rich mathematical tasks - everyone graduates center - enabling...
TRANSCRIPT
“…being good at mathematics involves many different ways of working…it involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods, and representing ideas in addition to calculating with procedures.”
-Jo Boaler, Professor of Mathematics Education, Stanford University
Working with Rich Mathematical Tasks
aski
ng q
uest
ions
draw
ing/
crea
ting
pict
ures
and
gra
phs
reph
rasi
ng p
robl
ems
just
ifyin
g m
etho
ds
repr
esen
ting
idea
s/co
ncep
ts/p
atte
rns
calc
ulat
ing
with
pro
cedu
res
Doe
s th
e ta
sk e
ntai
l…?
the
task
is in
quir
y ba
sed.
W
hy d
oes
this
wor
k? W
ould
doi
ng
____
_ he
lp a
ddre
ss _
____
? Wha
t w
ould
hap
pen
if I _
____
_?a
char
t/gr
aph/
visu
al is
cre
ated
in o
rder
to
com
mun
icat
e or
mak
e se
nse
of t
he
mat
hem
atic
s,
the
prob
lem
is
reco
ncep
tual
ized
in w
ay t
hat
faci
litat
es u
nder
stan
ding
the
need
to
appl
y m
athe
mat
ical
re
ason
ing
and
prov
ide
just
ifica
tion
is
embe
dded
with
in t
he t
ask
the
task
is m
ultid
imen
sion
al,
requ
irin
g flu
id r
epre
sent
atio
ns o
f the
m
athe
mat
ics
in d
iffer
ent
way
s(v
isual
ly, a
lgeb
raic
ally,
in w
ritin
g, or
gani
zed
in a
tabl
e, us
ing
colo
rs, e
tc.).
the
use
of s
kills
, co
mpu
tatio
ns, p
roce
dure
s, an
d al
gori
thm
s.
Ric
h m
athe
mat
ical
tas
ks
“…be
ing
good
at m
athe
mat
ics
invo
lves
man
y di
ffere
nt w
ays
of w
orki
ng…
it in
volv
es
aski
ng q
uest
ions
, dra
win
g pi
ctur
es a
nd g
raph
s, re
phra
sing
pro
blem
s, ju
stify
ing
met
hods
, and
repr
esen
ting
idea
s in
add
ition
to c
alcu
latin
g w
ith p
roce
dure
s.”
-Jo B
oale
r, Pr
ofes
sor
of M
athe
mat
ics
Educ
atio
n, S
tanf
ord
Uni
vers
ity
aski
ng q
uest
ions
draw
ing/
crea
ting
pict
ures
and
gra
phs
reph
rasi
ng p
robl
ems
just
ifyin
g m
etho
ds
repr
esen
ting
idea
s/co
ncep
ts/p
atte
rns
calc
ulat
ing
with
pro
cedu
res
Cre
ate
a pi
e ch
art t
hat r
eflec
ts y
our i
deal
bal
ance
bet
wee
n th
e si
x di
ffere
nt m
athe
mat
ical
com
pete
ncie
s in
dica
tive
of a
su
cces
sful
doe
r of
mat
hem
atic
s, a
ccor
ding
to B
oale
r.
.
.
Friday the 13th
This month there is no Friday the thirteenth, but this year there was one. Can you explain why every year must contain at least one Friday the thirteenth?
What’s the greatest number of Friday the thirteenths that can fall in one year?
Nrich Mathematicshttp://nrich.maths.org/610
Facilitator/Includer Resource Manager
Reporter Organizer
Remind your team to justify each mathematical statement
Search for connections among the different statements.
“How do you know that for sure?”
“How does that relate to…?”
Your group needs to organize your group’s results.
Your results need to be well organized, and use color, arrows, and/or other math tools to communicate your mathematics, reasons, and connections.
“How do we want to show that idea?”
Make sure your group reads all the way through the task before you begin. “Does everyone get what to do?”
Keep your group together. Make sure everyone’s ideas are heard.
“Did anyone see it a different way?”
“Are we ready to move on?”
Get and manage materials/resources for your team.
Make sure all questions are team questions; everyone has been tapped as a resource before you call the teacher.
Be prepared to join the teacher for a huddle and debrief your group.
Group Roles
Boaler, J. (2015). From Tracking to Growth Mindset Grouping. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.
Teacher Roles
• assign competence to all students • raise ‘status’ of students who think
they may be of lower status in a group
• teach students to be responsible for each other’s learning
• establish group norms of respect, listening, and collaboration
• encourage students to build off of each other’s ideas
• teach broad, open, multidimensional mathematics
• math is so much more than executing procedures!
• ensure students are in mixed-ability groupings
Boaler, J. (2015). From Tracking to Growth Mindset Grouping. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.
Going beyond…
Can you find more than one way to make each number with four 4s?
Can you go beyond 20?
Can you use four 4s to find negative integers?
www.youcubed.org
Course Two – 2005
MARS Tasks — High School Course 2 www.scoe.org/mars Page 3
MARS tasks available at https://www.scoe.org/
Designing Rich Mathematical Tasks
• Can you open the task to encourage multiple methods, representations, and pathways?
• Can you make it inquiry based?
• Can you present the task before teaching the method?
• Can you make it visual?
• Can you make it “Low Floor” and “High Ceiling”?
• Can you add requirement for students to convince, reason, and justify?
Boaler, J. (2015). Rich Mathematical Tasks. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.