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The use of Cuisenaire Rods on Learners’ Performance in Fractions in Grade 9 in Public High Schools in Chris Hani West District, South Africa.

Authors:
  • University of Fort Hare, South Africa, East London Campus
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The use of Cuisenaire Rods on LearnersPerformance in
Fractions in Grade 9 in Public High Schools in Chris
Hani West District, South Africa.
George Adom, Prof E.O. Adu
Faculty of Education, University of Fort Hare, South Africa.
DOI: 10.29322/IJSRP.10.06.2020.p10215
http://dx.doi.org/10.29322/IJSRP.10.06.2020.p10215
Abstract- This study was aimed at examining the use of Cuisenaire
rods on grade 9 learners’ performance in fractions. Pre-test, Post-
test, and Control group quasi-experimental design was used for the
study. The study group was made up of 250 grade 9 learners’. One
hundred and twenty-five (125) learners were selected into the
experiment group whiles One hundred and twenty-five (125)
learners’ were selected into the control group through systematic
simple random method. The data collected were analysed using
Analysis of Covariance (ANCOVA) to find the Mean, Standard
Deviation and Sample T-test. The mean and standard deviation
were used to compare the pre-test and post-test between the
Experimental group and Control group. The analysed results of the
means, standard deviations and T-tests were used to reject the null
hypotheses. The analysed results of Cuisenaire rods showed that
the pre-test (mean = 8.372, SD=1.770) and post-test (mean =
12,428, SD=4.732), t=13,024 p< 0.05. The hypotheses were tested
at 0.05 level of significance.
Index Terms- Cuisenaire rods, Educators, Fractions, Grade 9,
Learners’.
I. INTRODUCTION
overnments and stakeholders all over the world continue to
devise means and strategies to make the learning of fractions
in mathematics to learners very easy and practical to learners’ in
this modern world (Govan Mbeki Mathematical Development
Unit (GMMDU), 2013). The American Mathematics Society
(AMS) in collaboration with other mathematical organizations
promoted mathematics, science, and research through funding to
create awareness of mathematics education and to project the
mathematics profession (AMS, 2019). Eurydice (2011) asserted
that most European countries have reviewed their mathematics
syllabi, embracing an outcome-based method which was aimed at
developing learners’ competencies and skills rather than on
theoretical approach. This integral approached was focused on an
all-inclusive and flexible in meeting the needs of different levels
of learners’ as well as to their ability to comprehend the tenacity
of mathematics applications in their daily lives.
An assessment conducted by researchers on U.S. Grade 8
learners’ on fraction addition, the results showed that out of the
closest whole number to 12 13
+ 78
(The answer choices were
1; 2; 19; 21 and “I don’t know”) revealed that only 27% got the
correct answer to be (2) (Lortie-Forgues, Tian, & Siegler, 2015).
In a similar vein, the National Assessment of Educational Progress
(NAEP), conducted a test to a sample of U.S grade 8 learners. At
the end of the test, it was observed that only 50% of the
participants could correctly order 27
, 59
, and 112
from the
smallest to the largest (Martin, Strutchens, & Ellintt, 2007).
Siegler and Pyke (2013), observed that in addition and
subtraction of fraction problem, unequal denominator problems
elicited many more errors than equal denomitor ones. Learners’
in grade 6 correctly answered 41% of the problem and 57% of
grade 8 learners’ also correctly answered the problem. Siegler and
Pyke (2013), observed that 6th and 8th graders representing 68%
correctly answered decimal arithmetic problems. Performance
was high on addition and subtraction representing 90% and 93%
respectively but performance of learners’ was lower in terms of
multiplication and division representing 54% and 35%
respectively.
Fraction was introduced to Korean learners’ in grade three,
Japan in grade four to the elementary level whiles in Taiwan,
fraction was introduced to learners’ at grade three with much
emphasised on composition and decomposition of fractions (Son,
2011, Charalambous & Pitta-Pantazi, 2010, Watanabe, 2012). In
addition, East Asian countries used an amalgamation of carefully
selected mathematical materials that have prolonged existence in
terms of their application in demonstrating fractions and also
replicated the idea of fraction as a quantity. The focus was on the
linear model in connection with the bar model which was mostly
used in Japanese fractions instruction as well as Korean and
Taiwanese textbooks. This approached adopted by the East Asian
countries was in variance to the North American approached who
were preoccupied with the ‘pizza model’ or other circular area
models (Son, 2011, Charalambous & Pitta-Pantazi, 2010,
Watanabe, 2012).
Study conducted by (ICMI, 2009) showed that
Mathematics development was very low in Africa due to the few
numbers of secondary school educators teaching mathematics and
also the few number of graduates and post graduates pursuing
mathematics as a course at the masters and PhD levels and above
all the absence of innovations in most of our schools.
Van der Walt et al (2008) and Ndlovu (2011) were of the
view that the abysmal performance of learners in mathematics in
South African could be attributed to lack of inadequate learner
support materials, poor socio-economic background of learners,
G
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medium of instructions, lacked of motivation, poor quality of
educators and inadequate study orientation.
Researchers asserted that, an overwhelming majority of
South Africa learners’ Mathematical knowledge was uncertain.
South African learners’ encountered serious problems related to
Mathematics methodological terminology (Van der Walt, Maree
and Ellis 2008:490). Trends in International Mathematics and
Science Study (TIMSS, 2015) conducted a test in Mathematics
and Science to evaluate the performance of learners in grade Eight
among some selected Africa countries (Tunisia, Egypt, Ghana,
South Africa, Morocco and Botswana). At the end of the
competition, South Africa recorded the lowest mark in Science
and Mathematics (TIMSS, 2015). South Africa learners’ were
rated 30.0% in numeracy and 48.1% in literacy (UNICEF, 2005).
Siegler and Fazio (2010) observed that learners all over the world
were faced with challenges in learning fractions and it was evident
that an average learner never gained an abstract knowledge of
fractions. Many learners and educators were faced with the
challenge of fraction learning in mathematics due to the complex
nature of it. Research showed that learners were confronted with
the tasked of understanding the concept of the subject especially
fractions (Charalambous & Pitta-Pantazi, 2010).
II. RESEARCH OBJECTIVES
The present study aimed to find out the use of Cuisenaire
Rods on Learners’ Performance in Fraction in Grade 9 in Public
High Schools in Chris Hani West District South Africa.
III. HYPOTHESES
The following null hypotheses were tested at 0.05 level of
significance:
H01: There is no significant difference between the Pre-test
and Post-test of the control and experimental group.
H02: There is no significant relationship between
Cuisenaire rods and grade nine learners’ performance in fraction.
IV. RESEARCH QUESTION
What was the effect of Cuisenaire rods on learners’ academic
performance in fraction in grade 9?
V. LITERATURE
The literature of this study was based on what scholars had
written about the use of Cuisenaire rods in the teaching of fractions
both locally and internationally.
5.1 Theoretical framework
The theoretical framework of this study was anchored on
two theories; Cognitive Development theory and Constructivism
theory. Cognitive development theory was the ability to make
intellectual judgement through the process of involving all the
mental faculties (De Witt, 2011) whiles constructivism keenly
involved the collaboration efforts of learners with the educator in
constructing new meaning (Atherthon, 2010).
5.2 Conceptualisation of fraction
Olanoff, Lo and Tobias (2014), opined that fraction was an
aspect of rational numbers which was expressed in the form 𝑎
𝑏
where “a” and “b” were both numerals, and “b” ≠ 0. Fractions was
an aspect of study of rational numbers. In a similar vein Lortie-
Forgues et. al. (2015 p.206) asserted that a fraction was made up
of three components, a numerator, a denominator, and a line
separating the two numbers eg. 12
. Studies showed that for one
to advance in the understanding of the concept of rational numbers
in general, one must undertake a study of different interpretations
of fractions (Lamon, 2007, 2012). Ball (cited in Olanoff et al.
2014 p. 272) asserted that fractions may be inferred to as; (a) in
part-whole terms, where the whole unit may vary; (b) as a number
on the number line; (c) as an operator (or scalar) that could shrunk
or stretched another quantity; (d) as a quotient of two integers; (e)
as a rate; and (f) as a ratio.
Fractions was an essential aspect of mathematics that
formed the bedrock of every learner’s success in the subject as
stipulated by the National Mathematics Advisory Panel (NMAP,
2008). Lortie-Forgues, Tian and Siegler (2015) argued that, the
prominence of fraction and decimal calculation for academic
accomplishment was not restricted to mathematics courses only.
Rational number arithmetic was also ever-present in physics,
chemistry, engineering, psychology, sociology, biology,
economics, and other spheres of studies. Gould, Outhred, and
Mitchelmore (2006), asserted that educators, learners and
academics have typically described fraction learning as a difficult
aspect of mathematics syllabus. Researchers underscored the fact
that learners found it problematic to comprehend the idea of “a
part as a whole” relationship in mathematics.
5.3 Application of manipulative concrete materials in
classroom teaching.
In 2013, the National Council of Supervisors of
Mathematics (NCSM) issued a position statement on the use of
manipulative concrete materials in classroom teaching to develop
learners’ accomplishment in mathematics. “In order to develop
every student’s mathematically proficiency, NCSM recommended
that learners and educators must systematically integrate the use
of concrete and virtual manipulative into classroom instruction at
all grade levels” (NCSM, 2013).
Understanding mathematical skills was very important in
today’s technological world (Burns & Hamm, 2011; Carbonneau,
Marley, & Selig, 2013). Johann Pestalozzi (1746 1827)
influenced educators in the 19th century to use manipulative
concrete materials in teaching number sense at the basic level of
education including basic blocks (Saetter, 1990). Piaget’s
constructivism viewpoint of the 1970s, observed that theoretical
knowledge was established through discovering while using
physical materials rather than through auditory information via
person to person (Piaget, 1973). In this Morden world, there were
a variety of manipulative concrete materials stretching from
virtual computer software programmes to teacher-made materials
(Gaetano, 2014 p.5).
A manipulative concrete material was a physical object that
could be touched, felt, moved around by learners, appealed to the
faculties of the senses and also conveyed a mathematical
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knowledge (Swan & Marshall, 2011). In addition, Cramer and
Henry (2013) asserted that manipulative materials were physical
objects which ranged in size, shape, and colour. They
encompassed physical prototypes such as fraction circles, paper
folding, pie pieces, Cuisenaire rods, fraction bars, dice, and chips
that enabled learners to establish cognitive images of fractions.
However, many scholars were of the view that the use of
manipulative concrete materials does not necessarily warrant the
understanding of mathematical ideas. Researchers were of the
notion that virtual manipulative concrete materials in reality do not
help learners in cultivating mathematical comprehension (Moyer-
Packenham & Westenskow, 2013).
5.4 Cuisenaire rods
Elia, Gagatsis, and Demetrico (2007), asserted that
Cuisenaire rods were hands-on and minds-on physical material
used for mathematical instruction of abstract concepts. It was a
significant mathematical material used for modelling
mathematical concepts of what was taught in the mathematics
classroom and what pertained at homes relating to classroom
experience to everyday life activities. Cuisenaire Rods were
invented over the past nine decades by George Cuisenaire a
Belgian mathematics educator. This distinctive mathematical tool
was to help learners understand abstract mathematical concepts by
manipulating painted wooden strips of different dimensions called
Cuisenaire rods. A package of Cuisenaire rods consisted of 74
rectangular rods in 10cm different dimensions and 10 varied
colours. Each colour related to a particular length. The content of
the pack was made up of 22 white rods of 1cm each, 12 red rods
of 2cm each 10 light green rods of 3cm each, 6 purple rods of 4cm
each, 4 yellow rods of 5cm each, 4 dark green rods of 6cm each, 4
black rods of 7cm each, 4 brown rods of 8cm each, 4 blue rods of
9cm each and 4 orange rods of 10cm each. These rods were used
as physical objects to teach any concept in mathematics
(Kurumeh, 2010).
Figure 5.1: Using Cuisenaire rods to do addition of fractions. (Kurumeh, 2010).
This harmonious interconnection of the senses acted as a
tool to enhance learning and memory. Cuisenaire rods enabled
learners to discover mathematical problems on their own
(Akarcay, 2012). Using Cuisenaire rod teaching approach
prepared learners to meet daily standards with daily critical
thinking activities. It prepared learners for school success in
mathematics and meets the needs of every age group. Cuisenaire
rods enabled every learner to work individually and in groups on
important mathematical contents such as fractions while the
educator offered individual assistance to learners (Akarcay, 2012;
Van de Walle, 2007).
VI. METHODOLOGY
6.1 Research Paradigm
The researcher adopted a positivist research paradigm for
this study. Positivism was often associated with quantitative
research method. Collins (2010), was of the view that positivism
hang on quantifiable interpretations that led themselves to
statistical analysis. The researcher used treatments on
experimental and control groups in the classroom as stipulated by
the positivism theory of laboratory experiment of study.
6.2 Research Design
For this study, the researcher adopted a Pre-test, Post-test,
and Control group quasi-experimental design to determine the
effectiveness of Cuisenaire rods on learners’ academic
performance in fraction in grade nine (9).
6.3 Sample and Sampling Techniques
Two hundred and fifty (250) grade 9 learners whose ages
ranged between 13-16 years and ten (10) educators teaching grade
9 mathematics were selected from 40 public high schools with the
use of stratified, systematic random sampling, convenience and
purposive sampling methods. One hundred and twenty-five (125)
learners were put into the experiment group and another One
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hundred and twenty-five (125) learners’ were put into control
group through systematic random sampling method. One hundred
and two (102) learners were boys and One hundred and forty-eight
(148) learners were girls.
6.4 Data collection procedure
A Fraction Achievement Test (FAT) made up of multiple-
choice objective test of twenty (20) items were used. Each item
had one correct option (key) and three distractors, i.e. options A,
B, C, and D. The content area covered were; Proper fractions,
Improper fractions, Mixed fractions. A Pre-test was administered
to both the experimental group and the control group according to
their codes. The experimental group was then exposed to
Cuisenaire rods in solving different types of fractions with the help
of the researcher and the research assistant whiles the Control
group was not. On the third week, a Post-test was administered to
both experimental and control group. This was done according to
the codes assigned to them in the pre-test.
VII. DATA ANALYSIS
The data collected were analysed using Analysis of
Covariance (ANCOVA) to find the Mean, Standard Deviation and
Sample T-test. The mean and standard deviation were used to
compare the pre-test and post-test between the Experimental group
and Control group. The analysed results of the means, standard
deviations and T-tests were used to reject the null hypotheses. The
hypotheses were tested at 0.05 level of significance.
i). H01: There is no significant difference between the Pre-test and
Post-test of the control and experimental group.
Table 1.1 Summary result of Cuisenaire Rods Manipulative Tool Data Set.
Group
N
Trial
Mean
Min
Max
Controls
125
Pre-test
8.192
0
14
125
Post-test
7.992
1
11
Experiment
125
Pre-test
8.552
2
11
125
Post-test
16.864
12
20
Source: (Field study February, 2019).
Table 1.1, illustrated the descriptive statistics for
Cuisenaire Rods Manipulative Tool. The table showed the mean
scores and standard deviations of the experimental group and the
control group in the Pre-test (mean =8.552, SD=1.794) and
(mean =8.192, SD=1.735) respectively. The pre-test scores
showed that, there was no significant difference in the mean scores
and standard deviation between the experimental group and the
control group in the Pre-test. This could suggest that the initial
competencies of the two groups in fractions were equivalent prior
to the study. However, the mean scores and standard deviation of
the experimental group and control group in the Post-test were as
followed (mean =16.864, SD= 1.820) and (mean = 7.99,
SD=1.406) respectively. There was vast disparities in the mean
scores and standard deviation in the Post-test between the
Experimental Group and Control Group. (p < 0.05) therefor
hypothesis (H01) is rejected. The difference in the mean and
standard deviation scores could be attributed to the effects of
Cuisenaire Rods on the Experimental Group.
ii). H02: There is no significant relationship between Cuisenaire
rods and grade nine learners’ academic performance in fraction
Table 1.2: Shows the Paired Samples Statistics (N= 250)
Pair
Mean
Std. Deviation
Std. Error Mean
Cuisenaire rods manipulative
Post-test
12.428
4.732
.299
Pre-test
8.372
1.770
.112
Source: (Field work February, 2019).
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Table 1.2: Shows a Paired Samples Test from
Pair
Paired Differences
t
df
Sig.
(2-
tailed)
Mean
Std.
Deviation
Std. Error
Mean
95% Confidence Interval of the
Difference
Lower
Upper
Cuisenaire rods
manipulative Post-test -
Pre-test
4.056
4.924
.311
3.443
4.669
13.024
249
0.000
Source:(Field work February, 2019).
Mean
Std.
Deviation
Effect size
4.056
4.924
0.82
Effect size
To prove that there was a significant relationship between
Cuisenaire rods and grade nine learners’ performance in fractions,
the pre-test and post-test mean and standard deviations scores of
Cuisenaire rods were compared using sample paired t-test. Table
19 showed the Pre-test and Post-test mean and standard deviation
of Pre-test scores (mean =8.372, SD=1.770) and Post-test
scores (mean =12,428, SD=4.732) respectively. The scores
indicated that, there were increased in the mean scores and
standard deviation of the Post-test. The t-test (t=13,024, p < 0.05)
indicated that there was a significant relationship between
Cuisenaire rods and grade nine learners performance in fractions
therefore the null hypothesis (H02) was rejected.
VIII. CONCLUSION
The study showed that Cuisenaire rods have a great effect
on learners’ academic performance in fraction. Cuisenaire rods as
a manipulative concrete material has aided learners’ to discover
solutions to mathematical problems involving fractions, motivate
learners’ to work independently and in groups and also enhanced
learners’ understanding of fractions. Elia, Gagatsis, and Demetrico
(2007), suggested that Cuisenaire rods are hands-on and minds-on
physical material used for mathematical instruction of abstract
concepts and made mathematics real to learners. In support
(Akarcay, 2012) alluded to the fact that Cuisenaire rods enabled
learners to discover mathematical problems on their own.
Cuisenaire rods motivate every learner to work individually and in
groups on important mathematical contents such as fractions while
the educator offered individual assistance to learners (Akarcay,
2012; Van de Walle, 2007). Cuisenaire rods made mathematics
real to learners since it was learner friendly, activity oriented, and
stimulated learners’ comprehension of the mathematical concepts
and facilitated higher understanding of mathematical concepts,
facts and principles Kurumeh (2010).
IX. RECOMMENDATIONS
1. Learners’ ought to use Cuisenaire rods frequently in their
mathematical lessons so that they would be abreast with
it and also increased their understanding in fractions.
2. Mathematics educators should ensure that they
incorporated Cuisenaire rods in their mathematical
instructions.
3. Educators ought to motivate and sustained the interest of
their learners’ during mathematics instruction by the use
of different teaching methods. Mathematics class must be
learner centred and not teacher centred form of
instruction.
4. Principals ought to ensure that there were adequate
manipulative concrete materials in their schools to
enhance the teaching and learning of mathematics.
5. It was obligatory for the Department of Education to
ensure that every school was well resourced with
manipulative concrete materials to enhance the
mathematical proficiency of the learners’.
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AUTHORS
First Author Adom George, University of Fort Hare, East
London Campus, South Africa, Email:
georgeadom90@gmail.com
International Journal of Scientific and Research Publications, Volume 10, Issue 6, June 2020 116
ISSN 2250-3153
This publication is licensed under Creative Commons Attribution CC BY.
http://dx.doi.org/10.29322/IJSRP.10.06.2020.p10215 www.ijsrp.org
Second Author Second Author Prof. E.O Adu, University of
Fort Hare, East London Campus, South Africa. Email: eadu@ufh.ac.za
... It has led to a renewed attention to equational reasoning. Some of this activity builds explicitly on the pioneering work of Caleb Gattegno and his collaborators working with Cuisenaire rods in the 1950's (Mason, 2008;Benson, 2011;Goutard, 2017;Adom and Adu, 2020). Other researchers, working from first principles, have independently discovered many of Gattegno's findings especially those relating to the central importance of early algebra, pattern making, and mathematical equivalence (Davydov, 1962;Kaput, 1995a,b;Healy et al., 2002;Schmittau and Morris, 2004;Carraher et al., 2005;Schliemann et al., 2007;Baez, 2009;Mulligan and Mitchelmore, 2009;Blanton and Kaput, 2011;Cai and Knuth, 2011;Empson et al., 2011;McNeil et al., 2011;Rittle-Johnson et al., 2011;Kieran et al., 2016;Gadanidis et al., 2018;Kieran, 2018;Matthews and Fuchs, 2018;Simsek et al., 2021). ...
... These encourage the learner to pay attention to the relationship between quantities. They give rise to a substantial experience with integers and rational numbers Gattegno, 1953, 1962;Gattegno, 1959Gattegno, , 2010aGattegno, , 2011aBenson, 2011;Goutard, 2017;Adom and Adu, 2020). ...
... Ellis (1964) doesn't mention p-values, T or F statistics or standard error of difference so we were not able to recover the standard deviation. Adom and Adu (2020) reported an effect size of 5 with a T2X standard deviation more or less the same as the T1X data. Since the standard deviation is normally proportional to the mean, and the mean doubled we . ...
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