GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
Survey of Symbolic Learning Impairments among
Primary School Pupils in Mathematics
Olaoye Adetunji Abiola and Olaleru, Comfort Temilade
a function of different school subjects at any level. Many
subjects abound in the school system but each of these
subjects has different role towards the actualization of the
goal for which the society has established the schools for.
Mathematics is one the core subjects which every society
place an important value on its teaching due to its multidimensional roles in the past as well as in the future.
Infact there is no nation in the world that underrate the
teaching and learning of the subject in her stratum of
educational system, and this is why it has major
frequencies of teaching in the school time table relatively
to other school subjects. Mathematics is one of the most
important subjects in the school curriculum. There is
hardly any aspect of life that is not touched by this allimportant and cross-cutting subject. Young people being
unaware of its crucial importance often study the subject
as though they were under duress. Their teachers know
better and are fully aware that their pupils cannot cope
with challenges of life if they do not acquire some basic
understanding of Mathematics. In contrast the academic
performance of pupils in this core subject continue to be
on decline in spite government effort to stabilize the
nation educational system via the most two core subjects
viz-a-viz Mathematics and English in the school system.
With prominent studies conducted by Ozoji (2006) and
Ajibola (2008) one is not sure when this failure syndrome
could be nip-bud on one hand, and other hidden factors
that might have been contributed to the dismal
performance of pupils in Mathematics. It was based on
this premise among others that the study was designed to
survey some symbolic learning impairments among
primary school pupils in Mathematics along with their
achievement with a view to contribute to knowledge.
Abstract - The study was conducted to survey some of the
symbolic learning impairments that caused phobia among
primary school pupils in Mathematics. As a descriptive
study which made use of two research questions that were
later transformed into two hypotheses, purposive sampled of
five selected primary schools with ten Mathematics teachers
and two hundred pupils of primaries two and four of intact
class were used in the study. Three instruments that were
developed and used in the study included primary two
achievement test in Mathematics (r =0.68), primary four
achievement test in Mathematics(r=0.65) and Mathematics
teachers’ perceived symbolic learning impairment
instrument (r=0.72). Data collected and scoring were done
descriptively with one way ANOVA used to analyse data at a
significant level of 0.05. Findings revealed that there was
significant difference in the academic performances of the
past and present pupils’ understanding of counting system
that is more than thousandth in the achievement test (F-cal >
F-table, df=(4,188), P < 0.05*). It was also observed that
there was significant difference in the past and present
pupils’ understanding of an arithmetic operation (b-a) and
(a-b) where a ≠ b with teachers’ symbolic learning
impairment caused phobia among primaries pupils’
achievement test (F-cal > F-table, df=(4,188), P < 0.05*).
Discussions of these findings were extensively elaborated
along with their implications towards learning of
Mathematics among the primary school pupils on one hand,
and teachers’ omission or commission of symbolic
learning/teaching impairments on the other hand. At the end
suggestions and recommendations were proffered to guide
against such symbolic impairments among pupils with a
view to encourage more pupils to learn and not to develop
phobia for Mathematics at an early stage.
Keywords - Symbolic, Learning, Impairments, Primarypupils, Mathematics
I.
A. Theoretical and Conceptual frameworks
Impossibility, Infinity, Concepts and Phobias
INTRODUCTION
If it were easy to open children’s mind one would
have observed how flexible they are to assimilate
knowledge rather than discountenance of fact. This
underline assumption makes every concerned stakeholder
of children’s education to place a premium importance on
how they handle these children as what is taught and
learnt at this stage tends to have significant influence on
their life and performance in any chosen career. Whatever
anyone desires to become in life depends on the nature of
education which such a person undergoes, and this is also
on
A proof of impossibility is a proof demonstrating
that a particular problem cannot be solved. Proofs of
impossibility are usually expressible as universal
propositions in logic. One of the oldest and most famous
proofs of impossibility was the 1882 proof of Ferdinand
von Lindemann showing that the ancient problem of
squaring the circle cannot be solved, because the number
π is transcendental and only algebraic numbers can be
constructed by compass and straightedge. Another
classical problem was that of creating a general formula
DOI: 10.5176/2251-3388_3.1.62
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
using radicals expressing the solution of a polynomial
equation of degree 5 or higher. Galois showed these
impossible using concepts such as solvable groups from
Galois theory, a new subfield of abstract algebra that he
conceived. Among the most important proofs of
impossibility of the 20th century were those related to undecide-ability, which showed that there are problems that
cannot be solved in general by any algorithm at all. The
most famous is the halting problem. Although not
usually considered an "impossibility proof", the proof by
Pythagoras or his pupils that the square-root of 2 cannot
be expressed as the ratio of two integers or counting
numbers has had a profound effect on Mathematics: it
bifurcated "the numbers" into two non-overlapping
collections—the rational numbers and the irrational
numbers. This bifurcation was used by Cantor in his
diagonal method, which in turn was used by Turing in his
proof that the Entscheidung’s problem (the decision
problem of Hilbert) is un-decidable. Three famous
questions of Greek geometry were: "...with compass and
straight-edge to trisect any angle, to construct a cube with
a volume twice the volume of a given cube, and to
construct a square equal in area to that of a given circle.
For more than 2,000 years unsuccessful attempts were
made to solve these problems; at least, in the nineteenth
century it was proved that the desired constructions are
logically impossible"
automatically finite, whereas the same is not valid for
rational numbers. For example, a nomenclature for
unattainable and large figures as for large numbers varies
in different countries. In the United States, numbers
advance by increments of a thousand: billion
1,000,000,000 1 × 109 trillion 1,000,000,000,000 1 × 10 12
quadrillion 1,000,000,000,000,000 1 × 10 15 United
Kingdom and Germany However, in the UK and
Germany numbers have traditionally advanced by
increments of a million: million 1,000,000 1 × 10 6 billion
1,000,000,000,000
1
×
1012
trillion
1,000,000,000,000,000,000 1 × 10 18 quadrillion
1,000,000,000,000,000,000,000,000 1 × 1024 This has a
certain amount of logic on its side, particularly for
classical scholars: billion = million2 (bi-) trillion =
million3 (tri-) quadrillion = million4 (quadr-). Higher
numbers the U.S. usage is becoming prevalent in the UK
and Germany, particularly as it is now universally used
by economists and statisticians. The higher numbers, in
both styles, are as follows: Numbers in the United States
United Kingdom like quintillion 1 × 10 18 1 × 1030 .
Sextillion 1 × 1021 1 × 1036 . Septillion 1 × 1024 1 × 1042 .
Octillion 1 × 1027 1 × 1048 . Nonillion 1 × 1030 1 × 1054 ,
Decillion 1 × 1033 1 × 1060 , Vigintillion 1 × 1063 1 ×
10120 and Centillion 1 × 10303 1 × 10600 etc.
Concepts -Mathematics in primary school involves
learning about numbers, quantities and relations, as well
as about the connections and distinctions between these
three concepts. While numbers and quantities are not the
same, quantity can be represented by a number which is
not always used to measure a quantity and represent it by
a number but used to compare one person’s height to
another without any measurements or numbers.
According to an old French Mathematician
a
Mathematical theory is not to be considered complete
until one could make it so clear that one could explain it
to the first man whom one meets on the street.
Mathematical problem could be difficult in order to
entice, but not completely inaccessible, lest it mocks at
our efforts. It should be a guide post on the mazy paths to
hidden truths, and ultimately a reminder of pleasure in the
successful solution. The Mathematicians of past centuries
were accustomed to devote themselves to the solution of
difficult particular problems with passionate zeal. The use
of geometrical signs as a means of strict proof
presupposes the exact knowledge and complete mastery
of the axioms which underlie those figures; and in order
that these geometrical figures may be incorporated in the
general treasure of Mathematical signs, where there is
necessary a rigorous axiomatic investigation of their
conceptual content. Just as in adding two numbers, one
must place the digits under each other in the right order,
so that only the rules of calculation, i. e., the axioms of
arithmetic, determine the correct use of the digits, such
that the use of geometrical signs is determined by the
axioms of geometrical concepts and their combinations.
The agreement between geometrical and arithmetical
thought is shown also in that one does not habitually
Infinity-Most primary children are very interested in
infinity, which awakes curiosity in them before they enter
school: This is predominant among preschool and young
elementary school children that show intuitions of
infinity (Murenluto, Wheeler and Pehkoron. 2002).
However, this early interest is not often met by school
Mathematics curriculum as infinity remains mysterious
for most pupils throughout schools years. A lot of
questions often arise as ‘Is infinity a number? Is there
anything bigger than infinity? How about infinity plus
one? What’s infinity plus infinity? What about infinity
times infinity? Children, whom the concept of infinity is
brand new, pose questions like this and do not usually get
very satisfactory answers. In Mathematics and
Philosophy , two concepts of infinity namely potential
and actual infinity abound where former is a process
which never stops, and latter is supposed to be static and
completed, so that it can be thought of as an object. The
question of infinity has its roots already in the
Mathematics of ancient Greece, for example, the famous
paradox of Zenon. However, the transition from potential
to actual infinity includes a transition from process to a
Mathematical object. The foundation of infinity as
modern Mathematics sees it was laid when Dedekind and
Cantor solved the problem of potential infinity at the end
of the 19th Century, and Cantor developed his theory of
cardinal numbers. (Novotna, Moraova, Kratka &
Skehlikova; 2006). The set of natural numbers has
infinitely many elements, and it has no upper bound.
Therefore, the numbers may become bigger and bigger.
But every bounded subset of natural numbers is
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
follow the chain of reasoning back to the axioms in
arithmetic any more than in geometrical discussions. On
the contrary one applies, especially in first attacking a
problem, a rapid, unconscious, not absolutely sure
combination, trusting to a certain arithmetical feeling for
the behaviour of the arithmetical symbols, which one
could dispense with as little in arithmetic as with the
geometrical imagination in geometry. Two problems
illustrating two types of relations between quantities are
enumerated below: Rob and Anne have 15 books
(quantity) but Rob has 3 more books than Anne (or Anne
has 3 books fewer than Rob) (relation), the question is
‘How many books does each one have? (quantity). One
characteristic of relations, which distinguishes them from
quantities, is that they have a converse: if A is greater
than B, then B is smaller than A. So understanding
relations involves understanding the connections between
these two ways of thinking about the same relation. In
order to learn Mathematics, children must be able to
coordinate their understanding of quantities with their
understanding of relations, and must also distinguish
between them. One can think about relations between
quantities and represent the relation by a number even if
one does not know what the quantities are.
performance. Recently, Mathematics anxiety literature
has included studies on the cognitive impairments
associated with Mathematics anxiety (Ashcraft, 2002;
Ashcraft & Kirk, 2001; Ashcraft & Ridley, 2005). Even
the most accomplished Mathematicians and college level
professors sometimes experience symptoms related to
Mathematics anxiety. Ashcraft [1] (2002) suggests that
highly anxious Mathematics pupils avoid situations in
which they have to perform Mathematical calculations.
Unfortunately, Mathematics avoidance results in less
competency, exposure and Mathematics practice, leaving
pupils more anxious and mathematically as young as first
grade. Research by Sian Beilock unprepared to achieve.
According to Sian Beilock etal (2010), Mathematics
anxiety can start in children (Op cit) and colleagues
demonstrated that not only do young children experience
Mathematics anxiety, but this anxiety is associated with
poor performance in Mathematics. Phobia and fear
objects or situation comprises of 49 types and prominent
of these phobia and the objects or situation concerned are
Acrophobia(Heights),
Aerophobia(Flying),
Agoraphobia(Open spaces, public places), Aichmophobia
(Sharp
pointed
objects),
Ailurophobia
(Cats),
Amaxophobia (Vehicles, driving), Anthropophobia
(People), Aquaphobia (Water), Arachnephobia (Spiders),
Astraphobia (Lightning), Batrachophobia (Frogs,
amphibians), Blennophobia (Slime), Brontophobia
(Thunder),
Carcinophobia
(Cancer),
Claustrophobia(Closed
spaces,
confinement),
Clinophobia (Going to bed), Cynophobia (Dogs),
Dementophobia (Insanity), Dromophobia (Crossing
streets), Emetophobia (Vomiting), Entomophobia
(Insects), Genophobia (Sex), Gephyrophobia (Crossing
bridges),
Hematophobia
(Blood),
Herpetophobia
(Reptiles), Homilophobia (Sermons), Linonophobia
(String), Monophobia(Being alone), Musophobia (Mice),
Mysophobia (Dirt and germs), Nudophobia (Nudity),
Numerophobia (Numbers), Nyctophobia (Darkness,
night), Ochlophobia (Crowds), Ophidiophobia (Snakes),
Ornithophobia
(Birds),
Phasmophobia
(Ghosts),
Phobophobia (Phobias), Pnigophobia (Choking),
Pogonophobia
(Beards),
Pyrophobia
(Fire),
Siderodromophobia (Trains), Taphephobia (Being buried
alive), Thanatophobia (Death), Trichophobia (Hair),
Triskaidekaphobia(The number 13), Trypanophobia
(Injections), Xenophobia (Strangers) and Zoophobia
(Animals) the study as follow:
All these and some teachers’ introduced symbols
were considered as some of the symbolic learning
impairment caused dismal performance among pupils in
the primary school Mathematics achievement with
Numerophobia which refers to fear of numbers especially
among liberal oriented pupils and Triskaidekaphobia
which refers to fear of number 13 that is considered as an
irrational, thereafter given the study a strong baseline for
execution.
Statement of the problem-The study was conducted
to survey some of the symbolic learning impairments that
caused phobia among primary school pupils in
Mathematics. As a descriptive study it was conducted in
Ojo local government area of Lagos State, with two
research questions that were later transformed into two
hypotheses raised in Phobias-Many pupils experience
Mathematics phobia, which can be refer to as “feelings of
tension and anxiety that interfere with the manipulation
of numbers and solving of Mathematical problems in a
wide variety of ordinary life and academic situations”.
Mathematics is a subject and Phobia means fears/anxiety.
Then by putting the two together means: Mathematics
phobia is 'fear' of Mathematics. Mathematics phobia is a
phenomenon that is often considered when examining
pupils’ problems in Mathematics. It can also be called
Mathematics anxiety. The construct of Mathematics
phobia therefore falls within the larger construct of
anxiety, where anxiety has been broadly defined to be a
tense emotional response to the intellectual appraisal of a
threatening stimulus. Miller and Bichsel (2004) found
that state anxiety, trait anxiety, and Mathematics anxiety
were correlated, but Mathematics anxiety was the only
type of anxiety that correlated with Mathematics
B. Research Questions
RQ1: What is the past and present pupils’
understanding of counting system that is more than
thousandth in the achievement test?
RQ2: What is the past and present pupils’
understanding of an arithmetic operation (b-a) and (a-b)
where a ≠ b with teachers’ symbolic learning impairment
caused phobia among primaries pupils’ achievement test?
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
As a result the above two research questions were
transformed into two research hypotheses that were
under-listed below for testing at 5% level of significance.
randomly selection could not be used in a public school
for a study longer than a session without disrupting
already laid down academic calendar and administration.
The whole study lasted for three sessions as not all the
selected pupils in primary two continued their study in
primary four of the same school, though there was minor
attrition rate yet it could not affect the study in a
meaningful way.
C. Research Hypotheses
Ho1: There is no significant difference in the
academic performances of the past and present pupils’
understanding of counting system that is more than
thousandth in the achievement test.
D. Instruments
Ho2: There is no significant difference in the past
and present pupils’ understanding of an arithmetic
operation (b-a) and (a-b) where a ≠ b with teachers’
symbolic learning impairment caused phobia among
primaries pupils’ achievement test.
Two sets of achievement tests were developed for
the pupils in the study namely primary two achievement
test in Mathematics and primary four achievement test in
Mathematics with latter slightly higher in contents to the
former but based on the primary school Mathematics
module. While primary two achievement test comprised
of counting systems and some mathematics operational
and symbols that represent the survey impairments,
primary four achievement test comprised of simple and
similar equation related to the symbols that were made
use in the primary two achievement test. Each
achievement test comprised of ten questions in a multiple
form. The last instrument on some perceived symbolic
learning impairment was developed for the Mathematics
teachers to elicit their responses if these were introduced
by omissions or commissions in their course of teaching
but in all there were three instruments developed and
used for the study.
II. METHODOLOGY
Study was conducted to survey some of the
symbolic learning impairments that caused phobia among
primary school pupils in Mathematics. As a descriptive
study, two research-questions but later transformed into
two hypotheses that were used to conduct the research
among some selected primary schools in Ojo local
government area of Lagos State.
A. Population
Study made use of primary schools in Ojo local
government area of Lagos State along with their teachers
that taught these pupils in primaries two and four
respectively. The rationale behind this is not unconnected
to the fact that learning impairments in context
commences and pronounced in these two classes ahead,
and inhibiting subsequent Mathematics’ knowledge
acquisitions and application in future endeavours.
E. Validation
The instrument developed for the Mathematics
teachers was given to ten sandwich students of
Mathematics to ensure both facial and content validation,
and in line with scope of the study. These in-service
training teachers were instructed to select six pupils in
their primaries two and four, and administered the
instruments to them based on stipulated guidelines. A
split-half method of ensuring the validation of instrument
was later adopted among the in-service training teachers’
instruments and on the pupils’ instruments that were
submitted.
B. Sample
In the five selected primary schools ten
Mathematics teachers (five from primary two arms and
five from primary four arms) that had taught these pupils
were drawn into the sample on the pretext that they once
introduced these symbolic learning impairments by
omission or commission at the lower levels and the same
time trying to correct or otherwise of what they had
taught these pupils in the upper class. Forty pupils of an
intact class were selected from each school whereby a
total of two hundred pupils participated in the entire
study.
F. Reliability
Based on the split-half method employed the
correlation coefficient obtained for the teachers’
instrument was 0.72 while instruments for primaries two
and four had the correlation coefficients of 0.68 and 0.65
respectively. These values were considered relatively
high to ensure that these instruments were unbiased to
measure what they were purported to measure. The set of
pupils and Mathematics teachers used to validate these
instruments did not participate in the main study any
longer so as to prevent hawthorn /recollection effect.
C. Sampling Technique
Intact sampling techniques was adopted for the
pupils’ selection while purposive sampling techniques
was used for the selection of Mathematics teachers based
on their intention to be part of research, after an extensive
explanations had been made clear on the rationale for the
study. These teachers in turn assisted the researcher to
ensure that the study was strict to the use of intact class as
G. Administration
The validated instruments was administered by the
researcher to the selected Mathematics teachers in their
schools to elicit their responses, while pupils’ instruments
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
Table 2: One way Analysis of Variance (ANOVA) of pupils’
understanding of arithmetic operation system
was indirectly administered so that pupils selected would
be saved from seeing the strange face of the researcher
whom might be seen as threat to give credible responses.
All the instruments were collected by the researcher from
each Mathematics teacher a day after the administration
for better collation
Variables
PreAchieveme
nt test of
pupils at
primary
two level
Post
Achieveme
nt test of
pupils at
primary
four level
H. Data & Statistical Analysis
Data collected were administered according to level
though interrelated by the research questions and
hypotheses raised in the study, with descriptive scoring.
Anchored with the pupils’ performances in the previous
classes from their Mathematics teachers one way
ANOVA was subsequently used to analyse the collected
data at a significant level of 5%.
Table 1: One way Analysis of Variance (ANOVA) of pupils’
Understanding of counting system
SS
df
MS
Btw
1232.253
4
308.632
With
17641.818
195
90.471
Total
18874.071
199
Btw
5031.320
4
1257.830
With
23052.595
188
122.620
Total
28083.915
F-cal
df
MS
3450.727
4
862.682
With
43981.767
195
225.547
Total
47432.494
15199.362
4
3799.841
Within
348825.385
188
1855.454
364024.747
Sig.
10.054
.000
*
2.5238
.083
*
199
Btw
Total
F-cal
192
Table 2 described the academic performances of
pupils in the arithmetic operation (b-a) and (a-b) where a
≠ b with teachers’ symbolic learning impairment caused
phobia among primaries pupils’ achievement test where it
was found that at primary two and four that there was
significant difference in the academic performances
across the school used in the study(F-cal > F-table,
df=(4,195), P < 0.05*) and (F-cal > F-table, df=(4,188), P
> 0.05), respectively.
Ho1: There is no significant difference in the
academic performances of the past and present pupils’
understanding of counting system that is more than
thousandth in the achievement test.
Var
SS
Btw
*Significance, MS=Mean Square, SS= Sum of Squares, Btw=Between
Groups, With=Within Group, Var= Variations
III. FINDINGS
Variables
Precountin
g test of
pupils at
primary
two
level
Postcountin
g test of
pupils at
primary
four
level
Var
Sig.
IV. DISCUSSIONS
5.265
.006
*
19.230
.000
*
Different revelations were observed in the course of
the findings of the study which showed that Mathematics
like other school’s subject is a language which pupils
could learn and understand the way they pick their
mother’s language whenever some of the barriers in the
course of teaching and learning are removed. At first it
was observed that these pupils were good in counting
system to an extent that majority of them counted offhand beyond 500 though recognition was slightly not
encouraging. This might be as a result of the noncomplementary effort from previous class and home.
Situation arose when some of these pupils could not go
beyond 999 stressing that they were uncountable at the
primary two levels, and this might not be unconnected
with the teaching and learning that transpired within that
period. The belief of uncountable made the pupils to
assume that there was nothing beyond that point and saw
‘uncountable’ as part of the integers in Mathematics as at
then.
192
*Significance, MS=Mean Square, SS= Sum of Squares, Btw=Between
Groups, With=Within Group, Var = Variations
Table 1 described the academic performances of
pupils in the counting system that was more than
thousandth where it was found that at primary two and
four that there was significant difference in the academic
performances across the school used in the study( F-cal >
F-table, df=(4,195), P < 0.05*) and (F-cal > F-table,
df=(4,188), P < 0.05*), respectively.
Apart from this it was observed that pupils could
perform some elementary arithmetic operation whenever
symbol was never used. Such operation like 3-2=1, 64=2 etc were easy for the pupils to solve and teachers as
that time found their work stimulating unlike situation
where pupils were confronted with other concept of
‘impossible’ in solving problems like 2-3= ‘impossible’,
4-6=’impossible’ etc. These answers signalled to the
pupils at these levels a stumbling block and rest their
Ho2: There is no significant difference in the past
and present pupils’ understanding of an arithmetic
operation (b-a) and (a-b) where a ≠ b with teachers’
symbolic learning impairment caused phobia among
primaries pupils’ achievement test.
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
mind on impossible and uncountable as two distinct
concepts in Mathematics, and which they carried to the
subsequent classes.
learning which has the strong foundation in the
elementary teaching and learning period.
At the primary four, the pupils maintained the
status-quos of what they had learnt in the previous classes
with some modification and confusions of those concepts
as earlier learnt, thereby making the understanding of
Mathematics become strange to their liking. In one of the
utterance of a pupil it was posited that what he was taught
in primary two was ‘impossible’ for problem like (2-3),
(5-6) etc since the succeeding integer is greater than the
preceding ones, thereby creating confusion. Now the
situation has changed that ‘impossible’ is now ‘possible’
thereby making the pupil to believe that there was
inconsistence in Mathematics. Earlier, the extension of
figures beyond 1000 was seen as corollary to what was
obtained in the previous class as uncountable which was
a wrong notion previously injected into their learning
system.
V. CONCLUSION
Academic wastage is better minimized at the
elementary stage than at later part of pupils’ life as this is
synonymous to saying that the prevention is cheaper than
curative measure. Teaching and learning of Mathematics
at the elementary stage should be absolutely not being
done in abstract. It should devoid the use of regurgitation
in its entirety so that pupils would appreciate the beauty
and the need to learn the subject. This in turn would make
the pupils to show more interest in the subject and
transfer such to the teacher that is handling it. It is a
Divine favour that mathematics teachers have by
appropriate authority to have compelled the subject for
the pupils to learn and pass, otherwise they (mathematics
teachers) would have gone extra miles to look for clients
to register for the subject so as to sustain their livelihood.
Furthermore, study observed that much of the
phobias experienced by pupils in the course of learning
Mathematics were symbolic misrepresentations by the
assigned teachers that handled the subject from the
beginning and in which the subsequent teachers might
find difficult to correct among pupils. It should be noted
here that pupils believe so much in whatever their
teachers tell them in the classroom than what majority of
their parents teach them afterward at home. Infact these
pupils tend to report the weakness of their parent to the
teachers when in a real sense it was the fault of the
teacher and not the parent as whole. Though parent has
portion of blame of not liaise with the teacher at
appropriate time to correct the anomaly ahead of its
multiplier effect which often pronounced in the dismal
academic performance of these pupils later in life.
VI. IMPLICATION
Assume the current trend of teaching and learning
mathematics in the primary schools persist without
modifications that make the subject non-phobia to the
pupils especially in both developing nation like Nigeria
which has her educational goal of ‘self-reliance’ the
dream might be a mirage. The reason is not far-fetched
when one looks at the importance of the subject in the
area of science and technological advancement. No
nation in the contemporary period can survive without
developing her technology potentials which is domicile in
science that could only be ascertained through the
understanding of Mathematics. As a subject that
embraces the laid down foundation to the subsequent one
it means the weaker the foundation the immediate
collapse the entire structure, and so the nation is enslaved
since her educational system has collapsed.
Also, the study observed that most confusing
learning of Mathematics emanated from the shying away
from the reality of some mathematics teachers who might
not understand particular concept as at when confronted
by these pupils but looking for an escape route of given
wrong answer, instead of deferring such answer to the
time they might have made consultations with materials
or learned colleagues on the subject-matter. There is no
sin to inform these pupils of coming back some other
time for the solution of any unknown concept at a time
but great sin and error in teaching these pupils a wrong
concept that would last longer in their life. By extension,
a havoc committed by a quack mathematics teacher to the
pupils might be difficult to correct by professional
teacher later in life when there are much time lag in
between.
VII. RECOMMENDATIONS
Lots have been cited on the possible way forward
from the findings of the study but this does not mean the
micro-recommendations are not important so as to help
pupils overcome fear of Mathematics. First and foremost,
teacher should try the followings:
Mathematics teacher should figure out a way of
increasing the pupils confidence in him by allowing
pupils see interrelationship between the subject and their
immediate environment through his perform in
Mathematics. Teachers should assist the pupils develop
skills in which they are lacking to confront problems in
Mathematics. These could be basic numeracy skills or
However, everything is not lost at this period as the
study observed that much is needed to salvage the system
if immediately confronted ahead of the time it must have
grown a very hard wing to curtail ahead of higher level of
©The Author(s) 2015. This article is published with open access by the GSTF
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GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
skills required to solve complicated word problems, or
skills required to compute large calculations. They should
never ridicule or disrespect the pupils, especially in the
presence of classmates).
the understanding of the subject real to them. So a very
important factor in motivating pupils to study
Mathematics is:
Pupils might get more motivated if they know where
all Mathematics is needed, understanding large numbers,
and basic statistics that are essential to comprehend
information in school books. Pupils could be much more
motivated if involved and given open questions, involved
in the development of concepts, given very open-ended
exercises as this kind of teaching style require a lot of
planning from the teacher, probably a good understanding
in Mathematics, and good materials.
In fact, even if pupil has done something wrong,
praise him for all the steps he has got correct as the more
you praise, the more he tries to do better but the
correction of the wrong-doing should be within. Teachers
should always identify if pupils are under any pressure
from parents to perform up to certain standards. The
pupils might have created some lofty goals for
themselves to compete with others, teacher should make
the pupils set realistic goals and achieve them. So, if a
pupil has been failing in Mathematics, ask him/her to
target 60% in the next examination and not 90% marks,
as setting too high standards ultimately make him/her a
loser again and, increases his/her anxiety. Teacher should
review and learn basic Mathematics principles and
methods through short courses in Mathematics which is
often a significant first step towards decreasing the
anxiety response to Mathematics by pupils.
Teacher should not put a wrong answer down
instead; say "Please can someone explain how one comes
up with that?" In a classroom, teacher may ask, "Did
someone else get the same result as you (specific to
someone)? Did somebody get a different result? If we
have two (or three) different answers here, let us figure
them out" as wrong answers are not valuable. Teacher
should get in sight into pupils' thinking and where they
go wrong, and determine what needs to be re-taught.
Pupils need to be treated as humans and not to be scolded
with vulgar language of any sort for given wrong
answers.
Apart from these, parental influence cannot be
underestimated to ensure that pupil overcomes
Mathematics anxiety through positive reinforcement of
the child's intelligence and Skills. Rather than given pupil
negative criticism for doing poorly on a test building of
positive attitude towards Mathematics should be
encouraged, and this would build self-confidence and
thus reduce anxiety. Ones attitude in life determines ones
altitude Parents should be aware of thoughts, feelings,
and actions as they are related to Mathematics as
irrational thoughts could work against those thoughts
with more positive and realistic ones. A positive attitude
comes with quality teaching for understanding which
often is not the case with many traditional approaches to
teaching Mathematics. Teachers should ask questions that
could substantiate the 'understanding the Mathematics'
and not settle for anything less in course of instruction.
Clear illustrations or demonstrations or simulations,
practice regularly, especially when having difficulty
among pupils made the learning less tedious, and these
should be emphasized by the teachers. Pupils should be
encouraged of total understanding via complementary
tutor or work with peers that understand the Mathematics.
VIII.
SUGGESTION FOR FURTHER STUDIES
Based on the findings and the relative importance of
Mathematics in a any nation educational development
similar studies should be done at the secondary school
levels such as juniors and senior secondary to determine
various form of phobias constituted points to the dismal
performance of students in Mathematics.
Apart from that study should be conducted in other
core subject where dismal performance has been
identified with a view to nip the problem at the scratch
since the cost of prevention is, in most cases, not as
higher as curative. Teachers at the elementary school
should be encouraged not to disseminate unknown
concept as an escape route as it was done as impossible to
the pupils for at least two reasons. The havoc this might
have caused these young ones might not be easy for the
future professional to correct. Secondly, it might be
difficult for even the parent to diffuse the mind of the
young pupils against whatever their teachers teach them
in the classroom as teachers hold premium position in
their mind.
Pupils should be encouraged not only to read over
notes but practice Mathematics and state the level of
understanding relatively to what pupils are doing. Pupils
should be encouraged to be persistent and not over
emphasize the facts that constitute mistakes. Most
powerful learning stems from mistake. One thing that is
well known is that good teachers love the subject they
teach, and when teachers feel negative towards
Mathematics, its transitive effect would manifest in their
pupils and affect them similarly. Children who often like
numbers and Mathematics in public school might develop
'Mathematics anxiety or phobia' or end up disliking
Mathematics if the knowledge facilitators could not make
ACKNOWLEDGEMENT
Researcher seize this opportunity to express
appreciations to all the Mathematics teachers used, some
out-gone sandwich students’ teachers and the Microsoft®
Encarta® 2006 [DVD] in the aspect of literature review.
©The Author(s) 2015. This article is published with open access by the GSTF
49
GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR) Vol.3 No.1, September 2015
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AUTHORS’ PROFILE
Dr. Olaoye Adetunji Abiola is a Faculty Member of Department
of Science and Technology Education, Lagos State University,
Nigeria.
Olaleru, Comfort Temilade is a Faculty Member of Education in
the department of Science and Technology Education at Lagos
State University, Nigeria.
©The Author(s) 2015. This article is published with open access by the GSTF
50