Profile of Understanding Layers Function Derivatives And Folding Back Of College Student Prospective Teachers Of Mathematics By Gender

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Acceleration of Scientific K
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University o f Dr. S o e t o m o Surabaya,

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of Dr. SOETOMO

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University University

of Queensland

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PROCEEDINGS 1^^ ADRI-UNITOMO 2016
International Multidisciplinary Conference

PREFACE

This

book

reports

the

proceedings

of

the

1st

ADRI-UNITOMO

2016

International Multidisciplinary Conference held at University Dr. Soe
from November 9 to November 10, 2016. T h e purpose of this conference
was

to explore

scientific

knowledge

development

in the

era

of

ASEA

Economic Community that integrates the immediate and long-term, loca
and

global

needs.

needs,

The

and

regards

participants

social,

included

economic

lectures,

and

environmental

researchers,

economis

development planners, and national and international administrators.

Papers and discussion focused on the challenges of scientific
development
most

in business,

feasible

included

from

means
the

of

management,
addresseing

United

States,

knowle

education, engineering and
the
the

challenges.
United

The

the

participan

Kingdom,

Australia

Thailand, Malaysia, and Indonesia. An attempt was made to represent
many as possible of the groups and institutions working in areas
to

the

conference

Conference
published

theme.

Proceeding

All

with

papers

ISBN.

in International Journal

will

Selected
indexed

be

published

manuscripts

by Scopus,

in

rel

onli

will

by firstly

be

co

the authors

The

Editors

also

wish

to

thank

all the

organizing

committee

valuable assistance.

Surabaya, 8 November 2016
Chairman
CONFERENCE

of

THE

1'^

ADRI-UNITOMO

2016

INTERNATIONAL

for

t

1.

CHARACTER EDUCATION BASED ON PANCASILA VALUES THROUGH
CURRICULUM 2013 ON PRIMARY EDUCATION CHILDREN IN MADURA
Dian Eka IndrlanI

2.

STUDY OF PRIMARY SCHOOL TEACHER COMPETENCE IN TANAH BUM
REGENCY
Dwi Atmono, Muhammad Rahmattullah

3.

IDENTIFYING THE MISCONCEPTIONS OF NATURAL SCIENCE (IPA)
CRI (CERTANTY OF RESPONSE INDEX) AT THE PRIMARY SCHOOL
STUDENTS IN TARAKAN
Muhsinah Annlsa, Ralna Ylinda, Kartlnl

4.

PROFILE OF UNDERSTANDING LAYERS OF FUNCTION DERIVATIVES
FOLDING BACK OF COLLEGE STUDENT PROSPECTIVE TEACHERS OF
MATHEMATICS BY GENDER
Viktor Sagaia

5.

TEACHERS PROFESSIONALISM AND THE CHALLENGE OF EDUCATION
GLOBAL ERA
Sudrajat

6.

LESSON STUDY: COLABORATION BETWEEN TEACHER TRAINEES’
COMPETENCE AND STUDENTS’ ACHIEVEMENT
Arifin

7.

FACTORS INFLUENCING THE SCHOOL CLIMATE AT INDONESIA SC
KUALA LUMPUR (SIK), MALAYSIA
Muhajir

8.

RISING STUDENT’S ACADEMIC HONESTY: THE IMPLEMENTATION
CLASSROOM DEVELOPMENTAL BIBLIOTHERAPY (CDB) IN BAHASA
INDONESIA LEARNING AT MADRASAH IBTIDAIYAH
Siti KhorriyatuI Khotimah

ABSTRACT

The objective of this study is to identify the misconcepti
(IPA) on primary school students in Tarakan. The output of t
into a national scientific journal with ISSN. This study abso
schools and the education providers (universities). This s
misconceptions of what happens to the students, so that tea
handle and remediate these misconceptions. This study empl
descriptive research. The population is the sixth grade s
schools in Tarakan. It is because the students of this grade
material on force, light, and simple machine. The technique.
sample is cluster sampling by considering on the three crite
medium, and low school category which is based on the mean s
(UAS) on natural science subject. So, the sixth grade stude
Tarakan, and SDN C Tarakan are chosen as the sample of
instrument of this research is a written test in a form
equiped with the CRI (certainty of response index) answer
collected by distributing multiple-choice test which is cons
that are equipped with the CRI answer sheet.

Keywords: Misconceptions, Natural Science, CRI, Primary Schoo

PROFILE OF UNDERSTANDING LAYERS OF FUNCTION DERIVATIVES AN
BACK OF COLLEGE STUDENT PROSPECTIVE TEACHERS OF MATHEMAT
GENDER
Viktor Sagaia
Mathematics Education FKIP Dr. Soetomo University, Surabaya,
email: viktorsagala@gmaiLcom

ABSTRACT

This research aimed to describe the profile of understanding
the function’s derivative and folding back college student pr
mathematics by gender. This study used a qualitative descri
data obtained is validated, then the analysis step-by-st
presentation, categorization, interpretation and inference. T
guided to the understanding of the model which hypothesizes
eight layers understanding. The results showed that there
between the achievement of a layers of the subject of wome

them have an indicator layers of understanding ie; primiti
making, image having, property noticing, formalising, observi
then reaching also the first indicator (Inl) of inventising l
questions about graphs the third-degree polynomial function"
second indicator (in2) of inventising layer. Based on the ind
subjects understanding layer ie inventisingoid. But both subj
items the process of achieving this understanding. Women p
folding back the form of "off-topic", and man made that once
performed twice folding back the form "working on the deep
subjects do not perform folding back the form "cause discontin
Keywords: understanding layers, folding back, gender.

TEACHERS PROFESSIONALISM AND THE
ERA

CHALLENGE OF EDUCATION IN A

Sudrajat

Graduate Program, Muhammadiyah University of Yogyakarta, Indo
email:

jhon.ajat@yahoo.co.id

ABSTRACT

The professional Attitude of a teacher is very necessary in t
this global era. The task of the teacher is not only teachi
nurture, guide and shape the personality of the student. Mi
understanding the profession will result in the shifting of
slowly. The relationship between teachers and students who
turns into a relationship of mutually indifferent, not b
Professionalism of teachers is determined by behavior, will
condition that Prime. Professionalisation should be viewed
process, so that the attitude and professional teachers act
process, pre-service education, educational upgrading, includ
from professional organizations and the workplace, the soc
profession of teacher training, enforcement of the code
profession, certification, improved quality of prospective t
collectively determine a person including professional develo
This article presents an attempt discussion space for educ
educators, and related parties in order to better understan
develop attitudes and behavior in the world of education thro
mind, speech, and action.

47

Profile of Understanding Layers of Function
and Folding Back of College Student Pros
Teachers of Mathematics by Gender

Viktor Sagaia
Mathematics Education FKIP Dr. Soetomo University, Surabaya, Indonesi
v i k t o r s a g a l a g g i n a i l • com

Abstract: This research aimed to describe the profile of undersUndiiie layers the concept of
folding back college student prospective teachers of mathematics by gender. This study us
approach . The data obtained is validated, then the analysis step-by-step reduction, data
interpretation and inference. The analysis process is guided to the understanding of the
Pirie-Kieren owned eight layers understanding. The results showed that there was no differenc
a layers of the subject of women and man, both of them have an indicator layers of understan
image making, image baring, property noticing, formalising, observing and structuring, then re
(In!)
of inventising layer, and indicators "ask questions about graphs the third-degree polyn
second indicator (In2) of inventising layer. Based on the indicators of these, both su
inventisingoid.
But both subjects distinc 10 (ten) items the process of achieving this unders
folding back the form of "off-topic", and man made that once. Instead of man performed twi
"working on the deeper layers", both subjects do not perform folding back the form "cause disco
Key words : understanMng layers^ foUmg back^ gender.

Scientific understanding
is rational mind
authentic explanation, while the suchness
depends
on contextual experience. For example
Experts and researchers predecessor Dubinsky,
as Bruner
school children understand the commutafivity
and Piaget concentrated on the growing of mathematical
original
number when he observed and merge 2 ma
understanding at an early age, rarely go beyond
adolescence.
which was the same as the surviving 3
Dubinsky interested in doing research with the marbles,
same approach
marbles
withof
which the result is 5 marbles.
and expanded to the topic higher up the subject
matter
mathematics for high school and even college. APOS
theory
Pegg
& Tall (2005) identified two types o
has been introduced by Dubinsky (in Tall, 1999),
which
cognitive
growth, namely 1) the theory of globa
describes how the mental activity of a student long
in the
of
termform
(global
theory of longterm growth) in
actions, processes,objects,and schema when as
constructing
the theory of stages of cognitive developmen
mathematical concepts. Pirie-Kieren (1994) has2) provided
a
the theory
of local growth such conceptual
theoretical framework of eight levels (layers)(action,
understanding,
processes, objects, schema) o f Dubi
that primitive knowing, image making, image having,
property
global
theory starts from the physical inte
noticing, formalizing, observing, structuring, inventising.
Thisthe world around you, and the
individual with
theory also introduces folding back, namely thelanguage
return of
and the
symbols toward abstract form. In
next layer of the previous understanding to advance
to the
next also juxtaposing four theorie
and Tall
(2005)
layer of understanding.
development; 1) stages o f sensory motors, p
concrete operational
and formal operational fro
Authors interested in the profile o f understanding
of
level
of
recognition,
analysis, sequence, deduc
College Student Prospective Teachers o f Mathematics guided
Van Hiele,
Pirie-Kieren model, with material derivatived the
function.
In 3) sensory motor, the iconic, co
formalresearch
and post-formal of Model SOLO and 4) enac
connection with the above descriptioa the proposed
and symbolic
questions: How is the profile layers of understanding
theof Bruner. Local theory focused
cyclewoman
o f growth
in learning a concept. For e
concept of the derivative function and folding back
and
model o
SOLO
cycle focused on three levels
man
of
College
Student
Prospective
Teachers
f
unistructural
Mathematics? The research objective was to describe
the (U), multistructural (M), and rela
application contains at least two cycles
profile layers of understanding the concept ofmodel
the derivative
wage Student
in each model. The response rate of R i
function and folding back woman and man of College
cycle for the response rate of the new U in
Prospective Teachers of Mathematics
According Susiswo (2014), it became a base for
concepts acquired and also explains the cogniti
a
T H E O R m C A L STUDY
of students.
A. Understanding of Concept
Cycle two offer types of development that fo
primary and secondary school. Furthermore, acco
Skemp (1976) identified two forms of understanding,
& Tall (2005) is
theory other locales is b) proced
namely relational and instrumental. Relational understanding
processes and entities o f Davis, c) APOS of
defined as knowing what to do and why. Relational
condensation and reification of
understanding is the ability to draw conclusionsinteriorisasi,
on the specific
procedures,
processes
and prosep of Gray & T a l
rules into mathematical relationships are more common.
also to
reconcile the following four local
Meanwhile instrumental understanding defined as (2005)
the ability
theory ofof
Dubinsky
can also be compared with t
apply an appropriate remembered rule to the solution
a
understanding
problem without knowing why the rule works.
So
this is an of the four levels of Herscovic
intuition, procedural, physica
instrumental understanding of students' ability (1983),
to learnnamely
by rote.
In this case the action begins
The later period Skemp (1987) distinguishes formalization.
between "to
proceed with the procedure, while Herscovics
understand
something"
with
"understanding".
with intuition, followed by procedural.
Understanding associated with the ability, whilestarted
understanding
APOS
somewhat
different objects with physic
something associated with assimilation and an
apropirate
prominent physical
action, but in the end the
scheme. Scheme is a group of concepts that are connected,
each
very close
to the intended formalizafion H
concept is formed of abstraction invariant properties
of sensory
Bergeron.
input the motor or other concepts. The relationship
between
these concepts are linked by a relation or transformation.
Based on the opinion o f experts that has bee
Furthermore Skemp (1987) states that the scheme
canisbeused
saidnot
that the understanding of the mathe
only when the student has previous experience of
related
to the
a student
is the ability to perform mental
present situation, but also when solving problems
form owithout
f actions, processes, objects, and
having the experience o f the present situation.
For example,
constructing
the concept as well as the ability
students understand
the concept of extreme draw
points
of
conclusions
from specific rules into
polynomial fiinctions when he already has a scheme
in the form are more common.
relationships
of a bunch of concepts, including the completion of the
. Abstraction,
equation, the definition o f the derivative B function,
the construction, representation a
properties of the derivative function, derivative understanding
of polynomial
functions are mutually related.
According to Bruner (in Tall, 1996) there are

L INTRODUCTION

namely enactive, iconic
According Mousley (2005) there are three mental
models representation,
of
grew sequentially in the indi
mathematical understanding, that understanding Representations
as structured
from enaktif,
then finally iconic and symbolic.
progress,
understanding
as
forms
of
knowing
and
representation
understanding things as a process. Understanding as structuredhas its own strengths are then l
enactive
and iconic representations. Piaget (in
progress illustrates that growth in understanding
who follow
develops the theory of acquisition or con
the trend of construcfivism, namely the process also
o f constructing
which he called the theory o f abstr
knowledge from basic to higher level. Piaget to
(inBruner,
Mousley,

2

Representation
Knowledge of the properties themselves
are is a process o f mental devel
is already owned by someone, who revealed and
internal and are the result of construction created
a variety of mathematical models, namely: ve
internally
as
well.
Second
abstraction
concrete objects,is
tables, models manipulative o
pseudo-empirical described by Piaget
(in (Steffe,
Dubinsky,
thereof
Weigel, Schultz, Waters, Joi
Hudojo
, 2002: 47).
2002) as follows: "pseudo-empirical
abstraction
isCai, Lane, and Jacabcsin
states
that
a
mode
intermediate between empirical and reflective of representation that i
communicating mathematics include: tables, imag
abstraction and teases out the properties
that the
mathematical statements, written text, or a co
actions of the subject have introduced
into
objects".
of them. Hiebert
& Carpenter (in Hudojo, 2002)
So in pseudo-empirical abstraction itsubject’s
actions
is basically
a representation can be divide
have started to lead to interest internal
in therepresentation
propertiesand external represent
mathematical
owned by the object. Furthermore,about
according
to ideas which are then co
require external representation of his form,
Dubinsky (2002), reflective abstraction
is a concept
verbal, pictures and concrete
objects.
Th
introduced by Piaget to describe the
development
of allows a person's min
mathematical ideas that
logico-mathematical structure by basis
an of
individual
the idea is the internal representatio
C
Understanding
during cognitive development. Two
important Layers of Pirie-Kieren *s M
Folding
observations were made by Piaget is
theback
first
abstraction reflective not have absolute
beginning
Pirie-Kieren (1994) has provided a theoretic
of eight
(layers) understanding, that p
but was present at a very early
age levels
in the
image
making,
image
coordination structure sensory-motor (Beth & having, property noticing,
and inventising. This
Piaget, 1966 Dubinsky, 2002) and observing,
second, structuring,
that
"understanding does not necessarily
grow l
abstraction was
continuously evolved
through
continuously.
Someone often back to the prev
mathematical higher. As far as the understanding
whole history
of
to further
advance to the n
that activity namely folding
the development of mathematics fromunderstanding,
ancient times
(1994)
describes the indicator la
to the present can be considered as Pirie-Kieren
an example
of the
that understanding. The first layer understa
process of reflective abstraction primitive
(Piaget,
1985 in
knowing is the initial efforts made b
Dubinsky, 2002).
understanding the new definition, bring previou

Bruner and Piaget in most of his own work concentrates
on
the next layer
of understanding through actio
the development of mathematical knowledge at an
early
age,
the definition or definitions represents (Pir
rarely go beyond adolescence, however Dubinsky The
interested
second in
layer of understanding namely image
doing research with the same approach and expanded
stage to
in the
which students create an understan
topic higher up the subject matter of mathematics
for and
high use it in new knowledge (Pirie-K
knowledge
school and even college. When it Dubinsky see The
possibilities,
third layer of understanding namely image
not only to discuss and suspect, but to provide stages
evidence
to show
where
students already have an idea ab
that concepts such as mathematical induction, propositions
andpicture on the subject without h
make a mental
processes,
linear
predicate calculus, fiinctions as objects and examples
(Pirie-Kieren,
1994; Manu, 2005). The
independence, duality vector spaces, topology,
even
of and
understanding
namely property noticing i
category theory can be analyzed in terms o fwhich
renewal
or
students
are able to combine aspects o f
extension of the same idea as that of Piaget, is specific
used to describe
a
to the nature
of the subject (Pirie-K
child's construction o f concepts such as arithmetic,
proportion,
fifth layer
of understanding namely formalizin
and simple measurements (Dubinsky, 2001).
where students create an abstract mathematical
APOS theory has been introduced by Dubinskyon(in
theTall,
properties that appear (Pirie-Kieren, 19
1999), which describes how the mental activity able
of a to
student
understand
in
a concept definition or form
the form of actions, processes, objects, andalgorithm
scheme when
(Parameswaran,
2010).
The
sixth
constructing mathematical concepts. According to
understanding
this APOS namely observing is a stage wher
theory, a student can construct a mathematicalcoordinate
concept well
formal activity on formalizing leve
when he suffered the actions, processes, objects,
them on
and issues
has a related to the faces (Pirie
scheme. A child is said to have performed an students
action, iare
f thealso able to link the understa
child is to concentrate in an effort to understand
concepts
he
the has with
the new knowledge
mathematical concepts that it faces. A student (Parameswaran,
said to have had
2010). Seventh layer of understa
a process, i f thinking is limited to a mathematical
structuring,
concept that
is the phase where the students
it faces and is characterized by the emergence the
of the
relationship
ability to between the theorems of the
discuss the mathematical concept Furthermore, and
thebeing
students
able to prove it with logical argumen
said to have had the object, i f he had been able
1994).
to explain
Students
theare also able to prove the con
properties of mathematical concepts. Finally, students
one and the
are other
said theorems axiomatically (Pirie
to have had a scheme, i f he had been able Inventising
to construct
eighth layer o f understanding is
examples of mathematical concepts in accordance
students
with the
have a complete understanding of stru
requirements specified.
to create new questions that grow into a
(Pirie-Kieren,
Representation is a model or a substitute form
o f a problem 1994). Mathematical understandin
is
situation that is used to find a solution. Forunlimited
example, and
a beyond the existing structures
the question
"what if?" (Meel, 2005).
problem can be represented with objects, pictures,
words, or
symbols math (Jones & Knuth, 1991). There are four
ideas
The linkage
between APOS of Dubinsky and Pir
that are used in understanding the concept of theory
representation.
o f knowledge can be presented below; Act

3

Furthermore, according to Piere-Kieren (1994), This
although
matter was given to the subject to be
understanding the concept of someone grow an
from
the
interview
based on the worksheet, the data
innermost layer (primitive knowing) toward the
outermost
form
o f a worksheet at the interview and the i
layer (inventising), but there are times when transcribed,
a person back
once validated the data is analy
into the deeper layers when facing problems. The
activity
became
the what
main instrument in data collection a
the person back into the deeper layers is called
back. presence can not be delega
the folding
researcher's
According to Martin (2008) and Susiswo (2014) there
are four
researcher
must collect data through task-bas
possibilities the form folding back, that; "working
check on
the deeper
validity of the data obtained, categ
layers", "collect the deeper layers", "off-topic",
and presenting
"causing
reduce,
and
interpreting the d
discontinuous". Subjects experienced a folding conclusions.
back the firstThe
research
reveals
profile
form o f "work on the deeper layers" occurredunderstanding
due to the the concept of derivative fia
limitations of understanding that exist in the outer
layer so
that
prospective
teachers
o f mathematics. The co
the subject back to the deeper layers without exiting
the fijnction
topic
derivative
is limited in terms of fu
and work there use of existing knowledge.derived
Subjects
basic functions, derivative of polyno
experienced a folding back the second form o f
"collecting
detennine
the extreme points of fiinctions,
layer deeper" when the subject tried to get prior
knowledge
for
polynomial
fijnctions.
Profile of understanding
a specific purpose by reading in a new way.
with Subjeas
guided the model of understanding Piere-K
experienced a folding back a third form that which
is "oflF-topic"
has developed some cognitive psychology
when it occurred, where subjects experienced aresearchers,
folding back also referring to a form of fo
to primitive knowing and working on the expansion
o f otherand used by Martin (2008) and Susis
recommended
topics effectively but separate to the main Indicators
topic. Subjects
the layer of understanding and fol
experienced a folding back the fourth form been
is "causing
studied and have been compiled and tab
discontinuous" occurs when the subject returnedadapted
to the to
deeper
be prepared for an interview about t
layers, but not related with the understanding the
thatsubject.
there is,When
in compared with the charac
this process occurs, where the subject can not
look at research
the
qualitative
is meant by Moleong (201
relevance or connection between pemahamnnya existing
withas qualitative research, because th
qualifies
new activity or problem that is being done. Thus
the growth
profile
layerof
o f understanding of the derivativ
understanding referred to by Piere-Kieren is is
notanlinear.
In part of community life (stud
important
connection with that, no folding back is teachers)
successfully
and
in real worid
conditions,
expanding knowledge, and conversely there are representing
folding back the views and
aspirations o f
ineffective broaden understanding of the subject.
Ativity what
(especially
student teachers), the third: inclu
pullback of the outer layer into the deeperconditions
layers, then
that
students
study
program
M
advanced to the possibility o f turning outer Education
layer, can
be passed the courses Calculus I ,
have
described in the form o f "folding back path" insight into who's understanding of the co
derivative function existing students that hel
About gender, according the results of research by
social behavior (especially student teachers),
Iswahyudi (2012), at any stage Polya problem solving, students
more than one source of evidence, the data is
are capable of high mathematics, both males and females have
verbally, the action of the data subject and do
very complete keterlaksanaan metacognition. But the level o f
completeness of metacognitive activity o f male students is
IV. RESULT AND DATA AN ALIZE
higher than women. According Radua et al (2010) part of the
male brain called the inferior parietal lobule greater
Problemthan
TLPKinhas been done by the subject
women. This makes men more capable in the and
fieldmenofelected from the student prospective
mathematical compared to women. Based on the mathematics
results of were interviewed based TLPK and w
research conducted by TIMMS mention that to then
solvethe
thedata obtained in the form o f a wor
problems of spatial given to groups of men and
groups and
of the transcript of the interview.
interview
women there is a difference in the process o f answering the
A.
Understanding
Layers
questions. Groups of men rely on spatial strategies
when
solving mental rotation task, while the women's groups
tend
Data indicator o f understanding of each s
mengandakan verbal strategies to accomplish thefollows:
same task. In
the next test groups o f women using verbal skills to spatial TABLE 1
visualization same tests rely on mathematical INDICATORS
instructionsOFto UNDERSTANDING LAYERS OF
complete visual image (Asmaningtyas: 2010).
FUNCTION
DERIVATIVES
BY THE SUBJECT

ffl.

RESEARCH METHOD

WOMEN AND MAN
Indicator

Concept Understandinf;

specify- in writing the first deri
Conducting
initial
This type of research is qualitative, because
the an
data
fiincUon/x)
UlbOOl namely Ulb003,
effort to understand
the
obtained through the observation o f the subject's
behavior thatspecify in writing denvatives the
new definition (PKl)
produces descriptive data in the form of oral, written and otherfix) UlbOOl namely Ulb005
actions. Qualitative research to further highlight
theknowledge
processstated orally that he wrote on Ulb
Bringing
LJlb002
to the next
of is the first derivative of t
and meaning in the perspective of the subject. prior
Therefore,
thelayer
(PK2)/ ( X ) UlbOOl,
researcher's presence serves as an instrumentunderstanding
at the same
Giving reasMis why write Ulb003 a
interpreter. The process and the data obtained will be
derivative of UlbOOl
meaningful when processed and analyzed by the researchers.
Gi\ing reasOTis why write Ulb005 a
Applied research approach is descriptive because it aims to second derivative of U1 bOO 1
Write understanding of the deriviativ
Doingobusiness
thrtnigh
explore and describe the profile o f understanding
f student
in the form of limit UW1 b003
the action invohingformula
the
teachers. Auxiliary instrument used is a matter definitiffli
of Task Layers
Explained wally in the form of under
or definitions
of
Understanding
Concept
(TLPK)
following:
the derivative fiinctitm limit fcwmula
represents (Pk3)
"Given function equationy(x) = 2r^ - 3^:^ + 2, where
- 2 ^ 3 ;based
Separating the
fijnction
given t
Make a picture
on iM^vious knowledge
fimctions by tribe

4

Indicator
Concept Understanding
Indicator
Concept Understanding
Creating an image of
Applying
a
the formula to prove that the Being
terms able
of
to look Finding
for a
patterns derived formulas pro
concept through pictures
the derivative of the first derivatiw -3x^
pattern
is -6x,
to determine
number
an
of functions
algorithm
a tlworem
or through examples(Xitlining the limit fimction in the fM-ocess
of
Finding patterns to describe the thir
tTm3)
proving the deri>'alive function of the (Ob4)
square
poljncHnial function graph is given.
Finding patterns to describe the difT
Applying the formula to prove that the terms of
of graphs third-degree polynomial fun
the derivative first derivative of the 2x^ is 6JP.
Finding patterns to describe the diff
Outlining the limit fimction in the process of
of charts fourth-degree polynomial fu
proving the derivative function of the cube
Explains the pros aiKl cons draw the
Having an idea about
a
Explaining
the formula to be applied when
polynomial functions by means of the
searching for the derivative fimction consisting
topic (flil)
application without the application o
of sewral tribes
and derivative
Describe the shape of the rank-n limit of the
bincmial (.r+h)" for proving process derivative
Outlined
steps
procedure
graphs
Capable of establishing
a
third-degree polynlaining the similarities and differences
Having a complete describe the steps and the reason
aspects of a topic between
to
the application of the derivative
of
describe
various
types
of
thir
of
understanding
estabhsh the natureformula
understanding
the
single suiictured
rate
(In 1) polynomial fimction graphs and expla
Recognizing similarities
polynomial fimction of degree two, three and
of the properties, existing algorit
and differences varied
degree of degree n (.the original), as well as its
[»occss; describe the steps and t
overview of a topicrelationship
and
with the formula derived number
logically
describe
different
ty
de\elop it into a of fiinctions, thus forming derivatives of
fouLTth-degree polynomial function gra
defmition of the concept
general formula polynomial fimction.
explanations of the properties, the
which was built between
Explaining the relationship between fimction
in the process
these images (Pn2) rises with the fnst derivative of a fimction,
andto create
Make
Being able
newinquiries about the form of gr
apply it to determine the fimction interval
ride.that can third-degree
polynomial fimction wit
questions
grow
Explaining the relationship betweeninto
the
of derivative
a new concept application
(ln2)
fimction dowTi to the first derivative of a
function, and sipp\y it to determine the interval
Based on Table 1, it appears that the subject
fimction down
men
understanding th
Creating a matliemalical
Write and explain the formula understanding to
of have indicators of
knowing
layer,
image
making,
image
having,
abstraction of a concept
the derivative fimction
based on the properties
Write and explain the formula derivednoticing,
number
formalising, observing and structurin
that appear (Fol) of functions
on the last layer o f the eighth inventising, t
Write down and explain the general formula
reached the first indicator, coupled with the
derived polynomial fimctions
the question
o f graphs the third-degree polyn
Write down and explain the terms fimctitm
\xp
and down.
that will be given to students" that leads
Write down and e)q)lain the terms fimctitm
indicator While the third indicator in this lay
reaches its maximum / minimum.
by
the subject. So that both subjects can be p
Write down and explain the terms fimction
layer undersstanding namely inventisingoid. Fi
reaches an inflection point.
Being able to understand
Write and explain the formula mKlerstanding
understanding
of
the concept o f the derivative fun
a formal definition the
or derivative fimction
women and men are as follows:
algt»ithms of
Write down and explain the fM-ocess of finding
mathematical concepts
a formula deri\ed number of fimctions
(Fo2)
Write down and explain the process of finding
a polynomial function derivatives of general
fi>rmula
Able to coordinate Explaining
the
langakah- steps describe a curve of
formal activities at
third-degree polynomial ftmcti 0 and / \x)