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The Effect of Computer-based
Mathematics on Problem Solving
Proponent: Daisy T. Emanuel
3rd Grade Teacher, Sadie Tillis
• Many people regard mathematics as the
crown jewel of sciences.
• Yet mathematics has historically lacked
one of the defining trappings of science:
– laboratory equipment
Physicists
A new particle accelerator, the Large Hadron
Collider, in Geneva, Switzerland.
Astronomers
Celestron Astromaster 70az Telescope
Mathematicians
Albert EinsteinArchimedes
Mathematicians
Leonhard Euler Carl Friedrich Gauss
Mathematics
Mathematics concerns not the physical
landscape but an idealized, abstract world.
For exploring that world, mathematicians
have traditionally had only their intuition.
Erika Klarreich Study (2004)
Computers are starting to give mathematics the lab instruments they have been missing.
Computers’ power is enabling mathematicians to make quantum leaps into mathematics.
Computers take only seconds to calculate and create beautiful graphics of three-dimensional shapes.
Computers can solve complex problems and computers can remediate students in mathematics.
Knowledge of Teaching with ICT
“He who can does,
and he who understands
teaches.”
- Dr. Lee Shulman
President Emeritus of the
Carnegie Foundation for the
Advancement of Teaching
(1997-2008)
Knowledge of Teaching with ICT
In the 80′s, Lee Shulman introduced the
concept of pedagogical content knowledge to
differentiate it from content knowledge and
knowledge of general pedagogy.
Pedagogical content knowledge or popularly
known as PCK is teachers’ knowledge of how a
particular subject-matter is best taught and
learned.
Pedagogical Content Knowledge
Most important elements of its description:
1. knowledge of interpreting the content;
2. knowledge of the different ways of representing
the content to the learner; and
3. knowledge of learners’ potential difficulties,
misconceptions, and prior conceptions about
the content and related concepts.
Concept Map
Set of Integers
Counting
Numbers
(Positives)
Opposite of
Positives
(Negatives)
Zero
consists of
less
than
less
than
r
e
s
u
l
t
w
h
e
n
2 positive
numbers
are added
2 positive
numbers
are
multiplied
or divided
2 negative
numbers
are
multiplied
or divided
a smaller
number is
subtracted
from a
larger
number
a negative and a
positive numbers
are added, the
positive is farther
from zero on the
number line
r
e
s
u
l
t
w
h
e
n
2 numbers
with
different
signs are
multiplied
or divided
a larger
number is
subtracted
from a
smaller
number
a negative and a
positive numbers
are added, the
negative is farther
from zero on the
number line
results when
Opposites
are added
a number is
taken away
from itself
it is divided by
other number
it is multiplied
by any number
closed under
Addition Subtraction Multiplication
Concept Map
Set of Integers
can be
represented by
Rules on
operations are
never learned
using
memorization.
Signed
numbers have
no meaning or
do not make
sense.
Quantitative relationship
involving directions or
ideas on opposites
Number
Line
+ and –
chips
Tables and
patterns
Source of
difficulties and
misconceptions
Failure to
relate to
whole
numbers
Knowledge of Teaching with ICT
• It is not a question of whether schools should
integrate these technologies in its curriculum.
• ICT courses have been offered as a subject in
many schools.
• Use of technology in teaching traditional
subjects like mathematics.
• Does knowledge of technology equip teachers
to use it to teach effectively?
Integrating ICT in Teaching
• Some mathematics teachers jumped to it
right away, used technology in teaching.
• Some teachers are still in testing-the-water
mode.
• Some, until now, are still totally in the dark,
sticking to their old method despite the
availability of technology, oblivious to the
reality in today’s ICT – driven world.
ICT – driven World
• The students are the natives and the
teachers are the migrants.
• The way students learn are influenced
by their experiences with many forms
of technology and the way these tools
think and do things.
Printing Machine
When the pen and
the printing press were
invented, everybody
thought that they will
give an end to illiteracy.
It didn’t take long for
us to realize that it didn’t
and can’t.
Using Computer to Teach
It is not enough to
know how to use
ICT just us it was not
enough to know
mathematics content to
teach mathematics so
that students learn it
with meaning and
understanding.
Technological Pedagogical
Content Knowledge
A teacher’s knowledge regarding
technology is multifaceted and that the
optimal mix for the classroom is a balanced
combination of technology, pedagogy, and
content.
It can be used as framework for designing
learning experiences for teachers and for
planning, analyzing and describing the
integration of technology in teaching.
Technological Pedagogical
Content Knowledge
References
• http://www.learningtoday.com/corporate/math-software.asp
• http://prime.isthe.com/no.index/chongo/merdigit/long-m42643801/prime-c.html
• http://www.tpck.org/tpck/images/tpck/b/b1/Tpack-contexts-small.jpg