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