Revolutionizing Our
Thinking About
Math Instruction
Building Mathematicians
"The mind is not a vessel to be filled but a fire to be kindled."
– Plutarch, Greek Historian
"We cannot hope that
many children will
learn mathematics
unless we find a way
to share our
enjoyment and show
them its beauty as
well as its utility.“
-- Mary Beth Ruskai
"The mind is not a vessel to be filled but a fire to be kindled."
– Plutarch, Greek Historian
or Mathematician
Computer…
…aka
Calculator…
"Mathematics
"Calculatorsiscan
noonly
morecalculate
computation
than
they
typing
cannot
is literature."
do mathematics."
-- John
A. Paulos,
Van de Walle
– NCTM,Professor,
Math Educator,
Author
-- John
Allen
Mathematics
Temple,
Author
Math Magician!!!
Building Mathematicians:
Laying a Firm Foundation
EQ: What is a mathematician?
EQ: What are the fundamental skills a
mathematician needs?
Math is…
the Science of Pattern and Order
"A surprising proportion of
"Mathematics is on the mathematicians are accomplished
artistic side a creation of musicians.
new rhythms,
Is it because music and
orders, designs, harmonies,
andhumans
on theshare
mathematics
patterns
"What
do with
the
knowledge side, is a systematic
study
of
that are
beautiful?"
language
of
mathematics
is
various rhythms,to--orders,
designs,
Martin Gardner,
Mathematics Writer
describe
patterns..."
and harmonies.“
-- Lynn A. Steen, Math Professor
-- William L. Schaaf, Math Professor, Author
Math is the Science of
Pattern and Order
Geometry
Trigonometry
Differential
geometry
Calculus
Vector
calculus
Differential
equations
Topology
Dynamical
systems
Fractal
geometry
Measure
theory
Chaos theory
Complex
analysis
Math is…
the Pursuit of Laziness
"Life is too short
"The essence of mathematics
for long division."
is not to make simple things
complicated, but to make
"You know we all became
complicated things simple."
mathematicians for the same
-- S. Gudder, Math Professor, Author
reason: we were lazy."
-- Max Rosenlicht, Mathematician
Math is the Pursuit of Laziness
Math is the Pursuit of Laziness
Many Paths, One Door
Math is the Pursuit of Laziness
Math is the Pursuit of Laziness
http://blog.aimsedu.org/2013/05/28/in-pursuit-of-laziness/
Excerpt:
Let’s take a look at what the pursuit of laziness in mathematics
might mean for our students and us.
Finally,
Second,
laziness
isdoes
not
inactivity.
notnot
imply
While
thoughtlessness
pencil might
or to be
First of laziness
all,
laziness
does
mean
an the
unwillingness
do still,
work;
carelessness.
the
mind
is active
Lazy
mathematicians
pursuing solutions
are
extraordinarily
to
the problem
rather,
it speaks
toand
an
unwillingness
to do
pointless
or at
thoughtful,
hand.
butwork
theyintake
care
think on the
things and
unnecessary
order
to to
accomplish
an right
objective.
avoid irrelevant or unproductive approaches.
Building Mathematicians:
Laying a Firm Foundation
EQ: What is a mathematician?
EQ: What are the fundamental skills a
mathematician needs?
Building Mathematicians:
Laying a Firm Foundation
Building Mathematicians:
Laying a Firm Foundation
Content vs. Skill
Standards of Mathematical Practice
Activity: Name that Standard
Strategy: Think, Pair, Pair Again
Standards of Mathematical Practice
Spider
SMP 1 – Make Sense of Problems
and Persevere in Solving Them.
Learned Helplessness:
I can’t do this problem
Low
"Too many students give up upon
encountering difficulties in math,
when just trying a few strategies
could mean the difference between
succeeding and failing."
-- Arthur E. Schwartz
Fast Processors:
This problem is wrong
High
"If there is a problem you can't
solve, then there is an easier
problem you can't solve: find it."
-- George Polya
SMP 1 – Make Sense of Problems
and Persevere in Solving Them.
I can solve problems
without giving up.
SMP 2 – Reason abstractly and
quantitatively.
Students move from:
tangible to intangible
with units to without
SMP 2 – Reason abstractly and
quantitatively.
I can think about
numbers in many ways.
SMP 3 – Construct viable arguments
and critique the reasoning of others.
Does the commutative
property work for
subtraction?
Johnny: Yes,
2-2=0 and 2-2=0
SMP 3 – Construct viable arguments
and critique the reasoning of others.
I can explain my
thinking and try to
understand others.
SMP 4 – Model with mathematics.
SMP 4 – Model with mathematics.
I can show my work
in many ways.
SMP 5 – Use appropriate tools
strategically.
Dickerson Summer Math Packet
5 * $4.97
$4.97 =$5 - 3¢
.5 * $14.70
.5 = ½
$14.70 =$14 + 70¢
SMP 5 – Use appropriate tools
strategically.
I can use math tools
and show why I
chose them.
SMP 6 – Attend to precision.
SMP 6 – Attend to precision.
I can work carefully
and check my work.
SMP 7 – Look for and make use of
structure.
1+2=3
10 + 20 = 30
.1 + .2 = .3
1/10 + 2/10 = 3/10
1/5 + 2/5 = 3/5
SMP 7 – Look for and make use of
structure.
I can use what I know
to solve new problems.
SMP 8 – Look for and express
regularity in repeated reasoning.
2+2+2+2+2+2=6x2
5 = 10 ÷ 2 so a x 5 = a x 10 ÷ 2
or a ÷ 2 x 10
Multiplying 11s
11 x 23
253
SMP 8 – Look for and express
regularity in repeated reasoning.
I can discover and
use shortcuts.
Intro to Number Talks
Students have the opportunity to:
Intro to Number Talks
Teachers have the opportunity to:
Assess student understanding quickly
Identify misconceptions or wrong thinking
Build mental math skills
Build computational fluency
Allow students time to construct knowledge
Math is a Foreign Language and it
is not Dead
•
•
•
•
•
•
•
Spoken and written
Symbols
Inferencing
Context Clues
Multiple meanings
Things Get Lost in Translation
Global