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Development and Implementation of Mathematics Instruction Programs Based on Students' Individual...
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Development and Implementation of Mathematics Instruction Programs Based on Students' Individual Cognitive and Developmental Abilities
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Description
Identifier
SPEC
8
Author
Keithan, Amy E.
Title
Development
and
Implementation
of
Mathematics
Instruction
Programs
Based
on
Students
'
Individual
Cognitive
and
Developmental
Abilities
Publisher
Central Connecticut State University
Date of Publication
2009
Resource Type
Special Project
Abstract
The
purpose
of this
project
is
to
develop
and
implement
instructional
,
mathematics
programs
that are
based
on the
students
'
individual
developmental
and
cognitive
levels
of
functioning
. The
goal
is
to
teach
students
with
meaning
so
that they
gain
a
deep
understanding
of
mathematical
concepts
such
as
addition
,
subtraction
,
regrouping
,
renaming
, and
place
value
.
Students
will
gain
a
strong
foundation
of
arithmetic
in
order
to
continue
to
learn
mathematics
concepts
and
knowledge
so
that they
can
solve
problems
in their
future
experiences
. The
subjects
for this
project
are
eight
third
grade
students
who
are
eight
and
nine
years
old
. They
attend
a
private
,
Catholic
school
located
in an
urban
environment
. In this
particular
school
, there
is
no
standard
curriculum
and
students
do
not
take
the
Connecticut
Mastery
Test
. The
textbook
serves
as the
basis
for
mathematics
instruction
.
Since
each
student
has
different
strengths
and
weaknesses
,
each
learns
in
different
ways
. This
creates
an
environment
in
which
the
students
are
functioning
on
different
levels
of
developmental
and
cognitive
abilities
. In
order
to
assess
a
student's
developmental
and
cognitive
levels
of
functioning
two
diagnostic
tests
were
administered
. The
developmental
test
consists
of
three
parts
which
is
based
on
Piaget's
theory
of
conservation
of
number
,
length
, and
area
.
Each
student
was
interviewed
individually
and was
continually
asked
to
explain
their
thinking
by
answering
the
question
"
Why?
" The
implications
for
instruction
are that
conservers
of
number
are
able
to
understand
place
value
,
conservers
of
length
are
able
to
understand
the
comparison
notion
of
subtraction
and the
missing
addend
notion
of
subtraction
, and
conservers
of
area
are
able
to
understand
the
repeated
addition
of
equal
measures
or
array
notion
of
multiplication
. The
developmental
level
demonstrates
the
concepts
that a
student
is
capable
of
learning
and
understanding
. The
second
assessment
task
is
to
determine
the
student's
cognitive
level
of
functioning
through
observation
and
questioning
. The
functioning
level
of
cognitive
development
is
assessed
through
the
modeling
with
manipulatives
,
verbal
explanations
, and
symbolic
representations
of the
arithmetic
operations
of
addition
,
subtraction
,
multiplication
and
division
that were
presented
as
word
problems
in a
real
world
context
. The
cognitive
assessment
tasks
indicate
prior
knowledge
as to what a
student
has
already
learned
about
mathematics
both
correctly
and
incorrectly
.
Meaningful
instruction
occurs
when
a
student
is
taught
based
on these
two
levels
of
functioning
. The
analysis
of the
developmental
assessments
indicated
that
7
students
or
87.5
%
are
conservers
of
number
,
4
students
or
50
%
are
conservers
of
length
, and
3
students
or
37.5
%
are
conservers
of
area
. The
cognitive
assessment
consisted
of
twelve
word
problems
each
illustrating
one
of the
twelve
notions.There
were
2
addition
,
4
subtraction
,
3
multiplication
, and
3
division
problems
that were
solved
using
algorithms
with
paper
and
pencil
and then they were
solved
using
manipulatives
. In
analyzing
the
cognitive
assessment
tasks
and
responses
,
some
general
misunderstandings
and
misconceptions
were
revealed
by
many
of the
students
. The
students
struggled
with
understanding
numeration
,
especially
regrouping
,
distinguishing
between
different
types
of
problem
solving
operations
and
modeling
them with
manipulatives
, and
many
students
had
memorized
facts
and
algorithms
without
any
meaning
in the
symbolic
mode
.
Overall
the
students
showed
tremendous
individual
progress
and have been
able
to
attach
meaning
to
many
mathematical
concepts
. They have been
able
to
demonstrate
their
learning
and
understanding
through
discussions
,
explanations
, and
written
work
. As a
result
of
teaching
students
what they are
both
developmentally
and
cognitively
ready
to
learn
, they
displayed
more
confidence
in their
written
work
and
explanations
.
Subject
Mathematics  Study and teaching (Elementary)  Connecticut
Department
Department of Mathematical Sciences
Advisor
Halloran, Philip P
Type
Text
Digital Format
application/pdf
Language
eng
OCLC number
713734939
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