pearson, inc.all rights reserved.Printed in the United States of america.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.3
Table of Contents
agenda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Section 1: Focus, coherence, and rigor: How cMP3 Meets the content and Pedagogical Shifts of the common core. . . . . . . . . . . . . . . . . . 8
Section 2: the inquiry-based Learning Structure of cMP3 . . . . . . . . . . . . . . . . 21
Section 3: Supporting teachers to build Mathematical communities capable of cMP3’s inquiry-based Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Section 4: inquiry-based classrooms: a Shift in Student Experience . . . . . . . . 33
Section 5: Developing Your Plan for Supporting teachers. . . . . . . . . . . . . . . . . 39
Reflection and Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.4
Agenda
Section
introduction
1. Focus, coherence, and rigor: How cMP3 Meets the content and Pedagogical Shifts of the common core
2. the inquiry-based Learning Structure of cMP3
3. Supporting teachers to build Mathematical communities capable of cMP3’s inquiry-based Learning
4. inquiry-based classrooms: a Shift in Student Experience
5. Developing Your Plan for Supporting teachers
Reflection and Closing
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.5
Outcomes
at the conclusion of this workshop, you will be able to
• understand the CMP3 inquiry-based lesson structure;
• investigate how CMP3 aligns with the focus, coherence, and rigor of the content and pedagogical shifts of the Common Core;
• apply best practices to support teachers to implement CMP3 with fidelity;
• support students to successfully adopt inquiry-based instruction; and
• develop a plan for supporting teachers to implement CMP3 in their classrooms throughout the school year.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.6
Introduction
Year One Professional Development Goals • Support teachers in learning how to teach with focus, coherence, and rigor of the Common
core Learning Standards in Mathematics (ccLSM) through the cMP3 curriculum.
• Learn strategies and best practices to support student learning through inquiry-based instruction.
• Support teachers in making instructional decisions within the CMP3 curriculum through an analysis of student and teacher work.
• Deepen teacher content knowledge through the effective implementation of the CMP3 curriculum.
Year One Professional Development Components • Intensive Sessions (A–E)
• Intensive Webinars (synchronous and recorded)
• Teacher Sessions (1–4)
• Teacher Webinars (synchronous and recorded)
• Teacher Tutorials (static, online Web resources)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.7
Introduction
Mathematical Task a. Mirari conjectures that, for any three consecutive numbers, one number would be divisible
by 3. Do you think Mirari is correct? Explain.
b. Gia claims that the sum of any three consecutive whole numbers is divisible by 6. is this true? Explain.
c. kim claims that the product of any three consecutive whole numbers is divisible by 6. is this true? Explain.
d. Does the product of any four consecutive whole numbers have any interesting properties? Explain.
(Pearson Education, inc. 2014c, 85)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.8
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Quick Write: The ShiftFocus:
coherence:
rigor:
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.9
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Focus: Two Out of Three Ain’t Badthe following chart is an excerpt from Student achievement Partners (n.d.). cross out the one area of major focus that does not represent an area of major focus for the indicated grade.
Grade Which 2 of the following represent areas of major focus for the indicated grade?
Kcompare numbers Use tally marks Understand meaning of
addition and subtraction
1add and subtract within 20 Measure lengths indirectly
and by iterating length unitscreate and extend patterns and sequences
2Work with equal groups of objects to gain foundations for multiplication
Understand place value identify line of symmetry in two dimensional
3Multiply and divide within 100
identify the measures of central tendency and distribution
Develop understanding of fractions as numbers
4Examine transformations on the coordinate plane
Generalize place value understanding for multi-digit whole numbers
Extend understanding of fraction equivalence and ordering
5
Understand and calculate probability of single events
Understand the place value system
apply and extend previous understandings of multiplication and division to multiply and divide fractions
6
Understand ratio concepts and use ratio reasoning to solve problems
identify and utilize rules of divisibility
apply and extend previous understandings of arithmetic to algebraic expressions
7
apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
Use properties of operations to generate equivalent expressions
Generate the prime factorization of numbers to solve
8Standard form of a linear equation
Define, evaluate, and compare functions
Understand and apply the Pythagorean theorem
Alg.1Quadratic inequalities Linear and quadratic
functionscreating equations to model situations
Alg.2
Exponential and logarithmic functions
Polar coordinates Using functions to model situations
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.10
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Stoplight Highlighting: Where is the focus?
(PAARC 2011, 29–30)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.11
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
CM
P3 F
ocus
es W
here
the
Stan
dard
s Fo
cus
Gra
de 6
Maj
or C
lust
erC
onte
nt o
f Maj
or C
lust
erLi
st a
nd T
ally
CM
P3 In
vest
igat
ions
on
Con
tent
of M
ajor
Clu
ster
6.R
P.1–
3: U
nder
stan
d ra
tio
conc
epts
and
use
ratio
reas
onin
g to
sol
ve p
robl
ems.
• U
nder
stan
d an
d us
e la
ngua
ge o
f rat
ios
to d
escr
ibe
the
rela
tions
hip
betw
een
two
quan
titie
s.•
Und
erst
and
unit
rate
s an
d us
e it
in th
e co
ntex
t of a
ratio
rela
tions
hip.
• S
olve
real
-wor
ld p
robl
ems
with
ratio
tabl
es, t
ape
diag
ram
s, d
oubl
e nu
mbe
r lin
e di
agra
ms,
or e
quat
ions
, inc
ludi
ng p
robl
ems
with
uni
t pric
ing,
per
cent
, sp
eed,
and
uni
ts o
f mea
sure
men
t.
num
ber o
f inv
estig
atio
ns: _
____
____
6.n
S.1
: app
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
m
ultip
licat
ion
and
divi
sion
to
divi
de fr
actio
ns b
y fra
ctio
ns.
• In
terp
ret a
nd c
ompu
te q
uotie
nts
of fr
actio
ns.
• S
olve
wor
d pr
oble
ms
usin
g di
visi
on o
f fra
ctio
ns b
y fra
ctio
ns.
• U
se v
isua
l fra
ctio
n m
odel
s an
d eq
uatio
ns to
repr
esen
t pro
blem
s an
d ju
stify
con
cept
ual u
nder
stan
ding
of t
he s
ituat
ion.
num
ber o
f inv
estig
atio
ns: _
____
____
6.N
S.5
–8: A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of
num
bers
to th
e sy
stem
of r
atio
nal
num
bers
.
• U
nder
stan
d po
sitiv
e an
d ne
gativ
e nu
mbe
rs in
real
-wor
ld c
onte
xt.
• U
nder
stan
d a
ratio
nal n
umbe
r as
a po
int o
n th
e nu
mbe
r lin
e.•
Ext
end
both
num
ber l
ine
diag
ram
s an
d co
ordi
nate
axe
s to
incl
ude
ratio
nal
num
bers
.•
Und
erst
and
orde
ring
and
abso
lute
val
ue o
f rat
iona
l num
bers
.•
Sol
ve re
al-w
orld
and
mat
hem
atic
al p
robl
ems
by g
raph
ing.
num
ber o
f inv
estig
atio
ns: _
____
____
6.E
E.1
–4: A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of a
rithm
etic
to a
lgeb
raic
ex
pres
sion
s.
• W
rite
and
eval
uate
num
eric
al e
xpre
ssio
ns w
ith w
hole
-num
ber e
xpon
ents
.•
Writ
e, re
ad, a
nd e
valu
ate
expr
essi
ons
in w
hich
lette
rs s
tand
for n
umbe
rs.
• A
pply
the
dist
ribut
ive
prop
erty
and
com
bine
like
term
s to
gen
erat
e eq
uiva
lent
exp
ress
ions
.•
Iden
tify
two
equi
vale
nt e
xpre
ssio
ns
num
ber o
f inv
estig
atio
ns: _
____
____
6.E
E.5
–8: R
easo
n ab
out a
nd
solv
e on
e-va
riabl
e eq
uatio
ns a
nd
ineq
ualit
ies.
• U
nder
stan
d so
lvin
g an
equ
atio
n or
ineq
ualit
y as
det
erm
inin
g w
hich
val
ues
mak
e it
true.
• W
ritin
g an
d so
lvin
g eq
uatio
ns a
nd in
equa
litie
s w
ith o
ne v
aria
bles
.•
Sol
ving
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s by
writ
ing
and
solv
ing
equa
tions
with
non
nega
tive
ratio
nal n
umbe
rs.
• R
epre
sent
sol
utio
ns o
f ine
qual
ities
on
num
ber l
ine
diag
ram
s.
num
ber o
f inv
estig
atio
ns: _
____
____
6.E
E.9
: rep
rese
nt a
nd a
naly
ze
quan
titat
ive
rela
tions
hips
bet
wee
n de
pend
ent a
nd in
depe
nden
t va
riabl
es.
• R
epre
sent
two
real
-wor
ld q
uant
ities
that
cha
nge
in re
latio
nshi
p to
eac
h ot
her w
ith d
epen
dent
and
inde
pend
ent v
aria
bles
.•
Ana
lyze
the
rela
tions
hip
betw
een
depe
nden
t and
inde
pend
ent v
aria
bles
us
ing
grap
hs, t
able
s, a
nd e
quat
ions
.
num
ber o
f inv
estig
atio
ns: _
____
____
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.12
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Gra
de 7
Maj
or C
lust
erC
onte
nt o
f Maj
or C
lust
erLi
st a
nd T
ally
CM
P3 In
vest
igat
ions
on
Con
tent
of M
ajor
Clu
ster
7.R
P.1–
3: A
naly
ze p
ropo
rtion
al
rela
tions
hips
and
use
them
to
solv
e re
al-w
orld
and
mat
hem
atic
al
prob
lem
s.
• C
ompu
te u
nit r
ates
ass
ocia
ted
with
ratio
s of
frac
tions
, inc
ludi
ng le
ngth
s,
area
s an
d ot
her q
uant
ities
mea
sure
d in
like
or d
iffer
ent u
nits
.•
Rec
ogni
ze a
nd re
pres
ent p
ropo
rtion
al re
latio
nshi
ps.
• Te
st fo
r equ
ival
ent r
atio
s in
a ta
ble
or g
raph
ing
on th
e co
ordi
nate
pla
ne to
de
term
ine
if th
e gr
aph
pass
es th
roug
h th
e or
igin
.•
Iden
tify
the
cons
tant
of p
ropo
rtion
ality
in ta
bles
, gra
phs,
equ
atio
ns,
diag
ram
s, a
nd v
erba
l des
crip
tions
of p
ropo
rtion
al re
latio
nshi
ps.
• R
epre
sent
pro
porti
onal
rela
tions
hips
by
equa
tions
.•
Sol
ve m
ulti-
step
ratio
and
per
cent
pro
blem
s.
num
ber o
f inv
estig
atio
ns: _
____
___
7.N
S.1
–3: A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of
oper
atio
ns w
ith fr
actio
ns to
add
, su
btra
ct, m
ultip
ly a
nd d
ivid
e ra
tiona
l num
bers
.
• A
dd a
nd s
ubtra
ct ra
tiona
l num
bers
.•
Rep
rese
nt a
dditi
on a
nd s
ubtra
ctio
n of
ratio
nal n
umbe
rs o
n ho
rizon
tal a
nd
verti
cal n
umbe
r lin
e di
agra
ms.
• U
nder
stan
d su
btra
ctio
n as
add
ing
the
inve
rse.
• M
ultip
ly a
nd d
ivid
e ra
tiona
l num
bers
.•
Con
vert
a ra
tiona
l num
ber t
o a
deci
mal
usi
ng lo
ng d
ivis
ion
and
know
why
de
cim
als
can
term
inat
e or
repe
at.
• S
olve
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s us
ing
the
four
ope
ratio
ns o
n ra
tiona
l num
bers
.
num
ber o
f inv
estig
atio
ns: _
____
___
7.E
E.1
–2: U
se p
rope
rties
of
oper
atio
ns to
gen
erat
e eq
uiva
lent
ex
pres
sion
s.
• A
dd, s
ubtra
ct, f
acto
r, an
d ex
pand
line
ar e
xpre
ssio
ns w
ith ra
tiona
l co
effic
ient
s.•
Und
erst
and
that
rew
ritin
g ex
pres
sion
s in
diff
eren
t for
ms
can
help
to b
ette
r un
ders
tand
how
qua
ntiti
es a
re re
late
d.
num
ber o
f inv
estig
atio
ns: _
____
___
7.E
E.3
–4: S
olve
real
-life
an
d m
athe
mat
ical
pro
blem
s us
ing
num
eric
al a
nd a
lgeb
raic
ex
pres
sion
s an
d eq
uatio
ns.
• S
olve
mul
ti-st
ep re
al-li
fe a
nd m
athe
mat
ical
pro
blem
s w
ith p
ositi
ve a
nd
nega
tive
ratio
nal n
umbe
rs re
pres
ente
d as
who
le n
umbe
rs, f
ract
ions
, and
/or
dec
imal
s.•
Con
vert
betw
een
who
le n
umbe
rs, f
ract
ions
, and
dec
imal
s an
d kn
ow h
ow
to a
sses
s th
e re
ason
able
ness
of s
olut
ions
.•
Use
var
iabl
es to
repr
esen
t qua
ntiti
es in
real
-wor
ld a
nd m
athe
mat
ical
pr
oble
ms.
• C
onst
ruct
sim
ple
equa
tions
and
ineq
ualit
ies
to s
olve
pro
blem
s by
re
ason
ing
abou
t qua
ntiti
es.
• S
olve
wor
d pr
oble
ms
with
equ
atio
ns o
f the
form
px
+ q
= r a
nd p
(x +
q) =
r,
whe
re p
, q, a
nd r
are
spec
ified
ratio
nal n
umbe
rs.
• S
olve
wor
d pr
oble
ms
with
ineq
ualit
ies
of th
e fo
rm p
x +
q >
r or p
x +
q <
r, w
here
p, q
, and
r ar
e sp
ecifi
ed ra
tiona
l num
bers
.•
Gra
ph s
olut
ion
sets
of i
nequ
aliti
es.
num
ber o
f inv
estig
atio
ns: _
____
___
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.13
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Gra
de 8
Maj
or C
lust
erC
onte
nt o
f Maj
or C
lust
erLi
st a
nd T
ally
CM
P3 In
vest
igat
ions
on
Con
tent
of M
ajor
Clu
ster
8.E
E.1
–4: W
ork
with
radi
cals
and
in
tege
r exp
onen
ts.
• A
pply
pro
perti
es o
f int
eger
exp
onen
ts.
• U
se s
quar
e ro
ots
and
cube
root
s to
sol
ve e
quat
ions
of t
he fo
rm x
2 = p
and
x3 =
p,
whe
re p
is a
pos
itive
ratio
nal n
umbe
r.•
Find
squ
are
root
s of
sm
all p
erfe
ct s
quar
es a
nd c
ube
root
s of
sm
all p
erfe
ct c
ubes
.•
Exp
ress
a n
umbe
r as
a w
hole
num
ber t
imes
a w
hole
-num
ber p
ower
of t
en.
• P
erfo
rm o
pera
tions
with
num
bers
exp
ress
ed in
sci
entifi
c no
tatio
n, in
clud
ing
prob
lem
s w
here
bot
h de
cim
al a
nd s
cien
tific
nota
tion
are
used
.n
umbe
r of i
nves
tigat
ions
: ___
__
8.E
E.5
–6: U
nder
stan
d th
e co
nnec
tions
bet
wee
n pr
opor
tiona
l re
latio
nshi
ps, l
ines
and
line
ar
equa
tions
.
• G
raph
pro
porti
onal
rela
tions
hips
and
und
erst
and
the
unit
rate
as
the
slop
e.
• U
se m
ultip
le re
pres
enta
tions
to c
ompa
re tw
o di
ffere
nt p
ropo
rtion
al re
latio
nshi
ps.
• U
se s
imila
r tria
ngle
s to
exp
lain
con
stan
t slo
pe o
f a n
on-v
ertic
al li
ne o
n th
e co
ordi
nate
pla
ne.
• D
eriv
e y
= m
x as
a li
ne th
roug
h th
e or
igin
and
y =
mx
+ b
as a
line
inte
rcep
ting
the
verti
cal a
xis
at b
.n
umbe
r of i
nves
tigat
ions
: ___
__
8.E
E.7
–8: a
naly
ze a
nd s
olve
line
ar
equa
tions
and
pai
rs o
f sim
ulta
neou
s lin
ear e
quat
ions
.
• S
olve
line
ar e
quat
ions
in o
ne v
aria
ble.
• D
eter
min
e if
linea
r equ
atio
ns in
one
var
iabl
e ha
ve o
ne, i
nfini
tely
man
y, o
r no
solu
tions
.•
Sol
ve li
near
equ
atio
ns w
ith ra
tiona
l coe
ffici
ents
.•
Ana
lyze
and
sol
ve p
airs
of s
imul
tane
ous
linea
r equ
atio
ns a
nd u
nder
stan
d th
e so
lutio
ns. c
orre
spon
d to
poi
nts
of in
ters
ectio
n of
thei
r gra
phs.
• S
olve
sys
tem
s al
gebr
aica
lly a
nd e
stim
ate
by g
raph
ing.
•Sol
ve re
al-w
orld
and
m
athe
mat
ical
pro
blem
s.
num
ber o
f inv
estig
atio
ns: _
____
8.F.
1 –3:
Defi
ne, e
valu
ate
and
com
pare
func
tions
.•
Und
erst
and
a fu
nctio
n as
a ru
le th
at a
ssig
ns e
ach
inpu
t exa
ctly
one
out
put.
• C
ompa
re p
rope
rties
of t
wo
func
tions
alg
ebra
ical
ly, g
raph
ical
ly, n
umer
ical
ly, in
ta
bles
, or b
y ve
rbal
des
crip
tion.
• Id
entif
y y
= m
x +
b as
a li
near
func
tion
with
the
grap
h of
a s
traig
ht li
ne.
num
ber o
f inv
estig
atio
ns:
____
_
8.G
.1–5
: Und
erst
and
cong
ruen
ce
and
sim
ilarit
y us
ing
phys
ical
mod
els,
tra
nspa
renc
ies
or g
eom
etry
sof
twar
e.
• Ve
rify
expe
rimen
tally
the
prop
ertie
s of
rota
tions
, refl
ectio
ns, a
nd tr
ansl
atio
ns.
• U
nder
stan
d th
at tw
o-di
men
sion
al fi
gure
s ar
e co
ngru
ent i
f one
can
be
obta
ined
from
th
e ot
her t
hrou
gh ro
tatio
ns, r
eflec
tions
, and
tran
slat
ions
.•
Use
coo
rdin
ates
to d
escr
ibe
the
effe
ct o
f dila
tions
, tra
nsla
tions
, rot
atio
ns, a
nd
refle
ctio
ns.
• U
nder
stan
d th
at tw
o-di
men
sion
al fi
gure
s ar
e si
mila
r if o
ne c
an b
e ob
tain
ed fr
om th
e ot
her t
hrou
gh d
ilatio
ns, r
otat
ions
, refl
ectio
ns, a
nd tr
ansl
atio
ns.
• U
se in
form
al a
rgum
ents
to e
stab
lish
fact
s ab
out a
ngle
sum
and
ext
erio
r ang
le
of tr
iang
les,
ang
les
crea
ted
whe
n pa
ralle
l lin
es a
re c
ut b
y a
trans
vers
al, a
nd a
a tri
angl
e si
mila
rity.
num
ber o
f inv
estig
atio
ns:
____
_
8.G
.6–8
: Und
erst
and
and
appl
y th
e P
ytha
gore
an t
heor
em.
• E
xpla
in a
pro
of o
f Pyt
hago
rean
The
orem
and
of i
ts c
onve
rse.
• A
pply
Pyt
hago
rean
The
orem
.•
Use
Pyt
hago
rean
The
orem
to fi
nd d
ista
nce
betw
een
two
poin
ts in
the
coor
dina
te
syst
em.
num
ber o
f inv
estig
atio
ns:
____
_
(New
Yor
k S
tate
Mat
hem
atic
s C
omm
on C
ore
Wor
kgro
up, n
.d.,
36–3
8, 4
1–42
, 46–
48)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.14
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Notes on the Content of Major Clusters • Grade 6
• Grade 7
• Grade 8
Discussion on CMP3’s FocusWhere do you see the focus of the ccLSM in cMP3?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.15
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Discussion on CMP3’s CoherenceWhere do you see the coherence of the ccLSM in cMP3?
CMP3’s Rigor of the Common Core
Quick WriteGiven the descriptions of the instructional shifts in the “crosswalk of common core instructional Shifts: Mathematics” document, what will you see when there is rigor in the classroom?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.16
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Achieving Rigor through the Math PracticesUse the following UrL: http://www.p12.nysed.gov/ciai/common_core_standards/pdfdocs/nysp12cclsmath.pdf
Component of RigorIdentify One Math Practice for Each
Component of Rigor, and Explain How Students Will Use the Math Practice to Achieve the Rigor of the Common Core
Fluency: Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions (found in the attached list of fluencies) such as multiplication tables so that they are more able to understand and manipulate more complex concepts.
Deep Understanding: teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.
Application: Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. teachers in content areas outside of math, particularly science, ensure that students are using math—at all grade levels—to make meaning of and access content.
Dual Intensity: Students are practicing and understanding. there is more than a balance between these two things in the classroom—both are occurring with intensity. teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. the amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.
(nYSED, n.d.)
Rig
or: r
equi
re fl
uenc
y, a
pplic
atio
n, a
nd d
eep
unde
rsta
ndin
g
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.17
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Growing, Growing, Growing: Problem 4.1 a. the paper chen starts with has an area of 64 square inches. copy and complete the table
to show the area of a ballot after each of the fi rst 10 cuts.
b. How does the area of a ballot change with each cut?
c. Write an equation for the area a of a ballot after any cut n.
Number of Cuts Area (in.2)
0 64
1 32
2 16
3
4
5
6
7
8
9
10
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.18
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
D. Make a graph of the data.
(Pearson Education, inc. 2014c)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.19
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
In the following dialogue, from a CMP class, students compare their graphs for Problem 4.1 to their graphs of an inverse variation relationship.
Collin: i looked at one of the inverse graphs as well and i realized something, that this one has a Y intercept and inverse graph never had a Y intercept.
Teacher: Let’s investigate that idea. Does anybody remember one of the situations that was an inverse proportion relationship? that could help us talk about it.
James: it’s like, uh, factor pairs of each other that makes the graph. Like if there were 24, you know, if you were going to buy 24, um, 240,000 square feet of land, or something, um, then you could. . .you’d find all the factor pairs, like, you’d. . . Like, whatever the X is, like if the X was 2, then, then it’d be like 120,000 because, yeah, because the one would be 240,000, so then, yeah, it’s, it’s like factor pairs of each other, 2 times 120,000, that’s 240,000. . .and then you just like multiply the X by the Y and get 240,000.
Teacher: So you’re thinking of that problem back in the last unit where there were the pieces of land - it could be a 2 by 120,000. and then you listed several of those and that’s the factor pairs you were talking about. is that pattern also true on the graph and table for today’s problem?
James: Um, no. these are not the factor pairs idea that i was talking about.
Teacher: So it is a different relationship between variables. Why isn’t there a Y intercept on the inverse proportion graph, like collin said?
Sarah: Um, well, um, zero times nothing would ever give you 240,000, so there can’t be a y-intercept.
Teacher: Does a zero exist for this situation? at zero cuts, did he have an area?
Sara: Yup. 64.
Teacher: So there would be a Y intercept on this one, and the relationship between the X and the Y for an inverse proportion relationship is not exactly the same relationship between the X and the Y that we’re finding here. But the shapes of the graphs look alike.
(Pearson Education, inc. 2014c)
Rigor and Math Practices in CMP3annotate your work and the cMP3 classroom dialogue to indicate where and how you use rigor and the math practices in your problem solving and the cMP3 dialogue. Space is also provided here for notes.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.20
Section 1: Focus, Coherence, and Rigor: How CMP3 Meets the Content and Pedagogical Shifts of the Common Core
Revisit the Section 1 Big Questions • In what ways does CMP3 align with the focus, coherence, and rigor of the CCLSM?
• How do students experience rigor of the CCLSM in the investigation of CMP3 problems?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.21
Section 2: The Inquiry-Based Learning Structure of CMP3
What is inquiry-based learning?
Types of Problem SolvingThe following excerpt appears in Van de Walle, Karp, and Bay-Williams’ Elementary and Middle School Mathematics: Teaching Developmentally (2013, 32):
in a classic publication on the types of teaching related to problem solving, Schroeder and Lester (1989) identified three types of approaches to problem solving:
1. Teaching for problem solving. this approach can be summarized as teaching a skill so that a student can later problem solve. teaching for problem solving often starts with learning the abstract concept and then moving to solving problems as a way to apply the learned skills. For example, students learn the algorithm for adding fractions and, once that is mastered, solve story problems that involve adding fractions. (this approach is used in many textbooks and is likely familiar to you.)
2. Teaching about problem solving. this second approach involves teaching students how to problem solve, which can include teaching the process (understand, design a strategy, implement, look back) or strategies for solving a problem. an example of a strategy is “draw a picture,” in which students use a picture or diagram to help solve a problem. See “teaching about Problem Solving” in this chapter.
3. Teaching through problem solving. this approach generally means that students learn mathematics through real contexts, problems, situations, and models. the contexts and models allow students to build meaning for the concepts so that they can move to abstract concepts. teaching through problem solving might be described as upside down from teaching for problem solving—with the problem(s) presented at the beginning of a lesson and skills emerging from working with the problem(s). For example, in exploring the situation of combining 1/2 and 1/3 feet of ribbon to figure out how long the ribbon is, students would be led to discover the procedure for adding fractions.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.22
Section 2: The Inquiry-Based Learning Structure of CMP3
Ana
lyzi
ng C
MP3
’s L
esso
n St
ruct
ure:
Who
’s d
oing
wha
t whe
n?
Laun
chEx
plor
eSu
mm
ariz
e
Stud
ents
Wha
t are
stu
dent
s do
ing?
Wha
t are
stu
dent
s sa
ying
?
Use
one
wor
d to
des
crib
e a
stud
ent’s
role
.
Teac
hers
Wha
t is
the
teac
her d
oing
?
Wha
t is
the
teac
her s
ayin
g?
Use
one
wor
d to
des
crib
e th
e te
ache
r’s ro
le.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.23
Section 2: The Inquiry-Based Learning Structure of CMP3
Scrambled Sentencesthe role of a student during the Launch phase:
the role of a student during the Explore phase:
the role of a student during the Summarize phase:
the role of the teacher during the Launch phase:
the role of the teacher during the Explore phase:
the role of the teacher during the Summarize phase:
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.24
Section 2: The Inquiry-Based Learning Structure of CMP3
Revisit the Section 2 Big Questions • What is CMP3’s lesson structure?
• What are the roles of the teacher and the students in each phase of a CMP3 inquiry-based lesson?
• What is CMP3’s instructional philosophy?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.25
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Quick Write: What is the difference?
Traditional Classroom CMP3 Classroom
curriculum is presented part to whole, with emphasis on basic skills.
curriculum is presented whole to part, with the emphasis on the coherence of concepts per the ccLSM.
Strict adherence to fixed curriculum is highly valued.
Problems have multiple entry points, and students can use multiple pathways to find the solution. the most important aspect of the classroom is ongoing assessment of students’ thinking.
Students are viewed as ‘blank slates’ onto which information is etched by the teacher.
Multiple entry points to problems and the Launch-Explore-Summarize (LES) lesson structure provide opportunities for students to activate, construct, and critique their own knowledge while they investigate new concepts.
teachers generally behave in a didactic manner, disseminating information to students.
teachers generally launch the lesson to make sure students understand the Focus Question, and then they act as a guide or a facilitator as students construct and critique their own ideas as they discover new concepts.
teachers seek the correct answer to validate student learning.
teachers seek students’ thinking to determine misconceptions and students’ solution methods that employ multiple representations to discuss and make connections during the Summarize phase.
assessment of student learning is viewed as separate from teaching and occurs almost entirely through testing.
assessment of students’ learning occurs constantly through observation of student work, presentation, and discourse. Student notebooks are a key source of ongoing formative assessment.
Students primarily work alone. Students work in groups as a community of mathematicians engaged in mathematical discourse.
(brooks and brooks quoted in brahier 2009, 60)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.26
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
How will teachers’ cMP3 classrooms be different from their past classrooms?
What strategies will teachers need to employ to transform their classrooms to function as cMP3 classrooms?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.27
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Supp
ortin
g Te
ache
rs to
Bui
ld M
athe
mat
ical
Com
mun
ities
Gui
delin
es fo
r Bui
ldin
g a
Mat
hem
atic
al C
omm
unity
“Tee
n-Fr
iend
ly”
Cla
ssro
om
Nor
ms
Bes
t Pra
ctic
es fo
r Pro
mot
ing
Nor
ms
CM
P3 C
ompo
nent
s fo
r Pr
omot
ing
Nor
ms
View
our
cla
ss a
s a
com
mun
ity
in w
hich
eac
h pe
rson
wan
ts a
ll of
th
e ot
hers
to b
e su
cces
sful
in th
eir
lear
ning
exp
erie
nces
. try
not
to
see
the
clas
sroo
m a
s a
com
petit
ive
envi
ronm
ent i
n w
hich
you
r rol
e is
to
outd
o ot
hers
.
crit
iciz
e id
eas,
not
peo
ple
(e.g
., sa
y,
“i di
sagr
ee w
ith th
e w
ay y
ou s
olve
d th
at p
robl
em b
ecau
se .
. .,”
rath
er
than
, “Yo
u’re
stu
pid;
I ca
n’t b
elie
ve
you
got t
hat a
nsw
er!”)
.
Mak
e fre
quen
t con
tribu
tions
to
clas
sroo
m d
iscu
ssio
ns b
y as
king
qu
estio
ns, a
nsw
erin
g qu
estio
ns,
and
reaf
firm
ing
or d
isag
reei
ng w
ith
com
men
ts m
ade
by o
ther
s.
take
resp
onsi
bilit
y fo
r the
lear
ning
of
othe
r stu
dent
s. if
you
und
erst
and
a co
ncep
t, ta
ke it
upo
n yo
urse
lf to
hel
p ot
hers
(at y
our t
able
or i
n th
e w
hole
cl
ass)
und
erst
and
it as
wel
l.
ask
que
stio
ns a
nd le
t the
teac
her
and
team
mat
es k
now
whe
n yo
u do
n’t
unde
rsta
nd s
omet
hing
. rem
embe
r, th
at n
o on
e ca
n re
ad y
our m
ind—
you
will
nee
d to
com
mun
icat
e yo
ur la
ck
of u
nder
stan
ding
to g
et s
omeo
ne to
he
lp y
ou.
(con
tinue
d on
nex
t pag
e)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.28
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Gui
delin
es fo
r Bui
ldin
g a
Mat
hem
atic
al C
omm
unity
“Tee
n-Fr
iend
ly”
Cla
ssro
om
Nor
ms
Bes
t Pra
ctic
es fo
r Pro
mot
ing
Nor
ms
CM
P3 C
ompo
nent
s fo
r Pr
omot
ing
Nor
ms
Enc
oura
ge c
lass
mat
es to
par
ticip
ate.
D
on’t
let i
ndiv
idua
ls s
it, d
ay a
fter d
ay,
with
out c
ontri
butin
g th
eir t
houg
hts
(e.g
., en
cour
age
the
pers
on s
ittin
g ne
xt to
you
to ra
ise
the
ques
tion
with
the
clas
s th
at th
e in
divi
dual
has
ex
pres
sed
to y
ou).
rec
ogni
ze th
at th
ere
is n
o su
ch th
ing
as a
wro
ng a
nsw
er in
a m
athe
mat
ics
clas
sroo
m. i
t has
bee
n sa
id th
at
stud
ents
nev
er g
ive
a w
rong
ans
wer
; th
ey s
impl
y an
swer
a q
uest
ion
diffe
rent
from
the
one
the
teac
her
inte
nded
. See
min
gly
wro
ng a
nsw
ers
are
actu
ally
opp
ortu
nitie
s fo
r the
cl
ass
to e
xplo
re n
ew id
eas.
rea
lize
that
it is
nat
ural
to fe
ar fa
ilure
in
the
clas
sroo
m, b
ut re
cogn
ize
that
yo
ur c
lass
mat
es h
ave
this
sam
e fe
ar
and
that
risk
-taki
ng is
impo
rtant
for
succ
ess.
For
this
reas
on, n
ever
laug
h at
the
resp
onse
of a
cla
ssm
ate:
la
ught
er e
rode
s co
nfide
nce
and
feed
s th
at fe
ar. a
lso,
you
may
be
in
the
sam
e po
sitio
n on
the
next
day
.U
se fi
rst n
ames
. It c
reat
es a
muc
h m
ore
supp
ortiv
e en
viro
nmen
t whe
n yo
u sa
y, “i
thin
k Fr
ance
s is
cor
rect
, bu
t i d
isag
ree
with
Jos
eph’
s an
swer
, an
d he
re’s
why
. . .
” tha
n to
refe
r to
clas
smat
es s
impl
y as
“he”
and
“she
.”S
uppo
rt on
e an
othe
r. W
hen
you
resp
ond
in a
cla
ss d
iscu
ssio
n, m
ake
use
of p
revi
ous
poin
ts m
ade
by
sayi
ng, “
i agr
ee w
ith M
ark.
and
i al
so
thin
k th
at .
. .” i
f som
eone
com
es u
p w
ith a
uni
que
appr
oach
or s
olut
ion
to a
pro
blem
, it i
s ap
prop
riate
to
appl
aud
and
affir
m th
at p
erso
n.
(bra
hier
200
9, 1
90)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.29
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Best Practices for Promoting Mathematical Communities 1. Equity Sticks: Write the names of students on popsicle sticks, and place them in a cup or
bag. When calling on students to present or answer a question, randomly select a popsicle stick.
2. Excel® Random Generator: Enter the names of students into an Excel spreadsheet, and assign a student to use the random generator to select a student to present or answer a question. if possible, project the Excel random generator so that students see the fairness.
3. Student Fishbowl: Select students to act out group work, mathematical discourse, teamwork on a partner quiz, and so on while the other students observe and take notes on a graphic organizer. conclude the Fishbowl activity with a whole-group discussion of how students in the fishbowl interacted and functioned.
4. Assigning Roles in Group Work: By formally assigning roles, students have a specific set of responsibilities. Some commonly used roles are timekeeper, Gatekeeper/taskmaster, Facilitator, Skeptic, recorder, Summarizer, and Presenter.
5. Random Group Grading: randomly choose one member of a group to grade and assign that grade to the entire group. assign zeros for copying.
6. Graded Individual Exit Slips: at the conclusion of the Summarize phase, have students independently complete graded exit slips to assess the day’s learning.
7. Three Before Me: Have a standing rule that a student must pose his or her question to three other students before he or she can ask the teacher.
8. Questioning to Promote Teamwork: redirect all inquiries back to other group members in a form of a question (for example, say, “What can you say about tony’s question?”, or “Look at what Sara did. How can this help answer tony’s question?”)
9. Display Student Work: Display students’ work, and refer to it to help students make connections between multiple representations and mathematical concepts.
10. Word Wall: Display a word wall with the definition, multiple representations, and examples of student work on the concept in context.
11. Sentence Starters Wall: Display a wall with sentence starters for seeking clarification, asking for help, acknowledging someone else’s idea, affirming someone else’s thoughts or ideas, reporting a partner’s idea, presenting a group’s idea, paraphrasing what someone else says, predicting, making a suggestion, giving an opinion, and respectfully disagreeing.
12. Think–Pair–Shares: Students have the opportunity to sort out their own ideas and discuss them with a peer before the whole class engages in a discussion on a mathematical question. this strategy reduces the anxiety around contributing to classroom discourse and promotes student-student interaction.
13. KWL Charts: Students activate prior knowledge and construct questions, and teachers formatively assess students’ thinking and prerequisite concepts.
14. Peer Assessment: Students manage the learning of their classroom, and the process promotes student-student mathematical discourse.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.30
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
15. Student Behavior Self-Assessment: Use a rubric for students to grade how well their behavior was in accordance to the classroom norms.
16. Multiple Representations: as opposed to traditional direct instruction, encourage students to use their own math skills to solve problems and represent their solutions with any representation they can.
17. Talk Moves: When orchestrating classroom discussion, use revoicing, rephrasing, reasoning, elaboration, and wait time (Van de Walle, Karp, and Bay-Williams 2013, 43).
18. Star Student of the Week: recognize students when they help other students and/or contribute to building a community of mathematicians in the classroom. Post students’ pictures with examples of why they have been awarded the honor.
19. Got It!–Almost–Not Yet: Have these three sections somewhere on a wall near the door where students exit, and have a small name tag (magnetic or pin-up) of each student’s name. ask students to place their name tags under the Got it!, almost, or not Yet to describe their level of understanding of the day’s learning or a specified question or concept. Use this as a formative assessment for planning.
20. Display a Daily Participation Grade: Develop a participation grading rubric that aligns with class norms. Make it simple and transparent, post participation grades daily for students to see, and make the weight enough for students to see that good participation grades will raise their average.
21. What time is it?: Make a sign with Launch, Explore, Summarize, and any other phase(s) of a normal day (warm-up, exit slip, independent assessment, and so on). Label each phase with 0, 1, or 2, where 0 means no one talks, 1 means one person at a time talks, and 2 means everyone can use accountable talk. Use some way to indicate the phase of the lesson throughout each class.
22. Student Work Analysis: include presentation, discussion, and analysis of incorrect student work. Use this as both an opportunity for students to understand that incorrect solutions are just a way to rule out what does not work, as well as to make connections to the difference with correct solutions.
23. Equity Monitors: Have students designated as Equity coaches monitor other students’ participation. these students can motivate, assist, or even assess participation depending on the makeup of the class.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.31
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Brainstorm of Additional Best Practices for Promoting Communities of Mathematicians
CMP3 Components That Promote Mathematical Communities a. Partner quizzes
b. Problems with multiple entry points
c. Student-centered, collaborative Explore phase
D. Summarize phase in which students discuss and critique the work of multiple students
E. application problems from applications-connections-Extensions (acE) used as exit slips
F. Sample student work in teacher Place for students to analyze to make connections with their own work
G. Value of student thinking over correctness in LES lesson structure
H. cooperative learning groups in every lesson
i. Students ask questions of either the teacher or their group members during all three phases
J. Summarize phase in which the teacher sequences the discussion of multiple representations of solutions
K. Mathematical Reflections and Common Core Mathematical Reflections for students to reflect on how their groups investigated problems together
L. Problems with real-world context that engage students in discussion of the problem situation
M. teachers monitoring dynamics throughout the Explore phase
n. teachers orchestrating classroom discourse in the Summarize phase at the end of every lesson
o. teacher Place functionalities for keeping notes on students and communicating directly with families
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.32
Section 3: Supporting Teachers to Build Mathematical Communities Capable of CMP3’s Inquiry-Based Learning
Revisit the Section 3 Big Questions • What are the hallmarks of a CMP3 classroom?
• What best practices can teachers use to build a mathematical community capable of the inquiry-based learning of cMP3?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.33
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
What Students Need to Be Successful with the Shifts • Engaging, real-world problems
• Motivation to engage
• Communication skills
• Problem-solving skills
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.34
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
Motivation to Engage ProjectRead the following excerpt from Slavin (1996, 53–55), and then design a tool or rubric that teachers can use to motivate every student in every group every day.
WHAT FACTORS CONTRIBUTE TO ACHIEVEMENT EFFECTS OFCOOPERATIVE LEARNING?1
Research on cooperative learning has moved beyond the question of whether cooperative learning is effective in accelerating student achievement to focus on the conditions under which it is optimally effective. The foregoing discussion describes alternative overarching theories to explain cooperative learning effects, and an integration of these theories. Beyond this, it is important to understand in more detail the factors that contribute to or detract from the effectiveness of cooperative learning. There are two primary ways to learn about factors that contribute to the effectiveness of cooperative learning. One is to compare the outcomes of studies of alternative methods. For example, if programs that incorporated group rewards produced stronger or more consistent positive effects (in comparison to control groups) than programs that did not, then this would provide one kind of evidence that group rewards enhance the outcomes of cooperative learning. The problem with such comparisons is that the studies being compared usually differ in measures, durations, subjects, and many other factors that could explain differing outcomes. Better evidence is provided by studies that compared alternative forms of cooperative learning. In such studies, most factors, other than the ones being studied, can be held constant. The following sections discuss both types of studies to further explore factors that contribute to the effectiveness of cooperative learning for increasing achievement.
Group Goals and Individual Accountability
As noted earlier, reviewers of the cooperative learning literature have long concluded that cooperative learning has its greatest effects on student learning when groups are recognized or rewarded based on individual learning of their members (Slavin, 1983a, 1983b, 1989, 1992, 1995; Ellis & Fouts, 1993; Newmann & Thompson, 1987; Manning & Lucking, 1991; Davidson, 1985; Mergendoller & Packer, 1989). For example, methods of this type may give groups certificates based on the average of individual quiz scores of group members, where group members could not help each other on the quizzes. Alternatively, group members might be chosen at random to represent the group, and the whole group might be rewarded based on the selected member’s performance. In contrast, methods lacking group goals give students only individual grades or other individual feedback, and there is no group consequence for doing well as a group. Methods lacking individual accountability might reward groups for doing well, but the basis for this reward would be a single project, worksheet, quiz, or other product that could theoretically have been done by only one group member. The importance of group goals and individual accountability is in providing students with an incentive to help each other and to encourage each other to put forth maximum effort (Slavin, 1995). If students value doing well as a group, and the group can succeed only by ensuring that all group members have learned the material, then group members will be motivated to teach each other. Studies of behaviors within groups that relate most to achievement gains consistently show that students who give each other explanations (and less consistently, those who receive such explanations) are the students who learn the most in cooperative learning. Giving or receiving answers without explanation generally reduces achievement (Webb, 1989, 1992). At least in theory, group goals and individual accountability should motivate students to engage in the behaviors that increase achievement and avoid those that reduce it. If a group member wants her group to be successful, she must teach her groupmates (and learn the material herself). If she simply tells her groupmates the answers, they will fail the quiz that they must take individually. If she ignores a groupmate who is not understanding the material, the groupmate will fail and the group will fail as well. In groups lacking individual accountability, one or two students may do the group’s work, while others engage in “social loafing” (Latane, Williams, & Harkins, 1979). For example, in a group asked to complete a single project or solve a single problem, some students may be discouraged from participating. A group trying to complete a common problem may not want to stop and explain what is going on to a groupmate who doesn’t understand, or may feel it is useless or counterproductive to try to involve certain groupmates.
1 These sections are adapted from Slavin (1995).
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.35
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
Communication Skills ProjectWrite at least three sentence starters for each of the bullet points below, and display these sentence starters in every cMP3 classroom to provide models for students.
• Seeking clarification
• Asking for help
• Acknowledging someone else’s idea
• Affirming someone else’s thoughts or ideas
• Reporting on a partner’s idea
• Presenting on a group’s idea
• Paraphrasing what someone else says
• Making a prediction
• Making a suggestion
• Giving an opinion
• Respectfully disagreeing
For example, a sentence starter for paraphrasing might be, “So, you are saying that. . .”, and a sentence starter for asking for help might be, “i do not understand what they did, can you explain that to me?”
Finally, plan an exercise to make students aware of the display of sentence starters and to teach them how to use the sentence starters in the LES lesson structure of their cMP3 inquiry-based classrooms.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.36
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
Problem-Solving Skills ProjectRead the following excerpt from Van de Walle, Karp, and Bay-Williams (2013, 33–34). Choose a cMP3 problem in teacher Place, and use Polya’s four-step method to solve the problem and employ one or more of the problem-solving strategies outlined in the reading. include how you can support students to learn how to use the four-step problem-solving method and the problem-solving strategies in your presentation. if time permits, conclude your presentation by outlining additional problem-solving strategies to employ in a cMP3 classroom.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.37
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
Brainstorm School-Wide Efforts for Supporting Students through the Shift
notes:
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.38
Section 4: Inquiry-Based Classrooms: A Shift in Student Experience
Revisit the Section 4 Big Questions • What skills do students need to be successful in CMP3 inquiry-based classrooms?
• How can you support teachers to implement CMP3 with fidelity?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.39
Section 5: Developing Your Plan for Supporting Teachers
Collaborating with ColleaguesMany teachers have found it valuable to plan with a colleague before, during, and after teaching the unit. Very often, student work is a focus for their discussions, as it provides a platform for discussing the mathematics in the Unit, investigation, or Problem. Discussion can also cover effective teaching strategies and other issues related to teaching. the following sets of summary questions can be useful for working either alone or with colleagues.
(Pearson Education, inc. 2014c)
How, when, and where will you collaborate with colleagues?review the tool for collaborating before a Lesson and the tool for collaborating after a Lesson. Discuss at your tables how, when, and where you can use these at your school during the school year. complete the following table based on your table discussion.
Tool How? When? Where?
Before a Lesson
After a Lesson
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.40
Section 5: Developing Your Plan for Supporting Teachers
Tool for Collaborating Before a LessonMathematical Goals
What is the focus question for this lesson? (Primary learning goal)
What are some secondary mathematical goals that may arise?
Materials Vocabulary, Processes-notes
Launch How will i get kids to buy into the problem?
is there any prior knowledge that kids will need to do the problem?
Do i need to introduce any mathematics? any contextual information?
is there any way i can connect to the previous problems?
How can i keep from “giving away” how to do the problem?
What is the most effective arrangement (group them) for this problem? (individual, pair, group, whole class, combination)
How will i have them report out/share their learning from the Explore portion of the lesson?
Explore What do i expect to see students doing?
What struggles do I anticipate? (Areas of difficulty or misconceptions)
What questions might i ask to help kids sort out the ideas? (How will you scaffold?)
What might i ask to redirect a student’s thinking if they are off track?
What questions can i ask to check for understanding? extend learning?
Summarize How will i have students share what they learned from the problem?
What thinking went on in the individuals/pairs/groups that the whole class should hear?
What order should they hear it?
Does the order matter?
What are key mathematical questions that need to be answered to pull-out the mathematical opportunities in the problem? (to get at big ideas, strategies, skill practice)
What questions do i want to ask to check for understanding?
What questions do i want to ask to extend their learning?
How can i get students to: Listen to each others thinking,ask questions of me and each other, challenge ideas that are not clear/incomplete/incorrect,take notes on the essential ideas for future reference
How will i know if my students are understanding the mathematics?
What should i do tomorrow? next week? next unit?
HomeworkWhat homework is appropriate to assign and for what students?
(Pearson Education, inc. 2014c)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.41
Section 5: Developing Your Plan for Supporting Teachers
Tool for Collaborating After a LessonGeneral
a. How do you think the lesson went compared to what you expected?
b. What went well? What happened to make you feel that way?
c. Were there times in the lesson when students were struggling with the mathematical ideas?
d. What would you change or modify next time?
Overviewa. How comfortable are you with the level of sophistication your students achieved with ________________________
__________________________________________________________________________________________?
b. What ideas will you continue to emphasize?
c. What do students understand about _____________________________________________________________?
d. What were you thinking when you asked _________________________________________________________?
How did __________’s response compare to what you expected?
e. What do you think ____________ was thinking when he/she asked ________________________________________________________________________________________________________________________________?
f. Why do you think _____________ said ______________________________________________________________________________________________________________________________________________________?
g. What sense do you think ____________ is making from the ideas in this unit? How will you assess his/her level of understanding?
h. Where will you go with this idea tomorrow? in the future?
i. How would you modify the lesson if you had the chance to repeat the class?
Launch a. What did you have to think about when you planned the launch?
b. How did the launch engage the students in the problem?
c. What information/background did the students have to help them engage the problem?
d. What did you observe from the launch? Was there too much information? too little? Just right?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.42
Section 5: Developing Your Plan for Supporting Teachers
Explore a. Why did you decide to have students work individually, with a partner, in groups, or as a whole class?
b. What did you do to provide the individual differences in the class? (scaffold, extend)
c. What did students struggle with? What did they make sense of?
d. What did you observe during explore time that helped you shape the summary?
Summarizea. What did the students learn today? What is your evidence?
b. What misconceptions became apparent during class?
c. How did the summary compare to what you had anticipated?
d. Did all major mathematical ideas of the lesson surface during the summary?
no? When will you revisit them?
Yes? is there a way to extend students thinking?
e. What questions did the summary raise for students? For you?
(Pearson Education, inc. 2014c)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.43
Section 5: Developing Your Plan for Supporting Teachers
Taki
ng In
vent
ory:
Whe
re a
re y
ou n
ow?
Leve
l of E
ngag
emen
tW
ho in
you
r sch
ool d
istr
ict i
s at
this
leve
l no
w?
Wha
t str
ateg
ies
can
you
use
to m
ove
pe
ople
in y
our s
choo
l dis
tric
t to
the
ne
xt le
vel o
f eng
agem
ent?
Aw
aren
ess–
Indi
vidu
als
know
the
impa
ct
that
cM
P3’
s in
quiry
-bas
ed le
arni
ng a
nd
teac
hing
will
hav
e on
thei
r pra
ctic
e.
App
licat
ion
and
Expe
rimen
tatio
n–
indi
vidu
als
are
atte
mpt
ing
to tr
y ou
t bes
t pr
actic
e st
rate
gies
and
/or r
esou
rces
for
deliv
erin
g in
quiry
-bas
ed in
stru
ctio
n.
Ow
ners
hip–
Indi
vidu
als
are
able
to
judg
e av
aila
ble
reso
urce
s an
d ap
ply
thei
r und
erst
andi
ng to
mak
ing
thei
r ow
n de
cisi
ons
abou
t int
egra
ting
the
best
pr
actic
es o
f inq
uiry
-bas
ed te
achi
ng a
nd
lear
ning
into
thei
r pra
ctic
e
Adv
ocac
y an
d In
nova
tion–
Indi
vidu
als
are
able
to s
uppo
rt th
e de
velo
pmen
t of
thei
r col
leag
ues
and/
or th
ey g
o be
yond
ju
dgin
g re
sour
ces
to a
ctua
lly c
reat
ing
tool
s an
d re
sour
ces
for i
mpl
emen
ting
the
cM
P3
inqu
iry-b
ased
pro
gram
.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.44
Section 5: Developing Your Plan for Supporting Teachers
Revisit the Section 5 Big Question • What processes do you need to put into place to support teachers in their classrooms
throughout the school year?
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.45
Reflection and Closing
Homework to Complete Prior to the Next Intensive Session • Use the provided planning template to plan and collaborate with teachers to support
implementation.
Suggested Ideas • Following Teacher Session 1, select a lesson from CMP3. Write a one-page narrative of
how you envision the lesson will play out in the classroom. once others complete the same assignment, collaborate to compare and contrast the narratives.
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.46
Appendix
(nYSED, n.d.)
Crosswalk of Common Core Instructional Shifts: Mathematics
6 Shifts: EngagenYwww.engageny.org
3 Shifts: Student achievement Partners www.achievethecore.org
1: Focus: Teachers use the power of the eraser and signifi cantly narrow and deepen the scope of how time and energy is spent in the math classroom. they do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.
2: Coherence: Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
3: Fluency: Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions (found in the attached list of fl uencies) such as multiplication tables so that they are more able to understand and manipulate more complex concepts.
4: Deep Understanding: teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics of discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.
5: Application: Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. teachers in content areas outside of math, particularly science, ensure that students are using math — at all grade levels — to make meaning of and access content.
6: Dual Intensity: Students are practicing and understanding. there is more than a balance between these two things in the classroom — both are occurring with intensty. teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. the amount of time and energy spent practicing and understanding learning environments is driven by the specifi c mathematical concept and therefore, varies throughout the given school year.
1: Focus strongly where the Standards focus
2: Coherence: Think across grades, and link to major topics within grades
3: Rigor: require fl uency, application and deep understanding
=
=
=
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.47
Appendix
Dai
ly In
stru
ctio
nal F
low
(P
ears
on E
duca
tion,
inc.
, n.d
., 2)
Connect Mathematics Project 3: Preparing for the Transition: Supporting Teachers to Successfully Implement CMP3, Participant Workbook
© 2013 Pearson, Inc.48
References
brahier, Daniel J. 2009. Teaching Secondary and Middle School Mathematics, 3rd ed. Upper Saddle river, nJ: Pearson Education, inc.
Lappan, Glenda, and Dennis Raskin. 2013. “CMP3 Lesson Structure.” Pearson Education, Inc.; 9 min., 22 sec. MP4.
national Governors association center for best Practices (nGa center), council of chief State School Officers (CCSSO). 2010. “Common Core State Standards for Mathematics.” Washington, Dc: national Governors association center for best Practices, council of Chief State School Officers. Accessed June 28, 2012. http://www.corestandards.org/assets/ccSSi_Math%20Standards.pdf.
new York State Education Department (nYSED). n.d. “crosswalk of common core instructional Shifts: Mathematics.” accessed May 28, 2013. http://schools.nyc.gov/nr/rdonlyres/9375E046-3913-4aF5-9FE3-D21baE8FEE8D/0/commoncoreinstructionalShifts_Mathematics.pdf.
new York State Mathematics common core Workgroup. n.d. “P-12 common core Learning Standards for Mathematics.” new York, nY: new York State Mathematics common core Workgroup. accessed May 28, 2013. http://www.p12.nysed.gov/ciai/common_core_standards/pdfdocs/nysp12cclsmath.pdf.
Partnership for assessment of readiness for college and careers (Parcc). 2011. “Parcc Model Framework Mathematics 3-11.” accessed May 28, 2013. http://ok.gov/sde/sites/ok.gov.sde/files/C3PARCC%20MCF%20for%20Mathematics_Fall%202011%20release.pdf.
Pearson Education, inc. n.d. CMP3: Core Middle Grades Mathematics Program. Upper Saddle river, nJ: Pearson Education, inc.
———. 2014a. CMP3: Growing, Growing, Growing. Upper Saddle river, nJ: Pearson Education, inc.
———. 2014b. CMP3: Prime Time. Upper Saddle river, nJ: Pearson Education, inc.
———. 2014c. CMP3 Program and Implementation Guide. Upper Saddle river, nJ: Pearson Education, inc.
Slavin, robert E. 1996. “research for the Future: research on cooperative Learning and achievement: What We know, What We need to know.” Contemporary Educational Psychology 21, no. 0004: 43–69. Accessed May 28, 2013. http://www.konferenslund.se/pp/taPPS_Slavin.pdf.
Student achievement Partners. n.d. “Practicing with the Shifts: common core State Standards for Mathematics.” accessed May 28, 2013. http://www.achievethecore.org/math-common-core/professional-development/introduction-math-shifts.
Van de Walle, John A., Karen S. Karp, and Jennifer M. Bay-Williams. 2013. Elementary and Middle School Mathematics: Teaching Developmentally, 8th ed. Upper Saddle river, nJ: Pearson Education, inc.