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A study of students' achievement in algebra: Considering the effect of gender and types of schools

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Algebra is a branch of mathematics that deals with symbols and also the rules for manipulating those symbols, which are used to represent numbers and quantities in mathematical formulae and equations. It is needed and used in our everyday lives. The purpose of this study was to examine students' performance in algebra related to gender and types of schools.The research sample consisted of 317 students (135 boys and 182 girls) from three types of schools in Malaysia ie; national schools, Islamic-religious schools and boarding schools. Data were collected through an instrument known as the Algebra Achievement Test (AAT), and were then analyzed quantitatively using a two-way ANOVA test. Research findings showed that there were statistically significant main effects for gender and types of schools towards students' achievement in algebra. However, no interactional effects were found between gender and types of schools that could influence the results obtained.It is concluded that gender and types of schools do effect students' achievement in algebra.
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European Journal of STEM Education, 1:1 (2016), 19-26
Copyright © 2016 by Lectito BV, Netherlands
ISSN: 2468-1954
*Correspondence to: salmiza@usm.my
A study of students' achievement in algebra:
Considering the effect of gender and types of
schools
Salmiza Saleh1* & Muhamad Asyraf Abdul Rahman1
1 Universiti Sains Malaysia, MALAYSIA
ABSTRACT
Algebra is a branch of mathematics that deals with symbols and also the rules
for manipulating those symbols, which are used to represent numbers and
quantities in mathematical formulae and equations. It is needed and used in
our everyday lives. The purpose of this study was to examine students’
performance in algebra related to gender and types of schools.The research
sample consisted of 317 students (135 boys and 182 girls) from three types of
schools in Malaysia ie; national schools, Islamic-religious schools and
boarding schools. Data were collected through an instrument known as the
Algebra Achievement Test (AAT), and were then analyzed quantitatively
using a two-way ANOVA test. Research findings showed that there were
statistically significant main effects for gender and types of schools towards
students’ achievement in algebra. However, no interactional effects were
found between gender and types of schools that could influence the results
obtained.It is concluded that gender and types of schools do effect students'
achievement in algebra.
Keywords
earth, rock,
middle school (ages 11-14),
vocabulary,
discourse
Received:
Revised:
Accepted:
Published online:
3 Feb 2016
10 Feb 2016
02 Mar2016
DOI: 10.20897/lectito.201603
INTRODUCTION
Algebra has always been one of the main subjects in mathematics the world over. This fact is concurred by
65 countries around the world which participated in the Programme for International Student Assessment
(PISA), including Malaysia. This is probably due to the fact that algebra is the door to the extension of complex
arithmetic articulations, and a progression leap from concrete to abstract concepts in learning mathematics
(Skouras 2014). The placement of algebra, as subject of study in mathematics within a school’s syllabus, might
be different as some countries might offer it in an integrated syllabus, while others might employ it as unified
body strands within their mathematics curriculum, like algebra, arithmetic and geometry.
In Malaysia, algebra is integrated into the mathematics syllabus via chapters. It is first introduced to students
at the primary school level, and the syllabus progresses into the more comprehensive and advanced stages at
the secondary school level. To ensure proficiency in mathematics, students generally have to sit for mathematics
classes for at least four to five periods a week. However, regardless of the fairly well thought of syllabus, the
Malaysian average mathematics output, as found by the Trends in International Mathematics and Science Study
(TIMSS), was still lags far behind other Asian nations such as Japan, Hong Kong, Korea and also Singapore
(Mullis et al. 2004). Furthermore, Malaysia has never performed well in mathematics in PISA, and is known as
one of the worst performers in 2012, when it ranked below 50, together with countries such as Columbia, Peru
and Albania. In addition, the analysis of TIMSS-2007 showed that Malaysia scored the lowest, with only 24%
and 2.1 points, which ranks far below the International Average Score, set at 34% with 0.3 points, and has to
European Journal of STEM Education, 1:1 (2016), 19-26
20 © 2016 Lectito BV
settle for the last place, even below Thailand and Indonesia. In the Malaysian context, the condition gets worse,
as there is a lack of data for researchers to further investigate the factors affecting mathematics achievement,
especially at the secondary school level (Lim & Saleh 2002; Lim 2003).
This has led to more interest in many parties to investigate students’ achievement in mathematics, as the
subject has always been correlated with greater chance of employment, better wages and higher on-the-job
productivity (Geary & Hamson 2000). With that reason, it is significantly important to recognize the factors
that affect students’ mathematics achievement, in order to make good progression and prediction for the future,
relating to mathematical decisions. However, this paper will focus only on equity, in relation to two dimensions:
gender and types of schools.
LITERATURE REVIEW
Each student is unique in terms of acquiring knowledge in learning. In terms of results, student performance
may be poor, not necessarily because they do not have the skills, but more to the fact that they have not been
able to optimize their skills (Bandura 1977). Some said that it is important to measure student achievement in
mathematics, as their achievement in high school can have a direct and influential effect on their mathematics
performance at the tertiary level (Ismail & Awang 2007). Furthermore, according to the Centre for the Study
of Testing, Evaluation, and Educational Policy (SCTEEP) at Boston College, a test in mathematics is also used
to describe students’ overall achievement in a non-hierarchical way. Hence, assembling a student’s overall
results may just be the right kick start needed to assess and elicit a wider range of skills from students, in algebra.
As previously mentioned, it has been found that Malaysian students’ achievement, particularly in the subject
of mathematics, is on a heavy decline. Analysis showed that in TIMSS-1999, Malaysia was placed 10th out of 38
participating countries, with an average score of 519 points. It was the highest place that Malaysia has ever
reached, as it then flunked to 16th out of 46 countries in TIMMS-2003, with an average score of 508 points,
before falling down further to 20th place out of 50 participating countries in TIMSS-2007, with a score of 474
points. The downward spiral got worse in TIMSS-2011, when Malaysia stumbled to 26th place with 440 points,
and continued its decline in PISA 2012, when it ranked 57th place in mathematics, out of 74 countries which
took part in the examination.
It is an irrefutable fact now that Malaysian students are facing a problem in mathematics proficiency, and
much can be said about their achievement in mathematics, compared to their counterparts worldwide, and even
within neighboring countries. The disparity is obvious, when comparison is made with Singapore, our closest
neighbor. Ismail and Awang (2008) found that more than 50 percent of students in Singapore scored higher
than the average score of 603 in TIMSS-2003, compared to only 10 per cent of student in Malaysia who
managed to do so in the same exam. By comparing the contents tested in TIMSS, such as geometry,
measurement, fractions and algebra, researchers found out that Singaporean students have always scored
significantly higher than Malaysian students, regardless their gender. Results also showed that girls have always
outperformed boys in every area tested, with girls averaging a mean of 53.0, while boys generally hover around
the mean of 47.0.
Based on the secondary data of TIMSS-1999, Ismail and Awang (2007) found that there was a significant
difference between Malaysian boys’ and girls’ performance. The research shows that out of 5,577 Malaysian
students (girls - 55.2 per cent, boys - 44.4 per cent) involved in TIMSS-1999, aging on average of around 14.4
years old, with a standard deviation of 0.36, girls outperformed boys in mathematics. Four years later, using the
same procedures, Ismail and Awang (2011) once again found out that girls (M = 479.88, SD=75.94) still scored
better than boys (M = 468.27, SD = 80.37) in their test. The results were analyzed using data from TIMSS-
2007, which involved 4,466 students from 150 schools in Malaysia. This finding was consistent with the results
obtained from TIMSS-2007 participating countries such as Serbia, Macedonia, Armenia, Moldova, Singapore,
Philippines, Cyprus, Jordan and Bahrain (Ismail & Awang 2008; Mullis et al. 2008) This pattern continuously
shows that girls consistently score higher than boys in mathematics in a stable manner, most everywhere around
the globe.
Likewise, in the context of students’ perceptions towards the mathematics classroom environment and
mathematics achievement, Rajoo (2013) also found that girls performed better than boys. Using 445 students
as his research sample, Rajoo (2013) found that girls tend to be more involved (more active and joyful) during
mathematics lessons, as compared to boys. In relation to that, a study conducted by Abd. Razak, Thien and
Darmawan (2014) found that there was also a significant relationship between teachers’ gender and eighth grade
student achievement in mathematics. In their research entitled “Relationship of Students and Classroom-level
Variables with TIMSS 2011 Mathematics Achievement in Indonesia, Malaysia and Thailand”, it was found that
Saleh & Rahman / A Study of student’s achievement in algebra
© 2016 Lectito BV 21
teachers’ gender had a significant impact towards eighth grade student achievement in mathematics.
Furthermore, when students’ scores were correlated with teachers’ gender, in the context of Malaysia, the results
also showed that female teachers taught better than male teachers. However, unlike the previous studies,
Ainuddin Dahlan et al. (2010) found that there was no significant difference between boys and girls
achievements in four national schools in Kuala Lumpur, in terms of mathematics results in the Lower-
Secondary National Examination (PMR).
Besides gender, studies also show that school types also effect students’ achievement in mathematics
(Lubienski & Lubienski 2006; Newhouse, 2006; Lubienski, Lubienski & Crane 2008; Esposito 2010). In the
context of Malaysia, there are many different types of schools that have been set up to cater to the different
needs and levels of students nationwide. Among the mainstream schools are national schools and national-type
of schools (open to all residents, regardless of race, religious beliefs and gender), boarding schools (special
school for selected high achievers), and Islamic religious schools (to Muslims who want to learn more about
the teaching of Islam). It is a well known fact that boarding school students have always scored high marks in
mathematics (particularly in the Malaysian standard examinations) compared to students from other schools
(Nordin, et al. 2003). National and national-type rural schools students, on the other hand are generally left
behind in terms mathematics achievement (Baharun et al. 2008). As elements in Islam are manifested through
various aspects of the educational system (Joseph, 2008), the number of Islamic religious school is also on the
rise. However, there is not much research done pertaining this type of school in the country. Although previous
studies show that generally, students from religious schools perform better than those from public and private
schools (Chubb & More 1990; Jeyness 2002, 2008; Nordin et al. 2003), this fact cannot yet be corroborated in
Malaysia. There is lack of data available in relation to the comparison of students’ academic achievement among
different types of schools in Malaysian, as the issue is seen as ‘sensitive’ by the Malaysian Government (Joseph
2006, 2008).
RESEARCH QUESTION
What are the effects of gender and types of school on student’s achievement in algebra?
a. Is there a significant main effect in terms of student’s achievement in algebra between boys and girls?
b. Is there a significant main effect in terms of students’ achievement in algebra amongst national schools,
religious schools and boarding schools?
c. Is there a significant interaction effect between gender and types of schools in terms of students’
achievement in algebra?
METHODOLOGY
This research adopted a survey research design to collect the required data. Purposive sampling technique
has been used to select the schools and students. A total of 317 students (see Table 1) from 12 schools (four
national schools, four Islamic religious schools and four boarding schools) with the similar status (government
aided high performing school) were required to complete a test known as the Algebra Achievement Test (AAT)
within 60 minutes, administered during the school hours. The AAT consisted of 30 multiple-choice questions
(5 questions on knowledge, 17 questions on concept and 8 questions on higher order thinking skills). Data
obtained were then analyzed quantitatively using Two-Way ANOVA analysis.
RESULTS
What are the effects of gender and types of schools on students’ achievement in algebra?
Table 2 shows mean and standard deviation for gender in national schools, religious schools and boarding
schools. Table 2 shows that the total mean score for boys (M = 20.73, SD = 4.82) is lower than the total mean
Table 1. Number of samples for national school, religious school and boarding school
Types of schools
Girl
Boy
Total
National school
67
39
106
Religious school
59
47
106
Boarding school
56
49
105
Total
182
135
317
European Journal of STEM Education, 1:1 (2016), 19-26
22 © 2016 Lectito BV
score for girls (M = 22.02, SD = 4.22). Regardless of the types of schools, it can be concluded that girls (N =
182) outperform boys (N = 135) in algebra achievement in each school.
Table 3 shows results for Levene’s test of equality of error variances. The significant (p) value is 0.03 (>
0.01), implies that the assumption for homogeneity of variance is not violated. Therefore, it can be said that
each school and gender has equal variance in the mean scores of algebra.Table 4 shows results for the test of
between-gender and types of schools effect.
Is there a significant main effect in terms of students’ achievement in algebra between boys and
girls?
Alternative hypothesis: There is a significant difference in terms of students’ achievement in algebra
between boys and girls.
Table 4 shows that there is a statistically significant main effect for gender [F (1,311) = 10.83, p = 0.00].
Although the effect size for gender is small, with eta squared value 0.03 (Cohen, 1988), it gives significant
impact to a large sample (in this case, N = 317) (Pallant 2001). Thus, the alternative hypothesis cannot be
rejected due to the p-values results (0.00 < 0.01). Hence, there is a significant main effect in terms of students’
achievement in algebra between boys and girls.
Is there a significant main effect in terms of students’ achievement in algebra amongst national
schools, religious schools and boarding schools?
Alternative hypothesis: There is a significant difference in terms of students’ achievement in algebra
amongst national schools, religious school and boarding school.
Table 4 shows that there is a statistically significant main effect for schools [F (2, 311) = 25.57, p = 0.00].
The effect size for schools is considered as large (eta squared = 0.14). Thus, the alternative hypothesis cannot
be rejected due to the p-values results (0.00 < 0.01). Hence, there is a significant main effect in terms of students’
achievement in algebra amongst national schools, religious schools and boarding schools.
Table 2. Mean and standard deviation for gender in national schools, religious schools and boarding schools
Gender
School
Mean
Std. Deviation
N
Boy
National school
18.72
4.40
39
Religious school
20.36
4.32
47
Boarding school
Total
22.67
20.73
4.95
4.82
49
135
Girl
National school
20.10
4.60
67
Religious school
21.88
3.46
59
Boarding school
Total
24.46
22.02
3.17
4.22
56
182
Total
National school
19.59
4.56
106
Religious school
21.21
3.92
106
Boarding school
23.63
4.17
105
Total
21.47
4.53
317
Table 3. Levene's Test of Equality of Error Variances
F
df1
df2
Sig (p)
2.52
5
311
.03
*The mean difference is significant at 0.01 level
Table 4. Tests of between-gender and types of schools effect
Source
Types III Sum of
Squares
Df
Mean Square
F
Sig.
Partial Eta
Squared
Noncent.
Parameter
Observed
Power
Corrected Model
1061.08
5
212.22
12.20
.00
.16
60.98
1.00
Intercept
140410.29
1
140410.29
8068.83
.00
.96
8068.83
1.00
Gender
188.47
1
188.47
10.83
.00
.03
10.83
.76
School
889.84
2
444.92
25.57
.00
.14
51.14
1.00
Gender * School
2.17
2
1.09
.06
.94
.00
.13
.01
Error
5411.89
311
17.40
Total
152598.00
317
Corrected Total
6472.97
316
*The mean difference is significant at 0.01 level
Saleh & Rahman / A Study of student’s achievement in algebra
© 2016 Lectito BV 23
Is there a significant interaction effect between gender and types of schools in terms of students’
achievement in algebra?
Alternative hypothesis: There is an interaction effect in terms of students’ achievement in algebra between
gender and types of schools.
Table 4 shows that there is no statistically significant interaction effect gender*schools [F (2, 311) = .06, p
= 0.94]. The profile plot is shown in Figure 1. Therefore, the alternative hypothesis is rejected (p-value = 0.94
> 0.01). It can be concluded that there is no interaction effect in terms of students’ achievement in algebra
between gender and types of schools.
DISCUSSION
The results show that boarding schools’ students (both boys and girls) outperform Islamic religious schools’
and national schools’ students in algebra achievement. Boarding schools’ students obtain the highest mean
score in the test administered, followed by Islamic religious schools’ students and national schools’ students.
This may be due to the reason that boarding schools generally induct the best students and offer the most
conducive learning environment, compared to the Islamic religious schools and national schools. Compared to
national schools, the Islamic religious schools also take in better students and present a more conducive learning
environment than national schools.
On the overall, it was found that girls (M = 22.02, SD = 4.22) outperform boys (M = 20.73, SD = 4.82) in
terms of achievement in algebra, in all types of schools. Results obtained are parallel with the findings of Ismail
and Awang (2007, 2012), Alkhateeb (2001), the US Department of Education, National Center for Education
Statistic (2001), Mullis et al. (2008) and Rajoo (2013). However, the results are inconsistent with the findings of
the American Institute of Research (2005), which found that boys perform better in things related to application
problems.
The results are also in line with Freeman’s (2005) findings, in which girls are found to develop greater
confidence in their abilities to adopt with mathematical concepts and merge well with curriculum and
assessment methods. Boys seem to understand the concepts of algebra faster than girls. However, girls often
outperform boys as they tend to immerse themselves in practices and homeworks in order to polish their
understanding about abstract concepts. Moreover, boys generally seem to view that doing homework as non-
masculine-like (or feminine-like), and thus explains the reason why girls tend to become more superior in
algebra, as compared to boys (Ainuddin Dahlan et al. 2010).
Moreover, this research finding is correlated with the research done by Ainuddin Dahlan et al. (2010), which
found that even though boys have advantages in spatial and mathematical abilities, girls have always been
consistent in adopting themselves with the curriculum. Besides, girls can most often tolerate lengthy lectures
Figure 1. Profile plot for interaction effect between gender and types of schools
European Journal of STEM Education, 1:1 (2016), 19-26
24 © 2016 Lectito BV
(traditional approach) given by the teacher, as the lower level of testosterones in their body makes it possible
for them to adopt with this type of instruction, and as a result, excel more in mathematics. Compared to boys,
girls also favor learning that involves solving problems related to real world situations, thus making them
perform better in examinations.
Apart from that, girls also seem to outperform boys because the teacher-gender ratio is imbalanced at
schools in Malaysia. Research by Abd. Razak, Thien and Darmawan (2014) showed that students who were
taught by female teachers scored higher in eighth grade mathematics test, compared to those who were taught
by male teachers. At the moment, according to the Educational Management Information System [EMIS]
(2014), there is a huge gap between female teachers (127,030) and male teachers (55,385) at the secondary
school level in Malaysia. This explains the reason for the learning style and curriculum at schools, which is more
female-biased, where the interaction effect between teacher-gender and students’ achievement has been found
significant (Dee, 2006). On the contrary, the current findings also disagree with the research findings by
Antecol, Eren and Ozbeklik (2012), which found that female teachers will lead to poorer results in mathematics
among girls, not boys.
CONCLUSION AND IMPLICATION
This study has found that there is (i) a significant main effect in terms of students’ achievement in algebra
between boys and girls, (ii) a significant main effect in terms of students’ achievement in algebra amongst
national schools, religious schools and boarding schools, and (iii) no interaction effect in terms of students’
achievement in algebra between gender and types of schools.
The findings of this study provide direct implications on the implementation of mathematics education in
Malaysia, especially at the secondary level. There are several things that can be addressed in the context of
student interest in mathematics. The Malaysian Ministry of Education (MOE) policy-makers should focus on
the fair distribution of educational resources, particularly for the national and Islamic religious schools.
Undoubtedly, teachers must also have the credibility and the responsibility to educate mathematics as equally
fair as they can, without being biased towards any gender. And, ultimately, the school environment should also
be cultivated towards fostering students’ interest in mathematics more, as the benefits of this far outweigh other
types of improvements for the students’ future in the real world. Conclusively, the implications of this research
could serve as referral data for the Malaysian Ministry of Education (MOE), to enable them to better monitor
the gaps in terms of students’ mathematics achievement amongst national schools, religious schools and
boarding schools. Furthermore, educators should also be more creative and active in teaching mathematics, to
ensure a more meaningful and fruitful participation of both boys and girls in learning process. Gender-
imbalance in achievement at schools, if not remedied properly, may contribute to a wide gender gap, especially
in terms of university enrollment, at the tertiary level.
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... Studies by Asoma et al. (2022) showed that contexts appeared to influence the solution paths when solving Mathematical word problems. On the contrary, Saleh and Rahman (2016) reported no significant differences in contextualized word problems. However, Arnawa et al. (2019) found differences in gender ability in problem-solving. ...
... Thus, the critical P-value obtained (.960, 2-tailed) was greater than the alpha level of .05 and the confidence interval included 0, indicating that the difference in mean scores between male and female students was not statistically significant. Therefore, the researchers failed to reject the null hypothesis and concluded that there were no statistically significant differences between males and females in terms of their ability to solve algebraic word problems (Saleh & Rahman, 2016). The results in Table 5 show that some students were not attempting some test items, indicating a lack of confidence or understanding of the concepts involved. ...
... On the contrary, Saleh and Rahman (2016) reported no significant increase in student achievement when mathematical word problems were contextualized. This argument notwithstanding, Pratiwi and Widjajanti (2020) showed many students neither master the mathematical context nor the real-life context of the problem. ...
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... Considering that algebraic representation of arithmetic content involves writing one expression after another, or simpler equations equivalent to another equation, and similar aspects, it turns out that the presence of clear and systematic notes of algebraic representations of concepts means much more to female students compared to male students. The research results of Saleh & Rahman (2016), which indicate better achievements of female students in algebra compared to male students, provide additional confirmation of this conclusion. ...
... Another difference in the attitudes of students of different genders concerns the importance of using a pen tablet in the implementation of arithmetic mathematical content because solving these tasks step by step with appropriate algebraic notation is something students, especially female students, are accustomed to in regular mathematics classes that take place in face-to-face school environments. This attitude of female students can be linked to their higher levels of achievement in working with algebra content, confirming the findings of earlier studies (Murugan & Rajoo, 2013;Saleh & Rahman, 2016). ...
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... Rahman and Saleh, on the other hand, conducted research (N = 317) on students' performance in algebra content. The data suggest that students from Islamic boarding schools had the highest average score, followed by students from Islamic religious schools and national school pupils (Saleh & Rahman, 2016). This at least demonstrates that children from Islamic boarding schools perform good academically. ...
... This is why this variable has no impact on working memory systems. According to research (Saleh & Rahman, 2016) Islamic boarding school pupils are better at algebra. This finding surely inspires educators to further reformulate learning in order to maximize the potential of pupils, particularly those in Islamic boarding schools. ...
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... Earlier studies involving TIMSS data mostly concentrated on separate examination of the factors influencing mathematics achievement or science achievement (Caponera & Losito, 2016;Eriksson, Helenius & Ryve, 2019;Geesa et al., 2019;Henry, Nistor, & Baltes, 2014;Ismail et al., 2018;Lay & Chandrasegaran, 2016;Mohtar et al., 2019;Mokshein, 2012;Mubarak & Abdul Razak, 2017;Saleh & Abdul Rahman, 2016). For example, Geesa et al. (2019) explored the influence of home resources and attitudes towards mathematics and mathematics achievement in South Korea, Turkey, and the United States while Saleh and Abdul Rahman (2016) examined the effects of gender and school type on students' achievement in algebra. ...
... Earlier studies involving TIMSS data mostly concentrated on separate examination of the factors influencing mathematics achievement or science achievement (Caponera & Losito, 2016;Eriksson, Helenius & Ryve, 2019;Geesa et al., 2019;Henry, Nistor, & Baltes, 2014;Ismail et al., 2018;Lay & Chandrasegaran, 2016;Mohtar et al., 2019;Mokshein, 2012;Mubarak & Abdul Razak, 2017;Saleh & Abdul Rahman, 2016). For example, Geesa et al. (2019) explored the influence of home resources and attitudes towards mathematics and mathematics achievement in South Korea, Turkey, and the United States while Saleh and Abdul Rahman (2016) examined the effects of gender and school type on students' achievement in algebra. Contributing factors of science achievement using TIMSS data were studied by Mokshein (2012), Lay and Chandrasegaran (2016), Mubarak and Abdul Razak (2017), and Ismail et al. (2018). ...
... These include policies and interventions to improve access to high-quality education, reduce socioeconomic segregation, foster inclusive school environments and address the root causes of social inequalities. Gender differences have been observed in different subjects, including mathematics (Ajai & Imoko, 2015;Saleh & Rahman, 2016). As scholars work to address the underrepresentation of girls at the senior school level of mathematics, gender disparities in mathematics achievement have become a significant concern (Asante, 2010). ...
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... Studies conducted in Nigeria show that poor achievement of students in linear algebraic expressions is the main reason for failure in mathematics, especially at junior secondary schools (Banerjee and Subramaniam, 2012;James and Adewale, 2015;Salmiza and Muhamad, 2016;Marilou and Charita 2022). Learning of linear algebraic expression requires the students to actively participate in constructing knowledge, which could lead to creativity and high cognitive reasoning. ...
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... Since decades ago, algebra is used in our daily lives to represent numbers and quantities in mathematical formulae and equations (Kilpatrick & Izsak, 2008;Saleh & Rahman, 2016). Algebra is also a gate-keeper course determining for entry into most colleges and whether the students can go on to the higher-level STEM courses (Remillard et al., 2017). ...
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