


































Frontiers of Contemporary Education 
ISSN 2690-3520 (Print) ISSN 2690-3539 (Online) 

Vol. 4, No. 3, 2023 

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1 
 

Original Paper 

Differentiating Instruction in a Mathematics Classroom: Its 

Effects on Basic 7 Learners’ Academic Performance and 

Engagement in Common Fraction 

Edward Abatanie Padmore
1
, Joseph Kafui letsa-Agbozo

2
, Gabina Susuoroka

3* 
& Dennis Offei Kwakye

4
 

1
 Nusrat Jahan Ahmadiyya College of Education, Department and mathematics and ICT, Wa, Ghana 

2
 Akatsi College of Education, Department of Mathematics and ICT Education, Akatsi, Ghana 

3
 University Business Integrated Development Studies, Department of Business Education, Wa, Ghana 

4
 FMS, Fairmont, NC, Department of Mathematics, USA 

*
 Gabina Susuoroka, University Business Integrated Development Studies, Department of Business 

Education, Wa, Ghana  

 

Received: August 6, 2023     Accepted: August 23, 2023    Online Published: September 12, 2023 

doi:10.22158/fce.v4n3p1                URL: http://dx.doi.org/10.22158/fce.v4n3p1 

 

Abstract  

Differentiated instruction is a method that can be utilised to help learners with different characteristics 

master mathematics in every area covered. In this paper, a pre-test and post-test quasi-experiment 

design was used. The participants in this study were 83 students chosen at random from basic 7. This 

includes 41 students in the experimental group and 42 students in the control group at St Andrew’s 

Junior High School in Wa, Ghana’s Upper West Region. The learners were thoroughly matched based 

on their learning styles and numerous intelligences. The pre-test was used to assess learners’ academic 

performance prior to the intervention, and the post-test was used to see if there was a difference in the 

effect of differentiated instruction versus non-differentiated instruction between the control and 

experimental groups. The study looked into common fractions, specifically converting improper 

fractions to common fractions, converting mixed fractions to improper fractions, and solving problems 

requiring fraction addition and subtraction. According to the findings of the study, learners in the 

experimental group had interactive, analytic, and introspective learning styles. The experimental group 

has (differentiated class) and the control group’s (non-differentiated class) pre-test mathematical 

achievement was comparable to “low”, however, their critical thinking skills were “unreflective”. 

Post-test results, on the other hand, show that the experimental group (differentiated class) has “high” 

mathematics achievement and “developing” critical thinking skills, whereas the control group 



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(non-differentiated class) has “average” post-test mathematics achievement and “developed” critical 

thinking skills. The experimental group outperformed the control group in terms of pre-test and 

post-test mean improvements in mathematics achievement and critical thinking skills. As a result, the 

article recommended that practitioners understand the components of differentiation in order to 

develop lessons that meet the requirements of all learners. Mathematics facilitators must attend 

workshops and seminars on a regular basis to keep their knowledge and abilities in differentiated 

instruction up to date.  

Keywords 

Differentiated Instruction, fractions, facilitators, learners experimental, control   

 

1. Introduction  

In this century, facilitators are urged to use diversified instruction approaches in the classroom to 

accommodate the varying requirements of all learners from various cultural and social backgrounds. 

Differentiated instruction is a practice that focuses on learners and seeks to reduce inequities and 

discrepancies between individuals due to their diverse learning styles, abilities, and skills (Chamberlin 

& Powers, 2010). Differentiated instruction is a teaching technique that implies each classroom has a 

diverse set of students who may be reached via a range of methods and activities. Differentiated 

instruction detects individual students’ requirements and adjusts the classroom to fit those needs. No 

two students are alike because they learn at different rates. Based on this notion, variable instruction is 

a teaching and learning strategy that gives students with a range of ways to absorb knowledge and 

make sense of topics. Differentiated instruction is founded on the premise that educational approaches 

in the classroom should alter and adapt to the needs of individual and diverse students. Instead of 

expecting students to adapt to the curriculum, differentiated instruction demands teachers to be flexible 

in their approach to teaching and to modify the curriculum and presentation of content to learners 

(Tomlinson, 2013). The implementation of the basic curriculum in Ghana to improve junior high 

school mathematics learning and the investigation by Muthoni and Mbugua (2014) on the effects of 

differentiated instruction on student’s achievement in mathematics revealed that differentiated 

instruction significantly improved students’ achievement in mathematics when compared to traditional 

instruction.  

Differentiated instruction has existed for quite some time. Facilitators have to think outside the box in 

order to satisfy the requirements of all learners, regardless of age or aptitude. Differentiated instruction 

allows facilitators to draw on best practices to reach all learners. To improve learning in mixed-ability 

classrooms, this approach employs grouping strategies, brain-based learning methodologies, and 

current research on multiple intelligences.  

 

 

 



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Facilitating fractions with differentiated instruction at the fundamental level can make a significant 

difference. Some students struggle to understand fraction concepts such as equivalent fractions, 

comparing fractions, mixed numbers, and adding fractions. This could be due to a few inadequacies in 

their fundamental understanding of fractions in general. Allow these students to study content from 

prior stages in order to get a better knowledge of fractions as parts of a whole and fractions as parts of a 

group. While the high-achieving students in class frequently complete third-grade fraction tasks 

quickly, they begin to show signs of boredom if they are not appropriately challenged. Allow these 

types of learners to participate in lesson extension activities and study more complex fraction ideas to 

differentiate instruction. 

1.1 Problem Statement  

Several studies investigated differentiated mathematics instruction. Numerous research has been 

conducted to evaluate the effects of differentiated education on academic achievement and other 

characteristics. Significant disparities in outcomes were discovered (Aranda & Zamora, 2016; Muthomi 

& Mbugua, 2014; Konstantinou-Katzi et al., 2013; Lewis, 2013; Stager, 2007). The majority of studies 

discovered that modifying instruction based on learning needs, scaffolding, and flexible grouping 

resulted in improved performance among learners (Williams, 2012; Thorton, 2012; McAdamis, 2001). 

Recent research has also demonstrated the effectiveness of using tailored instruction in the mathematics 

classroom. According to Awofala and Lawani (2020), differentiated instruction improves pupils’ maths 

achievement. Differentiated instruction increases student motivation and involvement (Hapsari, Darhim 

& Dahlan, 2018). Professional development for teachers in differentiated instruction in the mathematics 

classroom improved students’ achievement (Prast, Van de Weijer-Bergsma, Kroesbergen & Van Luit, 

2018). Ismajli and Imami-Morina (2018) demonstrated that differentiated education is successful when 

teachers use interactive tactics to suit the requirements of all pupils. 

Despite the fact that the 2019 Ghana curriculum embraced the use of differentiated instruction in the 

mathematics classroom to improve learning at the basic level, some studies pointed out barriers and 

constraints such as insufficient training, support, and resources to be overcome in order to provide 

opportunities for learners to have differentiated lessons (King, 2010; Lange, 2009; Grey, 2008; 

Huss-Keeler & Brown, 2007). The curriculum aims to increase mathematics facilitation through spiral 

progression, in which learners are permitted to study topics and skills that are relevant to their own 

learning styles, resulting in good retention and mastery of mathematical content. This advancement is 

supposed to produce critical problem solvers, innovative, creative citizens, and educated 

decision-makers. Improvement of learners’ low performance in common fractions remains a difficulty 

for facilitators at Ancilla School, since students’ performance in that area remains very bad from their 

exercise, homework, assignment, and class test, as well as personal observation. Facilitators must be 

equipped with a variety of facilitating tactics and approaches in order to improve learners’ learning 

outcomes and, as a result, increase their performance in Mathematics (Gaylo & Dales, 2017). Against 

this backdrop, the researcher undertook a study to further evaluate the impacts of tailored instruction on 



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the performance of basic 7 learners in common fractions. The purpose of this study is to go deeper into 

the practical implementation of differentiated teaching and compare learners’ performance in 

understanding common fraction courses to the traditional technique. 

1.2 Research Question  

What is the difference in mathematics achievement in learners who have received differentiated 

instruction in common fractions as compared to learners who received traditional instruction? 

1.3 Significance of the Study 

The curriculum in schools has become standards-based, which means all learners are expected to 

achieve equally and meet high standards despite their varied abilities. Educators are therefore 

challenged to meet the diverse needs of the learner populations. The only way to meet the objective of 

the standards-based curriculum is to personalize or differentiate the instruction. Educators must face the 

challenges of changing from traditional lecture-style instruction to instructional methods that meet the 

diverse needs of their learners. Differentiated instruction is believed to be an effective instructional 

strategy because it advocates beginning where individuals are rather than with a prescribed plan of 

action, that disregards learner readiness, interest, and learning profile. This study is significant and 

contributes to the existing research because it provides educational leaders with a comparative study of 

differentiated instruction and traditional instruction. Society has become more diverse and complex, 

which is also represented in our classrooms. Schools need to adopt learning strategies that enable all 

learners to meet high standards. 

 

2. Method 

2.1 Research Design  

The study employed a quasi-experimental pre-test-post-test design. In the second term of the 

2022/2023 academic year calendar, the design made use of the basic 7 classes of Ancilla Catholic 

School, namely basic 7A and basic 7B. The basic 7B class was randomly allocated as the experimental 

group to receive differentiated instruction. While the basic 7A class was the control group, it was 

taught using conventional instruction, not differentiated instruction. Both classes were given a pre-test 

on fractions prior to the study’s implementation and a post-test after the study’s implementation in the 

convectional facilitating and differentiated instruction in facilitating fractions. Both Lessons focused on 

the subtopics of converting improper fractions to mixed fractions, converting mixed fractions to 

improper fractions, and solving problems involving common fraction addition and subtraction. Based 

on the requirement assessment and the researcher’s observations, the topic of common fractions 

presented several obstacles to learners. A Task Analysis Matrix (TAM) created by the researcher 

supervised the preparation of differentiated lessons. Based on the Basic 7 curriculum, these included 

topics, concepts, instructional objectives, procedural activities for customised instruction, skills, 

assessment, and references. 

 



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2.2 Participants  

Thirty-four (34) out of the thirty-five (35) of the learners in the convectional class were present and all 

the thirty-five learners in the experimental class were present. All learners were used for the study and 

were however considered in the analysis of data. The town classes were considered to be part of the 

study because they were those classes considered the poor performing classes in understanding the 

concept of fractions. For instance, the researcher happens to be a part-time teacher in the school and 

was teaching those classes.   

2.3 Data Collection Procedures  

The researchers contacted the headmistress of the Ancilla School, Wa to discuss with her all the details 

of the study and to seek permission to use the basic 7 class (A and B) for the study in the second term 

of the 2022/2023 academic year calendar. The study gathered the participants/ learners in each class 

and codes were assigned to each participant/learner to ensure confidentiality. The basic 7A 

participant/learners’ codes range from A01 to A43 while basic 7B codes range from B01 to B44. Basic 

7B class was assigned randomly as the experimental group using differentiated instruction method in 

teaching fractions while the basic 7A class was the control group taught using the traditional method of 

instruction. Before the conduct of the study, both classes were given a pre-test on fractions and later a 

post-test after the implementation of the study in traditional teaching and differentiated instruction. 

After the pre-test and the post-test an interval of 10 weeks period between the administration of the test. 

The researchers recorded all test scores on a spreadsheet using the designated codes for the 

participants/learners. A pre-test and post-test were administered to determine learners’ abilities to solve 

problems involving fractions. Both Lessons were developed on the sub-topics of converting improper 

fractions to mixed fractions, changing mixed fractions to an improper fraction, and solving problems on 

addition and subtraction of common fractions. The test items were composed of 40 multiple choice and 

4 theoretical questions based on the learning core competencies proposed by the basic 7 curriculum. 

The same test was administered to the experimental group and the control group. The pre- and 

post-tests identified learners’ strengths and weaknesses before and after the intervention. The post-test 

provided a measure of what the learners had learned. The materials for the study consisted of the basic 

7 mathematics textbooks, mathematics curriculum, and the excellence series that were published in line 

with the standards of the Ghanaian curriculum for the control group while the group receiving 

differentiated instruction also used the same mathematics textbooks, mathematics curriculum and the 

excellence series, manipulatives, laptops, games, and activities. 

2.3.1 Data Analysis  

The data collected for this study was to determine if learners taught using differentiated instruction 

methods are different in terms of their mathematics achievement than learners taught using traditional 

methods of teaching. At the end of the intervention, the post-test that is similar to the pretest was 

conducted for both groups. The 40-item multiple choice researcher-made performance test is made up 

of every correct answer one (1) point making for a total of 40 marks and the 4 theory questions are 



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made up of 15 makes each making a total of 60 marks. The total score for the entire test was 100 marks 

based on the standards of the new curriculum (National Council for Curriculum and Assessment 

(NaCCA), 2019). The scores of the learners were presented using raw scores, percentages, and grades, 

which are in line with the standards as proposed by the basic 7 mathematics curriculum.  

2.4 Validity and Reliability  

The learning styles of the learners were considered in the development of the lessons. After the 

development of the lesson experts in the area of mathematics and education (Mathematics coordinator 

in the municipality, CISOs, and some Lecturers) validated the lesson before the conduct of the study. 

These were experts on content, pedagogy, and technicalities and evaluated the content and content 

accuracy, clarity, and appropriateness of the lessons. The research instruments utilized in the study 

were validated researcher-made performance tests. The academic performance test was crafted to 

assess the academic performance of learners in common fractions and was tried out for validity and 

reliability purposes. The test items were composed of 40 multiple choice and 4 theoretical questions 

based on the learning competencies proposed by the Basic 7 Curriculum. The same test was 

administered to the experimental group and the control group.  

 

3. Results  

3.1 Academic Performance of Learners in the Pre-test 

Table 1 below displayed the academic performance of learners based on the scores they obtained from 

the pre-test administered by the researcher on changing mixed fraction to improper fraction, changing 

improper fraction to mixed fraction, and addition and subtraction of common fraction. The table 

displayed scores, number of learners, and percentages of learners in both the experimental group and 

the control groups in the pre-test. The sample of the experimental group was 42 and that of the control 

group was 41.  

 

 

 

 

 

 

 

 

 

 

 

 

 



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Table 1. Pre-test Scores of the Experimental and the Control Groups 

  Experimental Group Control group 

Performances Grades 
Score 

(100) 

No. of 

learners 
Percentage 

No. of 

learners 

Perc. 

(%) 

Highest 1 90-100 0 0 0 0 

Higher 2 80-89 0 0 0 0 

High 3 70-79 0 0 0 0 

High Average 4 60-69 1 2.4 2 4.8 

Average 5 55-60 5 11.9 4 9.8 

Low average 6 50-54 2 4.8 1 2.4 

Low 7 40-49 7 16.7 10 24.4 

Lower 8 35-39 13 31.0 12 29.3 

Lowest 9 0-34 14 33.3 11 26.8 

  Total 42 100 41 100 

Source: Scores of learners (2023). 

 

From Table 1, the pre-test results show that the learners in both experimental and control groups had 

weak scores and were initially at par. It revealed further that learners in both groups did not meet 

established expectations with the topic considering the result displayed. For example, learners in both 

experimental and control groups could not score (90-100) the highest in the pre-test. Also, no (0%) 

score (80-89) was higher in both classes. Again no (0%) could score (70-79) high marks in both classes. 

While only 1 (2.4%) in the experimental class and 2 (4.8%) in the control class scored (60-69) high 

average. The score of (55-59) average saw a few 5 (11.9%) of the experimental group and a few 4 

(9.8%) of the control group. Again, the table indicated only 2 (4.8%) of the experimental group and 1 

(2.4%) of the control score (50-54) low average in the test. The score of (40-49) low average saw 7 

(16.7%) of the experiment group and 10 (24.4%) of the control group. While the score of (35-39) lower 

performance saw more 13 (31.0%) in the experimental group and 12 (29.3) in the control group and the 

score of (0-34) lowest saw many 14 (33.3%) of the experimental group and 11 (26.8%) of the control 

group. The results above indicated that before the intervention processes both the experimental group 

and the control group saw more than 70% of the learners scoring below average even though the scores 

of the learners in the experimental group were slightly different as compared with that of the control 

group in the pre-test results. The results indicated that both the experimental and control group were 

comparable in terms of performance before the intervention. The pre-test scores of the learners in the 

control group were almost the same. They weren’t a significant difference in the learner’s performance 

before that intervention. The results further indicated that learners never got good facilitating at the 



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initial stage and this suggests that proper pedagogical strategies used could increase learners’ 

performance academically in mathematics. Learners will continue to perform poorly in their studies if 

the right pedagogical strategies are not used in the mathematics classroom. 

3.2 Post-test Scores of the Experimental and the Control Groups 

Table 2 below displayed the academic performance of learners based on the scores they obtained from 

the post-test administered by the researcher on changing mixed fraction to improper fraction, changing 

improper fraction to mixed fraction, and addition and subtraction of common fraction. The table 

displayed the frequency and percentages of learners’ scores in both the experimental group and the 

control groups in the pre-test. The participants of the experimental group were 40 out of 42 and that of 

the control group was 41 out of 41. 

 

Table 2. Post-test Scores of the Experimental and the Control Groups 

  Experimental Group Control group 

Performances Grades 
Score 

(100) 

No. of 

learners 
Percentage 

No. of 

learners 
Percentage 

Highest 1 90-100 3 7.5 0 0 

Higher 2 80-89 15 37.5 5 12.2 

High 3 70-79 10 25 3 7.3 

High Average 4 60-69 7 17.5 4 9.8 

Average 5 55-60 3 7.5 12 29.3 

Low average 6 50-54 1 2.5 5 12.2 

Low 7 40-49 1 2.5 3 7.3 

Lower 8 35-39 0 0 2 4.9 

Lowest 9 0-34 0 0 5 12.2 

  Total 42 100 41 100 

Source: Scores of learners (2023). 

 

 

 

 



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From Table 2, the post-test score indicated that the score (90-100) highest score saw 3 (7.5%) of the 

experimental group and 0 (0%) of the control group obtaining that. Also, many 15 (37.5%) of the 

experimental group and only 5 (12.2%) of the control group scored (80-89) higher in the post-test. 

Again, more than 10 (25%) of the experimental group and only 3 (7.3%) of the control group scored 

(70-79) high in the post-test results. Again, 7 (17.5%) of the experimental group and 4 (9.8%) of the 

control group scored (60-69) high average of the post-test results. Also, the score (55-60) average saw 

only 1 (2.5%) of the experimental group and 12 (29.3%) of the control group, while 2 (5%) of the 

experimental group and 5 (12.2%) of the control group scored (50-54) low average in the test. Again, 

only 1 (2.5%) of the experimental group and 3 (7.3%) of the control group scored (40-49) low on the 

test. Also, only 1 (2.5%) of the experimental group and 2 (4.9%) of the control group scored (35-39) 

lower on the test and no 0 (0%) learners of the experimental group and few 5 (12.2%) of the learners in 

the control group scored (0-34) lowest in the post-test. 

 

4. Discussion of Results  

From the post-test results, both groups showed an increase in their academic performance. However, 

the experimental group had greater improvement than the control group comparing the post-test scores 

of the two groups. Based on the performance level, the experimental group had a much improvement 

than the control group.   

From the post-test results, there were learners in the experimental group who reached the highest score 

level while no learner in the control group reached that level. On average, more learners perform 

outstandingly in the experiment group than in the control group. The results confirmed that the use of 

differentiated instruction had increased learners’ performance significantly higher than the 

conventional method of facilitating. 

This finding confirms the study by Aranda and Zamora (2016) and Konstantinou-Katzi et al. (2013) 

that differentiated instruction had much improvements and positive impact on the academic 

performance of learners and Muthomi and Mbugua (2014) who investigated the effects of 

differentiated Instruction on learners’ achievement in mathematics in secondary schools in Meru 

County in Kenya wherein a significant increase in the learner’s achievement was noted. Likewise, the 

research of Tambaoan and Gaylo (2019) on Differentiating Instruction in a Mathematics Classroom: Its 

Effects on Senior High School Learners’ Academic Performance and Engagement in Basic Calculus 

showed that learners performed better when differentiated instruction was used in the instructional 

process in the classroom.  

In the course of the intervention, it was realized that learners in the experimental group were very 

active, attentive in class, and participated fully. Every learner there was seen doing something in the 

course of facilitating in the experimental class while the control group was not active, Learners were 

seen only observing the Facilitators facilitating and the class was not active and learners were not given 

the chance to express themselves this made the control class very bore leading to poor performance. 



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The class engagement was very good and all these gave learners a lot of opportunities to ask questions. 

From the results, it was viewed that most learners do not like mathematics because of the mode of 

facilitating the mathematics curriculum.  

4.1 Conclusion  

Using differentiation in the mathematics classroom in facilitating common fractions at the basic 7 

levels significantly increased the academic performance and participation of learners. It supported the 

improvement of the academic performance of learners and increased their participation. From the 

pre-test learners’ performance was very bad and their understanding of the topic was low. However, 

after the intervention using differentiated instruction in the classroom, most learners performed better 

in the experiment group than the conventional group in the post-test, meaning the use of differentiated 

instruction will help in solving the poor performance in the subject area because this method will give 

opportunities to all learners to participate in the classroom when facilitators incorporated it into their 

lessons. 

4.2 Recommendations  

Since the use of differentiated instruction in mathematics classrooms aids in the general good 

performance of learners, supervisors like mathematics coordinators, CISOs, heads, and facilitators, 

must ensure that facilitators use differentiated instruction in their classrooms. Also, mathematics 

facilitators must use differentiated instruction in the facilitating and learning process in the classroom 

to help enhance learners’ full participation and help improve their academic performance. 

Again, the Ministry of Education, Ghana Education Service, and other organizations in education and 

child development must periodically organise workshops in-service training, and Seminars in 

differentiated instruction to boost and equip facilitators with knowledge and skills as to the use of 

differentiated instruction in their lessons. Mathematics facilitators must also research the area of 

differentiated instruction to gain knowledge and skills in the use of differentiated instruction.  

 

 

 

 

 

 

 

 

 

 

 

 

 



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