Content uploaded by Gabriel Assamah
Author content
All content in this area was uploaded by Gabriel Assamah on Oct 03, 2024
Content may be subject to copyright.
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
170
Research Arcle
THE EFFECT OF COOPERATIVE LEARNING THEORY ON THE TEACHING OF TRIGONOMETRY
AT HIGH SCHOOLS
Richard Kyere Asomah1 Gabriel Assamah2 Millicent Narh-Kert3 Harriette Nusrat Manu4 Emmanuel Agyei5
1,3Department of Teacher Education, University of Ghana, Legon, Accra, Ghana.
2,4Directorate of ICT Services, University of Cape Coast, Ghana.
5Department of Mathematics, Illinois State university.
Corresponding author: rkasomah@ug.edu.gh
TO CITE THIS ARTICLE:
Asomah , R. K., Assamah, G. ., Narh-Kert, M., Nusrat Manu, H., & Agyei, E. (2024). THE EFFECT OF COOPERATIVE
LEARNING THEORY ON THE TEACHING OF TRIGONOMETRY AT HIGH SCHOOLS. Turkish Journal of Computer and
Mathematics Education (TURCOMAT), 15(2), 170–182. https://doi.org/10.61841/turcomat.v15i2.14647
ABSTRACT: The benefits of enacting lessons anchored on Cooperative learning (CL) in mathematics has been
well documented. However, in particular, the effect of CL on the teaching of trigonometry is rare at the second
cycled educational institutions. This study, therefore, is aimed at exploring the efficacy of CL in enhancing
meaningful teaching and learning of trigonometry at some selected Senior High School (SHS) in Ghana. Mixed
method research design was employed to collect data using a questionnaire with both close-ended and open-ended
items, and Trigonometric Achievement Tests (TAT) with essay type questions. A stratified sampling technique was
used to select 55 students as the participants in the study. Descriptive statistics, paired sample t-test and thematic
coding were used in analysing the data. The findings showed that, there were significant improvement in the
students’ learning outcomes in trigonometry. Further, the study revealed improved performance in students’ pre-
test and post-test scores after participating in CL lessons. Finally, the students’ overall positive dispositions towards
the CL-lessons were reflected in high means scores on the subscales of CL: Positive interdependence, Individual
accountability, Face-to-face promotive interaction, Social skills and Group processing, depicting favourable
experiences with the CL-lessons. To this end, the authors argue that, to develop higher order thinking skills in
students, the use of CL in the teaching and learning of trigonometry ought to be prioritised. It is recommended that;
management of educational institution should consider conducting professional development training for educators
who desire CL as a means of instruction. Implications for policy and further research are discussed.
KEYWORDS: Cooperative Learning, Positive Interdependence, Individual Accountability, Promotive,
Face-to-Face Promotive Interaction, Social Skills, Group Processing
Introduction:
Trigonometry is an inseparable part of mathematics in high school. It is the product of arithmetic, algebraic
techniques and geometrical realities (Gillman,1991). Although Trigonometry has been taught from elementary
school level, it is one field of mathematics still regarded difficult by high school students (Gur, 2009; Asomah et
al., 2023a). In particular, the use of improper equations, sequences of operations and misuse of sinuses and cosines,
misinterpretations of languages, illogical inferences, distorted definitions, and technical error calculations have been
identified as common slip-ups on the part of High School students in answering trigonometric questions (Tuna,
2013). Further, Ross et al. (2011) identified over-reliance on committing to memory as the short cut for learning
trigonometric ratios of sine, cosine and tangent of angles as well as the deficiency in the use of text book definitions
and mnemonics as an attributable function in the students’ inability to understand the concept of trigonometry.
Consequently, Jong and Brinkman (1997) indicate instructional and methodological problems as the bane of
teachers in ensuring proper understanding of trigonometry. As a result, inappropriate teaching methods are
employed to facilitate trigonometry in the learning environment. Thus, pitching students in a restricted situation that
causes them to misrepresent basic concepts in trigonometry (Asomah et al., 2023b). To this end, the meaningful
representation of concept of trigonometry is missed (Weber, 2005). Moreover, developing understanding based on
trigonometric links is not easy for learners, and traditional ways of teaching trigonometry do not overcome students’
difficulties (Demir, Sutton-Brown & Czermiak, 2012). For this reason, the medium of instruction employed to teach
the concept of trigonometry is very important. Field-knowledge and pedagogical knowledge of teachers play
important role in teaching (Cochran et, al.,1993). Besides, mathematics education researchers have raised concern
with regard to ‘rote learning’ of mathematics procedures (Kamii & Dominick, 1997), which limits opportunities to
explore the nature of mathematics problems (Hiebert et al., 1996). Although, there have been fundamental changes
in the nature of trigonometry in modern times, mathematic teachers, still, resort to traditional methodology of
teaching. This is because, in the past, conventional method of teaching employed to manipulate trigonometric
functions were regarded as critical in aiding students understanding in the classroom context (Asomah et al., 2023a).
Thus, it could be argued that, there are problems with the method of teaching trigonometry. In this way, basic
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
171
Research Arcle
concepts, thinking and creativeness which hitherto would have been acquired cognitively is lost in trigonometry. It
is in response to these gaps that varied pedagogical strategies have been researched to have effect on the
improvement of students learning in trigonometry (Asomah et al., 2023a; Delice & Roper, 2006; Kendal & Stacey,
2003). In developing students’ ideas and skills, experience and reflection play a major part in modern approaches
to teaching (Hammond et al., 2001). One of such teaching approaches is cooperative learning (CL). This is because
characteristically, cooperative learning is practically oriented, collaboratively and participatorily inclined, reflexive
in process, and purposefully constructed in bridging the loophole created in literature in relation to theory and
practice in the classroom context (Trauth-Nare & Buck, 2011).
In Ghana, however, literature on the use of CL as a pedagogical approach to teaching trigonometry in the SHS
classroom context have been rare. Even though, there have been several studies conducted in mathematics with
particular focus on CL in Ghana and elsewhere (e.g., Asomah et al., 2023a; Asomah et al., 2023b; Rohrbeck et al.,
2003; Slavin, 2014). Nevertheless, the studies of (Assan-Donkoh et al., 2019; Edekor & Agbornu, 2020; Bosson-
Amedenu, et al., 2021) using the CL focussed on the teaching and learning of circle theorem at the SHS and a topic
in mathematics at the Junior High School (JHS) and College of Education respectively. Thus, providing a limited
scope in literature on the prospects of the efficacy of CL on the teaching and learning of mathematics at the SHS
level and in particular, trigonometry as a concept. In view of the abysmal performance of Ghanaian students in
trigonometry as reflected in how they performed poorly in the WAEC examinations (WAEC, 2023), the current
study focusses on the effect of CL in the teaching and learning of trigonometry. This is because CL environments
are more relaxed and enjoyable in comparison with traditional methods of teaching (Roger, Olsen, & Kagan, 1992).
The choice of this instructional approach is appropriate since previous studies affirmed the difficulties
accompanying the methods of instructions used to teach trigonometry as well as student’s misunderstanding in
learning (Slavin, 2014). Therefore, this study is aimed at determining the efficacy of CL in aiding students to
overcome the conceptual difficulty in learning trigonometry.
The context of the study
Trigonometry as a course of study, takes an unparalleled place in mathematics curriculum in different learning
institutions in many countries. Although various nomenclatures attributed to it differ from one country to the other
(Delice & Roper, 2006). In the Ghanaian SHS mathematics curriculum however, trigonometry encapsulates seven
general objectives, to be specific, the units 2.11 and 3.40 of the second and third year aspects of the mathematics
syllabus are structured with eight content sections sequenced as: “tangent, sine and cosine of acute angles; the three
main ratios in trigonometry in respect of 30º, 45º and 60º; the use of calculators to read sine, cosine and tangent of
angles between 0º and 360º; inverse of trigonometric ratios; angles in respect of their elevation and depression in a
given right angled triangle; application of the concept of ratios of trigonometry; graphs of trigonometric equations”
(MOE, 2010, pp. 43-53). The problems associated with the teaching of concepts in trigonometry as identified in
literature cannot be different in the Ghanaian context. This is because it continues to be major highlighted as a
weakness in the Chief Examiner’s report of West African Examination Council (WAEC), a body charged with the
responsibility of an oversight administration of examinations in the West African Sub-region (WAEC, 2011; 2012;
2023). The WAEC Chief Examiners’ Report on mathematics has incessantly acknowledged the concept of
trigonometry as part of the difficult topics for most learners. For instance, in 2023, the report decried the poor
performance of candidates in answering question on trigonometry. Thus, the student’s inability to conceptualize and
apply their understanding of the various concepts (topics) under trigonometry to answer questions posed to them at
the end of their two-year learning of trigonometry at the SHS level. Again, in 2011, the Chief Examiner’s Report
delineated the pedagogical problems in teaching trigonometry as a result of which almost all the candidates who
attempted the trigonometric question got it wrong:
” Given that sin x = 0.6 and 0o ≤ 𝑥 ≤ 90o, find 1-tan x, leaving your answer in the form 𝑎
𝑏 where ‘a’ and ‘b’ are
integers. In (a) candidates were to find 1 - tan x in form 𝒂
𝒃 where a and b are integers given that Sin x = 0.6 and
0o ≤ 𝑥 ≤ 90o”
Similarly, in 2012, the Chief Examiner’s Report indicated students’ inability to diagrammatically represent the
trigonometric questions in right-angled triangle and thereby failed to apply the appropriate trigonometric ratios of
sine, cosine and tangent of an angle in solving the question. As such, the question was left unanswered by most
candidates and those who attempted it. In view of the limited literature on the teaching methods that enhances the
learning experiences of students in the concept of trigonometry especially at the SHS level (Asomah et al., 2023a),
it could be argued that, trigonometry is one of the mathematics topics which has become the bane to many students
such that they have to strive to obtain a pass (Usman & Muhammed, 2017). Further, the teaching and learning of
trigonometry is compulsory for all SHS students (its taught both as a common core course and an elective) (MOE,
2010). Thus, students at the SHS are forced to grind it with other courses. In light of this, the current study seeks to
explore the effectiveness of CL as a teaching method to overcome the difficulty students face in learning
trigonometry conceptually. This is because, student’s errors are unique and reflect their understanding of concept,
problem or a procedure ((Sarwadi & Shahrill, 2014) as expressed in the WAEC Chief examiners Report (WAEC,
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
172
Research Arcle
2011; 2012; 2023). To this end, since errors committed by students are symptomatic of misunderstanding in
trigonometry (Lai, 2006), the deployment of CL as pedagogical tool in the SHS mathematics classroom context,
could bridge the loophole created in literature in relation to theory and practice.
Theoretical underpinning of the study
Constructivism is ‘an approach to learning that holds that people actively construct or make their own knowledge
and that reality is determined by the experiences of the learner’ (Elliot, Kratochwill, Cook, & Travers, 2000, p. 256).
Scaffolding is an important feature of the theory of constructivism, it ensures an effective teaching, where the grown-
up incessantly fine-tunes the level of his or her assistance in response to the beginner's level of performance. In the
classroom context, scaffolding entails modelling a skill, providing hints or cues, and adapting material or activity
(Copple & Bredekamp, 2009). Thus, constructivism recognizes the individual student’s active participation in the
learning environment as a means of constructing one’s own knowledge and the realization that the knowledge
created will vary in its degree of validity as a true reflection of reality. Characteristically, constructivism is a theory
in continuum and depending on one’s perspective, it is categorised into three main types: Cognitive constructivism,
social constructivism and radical constructivism. In particular, the social aspect of the theory of constructivism was
defined as” learning is a collaborative process, and knowledge develops from individuals' interactions with their
culture and society” (Lev Vygotsky, 1978, p. 57). This assertion therefore suggests that, the development of the
cultural function of every child seems to occur twice: first, from the child’s social level and, later on, at the level of
the individual; first, between people (inter-psychological) and then inside the child (intra-psychological). The
tenants of social constructivist theory are achieved through Cooperative, collaborative and participatory forms of
teaching and learning. Nonetheless, the current study focusses on cooperative learning as a means of achieving
constructivist oriented pedagogical approach to teach trigonometry.
According to the Johnson & Johnson model (1998), cooperative learning is an instruction that involves student
working in teams to accomplish a common goal, conditioned on the inclusion of the constructs: Positive
interdependence, Individual accountability, Face-to-face promotive interaction, Appropriate use of collaborative
skills and Group processing. Again, Slavin and Karweit (1981) averred that cooperative learning can be referenced
as pedagogical approach where students conduct their work in small groups or teams purposed to master academic
materials and consequently are rewarded for doing well in their groups. Hence, the concept of cooperative learning
cannot be a substitute to a situation where students are merely allocated in group for the purposes of working in
activity. CL is reliably recognized for its efficiency in improving social, motivational and cognitive outcomes of
students (Rohrbeck et al., 2003; Slavin, 2014). Johnson and Johnson (1998) contended that lessons that are
cooperative based are characteristic of five main variables: positive interdependence, face to face promotive
interaction, social skills, individual accountability and group processing.
Positive Interdependence lends credence to the effect that, the student in the learning environment is successful if
such students is reliant on the ideas, involvement, and accomplishment of the others in the group (Johnson, Johnson,
& Smith, 1991). Individual accountability ensures that students learn together, but perform alone (Johnson et al.,
1998). According to Johnson et al. (2014) promotive face-to-face interaction occurs in the learning environments
where students are afforded the opportunity (time in class) to discuss, ask questions and offer the needed support to
each other in the completion of the task assigned to the group. Moreover, group processing, affords students, an
opportunity to reflect upon the correctness or otherwise of the work done by a group. This aids in the determination
of the quality of work as executed by the group in respect of the successfulness or otherwise of cooperative learning
teams (Johnson et al., 1991). Lastly on the tenant of social skills, Johnson et al., (1998) recognizes the need for
students in the cooperative learning environment to exhibit some competencies for cooperative learning to be
effective. Finally, this study was anchored on the social aspect of the theory of constructivism as an approach to
teaching. CL, as an instructional approach is one of the means through which the theory of constructivism is
achieved. In reviewing literature therefore, it is established that a learning environment is said to be cooperative
learning-based if and only if such pedagogical technique is anchored on the five main variables (Johnson & Johnson,
1998). Thus, positive interdependence, face to face promotive interaction, social skills, individual accountability
and group processing.
Research question
In evaluating the efficacy of CL as a pedagogical approach aimed at improving students learning outcome in
trigonometry, the question: “How effective is the CL in improving students learning outcome of concepts in
trigonometry?” guided the conduct of this study.
Research design
A mixed method research design that entailed the quantitative and qualitative data collection was employed in this
study. The rationale was to obtain different but complementary data on the effectiveness of CL in improving students
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
173
Research Arcle
learning outcome of concepts in trigonometry (Morse, 1991). The quantitative and qualitative data were used in
complementing the findings of the study (Creswell & Tashakkori, 2007). Thus, through triangulation of the data, a
deeper understanding of the students’ meaningful experiences of CL was accounted for in the study (Cresswell,
2020).
Sample and participants
Cape Coast is the only Metropolis out of Twenty-three (23) districts in the Central Region of Ghana. The Metropolis
is bounded to the South by the Gulf of Guinea. It hosts eleven (11) SHS (GES, Cape Coast Metropolitan Office,
2024). These schools constitute the population of the study. The availability of the different categories of SHS
informed the choice of this Metropolis as most suitable for the conduct of this study. Constructs such as the school’s
infrastructure, enrolment (numerical strength of teachers and students in the school), readily available teaching and
learning resources (state of the art laboratories and equipment) and academic excellence (Computerised School
Selection and Placement System [CSSPS], 2023) informed the placement of the 11 SHS into two strata (Tier A and
B). A school from each of the two strata was selected based on stratified and simple random sampling techniques.
Further, in determining numerical values of participants in the study, a probability proportional to size (PPS)
sampling approach was used. This technique eliminated biases and allowed an intact class to be selected on an equal
basis. Thus, a total of 55 (Tier A=29 and Tier B =26) students were engaged as the study’s sample. Subsequently,
these intact classes from the two-tier schools (Tier A and B) were instructed on the concepts of sine, cosine and
tangent of angles using the CL as the medium of instructions. Data was taken before and after instruction with the
CL lessons. With regards to the qualitative aspect, responses from six (6) participants were selected randomly on
stratified method of approach. Thus, Stud_10, Stud_11 Stud_12 Stud_13, Stud_14, Stud_15 (Stud-Student from
Tier A and B). Hence, positioned the authors to attribute specific statements made to their corresponding authors in
the respective schools. Participants inclusion or exclusion was by consent. Further, anonymity and confidentiality
of the participants were guaranteed. The gender distribution of the students in the study is shown in Table 1.
Table 1: Gender Distribution of Respondents (Students)
Gender
Frequency
Percentage (%)
Male
45
81.8
Female
10
18.2
Total
55
100.0
The Table shows that more than half of the respondents were males, representing 81.8% of the total sample size.
The average age of students in this study was 17 years (SD = 1.50). The minimum age was observed to be 15 years
while the maximum age was 24 years. From the test of frequencies and percentages, all 55 (100%) of the respondents
were SHS 2 students. This is because the teaching and learning of trigonometry excludes first year SHS students
(MOE, 2010).
Instrument
Two sets of instruments constructed in this study, were grounded on the loopholes and growing themes identified
in literature. The questionnaire was adapted from instruments previously developed by Agyei et al., (2013) and
employed by Asomah et al., (2022). In particular, a questionnaire with open-ended and closed ended items as well
as Trigonometric Achievement Test (TAT- a 30-item multiple choice question with an essay type question) were
administered in the study. The questionnaire consisted of 3 parts. The demographic information (e.g. sex, age, course
of study etc.), close-ended items relating to students’ experiences of CL Lessons constituted the first and second
parts of the questionnaires. Students disposition towards the experiences of the CL Lessons were characterised by
the extent to which they agree or disagree to each item on a 5-point Likert scale. To this end, negative and positive
observations were assigned and interpreted as 1=lowest score and 5=highest score respectively. The last part of the
questionnaire, afforded the respondents an opportunity to express their satisfaction or otherwise of the CL lessons
introduced in the class. The instruments were piloted with a smaller sample of students with similar characteristics
in some selected schools before administering it to the participants in this study. The two instruments were
administered personally by the first author in all the selected schools. Both instruments were in the English language
since it’s the medium of instruction used in senior high schools in Ghana. The inputs received at the pilot stage were
used in modifying the instrument in relation to its validity and reliability. Further, the reliability of the subscales of
CL as established were determined using Cronbach Alpha coefficients. Specifically, this questionnaire (closed
ended items) comprised 20 items grouped under the subscales of positive interdependence, promotive face to face
interaction, individual accountability, group processing and social skills. The Cronbach’s alpha reliability estimates
for all the subscales: individual accountability (3 items, α = .72), positive interdependence (5 items, α = .80),
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
174
Research Arcle
promotive face to face interaction (4 items, α = .75), group processing (3 items, α = .73) and social skills (5 items,
α = .83) were considered to be reliable according to Hinton, et al., (2014) for the conduct of a study. In addition to
the questionnaire, TAT was in the form of pre-test and repeated as post-test in the area of trigonometry was
employed. The questions were first constructed using the WAEC (2023) standardized questions on trigonometry.
Subsequently, an informed opinions of three experienced mathematics teachers at the SHS were sought for the
purposes of proof reading the questions to reduce ambiguity and improve clarity of trigonometric expressions used.
Finally, 3 experts in the field of mathematics education at the Teacher Education Department, University of Ghana
revised and contributed to the test items’ relevance and consistency in terms of the scope of the content and the
curricular practices in the SHS mathematics syllabus. The TAT was employed to quiz the students conceptual
understanding of the concepts taught during the CL-lesson.
Data collection and analysis
The first researcher submitted official letters of permission to heads of the SHS who in turn granted access to the
assistant academic heads, heads of mathematics departments and the mathematics students in the selected schools.
In consultation with the heads of the mathematics departments, the first researcher taught students at the two schools
(Tier A and B) who participated in the study.
The administration of the questionnaires, TAT and essay type question occurred at the respective schools of the
participants of the study (Tier A and B). This was purposed to report on the efficacy of CL in improving students
understanding of trigonometry in an uninterrupted environment of the participants (Cohen et al., 2017). The TAT
was scored out of hundred (100%) and analysed using paired sample t-test. The paired sample t-test was used in
determining the mean difference between the two sets of observations (pre-test and post-test) at the end of
instructions. The use of this tool of analysis was considered appropriate since observations were independent of one
another with insignificant outliers in terms of the scores and consequently, were found to be approximately normally
distributed. Hence, the use of paired sample t-test to determine the improvement (if any) in the students’ pre-test
and post-test scores in the study. Further, concerning the essay type question, a total mark of 5 was awarded (using
WAEC standardized marking scheme A0=Wrong Answer, A1=Correct Answer, Mo=Wrong Method, M1=Correct
Method, Bo=Wrong Basic Idea, B1=Correct Basic Idea) for which marks above 2.5 and below 2.5 were interpreted
as favourable (positive) score and unfavourable (negative) score respectively. Further, the responses to open-ended
items were coded, themed and analysed (Miles & Huberman, 1994).
Results
The effectiveness of the CL approach for teaching and learning of trigonometry was measured quantitatively by
administering a 5-point Likert scale questionnaire and qualitatively with use of the open-ended items and excepts
from the essay type questions administered to 55 (Tier A=29 and B=26) students at the two SHS during real
classroom implementation of the CL lessons designed by the authors. The results are presented in two sections:
Students’ disposition towards CL and an enhanced students’ learning outcomes in trigonometry.
Students’ disposition towards CL
The findings, in view of the subscales of CL (positive interdependence, promotive face to face interaction, social
skills, individual accountability and group processing) in promoting teaching and learning of trigonometry are
discussed.
Positive Interdependence
Student’s positive disposition towards the subscale of positive interdependence showed the extent of their
cooperation during group activities in the CL-lessons. Specifically, respondents unvaryingly agreed with all
statements related to positive interdependence. For instance, participants affirmed that the specific roles allocated
within the group facilitated their problem-solving abilities during classroom discussions (M = 3.85, SD = 1.18).
Additionally, they expressed satisfaction with the level of participation within the lesson, indicating a high level of
engagement (M = 4.15, SD = 0.95). The findings are presented in Table 2.
Table 2: Students reaction to the subscale of Positive interdependence
Items
M
SD
The specific responsibilities assigned to me in the group helped me to find solution to the
question in class.
3.85
1.18
The lesson was participatory enough in class.
4.15
0.95
In this lesson, I got the chance to interact with my group members on the topic throughout
the teaching period
3.93
1.10
Through the use of students’ worksheet and cooperation received from my group members,
I was able to solve realistic problems during the task stage of the lesson
3.73
1.19
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
175
Research Arcle
The teacher’s role in the lesson was more of offering support and guidance to the me.
Overall
4.44
4.02
0.74
1.03
M=Mean, SD=Standard Deviation
Furthermore, participants acknowledged the opportunity for continuous interaction with their group members
throughout the teaching session, highlighting the collaborative nature of the learning environment (M = 3.93, SD =
1.08). The utilization of student worksheets, coupled with the supportive efforts from group members, was perceived
as instrumental in undertaking real-world challenges during the task-oriented phase of the lesson (M = 3.73, SD =
1.19).
Moreover, participants recognized the teacher's supportive role, emphasizing guidance and assistance rather than
authoritative instruction, which contributed to a positive learning experience (M = 4.44, SD = 0.74). These results
give emphasis to the efficacy of positive interdependence in fostering collaborative learning environments
conducive to student engagement and problem-solving.
Similar observations were made from the responses to the open-ended items. Thus, student’s responses to the
question: “Describe how the placement of students into groups facilitated the lesson” were stated as:
Stud_12: Grouping us brought about the shared responsibilities to enable us to
coordinate and achieve our objectives as a group
Stud_10: Our group was assigned some activities on the topic by our teacher. The
brilliant ones helped the weak ones in the group.
Remarkably, all the items measuring positive interdependence, a subscale of CL recorded mean values greater than
3.73, which indicates high level of students’ disposition towards positive interdependence in trigonometric lesson
delivery.
Promotive Face to Face Interaction
A positive outlook from the perspective of the students concerning their active participation in the CL-lesson were
observed. The findings indicate unanimous agreement among participants regarding various aspects of face-to-face
promotive interaction. In particular, participants endorsed the statement "The lesson allowed me to share ideas with
my colleagues in the group on the concept taught in class" (M = 4.13, SD = 0.90). Similarly, participants affirmed
their engagement in lesson activities by way of sharing ideas on the topic during the instruction (M = 4.00, SD =
1.04). Table 3 presents views of the participants on the subscale of Promotive Face to face interaction
Table 1: Students reaction to the subscale of Promotive face to face interaction
Items
M
SD
The lesson allowed me to share ideas with my colleagues in the group on the concept
taught in class.
4.13
0.90
I was involved in activities that enabled me to share ideas on the topic during the lesson.
4.00
1.04
My views and contributions were respected by my mates during group discussions in the
lesson.
4.33
0.96
The teacher clearly defined the lesson’s objectives to guide me during the lesson
Overall
4.45
4023
0.79
0.92
M=Mean, SD=Standard Deviation
Additionally, participants felt that their viewpoints and contributions were respected by their peers during group
discussions within group discussions (M = 4.33, SD = 0.96). Also, participants acknowledged the effectiveness of
the teacher’s input in defining clearly, the lesson's objectives to guide them throughout the session (M = 4.45, SD =
0.79). Thus, these findings point out the importance of face-to-face promotive interaction in fostering active
participation, mutual respect, and clarity of objectives within educational settings.
Likewise, evidence from the responses to the open-ended items revealed by way of response to “In what way did
the lesson activities encourage you to share ideas on the concept taught?” Some specific responses gathered were:
Stud_13: In my group, we shared ideas on the task that was assigned to us, corrected
some mistakes of our colleagues and in fact it helped each and every one of us to improve.
Stud_11: I had misconceptions about certain aspects of the topic but got support from colleagues in the
group
Stud_15: It was made easier for us to acknowledge our strengths and weaknesses since such fault was
easily identified and corrected by our fellow counterpart during group discussions.
Overall, the 4.00 high mean recorded posits the relevance of this subscale in promoting fruitful discussions within
the inter an intra group activities during lessons with CL as the means of instruction.
Individual Accountability
The participants responded to closed-items on statements concerning their individual participation in the lessons
with CL. The findings indicate unanimous agreement among participants regarding the statements related to
Individual Accountability. For example, participants strongly affirmed the notion of viewing their group members
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
176
Research Arcle
as supportive allies in the learning environment rather than competitors within the classroom setting (M=4.16,
SD=.98). The results are presented in Table 4.
Table 4: Students reaction to the subscale of Individual Accountability
Items
M
SD
I see my group members as helpful mates in the learning process rather than competitors
in class
4.16
0.98
Through the group’s activities I have learnt to solve questions on my own without relying
on my colleagues in the group always
4.09
1.02
Teacher continually assesses my individual contributions during the group’s activities
throughout the lesson
Overall
4.02
4.09
1.08
1.03
M=Mean, SD=Standard Deviation
Furthermore, they expressed concurrence with the statement highlighting their ability to independently tackle
questions within the group's activities, diminishing reliance on their peers (M=4.09, SD=1.02). In addition,
participants acknowledged the teacher's consistent evaluation of their individual contributions throughout the group
activities within the lesson (M=4.02, SD=1.08). These results depict a robust endorsement of the principles and
practices associated with fostering individual accountability within the learning environment.
Further, the open-ended items elicited responses as to whether students were individually engaged in the lesson,
some of the responses in relation to the question: “Describe how you were engaged individually during the lesson”
were:
Stud_14: I was tasked to solve questions independently before being asked to put our individual solutions
together for the purposes of reaching consensus on a single solution as the answer for the group.
Stud_13: The individual activities assigned to us during the lesson, questions targeted at the individual
group members helped in mastering the concept during the lesson
Generally, participants expressed their participation in the CL-lessons with a high mean score (M=4.09 SD=1.03)
via the individual roles they actively played in mastering the content of the subject matter during the teaching and
learning sessions of the study.
Social Skills
The data portrays a positive attitude of students towards the congenial atmosphere created during instructions in
class. The analysis of the results indicates a strong consensus among participants regarding their social skills.
Specifically, participants demonstrated agreement with all the provided statements. For instance, participants
affirmed the effectiveness of disciplinary measures implemented during group activities to resolve issues with their
peers in the classroom (M=4.02, SD=.87). Table 5 depicts the views of the students in relation to the closed-ended
items.
Table 5: Students reaction to the subscale of social skills
Items
M
SD
The disciplinary measures that were put in place during group activities helped me to solve
problems with my group members in the classroom.
4.02
0.87
I understood better in the questions we solved together as a group
4.02
1.05
My teacher’s fairness in applying the rules in the lesson motivated me to work together
with my group members in solving questions.
4.09
0.97
There was respect for each other’s opinion during group work activities.
4.22
1.03
The rules for a successful group activity were formulated by myself and colleagues during
the lessons
Overall
3.93
4.10
0.86
0.96
M=Mean, SD=Standard Deviation
Furthermore, participants acknowledged enhanced comprehension during collaborative problem-solving sessions
(M=4.02, SD=1.05), attributing this to the joint effort within the group. Moreover, participants expressed
appreciation for their teacher's equitable enforcement of rules, which served as a motivating factor for co-operative
work (M=4.10, SD=.97).
Additionally, participants highlighted the presence of mutual respect for each other's viewpoints during group work
activities (M=4.22, SD=1.03). Besides creating an atmosphere devoid of disdainful remarks from each other during
group activities, participants attributed the successful group activities during lessons to their active involvement in
the formulation of guidelines (M=3.9, SD=.86) that aided their understanding of the concepts taught, emphasizing
a sense of ownership and collaborative decision-making within the group dynamic.
In addition to the above observations, the students’ responses in relation to the question: “Describe how the
guidelines facilitated the group activities during the lesson” were reported in the study. Some specific responses
gathered were:
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
177
Research Arcle
Stud_10: It ensured that each student in the group stayed focus and participated fully because the class
was under control.
Stud_12: I was put on my toes and as such was disciplined throughout the entire lesson, it helped us in
the class.
Stud_14: It actually guided our actions during the group discussions since there is little room for
interruptions. so, we attained the set goals in the lesson.
Stud_15: It created an environment where students defended their individual solutions in the group
without any fear or being mocked by their colleagues during discussions in the groups.
Thus, generally, social skill was perceived as positive from the perspective of students. This indicates high levels
of tolerance, respect for one another and cooperation from group members during the enactment stage of the lessons.
Group Processing
In view of the presentations conducted by the groups, during the teaching and learning of trigonometry, the
participants depicted positive disposition towards the statements asked about the relevance of this subscale in their
learning of trigonometry. The findings indicate a high level of agreement among participants regarding group
processing. Specifically, participants expressed consensus on various aspects. In particular, they acknowledged
understanding certain mathematical concepts through feedback received from their colleagues during the lesson
(M=4.20, SD=0.89). The views of the students are presented in Table 6.
Table 6: Students reaction to the subscale of Group processing
Items
M
SD
I understood some mathematical concepts through feedback from my colleagues in the lesson.
4.20
0.89
The group presentation experiences in the lesson helped me to develop problem-solving skills.
3.91
0.97
The teacher provides clarity to my questions which helped me to understand the lesson.
Overall
4.40
4.17
0.81
0.89
M=Mean, SD=Standard Deviation
Further, participants of the study affirmed that their problem-solving skills improved as a result of engaging in group
presentations during the lesson (M=3.91, SD=0.97). Moreover, participants acknowledged the effectiveness of the
teacher's explanations in clarifying their queries, thereby enhancing their comprehension of the lesson (M=4.40,
SD=0.81). These findings collectively suggest a positive perception of group dynamics and instructional support in
the learning process.
The quantitative findings further corroborate the comments obtained in response to the question: “In what way did
the group presentations enhance your understanding of the concept taught during the lesson? The responses elicited
from the students were observed as follows:
Stud_11: Our group presentation in class today helped in bringing clarity to the
alternative solutions proposed by other groups in the lesson.
Stud_13: The group presentations helped raise the confidence level of some of us since we got the
solution right.
Stud_14: This activity helped us to get swift feedback from our teacher, know what and where to improve
and stay clear of any misconception during the lesson.
Stud_15: It positioned us to be part and parcel of the teaching and learning process.
It could be observed from the overall mean recorded (M=4.17, SD=0.89), that students exhibited a positive
disposition toward the subscale of group processing during instructions.
Enhanced students’ learning outcomes in trigonometry
The improvements in students’ learning of trigonometry using CL were further understood and explained in the
students improved learning outcomes. Data collected particularly during the enactment stage of the lesson were
used in addressing this question. Application of trigonometric ratios as a topic in the mathematics teaching syllabus
in two different classes at the Tiered Schools were taught. Evidence of a particular student’s [De-Graft-pseudonym
for the purposes of this study] improvement in performance in connection to the essay type question administered
before and after the lesson is shown in Figures 1A and 1B. Thus, Figures 1A and 1B show excerpts of the
performances of De-Graft’s pre-test and post-test administered in the study. It could be observed that, De-Graft
showed improvement in the test scores after the lesson. This evidence follows through all the questions as the
student’s provided clarity to the various steps (working-proof of the solution) in solving the essay type question and
demonstrating conceptual understanding through the construction of appropriate diagram in the solution on the
answer booklet provided to the participants.
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
178
Research Arcle
A0=Wrong Answer, A1=Correct Answer, Mo=Wrong Method, M1=Correct Method, Bo=Wrong Basic Idea,
B1=Correct Basic Idea
Figure 1A: Excerpt of De-Graft’s Pre-Test Score.
A0=Wrong Answer, A1=Correct Answer, Mo=Wrong Method, M1=Correct Method, Bo=Wrong Basic Idea,
B1=Correct Basic Idea
Figure 1B: Excerpt of De-Graft’s Post-Test Score.
For example, from Figure 1A and 1B, De-Graft’s post-test score increased from 2 out of 5 to 5 out of 5 on the pre-
test and post-test respectively. As observed from the excerpts, De-Graft’ s could not account for the processes
leading to the answer that was asked in relation to the trigonometric ratios of sine, cosine and the tangent of an angle
given during the pre-test. In particular, the question (with the help of the diagram find the sine, cosine and the
tangent of an angle of 270 degree) could not be solved. Thus, De-Graft was unable to draw the proper right-angled
triangle diagram to illustrate the concept of the question. Again, his inability to apply the appropriate trigonometric
ratio to the tangent of an angle of 270 degree in the pre-test, implied rote method of learning the three ratios of
trigonometry with little or no relational understanding. Hence, the abysmal performance in relating to the question
before the CL lesson.
However, at the post-test, (thus, after the students were grouped with some assigned roles, provided with
opportunities to discuss at length their ideas on sine, cosine and the tangent of an angle through the provision of
related activities on the students work sheet individually and collectively as a group as well as the provision of
platform for the groups to project their solution on the chalkboard for the purposes soliciting alternate ideas and
views from non-group members during the teaching and processes) De-Graft’ s was able to account for the processes
that led to the solution of pre-test item. As such, De-Graft’s related to the question by displaying his conceptual
understanding of the diagrammatic representation of an appropriate trigonometric ratio to the tangent of an angle of
270 degree in the post-test. Specifically, De-Graft’s ability to construct an angle of 270 in a right-angled triangle
with the aid of a rule and a protractor accounted for his understanding of the question. Consequently, he related to
the definitions of the three ratios of trigonometry and solved for the angles as shown in the post-test (see Figure
1B). To this end, De-Graft answered the question with the correct methodology with a suitable diagram to represent
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
179
Research Arcle
the main ideas sought by the question he could not answer in the pre-test (see Figure 1A). Hence, it could be asserted
that, the effective utility of the CL as a pedagogy might have accounted for the improvement in De-Graft’s individual
pre-test score. Thus, students’ performance improved post introduction of the CL by the authors. In addition, the
results of the TAT were scored and analyzed using paired sample t-test. Table 7 shows the results of the paired
sample t-test of the TAT scores obtained before and after CL lessons with students in the two-tiered schools.
Table 7: Paired Sample T-test for the Two-Tiered Schools.
Paired differences
M
SD
Md
T
df
p
Post-test scores
7.92
1.093
5.54
37.131
54
.000
Pre-test scores
2.38
1.169
The results from the Table show the paired sample t-test with a significant (mean difference = 5.54, 95% CI: 5.23
to 5.85) mean difference. A very large eta squared (eta squared = 0.98) was obtained from the analysis which depicts
that, there was significant difference in the student’s pre-test and post-test scores obtained before and after CL
lessons. Thus, students’ performance in the Tiered A and B schools improved after they were introduced to the CL
lesson on the concepts taught.
In a nutshell, the qualitative findings corroborate the quantitative findings, highlighting that, the deployment of CL
as a pedagogical tool in the classroom context was effective in enhancing students meaningful learning of
trigonometry.
Discussions
The study sought to explain the effectiveness of CL in improving students’ learning of trigonometry. The discussions
in connection with this study was presented from two perspectives as reported in the results section as; enhanced
students’ learning outcomes and perceived students’ experiences with the CL-based lessons. Enhanced students’
learning of concepts in trigonometry with CL-lesson was explained based on the qualitative and quantitative analysis
of the improvements that occurred in students’ learning outcomes as depicted in Tables 2-7 and Figure 1A and
Figure 1B. In particular, analysis of the results (Figures 1A and 1B) at the individual pre-test and post-test scores of
the students showed that, the CL-lesson enhanced students’ mastery of the concepts of trigonometry. The results of
this study are consistent with the studies (Asomah et al., 2023a; Ahmadi, 2000; Oloyede et al., 2012; Shafiuddin,
2010) who assessed the impact of CL strategy in teaching mathematics students. These studies affirmed the effect
of CL on students’ performance, interest, motivation, conceptual understanding, and their attitudes toward
mathematics. The results of these studies established that, students performed better when they were taught with CL
than those in traditional sections and their attitude towards mathematics improved as was the case in the current
study where there were improvements in the performance and dispositions of students in the two schools taught (see
Tables 2-7). The authors indicated a better superiority of the CL as an instructional approach in mathematics courses
to a more traditional method of instruction. This observation was also implied in this study although the current
study did not compare the CL lessons directly with the traditional method of teaching. Specifically, the results align
with this study because the views of the students on the new teaching method (CL) agree with sentiments as
expressed in the study of Ahmadi (2000) (see qualitative analysis of students’ responses to the researcher interview).
Again, in the said studies of (Assan-Donkoh et al., 2019; Ahmadi, 2000; Edekor & Agbornu, 2020; Oloyede et al.,
2012), they averred that, CL is very dynamic, thus students are more actively involved in the exploration of
mathematical concepts and ideas as well as the resolution of specific task. This was also observed in the current
study as the introduction of the CL lessons made the students active participants in constructing their own
understanding of the subject matter. In relation to other disciplines, effectiveness of CL has proven to be effective.
In particular, the studies of Oloyede et al. (2012), Bukunola and Idowu (2012) who explored the effectiveness of
CL strategies on Nigerian Junior Secondary School students’ academic achievement; however, Bukunola and Idowu
(2012) concentrated on the Basic Science. Their study employed a number of intact classes in the selected co-
educational Junior Secondary Schools as the sample. The results revealed that CL had significant effects on students’
post-test academic achievement scores in Basic Science. Again, the results revealed that the CL had a significant
effect on students’ retention of Basic Science concepts taught. Thus, as student performance improved, their
retention also improved as was evidenced in this study. Moreover, this study resonates with the findings of Vaughan
(2002) who observed the effects of CL on the students’ performance and attitudes in relation to mathematics. The
analysis of pre- and post-test scores showed favourable changes in the students’ attitudes and performance. This
further affirms the current study’s position on SHS students’ improvement in their learning outcome. In addition,
Whicker et al. (1997) findings in their study aligns with similar observations in the current study. In their study, the
effects of CL on students’ achievement and attitudes in secondary school mathematics classroom were found to be
favourable. They found that students who experienced CL lessons performed better on the test scores than students
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
180
Research Arcle
in the comparison group and as such, affirms the current study’s pretest and post-test scores where students
improved on their pre-test scores as result of the introduction of the CL-lessons. Again, Bosson-Amedenu, et al.,
(2021); Shafiuddin (2010) also examined the effect of CL on mathematics. The main objectives of the study were
to find out the effectiveness of the CL approach over conventional method in learning mathematics at high school
level and compare the achievement of the high, average, and low achievers when taught using the CL method as an
instructional approach. The results showed a significant difference between the post-test scores of students in
cooperative learning method and conventional method group. Thus, students performed well when taught through
CL approach. The current study’s student’s performance on the pre-test and post-test corroborates the findings of
Shafiuddin (2010). This is because after exposing students to the CL-lessons, this study registered much improved
trigonometric performance in the students’ post-test in comparison with their pre-test scores.
At the crux of this study, was the relevance of CL as a means of instruction for the teaching and learning of
Trigonometry at the SHS. To this end, the authors contend that, in the wake of the student’s positive disposition
towards CL lesson, it is critical that CL-based materials in the form of exemplary lessons are designed to guide in-
service and pre-service teachers to maximise the gains and minimise the weaknesses associated with this pedagogy.
Further, it is important that teachers adopt activity-based lessons as a means of maximising the features (Positive
interdependence, Individual accountability, Face-to-face promotive interaction, social skills and Group processing)
of CL in teaching mathematics.
Conclusions and implications
The results showed that, the enhanced learning outcomes in the performances of the students as reported in the study
was one possible reason that explained the improvements in students’ learning of trigonometry using the CL
approach. The study further revealed improved and significant performance in students’ pre-post-tests scores after
participating in the CL lessons in all the two senior high schools involved in the study. Finally, the students’ overall
positive dispositions towards the CL-lessons which were reflected in high means scores on the subscales -Positive
interdependence, Individual accountability, Face-to-face promotive interaction, social skills and Group processing,
depicted favourable experiences with the CL-lesson is another reason that explained the improvements in students’
learning of trigonometry. To this end, the authors argue that, to develop higher order thinking skills in students the
use of CL in the teaching and learning of trigonometry ought to be prioritised. It is recommended that; management
of educational institution should consider conducting professional development training for educators who desire
CL as a means of instruction.
Limitations and further research
The study was limited to only students from public SHSs in the Cape Coast Metropolis. Hence, the deficit in the
generalization of the findings of this research over all SHS. Thus, it would be worthy to note of a replication of this
study in other subject disciplines such as biology, physics and chemistry as well as art related subjects at the SHS
level; since the deployment of CL as a pedagogical strategy is not limited to mathematics.
Conflicts of Interest
The authors declare no conflicts of interest.
Funding
The authors received no direct funding for this research.
Data availability statement
As a result of the anonymity and confidentiality of the participants in this study, the supporting data are exclusively
available@ rkasomah@ug.edu.gh
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
181
Research Arcle
References
[1] Ahmadi, M. H. (2000). The impact of cooperative learning in teaching mathematics. Primus, 10(3), 225-
240.
[2] Asomah R.K, Agyei, D.D., Assamah G., & Amponsah K.D (2024) Examining teachers’ perceptions of
the impact of government of Ghana’s wi-fi technology program on teaching practices: an empirical study
from the senior high schools in the cape coast metropolis, Cogent Education, 11:1,
2296455,DOI:10.1080/2331186X.2023.2296455
[3] Asomah, R. K., Agyei, D. D., & Ntow, F. D. (2023a). Developing in-service mathematics teachers’
pedagogical content knowledge and skills to teach trigonometry: Using cooperative teaching and learning
approach. Contemporary Mathematics and Science Education, 4(1),1-12.
https://doi.org/10.30935/conmaths/12540
[4] Asomah, R. K., Agyei, D. D., Ntow, F. D., & Benning, I. (2023b). Hypothetical Approach to the Teaching
of Trigonometric Concepts Using Cooperative Learning. Education Research International, 2023.
https://doi.org/10.1155/2023/2051776
[5] Asomah, R. K., Crankson, S., Asiedu, K. J., & Dapaah, B. A. (2022). Analysis of Ghanaian Junior High
School Pupils’ Perception of, and Attitude Towards, Mathematics. African Journal of Educational Studies
in Mathematics and Sciences, 18(1), 37-47.
[6] Assan-Donkoh I., Susuoroka, G., Baah D., Baah-Duodu, S., & Puotie, Z. (2019). Cooperative learning
strategy in teaching and learning of circle theorem in mathematics: A case of Nana Brentu senior high
school in Aowin Municipality in Ghana. Open Science Journal of Mathematics and Application. 7(1), 1-
13.
[7] Bosson-Amedenu S., Teku E., Vivian N., & Osei-Asibey E. (2021). A study of cooperative strategies that
enhance individual mathematical achievement among college of education students in Ghana. Teacher
Education and Curriculum Studies. 6(1), 28-32.
[8] Edekor L., K., & Agbornu S. (2020) Cooperative learning strategy and
students’ performance in mathematics in junior high school in Hohoe municipality, Ghana. American
Journal of Educational Research, 8(9), 693-697.
[9] Bukunola, B. A. J., & Idowu, O. D. (2012). Effectiveness of cooperative learning strategies on Nigerian
junior secondary students’ academic achievement in basic science. British Journal of Education, Society &
Behavioural Science, 2(3), 307-325.
[10] Cochran, K.F., Derutter, J.A and King, R.A. (1993), Pedagogical content knowing: an integrative model
for teacher preparation, Journal of Teacher Education,44,4.
[11] Creswell, J. W. (2020). A Framework for Design. Research Design: Qualitative, Quantitative, and Mixed
Methods Approaches.
[12] Creswell, J. W., & Tashakkori, A. (2007). Developing publishable mixed methods manuscripts. Sage
Publications.
[13] Computerized School Selection and Placement System [CSSPS]. (2023). Ghana Education Service SHS
Selection register. Retrieved from https://ghstudents.com/wp-content/uploads/2019/06/GES-SHS-
selection-REGISTER-2019.pdf.
[14] Gillman, L. (1991). The limit of x sin x/x. Teaching of Mathematics, 1(2), 346-352.
[15] Delice, A., & Roper, T. (2006). Implications of a comparative study for mathematics education in the
English education system. International Journal of the IMA, 25(2), 64-72.
[16] Demir, K., Sutton-Brown, C. & Czerniak, C. (2012) Constraints to changing pedagogical practices in
a. higher education: An example from Japanese lesson study. International journal of science
education
b. 34(11) pp.1709-1739.
[17] Elliot, S. N., Kratochwill, T.R., Cook, J., & Travers, J. (2000). Educational psychology: Effective teaching,
effective learning (3rd Ed.). Boston, MA: McGraw-Hill College.
[18] Gur, H. (2009). Trigonometry learning. New Horizons in Education, 57(1), 67-80
[19] Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., & Wearne, D. (1996). Problem
a. solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational
Researcher, 25(4), 12–21. https:// Doi. org/ 10. 3102/ 00131 89X02 50040 12
[20] Johnson, D. W., Johnson, R. T., & Smith, K. A. (1998). Cooperative learning returns to college what
evidence is there that it works? Change: The Magazine of Higher Learning, 30(4), 26-35.
[21] Johnson, D., Johnson, R., Holubec, E., & Roy, P. (2015). Cooperation in the classroom. Edina, MN:
Interaction Books.
[22] Johnson, D.W., Johnson, R.T., & Smith, K.A. (1991). Active learning: Cooperation in the college
classroom., MN: Interaction Book Company Edina.
[23] Jong, O. D., & Brinkman, F. (1997). Teacher thinking and conceptual change in science and mathematics
education, European Journal of Teacher Education, 20(2), 121-124.
Turkish Journal of Computer and Mathemacs Educaon (TURCOMAT) Vol.15 No.2(2024),170-182
182
Research Arcle
[24] Kendal, M., & Stacey, K. (2003). Tracing learning of three representations with the differentiation
competency framework. Mathematics Education Research Journal, 15(1), 22-41
[25] Kamii, C., & Dominick, A. (1997). To teach or not to teach algorithms. The Journal of Mathematical
a. Behaviour, 16(1), 51–61. https:// Doi. org/ 10. 1016/ S0732- 3123(97) 90007-9
[26] Lai, C. Y., & Wu, C. C. (2006). Using handhelds in a Jigsaw cooperative learning environment. Journal of
Computer Assisted Learning, 22(4), 284-297.
[27] Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis, (2nd ed.). Newbury Park, CA: Sage.
[28] Morse, J. M. (1991). Approaches to qualitative-quantitative methodological triangulation. Nursing
Research, 40(2), 120–123.
[29] Ministry Of Education. (2010). Teaching Syllabus for Core Mathematics (SHS). Accra: CRDD.
[30] Oloyede, E. O., Adebowale, O. F., & Ojo, A. A. (2012). The effects of competitive, cooperative, and
individualistic classroom interaction models on learning outcomes in mathematics in Nigerian senior
secondary schools. International Scholarly Research Notices, 9(1), 61-81
[31] Rohrbeck, R., & Schwarz, J. O. (2013). The value contribution of strategic foresight: Insights from an
empirical study of large European companies. Technological Forecasting and Social Change, 80(8), 1593-
1606.
[32] Roger, E.W., Olsen, B. & Kagan, S. (1992). About cooperative learning: A teacher’s resource book. In K.
Kesler (Ed.). Cooperative language learning. Prentice-Hall Inc.
[33] Ross, J., Bruce, C., & Sibbald, T. (2011). Sequencing computer-assisted learning of transformations of
trigonometric functions. Teaching Mathematics and its Applications, 30(5), 120 – 137.
a. service-learning, Journal Curriculum Studies, Vol 32,6,797-820.
[34] Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and
misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research,
2014(2014), 1-10.
[35] Shafiuddin, M. (2010). Cooperative learning approach in learning mathematics. International Journal of
Educational Administration, 2(4), 589-595.
[36] Slavin, R. E. (2014). Cooperative learning and academic achievement: Why do groupwork work? Anales
de Psicología, 30(3), 785–791.
[37] Slavin, R. E., & Karweit, N. L. (1981). Cognitive and affective outcomes of an intensive student teams
learning experience. Journal of Experimental Education, 50(1), 29-34.
[38] The West African Examinations Council [WAEC], (2011). Chief Examiners’ Report. Core Mathematics
Program: May/June West African senior school certificate examination. Accra: WAEC.
[39] The West African Examinations Council [WAEC], (2012). Chief Examiners’ Report. Core Mathematics
Program: May/June West African senior school certificate examination. Accra: WAEC.
[40] The West African Examinations Council [WAEC], (2023). Chief Examiners’ Report. Mathematics (core):
May/June West African senior school certificate examination. Accra: WAEC.
[41] Tuna A (2013). A Conceptual Analysis of The Knowledge of Prospective Mathematics Teachers
a. About Degree and Radian World J. Educ 3 1
[42] Usman, M. H., & Hussaini, M. M. (2017). Analysis of students' error in learning trigonometry among
senior secondary school students in Zaria Metropolis, Nigeria. IOSR Journal of Mathematics, 13(2), 1- 4.
[43] Vaughan, W (2002). Effects of cooperative learning on achievement and attitude among students of colour.
The Journal of Educational Research, 95(6), 359-364.
[44] Weber, K. (2005). Students’ understanding of trigonometric functions. Mathematics Educational Research
Journal, 17(3), 91–112.
[45] Whicker M. K., Linda B., & John A. N. (1997). Cooperative learning in the secondary mathematics
classroom, The Journal of Educational Research, 91(1), 42-48.
