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Sys Rev Pharm 2020;11(12):348-355
A multifaceted review journal in the field of pharmacy
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
348
MATHEMATICS LANGUAGE UNDERSTANDING OF
TEACHERS’ CANDIDATE IN MATHEMATICS LEARNING
Baiduri, Yus Mochamad Cholily, Dina Amalya Lapele
University of Muhammadiyah Malang, Malang, Indonesia
baiduriumm@gmail.com
ABSTRACT
This study aims to explore and describe the understanding of
prospective mathematical language in mathe-matics teachers in
learning. A qualitative approach with a descriptive type is used for
this purpose. Three Mathematics Teacher Professional Education
(TPEP) students at the University of Muhammadiyah Malang who
are currently pursuing Field Experience Programs (FEP) in high
schools are used as research subjects. Subjects were selected
based on the Achievement Index (IP) obtained namely, high,
medium, and low. Data obtained through the study of the Learning
Implementation Plan (LIP) and Student Worksheet (SW) docu-
ments, observations during the learning process, and interviews.
The data analysis technique is done by data reduction, data
presentation, and conclusion drawing. The results showed that
the understanding of the math-ematical language of subjects with
high and moderate IPs was classified as very good while the
understand-ing of the mathematical language of subjects with low
IP was classified as good
The subject has been able to understand several semiotic lists
accurately and be able to present a visual ap-pearance well.
Some grammatical patterns in the form of vocabulary and logical
relationships can also be used appropriately. There are some
mistakes in understanding the subject of mathematics. Errors in
the se-miotic aspects are errors in the use of symbols,
inconsistent use of symbols, and writing errors. Mistakes based
on aspects of grammatical patterns are implicit relationships that
are less precise and systematic in the application of concepts, as
well as the use of vocabulary that can confuse.
Keywords— Mathematical Language, Semiotic Understanding,
Grammatical Understanding, Teacher Can-didate
INTRODUCTION
The term language is defined as words in which the
pronunciation and methods used are understood by a
community [1]. Mathematics has its own language [2].
The language of mathematics is the system used by
mathematicians to communicate mathematical ideas
among themselves. This language contains natural
language with the use of technical terms and
grammatical conventions that are specific to
mathematical discourse, coupled with symbolic
notations that are very specific to mathematical
formulas [3]. Specifically, concerning mathematical
language, the ability to use words, explain, justify, and
communicate mathematically is important for the overall
development of mathematical abilities [1, 4].
Language in learning mathematics is understood as
a source for mathematical thinking in mathematical
activities with other people as well as activities to
interpret mathematics in other situations [5]. The main
function of language in teaching mathematics is to
enable teachers and students to communicate
mathematical knowledge appropriately [6].
Mathematical languages consist of natural
languages using technical terms and grammatical
conventions that are specific to mathematical
discourse, plus symbolic notations that are very specific
to mathematical formulas. The mathematical language
syntax includes a list of symbols, configuration of rules
for constructing language patterns, axioms, deductive
systems, and theorems. Elements in mathematical
language include symbols, concepts, definitions, and
theorems [3]. Mathematical terms and symbols are
clearly defined. Each statement in mathematical
language has only one meaning or is not ambiguous.
Each mathematical pattern has one structure that is
determined by operational rules [3].
Many advanced mathematical sentences have
complicated structures that are easy to understand if
one knows some basic mathematical terms [7]. Good
mathematical language skills require a strong base of
vocabulary knowledge; flexibility; fluency and ability to
understand numbers, symbols, and sentences [1]. Fact,
students have difficulty in understanding these
elements including using definitions of mathematical
terms and related concepts [6], formulating
mathematical models, transforming problems into
mathematical equations [8]. Students have difficulty in
determining the operations that must be carried out to
find solutions because they are unable to make
appropriate mathematical models [9].
Factors that cause students difficulty understanding
the language of mathematics are complex forms of
mathematics and students feel less familiar with the
words learned [8]. Mathematical language learning
activities will be difficult because of the abstractness of
the objects discussed and their consequences affect
the difficulty of expressing the things discussed [6].
Thus the teacher first needs to have good mathematical
language skills. This is because teacher knowledge will
have an impact on student achievement [10]. Teachers
who have good mathematical language skills will be
able to better teach students how to use sentences in
mathematics, symbols, and multi-representations [5].
Mathematics Language Understanding Of Teachers’ Candidate In Mathematics Learning
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
349
Teachers have an important role in learning because
teacher performance will affect student achievement
and student involvement in the learning process [11]. In
realizing the goals of mathematics learning, teachers
need to use structured languages, namely technical
vocabulary and symbolism that can be understood by
students [6]. This is because mathematics is
fundamentally procedural that focuses on techniques
that involve numbers, symbols, and equations. Patterns
and relationships between concepts consisting of
symbols and equations are real problems that must be
understood in depth. Therefore, mathematical logic and
grammar are very important to understand [12].
Teachers still have difficulty in explaining
mathematical concepts in the form of mathematical
language [13]. Even though the teacher claimed to
have mastered the concept but was confused to explain
it. Teachers also have difficulties in expressing
mathematical problems in mathematical symbols or
sentences [14]. This is a problem in learning
mathematics because teachers need to be able to give
mathematical meaning to students through the ability to
read, write, and discuss mathematical concepts [5]. The
challenge for mathematics teachers is not only the
complexity of the mathematical concepts taught and the
various prerequisite concepts needed but also the
sophistication of the semiotic system that exists in
mathematics [15]. Therefore, the preparation of
competencies for prospective teachers or teachers is
very important.
The teacher professional education program (TPEP)
is an effort by the Indonesian government to prepare
professional teachers to realize the goals of national
education. TPEP is an educational program held to
prepare graduates of Education and
Undergraduate/Non-Education IV who have the talent
and interest to become teachers to fully master
teachers’ competencies under national education
standards so that they can obtain a certificate of
professional educators [16] with a period of education
for one semester or two semesters. TPEP Mathematics
students are prospective mathematics teachers and will
become mathematics teachers after they are declared
graduated and obtain educator certificates. The
intended teacher competence consists of personality,
social, professional, and pedagogical competencies
[17]. The development of prospective mathematics
teachers using appropriate mathematical language is
an important aspect of teacher education [18, 19].
Professional and pedagogical competencies related
to the mastery of the content of the material and how to
teach them are two very important competencies for
prospective teachers [20]. Prospective teachers must
have the ability to understand the connection of one
notation to another or from one procedure to another
[13] which is one of the professional competencies
besides using clear language to express the reasons
behind mathematical procedures [13]. Through
mathematical vocabulary and definitions, students
explore the concepts involved and learn to mean [1].
Mathematical language teaching to students helps
teachers identify more clearly what is the source of
difficulty and helps them understand how to make the
mathematical language more meaningful to students
[21].
Mathematical language consists of semiotic and
grammatical/syntactic aspects [22]. Semiotics is the
study of signs, which can be in the form of words,
images, sounds, gestures, and objects [23]. Syntax
studies the relationship between one word and another,
or other elements as a whole. The syntactic unit
consists of words, phrases, clauses, sentences, and
discourse [24]. Semiotic aspects include mathematical
symbol notation and graphics or visual displays.
Whereas the grammatical effect consists of technical
vocabulary and implicit logical relationships [22]. The
syntactic unit observed in this study focuses on
vocabulary and sentences used.
Symbols have characteristics that can be viewed
from aspects of materiality, syntax, and meaning.
Materials symbols can be in the form of Latin letters,
operators, and physical attributes. Besides, the symbol
syntax states the position and conventions associated
with it. For example, the "" sign is used to express the
same value on both sides. In meaning, symbols are
placed in the domain that states the context of a
problem [25]. The meaning of mathematical symbols is
also expressed by [26] which states that mathematical
symbols consist of three categories, namely letters,
figures, and other templates that combine letters and
other figures in a two-dimensional form. Symbols in the
form of letters such as ,,,,. The symbols in the
form of figures such as ,,,,. Symbols in the
form of combined templates such as
[27].
Graphs are an example of visual appearance in
mathematics. Several other visual displays that can be
used in understanding mathematical concepts. In
mathematics, the choice of visual appearance is related
to what is to be expressed [28]. One example of a
visual display such as images of wake-up flat and wake
up space.
A word is a small unit of a sentence [29]. Sentences
can be interpreted in three understandings, namely
sentences as expressions with specific structures or
forms, sentences as expressions with specific contexts
or meanings, and sentences as specific uses [30].
Sentences in mathematics can be definitions,
theorems, or other statements containing elements of
logic. Logic sentences can be in the form of
implications, bi-implications, negations, or sentences of
office. Mathematical logic sentences must be proven
true [31]. Thus, a sentence has an implicit logical
relationship if the sentence is following the rules of
logic.
Some of the previous studies relating to the
language of mathematics are [32] which states that
mathematics becomes difficult to understand because it
contains terms and symbols that are difficult to
understand. Therefore, teaching about the language of
mathematics will increase the effectiveness of learning
Sys Rev Pharm 2020;11(12):348-355
A multifaceted review journal in the field of pharmacy
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
350
mathematics. The same thing was also expressed [1]
that learning of terms in mathematics became
something very important. In learning mathematics,
students have difficulty in translating terms in
mathematics [9] as well as making mathematical
models of the given problems [8]. The mathematical
language skills of prospective mathematics teachers
(mathematics education students) [33].
Because naturally mathematical content develops
from less complex skills to very complex ones and the
importance of the teacher's role in helping students use
mathematical language effectively, mastering the
mathematical language and the ability to teach it to
prospective teachers is very important. Therefore, this
study aims to explore the understanding of
mathematical language by prospective mathematics
teachers who are undergoing professional education
teachers. The problems examined in this study are:
how is the understanding of the mathematical language
of prospective mathematics teachers who are attending
professional education teachers?
THE RESEARCH METHODS
DESIGN
A qualitative approach with an explorative
descriptive type was used in this study, because the
aim of this study is to explore information about
understanding mathematical language of prospective
mathematics teachers who were obtained in depth and
describe a situation as it is, without giving any action
[34, 35].
SUBJECTS
The subjects of this study were three prospective
mathematics teachers who were attending professional
education teachers at the University of Muhammadiyah
Malang and taking the Field Experience Program (FEP)
at partner schools, namely public high schools 8 and 9
in Malang. Subjects are undergraduate mathematics
education graduates selected based on the
Achievement Index (IP) obtained. Subjects with high IP
(S1), medium IP (S2), and with low IP (S3).
DATA COLLECTION
The research data in the form of understanding of
the mathematical language were obtained through a
review of the Learning Implementation Plan (LIP) and
Student Worksheet (SW) documents made by
prospective teachers, observations during the learning
process in class, and interviews. Data collection was
carried out on each subject for three meetings, each
meeting using 2 x 40 minutes. Method triangulation and
time triangulation are used to obtain valid data [35, 36].
DATA ANALYSIS
Data analysis techniques in this study use an
interactive model [34, 35] namely: 1) data reduction
includes the activities of selecting, simplifying and
transforming rough data from document review,
interviews, and observations conducted during learning
activities; 2) data presentation, namely compiling
information in the form of narrative text and calculation
results tables that explain the understanding of
mathematical language and the pedagogical abilities of
teacher candidates used in analyzing data; 3) drawing
conclusions namely verification of data obtained during
the research process. Mathematical language
understanding of prospective mathematics teachers is
classified by the categories, very good if
, good if 0 , not good if 0
, and not very good if 0 , where U
is Understanding Mathematical Languages [37].
RESULTS
Understanding the mathematics language of
prospective teachers in terms of the use of semiotic
lists and also grammatical patterns are presented in
general and deepened discussed in each subject.
Percentage of understanding of the mathematics
language of prospective teachers is obtained through
the results of the document review, namely the LIP and
SW used at three meetings, the results of observations
in class during the learning activities taking place, and
interviews. The results of the document review
regarding the overall understanding of the mathematics
language of prospective teachers are presented in
Table 1.
Table 1. Understanding Mathematics
Language of Teachers Prospective
Su
bje
cts
LIP and
SW
Meeting
1
LIP and
SW
Meeting
2
LIP and
SW
Meeting
3
Av
era
ge
Cate
gori
es
Ri
gh
t
No
t
Ri
gh
t
Ri
gh
t
No
t
Ri
gh
t
Ri
gh
t
No
t
Ri
gh
t
S1
74
%
26
%
77,
5%
22,
5%
73,
5%
26,
5%
75
%
Very
good
S2
77,
47
%
22,
53
%
75
%
25
%
76,
10
%
23,
90
%
76,
19
%
Very
good
S3
60
%
40
%
60,
26
%
39,
74
%
57,
52
%
42,
48
%
59,
26
%
Goo
d
UNDERSTANDING MATHEMATICS LANGUAGE S1
Understanding S1 mathematical language is
classified as very good. This is seen in 75% of the use
of appropriate mathematical language. Some
mathematical concepts and ideas are also well
understood. One example is the following interview
excerpt.
Researcher
:
What do you think the symbols of
mathematics mean?
S1
:
Symbols in mathematics are an
agreement in representing a
mathematical definition or formula.
Researcher
:
What about graphics? How do you
view the graph?
S1
:
The graph is to presents data. On
the graph, there are 2 axes, the X-
axis and the Y-axis. We have to
know what X-axis represents what
data and Y-axis represent what
data.
Mathematics Language Understanding Of Teachers’ Candidate In Mathematics Learning
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
351
S1 understands symbols as a sign which is an
agreement in representing a mathematical idea. Also,
S1 understands graphs as displays used to present
data. Sometimes S1 has difficulty in explaining the
definition to students. This is because explaining new
vocabulary to students must use simple and clear
sentence structures so that students can understand it
well. Some mathematical languages can be used
well by S1 but there are also some mistakes. The
proper use of mathematical language, for example, is
described in Table 2.
Table 2. Accuracy of S1 in Using Mathematics
Language
No.
Appropriate
semiotic/grammatical
pattern
Description
1.
If we add up the
difference in data with
the average, we get
It contains
semiotic elements
(symbols) and
grammatical
patterns (use of
technical
vocabulary).
Representation of
words into
mathematical
sentence form.
The notation and
symbols used are
exact. The
vocabulary used is
precise and
logical.
2.
Projection in the
field is
It contains semiotic
elements in the
form of visual
appearance
(pictures).
The visual display
in the form of a
figure of space and
its projections are
presented
appropriately. The
images presented
represent the
conditions given.
From the semiotic aspect, S1 has used several
symbols appropriately such as the sigma symbol (
and also the average (
. Besides, from the aspect of
grammatical patterns the vocabulary used is also
appropriate and has a logical relationship. Visual
displays such as histograms and projected images of
space constructions are also well presented and
represent the conditions given. Besides, there are
some errors in the understanding of the S1
mathematics language as presented in Table 3.
Table 3. Errors of S1 in the Use of
Mathematics Language
No
.
Semiotic/grammatic
al patterns that are
not quite right
Correctio
n
Descriptio
n
1.
The use of colons
that are not in line
with the math
sentence (...)
Use a
triangle
which is in
line with
the math
sentence
()
Mistaken
use of
symbols
2.
frequency
frequency
of the i-th
data
Information
on notation
is
incomplete
3.
the point of the i-th
class is
the
midpoint
of the i-th
class is
Information
on notation
is
incomplete
4.
The line segment AB
denoted by AB
Mistaken
use of
symbols
Table 3 shows that there are some errors in the use
of mathematics language by S1. The mistake in terms
of semiotics is the mistake of using symbols. Besides,
there are also errors in terms of grammatical patterns,
namely the vocabulary used to explain the meaning of
symbols is not right.
UNDERSTANDING MATHEMATICS LANGUAGE S2
Understanding the S2 mathematics language is
classified as very good. S2 gained the largest
percentage compared to other subjects, reaching
76.19%. Some mathematical concepts and ideas are
also well understood. One example is the following
interview excerpt:
Researcher
:
What do you think the mathematical
symbols mean?
S2
:
Mathematical symbols are things
that express meaning about
mathematical ideas.
Researcher
:
What is the meaning of the graph?
S2
:
Graphs are used to present data.
The mathematical symbol according to S2 is
something that expresses the meaning of mathematical
ideas. Understanding the S2 language is better than
other subjects. Besides, S2 also admitted that he had
no difficulty in explaining a mathematical concept to
students. Some mathematical languages can be used
well by S2, but there are also some mistakes. The
proper use of mathematical language, for example, is
described in Table 4.
Table 4. Accuracy of S2 in Using Mathematics
Language
N
o.
Semiotic / grammatical patterns that
are appropriate
Descripti
on
Sys Rev Pharm 2020;11(12):348-355
A multifaceted review journal in the field of pharmacy
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
352
1.
Implicit
logical
relations
hips are
used
precisely
to
express
deviation
standard
and
variance
2.
N
o
fi
xi
fixi
xi-x
fixi-x
1
1
4
1
2
16
8
5,2
72,8
2
1
6
1
5
24
0
2,2
35,2
3
2
0
1
8
36
0
0,8
16
4
1
7
2
1
35
7
3,8
64,6
5
4
2
4
96
6,8
27,2
7
1
12
21
215,8
The
visual
display in
the form
of a table
is
presente
d with
elements
that are
complete
and
ordered
so that it
can lead
to
consider
the value
of the
deviation
standard.
From the semiotic aspect, S2 represents the
deviation standard and variety relations using the
correct symbols and also the right logical relationships
when viewed from aspects of grammatical patterns.
Visual displays such as tables are presented with
elements that are complete and ordered so that they
can lead to finding solutions. Besides, there are also
some mistakes in understanding the S2 mathematics
language as presented in Table 5.
Table 5. Mistakes of S2 in the Use
Mathematics Language
No
.
Semiotic/grammatic
al patterns that are
not quite right
Correctio
n
Descriptio
n
1.
The frequency the
class uses the
notation
sometimes uses
Use the
notation
to express
the class
frequency
Use of
inconsisten
t notations
2.
Use point
four (....)
which
states fill
in the
points with
the right
answer.
Mistaken
use of
symbols
Table 5 shows that there were some errors in the
use of mathematics by S2. These errors include the
use of inconsistent notations and the use of symbols.
Besides, there is also a mistake in the presentation of
the graph because the distance between the number
lines on the coordinate axis is not consistent (the scale
is inconsistent).
1.1 Understanding Mathematics language S3
The mathematical language understanding of S3 is
quite good with the acquisition of a percentage of
59.26%. Not much different from the views of other
subjects, S3 states that mathematical symbols are
meanings/signs that state something that must be
interpreted or done. This can be seen in the following
interview excerpt.
Researcher
:
What do you think is the meaning of
mathematical symbols?
S3
:
I think the mathematical symbol is a
sign of an idea or thing that has to
be done. For example, the addition
sign (+) means we have to do the
addition operation of two or more
numbers.
Researcher
:
How about the graph?
S3
:
The graph to state the relationship
between data
S3 sometimes experience confusion in using the
right mathematical language and following the concept.
For example, when teaching integers sometimes S3
uses the command word "forward/backward" and
sometimes uses the word "right/left". This can lead to a
misunderstanding of the basic concepts of integers. S3
is also often mistaken in distinguishing "plus" or "minus"
sign operations and "positive" or "negative" numbers.
This indicates that S3 has not differentiated the basic
concepts of number values and number operations.
This is important to note because number values and
number operations have different meanings.
Some mathematical languages can be used well by
S2 but there are also some mistakes. The proper use of
mathematical language, for example, is described in
Table 6.
Table 6. Accuracy of S3 in Using Mathematics
Language
No.
Semiotic/grammatical
patterns that are
appropriate
Description
1.
The form
is other writing from
[
which means the form
is a tribe of many
degrees 2.
The vocabulary used is
precise and has an
implicit logical
relationship to explain
the degree of a multi-
syllable
2.
Two is not a factor of
, because after
all the possible h
values are substituted,
no resulting hvalues
The vocabulary used is
precise and has an
implicit logical
relationship to explain
the concept of theorem
factor.
Mathematics Language Understanding Of Teachers’ Candidate In Mathematics Learning
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
353
are found
Some of the examples above state the accuracy of
the use of mathematical language by S3 in terms of
both semiotic and grammatical patterns. From the
semiotic aspect, S2 explains the concept of many tribal
degrees and factor theorems with languages that have
a logical relationship. From the aspect of grammatical
patterns, S2 also presents the horner chart
appropriately. In addition, there are also some mistakes
in understanding the S2 mathematics language as
presented in Table 7.
Table 7. Mistakes of S3 in the Use of
Mathematics Language
N
o.
Inappropriate
words/
phrases/sente
nces
Correct
words/phrases/sen
tences
Explanatio
n
1.
than
The
implicit
logical
relationshi
p which is
less
precise
because
the
teacher
does not
include the
notation
so
that
students
understan
d the
origin of
the
substitutio
n process
undertake
n
2.
produce
produce as
the initial term of
the quotient
The use of
vocabulary
that can
cause
confusion
in
understan
ding
concepts
3.
Polynomial
division h()
by
polynomial division
h() by
Writing
error
4.
Sometimes
teachers use
polynomial
denoting
with ,
Use consistent
only notation
Use of
inconsiste
nt
notations
sometimes
Table 7 shows that there are some errors in the use
of mathematical language by S3. The understanding of
S3 mathematics is low compared to other subjects.
This is indicated by the number of errors in the use of
S3 more than any other subject. Some errors in the use
of mathematical language by S3 include: 1) Implicit
logical relationships that are less precise; 2)
Misrepresentation of concepts; 3) The use of less
systematic concepts; 4) Use of vocabulary that
confuses; 4) Error writing symbols; 5) Erroneous use of
symbols, and; 6) Inconsistent use of notation.
Based on the description from Table 2 to Table 8 it
can be concluded that the understanding of the
mathematical language of prospective teachers is
following the rules of mathematics. But there are still
some mistakes in the use of mathematical language by
prospective teachers. Errors based on the semiotic
aspects include errors in the use of symbols, as well as
inconsistent use of symbols. While errors based on
aspects of grammatical patterns include implicit logical
relationships that are less precise and systematic in the
application of concepts, as well as the use of
vocabulary that can confuse.
DISCUSSION
Overall prospective teachers studied understand
mathematics as a language consisting of symbols,
graphics, definitions, and interrelationships among
them. Each symbol has a certain meaning. This states
that the language or terms used in mathematics can be
translated into a particular sign [32]. Prospective
teachers assume the language of mathematics is very
influential in learning. Explanation of mathematical
concepts to students must be done using the simple
language understood by students. This is very
important to note because when teachers use
mathematical language that is not appropriate then
students will not be able to explain mathematical ideas
and concepts in an appropriate language [33, 38].
Students have difficulty using mathematical terms and
related concepts so learning must be able to be
explained in simple languages so that students can
more easily understand [6].
Prospective teachers understand the material being
taught well. But this does not guarantee the teacher is
also able to explain it well to students. [13] argues that
although the teacher claims to have mastered the
concept, the teacher is still confused in explaining
mathematical concepts with appropriate mathematical
language and is understood by students. This is
indicated by the existence of some errors in the
mathematical language of the prospective teachers
studied.
Some of the mathematical errors of the prospective
teachers are viewed from the semiotic aspects and
aspects of grammatical patterns. Errors based on the
semiotic aspects include errors in the use of symbols,
Sys Rev Pharm 2020;11(12):348-355
A multifaceted review journal in the field of pharmacy
Systematic Reviews in Pharmacy Vol 11, Issue 12, December 2020
354
as well as inconsistent use of symbols and error writing
operations symbols. While errors based on aspects of
grammatical patterns include implicit logical
relationships that are less precise and systematic in the
application of concepts, as well as the use of
vocabulary that can confuse.
In learning activities prospective teachers solve
problems using mathematical symbols [14]. The most
common mistakes made by prospective teachers are
the use of symbols. Besides, the most frequent mistake
made by prospective teachers is the mistake in
mentioning the terms "minus vs negative" and "plus vs
positive". In addition to the teacher's weak awareness
of the meaning of the concepts "minus vs negative" and
"plus vs positive", the teacher is also still weak in the
meaning of the concept of "simplify vs. reduce",
"similarity vs congruence" which causes
misinterpretations of interpretations [33, 38].
Teacher candidates are sometimes inconsistent in
the use of symbols. Besides, the implicit logical
relationship of related sentences is also not well
presented. Both of these are mistakes of prospective
teachers in understanding the concept [18, 38] which
must not happen. Prospective teachers need to be sure
to master the language of mathematics well. Some
mathematical concepts are difficult for students to
understand so prospective teachers need to use
mother tongue to understand students. It is very
dangerous if the mother tongue used will make
students misunderstand [38]. Therefore, teachers and
prospective teachers need to explore the language of
mathematics.
The solution to these problems is that teacher
training needs to be focused on the use of appropriate
mathematical language to help teachers make effective
learning [18, 19, 38]. This is because the ability to
communicate effectively through mathematical
language requires mathematical understanding,
vocabulary, and a strong knowledge base; flexibility,
fluency, and ability to numbers, symbols, diagrams, and
understanding skills [1, 38].
CONCLUSIONS
Understanding the mathematical language of
prospective teachers with high and moderate IP is
classified as very good while the understanding of the
mathematical language of prospective teachers with
low IP is classified as good. Prospective teachers have
been able to understand some semiotic lists precisely
such as sigma symbols and have also been able to
present visual displays well. Some grammatical
patterns in the form of vocabulary and logical
relationships can also be used appropriately. But there
are also some mistakes in understanding the language
of prospective teacher mathematics. Errors in the
semiotic aspects are errors in the use of symbols,
inconsistent use of symbols, and writing errors.
Mistakes based on aspects of grammatical patterns are
implicit relationships that are less precise and
systematic in the application of concepts, as well as the
use of vocabulary that can confuse.
Understanding of the prospective teacher's
mathematical language is influenced by learning
achievement. This research focuses on understanding
language from the aspect of professional competence,
not on pedagogical competence with the subject of
TPEP participants in positions (already a teacher).
Therefore, it is necessary to further study the
pedagogical competence of TPEP participants, both in
positions and pre-positions (not yet becoming
teachers).
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