


































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

Vol. 3, No. 3, 2022 

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1 
 

Original Paper 

Effect of Inquiry-based Teaching Approach on Students 

Achievement in Circle Theorems 

Gabina Susuoroka
1*

, Richmond Adu-Gyamfi
2
, Emmanuel Boakye Adubofour

2
, Al-hassan 

Abdul-Mumin
2
 & Dennis Offei Kwakye

3
 

1
 Department of Business Education, University of Business and Integrated Development 

Studies-UBIDS, Wa, Ghana 

2 
Department of Mathematics, Ola SHS, NJA College of Education, Ghana 

3
 Department of mathematics and ICT, C. K. Tedam University of Technology and Applied Sciences, 

Navrongo, Ghana 

*
 Gabina Susuoroka, E-mail: susuorokag@yahoo.com 

Authors’ contribution: 

 Theoretical and conceptual framework: Gabina Susuoroka, Richmond Adu-Gyamfi, Emmanuel 

Boakye Adubofour, Al-hassan Abdul-Mumin & Dennis Offei Kwakye 

 Design and typesetting: Gabina Susuoroka, Richmond Adu-Gyamfi, Emmanuel Boakye 

Adubofour, Al-hassan Abdul-Mumin & Dennis Offei Kwakye 

 Data collection: Gabina Susuoroka, Richmond Adu-Gyamfi, Emmanuel Boakye Adubofour 

 Analysis and interpretation: Gabina Susuoroka, Richmond Adu-Gyamfi, Emmanuel Boakye 

Adubofour, Al-hassan Abdul-Mumin & Dennis Offei Kwakye 

 Supervision and Guidance: Gabina Susuoroka, Richmond Adu-Gyamfi, Dennis Offei Kwakye 

 

Received: June 15, 2022       Accepted: July 6, 2022      Online Published: September 20, 2022 

doi:10.22158/fce.v3n3p1              URL: http://dx.doi.org/10.22158/fce.v3n3p1 

 

Abstract 

This study investigated the effect of inquiry-based teaching approach on students’ achievement in 

Circle theorems in Senior High Schools. The study used sequential exploratory mixed method 

research design to collect quantitative and qualitative data to answer the various research questions. A 

sample of 105 students and 6 mathematics teachers from the two schools were randomly and 

conveniently selected respectively for the study. Circle Theorems Achievement Tests (CTAT) was 

administered to both intact classes (control and experimental) as pre-test and after the intervention a 

similar CTAT was administered as post-test. During treatment, the experimental group were taken 

through inquiry- based teaching approach instruction while the traditional instruction was applied to 



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the control group. Results from paired sample t-test showed that participants in the experimental group 

had increment in their post-test as compared to the pre-test. However, independent samples t-test 

results revealed that students in the experimental group achieved better in the post-test as compared to 

those in the control group. Interview data showed students negative attitudes and teachers’ teaching 

methods (use of traditional teaching method) were the main cause of students’ poor performance in 

circle theorems. The observation data also revealed that time factor was challenging since inquiry 

class activities needed more time to complete and also forming the small groups was a challenge in the 

class due to large class size and classroom not spacious. In conclusion, inquiry-based teaching 

approach was found to increased students’ achievement in circle theorem than the traditional 

instruction and hence recommended for teachers to implement it in their teaching. 

Keywords 

Circle, Theorem, Inquiry-Based, Teaching, Achievement and Students 

 

1. Introduction 

Mathematics is one of the most useful subjects worldwide. In view of this, its importance in everyday 

life cannot be undermined. The main objective of teaching mathematics at all levels is to enable the 

learner develop clear and logical thinking needed for analysis of both academic and everyday life 

situation (Scopes, 1973). Thus, mathematics aids in understanding other subjects, especially the science 

subjects. Mathematics is necessary for the development of scientific, technical, monetary and 

commercial activities around the life of an individual and the community (Ayot & Patel, 1992). 

Mathematics has become a compulsory subject up to a certain academic level in almost every nation of 

the world. According to Kinyua, Maina, and Odera (2003), mathematics helps the students to improve 

their skills in measurement, approximation and estimating. Such skills are necessary for any quest be it 

academic or business. The importance of mathematics is also highlighted by National Council of 

Teachers of Mathematics (2003) that “those who understand and can do mathematics will have 

significantly enhanced opportunities and options for shaping their future” (p. 5). Every student must 

study mathematics during the educational process for their personal development and achievement in 

today’s technological and progressing world. The mastery of mathematics is a key literacy component 

that influences children’s success in education and in future society (Engle, Grantham-McGregor, 

Black, Walker & Wachs, 2007). Asiedu-Addo and Yidana (2000) asserted that mathematics builds 

individual’s reasoning and problem-solving abilities, and also develops his/her personal qualities which 

include confidence, diligence, perseverance and cooperation. 

Secondary school mathematics is designed to help students in working out solutions to problems with 

accuracy, precision and speed both academic and functional life situation. The core mathematics 

syllabus at Senior High School (SHS) level in Ghana, is made up of the following content domains: 

Numbers and Numeration, Plane Geometry, Algebra, Vectors and Transformation in a Plane, Statistics 

and Probability, Trigonometry and Mensuration (Ministry of Education, 2010). Geometry, which is the 



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main focus of this study places emphasis on circle theorems. Geometry is a branch of mathematics that 

provides a rich source of visualization for understanding arithmetic, algebraic, and statistical concepts 

(Drickey, 2001). As such, the teaching and learning of geometry is very essential in everyday life since 

it provides a more complete appreciation of the world, we live in. The reason being that it appears 

naturally in the structure of the solar system, in geological formation of some rocks and crystals, in 

plants and flowers, and even in animals (Lie & Hafizah, 2008). Circle theorems is considered as a very 

important aspect of geometry. Its application is seen in ship navigation. Due to the usefulness of 

geometry in everyday life, it is not surprising that most international examinations always have some 

aspect of it. Examples of these examinations are the Trends in International Mathematics and Science 

Study (TIMSS), West African Senior School Certificate Examination (WASSCE), etc. 

Students showed high level of difficulty in identifying angles subtended at the centre and at the 

circumference by an arc. Moreover, in questions relating to angles subtended by a diameter at the 

circumference majority of the students encountered difficulties in the area of recognizing the theorem 

to be used as well as writing the correct mathematical statements. How well students retain taught 

circle theorems concept can be traced back to the teachers’ teaching approach used in class. 

Furthermore, there is empirical evidence that many students in Ghana face difficulties in solving 

questions involving geometry concepts (Baffoe & Mereku, 2010). This suggests that SHS students find 

geometry concepts difficult and mathematics teachers are faced with the challenge of how to present 

geometry concepts to students to promote conceptual understanding.  

As a result, the methods of teaching mathematics should be of great importance to mathematics 

educators. Generally, teaching requires that, the teacher creates an environment in which students are 

active leaners. Teaching also requires that the teacher integrates a range of assessment methods into 

their instruction to enhance students understanding (National Board for Professional Teaching 

Standards, 2009). Understanding mathematics means being able to justify procedures used or state why 

the process works. In other words, real understanding of mathematics concept is achieved when it is 

taught through proofs (Wiggins, 2016). Unfortunately, mathematics teachers in sub-Saharan Africa use 

the traditional method of teaching in their lessons where concepts are taught by giving a set of rules to 

students to be followed without the students knowing how those concepts came about (Akyeampong, 

Lussier, Pryor & Westbrook, 2013). According to Wood and Gentile (2003), educators are beginning to 

recognize that there are better ways to learn other than through the traditional methods. The traditional 

method of teaching, is passive rather than active. Students are made to act as spectators rather than 

partakers in the learning process. Also, the traditional method of teaching does not enhance critical 

thinking and collaborative problem-solving since “chew and pour” is the order of the day. Students 

should be exposed to skills in creating their own knowledge in order to enhance understanding of 

mathematical concepts rather than providing them with a set of rules without understanding. In order 

for the students to think mathematically, students should be exposed to various strategies of problem 

solving. One of such strategies is inquire-based teaching approach. Inquiry-based teaching approach is 



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a method of teaching in which teachers allow students to learn through investigations and discovery.  

According to Spronken-Smith (2007), inquiry-based learning is a pedagogy which enables students 

experience the processes of knowledge creation and the key attribute is learning stimulated by an 

inquiry is student centred, a more to self-directed learning and an active approach to learning. Similarly, 

Friesen and Scott (2013) also defined inquiry-based learning as an approach to teaching and learning 

that places student’s questions, ideas and observations at the center of the learning experience. 

According to Minner, Levy, and Century (2010), inquiry-based teaching strategy actively engage 

students in the learning process through scientific investigations which increase conceptual 

understanding. There is a positive impact in the student learning outcome when an inquiry-based 

learning method is used instead of traditional lecture-based learning (Minner, Levy & Century, 2010). 

With inquiry learning, students engage in learning by drawing upon their prior knowledge and 

experiences. Inquiry learning uses the student’s prior knowledge as a building block to integrate new 

understandings with prior learning (Lemlech, 1998). Learning has more meaning for students as it 

becomes a more relevant part of their lives and they begin to better understand the world around them. 

Inquiry-based learning involves students’ in explorations, theory building, and experimentation. It 

encourages active thinking and seeking rather than rote memorization. As stated by Baker et al. (2008), 

in our view, encouraging students’ problem solving and creative thinking is far better than testing their 

ability to memorize. The goal [of inquiry learning] is to help students develop skills that enable them to 

construct vital concepts and challenge their ingrained misconceptions.   

Inquiry learning is a student-centred approach that allows students to have more control over their 

process of knowledge-getting. Consequently, students are motivated by inquiry learning. Not only 

because students are actively involved in the process but because the expectation of finding the answer 

motivates the search for it as confirmed by Slavin (2006) that it arouses students’ curiosities and 

motivates students to continue to seek until they find answers. Inquiry-based learning develops 

independent problem-solving and critical-thinking skills in students, which is a benefit for both 

students and teachers. Lemlech (1998) stated that the goal of inquiry learning should be to challenge 

the student to engage in activity that requires higher level thinking and reflective processes. 

Inquiry-based learning also emphasizes students’ understanding concepts rather than acquiring skills. 

Inquiry-based learning encourages teachers to move away from the tradition in which knowledge is 

viewed as discrete, hierarchical, sequential, and fixed and toward an environment in which knowledge 

is viewed as an individual construction created by the learner (Draper, 2002). Inquiry-based learning 

offers students opportunities to discover knowledge by themselves (Longo, 2010). Students are allowed 

to discuss their own perspectives, reflect on the process of exploration, and explain their choices 

(Michalopoulou, 2014). 

 

 

 



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1.1 Statement of the Problem 

In discharging our duties in the classroom as mathematics teachers, we often encounter a lot of 

problems faced by learners. These problems sometimes discourage students in their learning of 

mathematics and eventually cause their failure in the subject. This came to light as a result of students 

showing fewer interest in circle theorems lessons leading to scoring low marks on circle theorems. 

Students showed high level of difficulty in identifying angles subtended at the centre and at the 

circumference by an arc, the relationship between the angles between the tangent and cord at the point 

of contact and angle in the alternate segment and the relationship between opposite angles of a cyclic 

quadrilateral. Moreover, questions relating to angles subtended by a diameter at the circumference and 

properties of parallel lines majority of the students encountered difficulties in the area of recognizing 

the theorem to be used as well as writing the correct mathematical statements (see Appendix A). 

Based on information gathered by the researcher, Teachers in the district still use traditional or teacher 

centred method to teach circle theorems. Traditional or teacher centred method makes students passive, 

act as spectators in the learning process, does not enhance critical thinking and collaborative 

problem-solving. In order for students to perform better in circle theorems, teachers should use student 

centred method such as inquiry-based teaching approach. In inquiry-based teaching approach, teachers 

allow students to learn through investigations and discovery, develops independent problem-solving 

and critical-thinking skills and emphasizes on students’ understanding concepts. This study therefore, 

sought to investigate the effectiveness of inquiry-based teaching approach in circle theorem in senior 

high schools in Asutifi North District in Ahafo Region in Ghana. 

1.2 Purpose of the Study 

The purpose of the study was to investigate the effect of inquiry-based teaching approach on Senior 

High Schools (SHS) students’ achievement in circle theorems in            the Asutifi North District of Ghana. 

1.3 Research Questions 

The study was guided by the following research questions: 

1) what are the causes of poor performance of students’ in circle theorems? 

2) what is the effect of using inquiry-based teaching approach on students’ achievement in circle 

theorems? 

1.4 Definition of Terms 

In the context of this study, the following definitions of terms have been used based on the objectives, 

scope, limitations and delimitations of the study. 

Circle Theorems: it is one of the geometry topics in senior high school syllabus. It is known as plane 

geometry II. It can be found in unit 2.10 in 2010 core mathematics teaching syllabus. 

Students’ Achievement: Student achievement refers to the amount of academic content learned by a 

student within a specified amount of time. The achievement can be measured using various assessment 

tools such as achievement tests, observation or interview. 

 



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Traditional Method of Teaching: For the purpose of this study, the traditional method of teaching 

mathematics is defined as the process by which mathematics teachers explain concepts to students by 

using board illustrations and then follow the explanations up with examples from textbooks. 

 

2. Theoretical Framework 

This study is anchored on constructivist theory. Constructivism is a theory about how we learn. It also 

suggests that children must be active participants in the development of their own understanding. 

Constructivist designers view instruction as “a process of supporting [knowledge] construction rather 

than communicating knowledge” (Cunningham & Duffy, 1996). The constructivist classroom is an 

environment where learners actively inquire and originate new knowledge and ideas through engaged 

dialogue, interaction, presentation, sharing, and negotiation. In this setup, teachers’ role is to guide and 

moderate the discussion rather than passively passing information to the learners. Constructivist 

teachers provide direction to the learners by engaging them in inquiry activities and by stimulating 

student centered active discussion and knowledge sharing, i.e., promoting active learning in a social 

setup where learners construct new knowledge according to their prior knowledge, social realities, 

peers’ perspectives, and new findings (Bruner, 1986). Again, constructivist teaching, emphasize that 

children have to build their own scientific knowledge and understanding. At each step-in science 

learning, they need to interpret new knowledge in the context of what they already understand. Rather 

than putting formed knowledge into children’s minds, in the constructivist approach, teachers help 

children construct scientifically valid interpretations of the world and guide them in altering their 

scientific misconceptions (Martins, Sexton, Franklin & Gerlovich, 2005).  

In constructivism, collaboration is emphasized (Adler, 1997) and this is in line with inquiry-based 

classroom which allows learners to collaboratively engage in decision making regarding the solution to 

a problem at hand with learners not losing their autonomy and control. In inquiry-based teaching 

approach, students experience the processes of knowledge creation and the key attribute is learning 

stimulated by an inquiry a student-centered approach, a more to self-directed learning and an active 

approach to learning (Spronken-Smith, 2007). The teacher’s role in a constructivist classroom is to 

prompt and facilitate discussion, and to guide students by asking questions that will lead them to 

develop their own conclusions on a subject. If inquiry-based teaching approach is based on the belief 

that knowledge is generated through the process of students working and conversing together to tackle 

real-life problems and makes discoveries, then constructivism and inquiry-based teaching approach are 

perfect match. 

2.1 Causes of Poor Performance of Students in Geometry and Circle Theorems 

A number of factors have been put forward to explain why students perform poorly in geometry and 

circle. Findings made by Noraini (2006); Aysen (2012) have shown that some factors are identified to 

make the learning of geometry concepts in mathematics difficult which include: teachers’ methods of 

instruction, geometric language, visualizing abilities. Fabiyi (2017) found out that the reasons given by 



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students for perceiving geometry concepts difficult includes: unavailability of instructional materials, 

teachers’ method of instruction and so on. 

The quality of instruction is one of the greatest influences on the students’ acquisition of geometry 

knowledge in Mathematics classes. According to Akyeampong, Lussier, Pryor, and Westbrook (2013), 

mathematics teachers in sub-Saharan Africa use the traditional method of teaching in their lessons 

where concepts are taught by giving a set of rules to students to be followed without the students 

knowing how those concepts came about. Traditional approaches in learning geometry emphasize 

more on how much the students can remember and less on how well the students can think and reason. 

Thus, learning becomes forced and seldom brings satisfaction to the students (Baffoe & Mereku, 2010). 

The problem with traditional instruction is the concept of rote learning. Marshal (2006) took the 

definition of “rote” from the Oxford English Dictionary as, a mechanical manner, by routine; especially 

by the mere exercise of memory without a proper understanding of, or reflection upon, the matter in 

question. Through traditional mathematics instruction, children are expected to use a mathematical 

concept before they have been able to experience it primarily focusing on how the teacher told them 

how to use it. This style of teaching is what Battista (2009) as cited by Marshal (2006) described as 

ineffective and seriously stunts the growth of students’ reasoning and problem-solving skills. 

2.2 Concept of Inquiry-Based Teaching Approach 

Inquiry-based learning is a pedagogy which enables students experience the processes of knowledge 

creation and a more to self-directed learning and an active approach to learning (Spronken-Smith, 

2007). Inquiry-based learning can also be defined as an approach to teaching and learning that places 

students’ questions, ideas and observations at the centre of the learning experience (Friesen & Scott, 

2013). 

There are forms of inquiry that are commonly used in inquiry-based instruction. They are confirmation 

inquiry, structured inquiry, guided inquiry, and open inquiry (Pappas, 2014). The first level of inquiry 

is confirmation inquiry in which students are provided with the question and method as well as the 

results, which are known in advance (Pappas, 2014). The second level of inquiry learning is structured 

learning where the students are introduced to the experience of conducting investigations or practicing 

specific inquiry skills like those of collecting and analyzing data (Banchi & Bell, 2008). This is where 

the teacher mainly directs the inquiry by providing questions to be investigated and will then provide a 

step-by-step instruction to help students arrive at the answer. This kind of inquiry is important 

because it enables students to gradually develop their ability to conduct more open-end ed  inquiry. It 

is also good level to start for teachers who are new to inquiry-based teaching method (Banchi & Bell, 

2008). The third level of inquiry is guided inquiry. It is the inquiry level where the question and 

procedure are provided by the teacher; however, the students arrive at an explanation supported by 

their investigations (Pappas, 2014). Here the teacher chooses the question and the students will take 

more responsibility for establishing the direction and methods of the inquiry. The teacher plays an 

important role in guided inquiry. This could be through feedbacks or posing further questions to help 



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lead the students in the right direction (Banchi & Bell, 2008). The final level of inquiry learning is open 

inquiry. In free inquiry, students form their own questions, design their own methods of investigation, 

and carry out the inquiry process without guidance from the teacher (Pappas, 2014). In open inquiry, 

students take the lead in establishing the question and methods while the teacher takes on a supportive 

role. Having students to ask questions is key to open inquiry and requires a high order thinking. 

However, it is possible to use a combination of the types mentioned and it is called the coupled inquiry 

(Banchi & Bell, 2008). 

The inquiry teaching style establishes itself as different from other constructivist guided approaches in 

the sense that it is not a minimally guided learning environment and that direct instruction can be used 

in the context of inquiry teaching and learning. Proper inquiry teaching approach requires that teachers 

carefully scaffold their students as they challenge them with new mathematical material (Hmelo-Silver 

et al., 2007). Once students are challenged, they are expected to engage in creating conjectures, 

analysing conjectures, communicating, working collaboratively, and engaging in mathematical 

argument (Stonewater, 2005). 

2.3 Effect of Inquiry-Based Teaching Approach on Students’ Achievement 

For teachers to have a proper understanding of students’ mathematical knowledge and know-how, there 

must be tangible ways teachers can gain insight into their students’ thought processes. Inquiry-based 

mathematics approach does just that (Ferguson, 2010). The teacher’s role has evolved from concept 

deliverer to concept facilitator where questions are posed to get students thinking and experiencing the 

mathematical concepts at hand. Students are encouraged to “show what they mean” and “explain” their 

thinking either orally or in written form (Ferguson, 2010). 

According to Ferguson (2010) the inquiry-based teaching approach has a positive effect on the 

mathematics achievement of students. In Ferguson (2010) study, two high school geometry classes 

were taught area formulation using a traditional lecture-based approach to instruction. A third geometry 

class was taught area formulation utilizing inquiry-based instructional methods. Students in both 

groups took both a pre- test and post-test. At the end of the exercise, Students involved in the 

inquiry-based lessons exhibited better retention, a better ability to problem solve, and better 

performance on decontextualized mathematical problems than their peers who were taught in the 

traditional fashion. He stated that, the inquiry-based mathematics instruction improves students’ 

mathematics achievement. He therefore recommended that teachers of mathematics should apply the 

inquiry-based teaching and learning approach in both at the junior levels through to the tertiary levels. 

A quasi-experimental study carried out by Riordan and Noyce (2001) compared two inquiry-based 

mathematics programmes; an elementary programme called Everyday Mathematics and a middle 

school programme entitled Connected Mathematics. The study compared state-wide standardized test 

scores for students using these curriculums to demographically similar students using a mix of 

traditional instruction methods. The results of this study showed that students in schools using either 

of these inquiry-based programmes as their primary mathematics curriculum performed significantly 



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better on the 1999 state-wide mathematics test than did students in traditional programmes. 

Similarly, Al-Qurashi (2002) conducted research on examining inquiry-based instruction in 

mathematics. Teachers were trained in professional development sessions and participated in an 

inquiry-based instruction project. He used videotapes, lesson plans of the participants, observations, 

and interviews to explore the implementation of inquiry-based instruction. Using the Engage, Explore, 

Explain, Elaborate and Evaluate inquiry-based design (5 E inquiry-based design), he developed a rubric 

to evaluate lessons. He concluded that inquiry-based instruction promoted student achievement. 

2.4 Summary of Review 

Findings from the review suggested that most students learn best when given problems to solve and 

that such problem-based learning improves retention and ownership of geometry (circle theorems) 

(Goos, 2004; Stonewater, 2005; Hmelo- Silver, Duncan & Chinn, 2007). Through the analysis of 

literature on inquiry-based approach it seems feasible that one could create a more optimal learning 

environment for most students. Few articles are dedicated to the detriments of inquiry instruction 

however, Lampert (1990) did indicate that not all students participate in inquiry environments. In 

particular, some students may not wish to participate in classroom discussions. Though there are 

concerns regarding inquiry-based instructional methods they are not severe enough that we should 

ignore the possible benefits of such an approach. In light of the current state of mathematics education, 

and the consideration that in current practice not all students are engaged in the learning processes, the 

inquiry-learning approach needed to be investigated. The possible benefits to students and mathematics 

education warrant a movement towards constructivist-based instruction and inquiry-based learning 

opportunities. 

 

3. Method 

3.1 Research Design 

Mixed methods design was used for the study since both quantitative and qualitative data set was 

collected. Mixed methods design is based on the premise that a single data set is not sufficient to 

answer all the research questions which are different in nature (Creswell, 2012). Not all, mixed method 

approach holds greater potential to address complex questions by acknowledging the dynamic 

interconnections that traditional research methods have not adequately addressed (Hesse-Biber, 2010). 

The use of the quantitative approach enables the researcher to use the students’ test data to ascertain if 

there was any positive or negative influenced of inquiry-based teaching approach on students’ 

achievement in circle theory. This was done by the use of independent and dependent t-tests to test for 

statistical significance in the differences in pre and post test scores of the students. The qualitative 

approach on the other hand, allow the use of semi-structured interview data to get an in-depth 

knowledge of causes of poor performance of students in circle theory from students’ and mathematics 

teachers’ perspective. Qualitative approach also enables the researcher to use observation data 

collected from mathematics teachers on challenges associated with inquiry-based teaching approach in 



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teaching circle theorem classroom. 

Mixed method was used to collect different and complementary data on the same topic for 

integration and interpretation to address the overall content aim of the study (Creswell & Clark, 2011). 

This method is justified on the basis that the researcher collected both quantitative and qualitative data 

within the study period to address the aim of this study. The reason for combining both quantitative and 

qualitative data was to bring together the strengths of both forms of data for this research work and 

better understanding of the results (Cohen, Manion & Morrison, 2007; Creswell, 2009). 

3.2 Population 

Field (2013) described population as an entire collection of things. Also, Nworgu (2006) classifies 

population as target and accessible where target population is all the members of a specific group to 

which the investigation is related while the accessible population is defined in terms of those elements 

in the group within the reach of the researcher. The target population for the study was all the 

third-year students and mathematics teachers in the public senior high schools in Asutifi North District 

in Ahafo Region of Ghana. There are two public senior high schools in the district with a total 

population of 657 students in third-year and 23 mathematics teachers these schools.  

3.3 Sample and Sampling Technique 

A sample according to Gerrish and Lacey (2010), is a subset of a target population, normally defined 

by the sampling process. The sample for the study consists of 105 students and 6 mathematics 

teachers selected from the two Senior High Schools in the District. Considering the purpose and the 

design of the study, the researcher employed simple random and convenience sampling techniques to 

select the sample from the population. Simple random sampling is a process of selecting a sample from 

a population in a way that every different possible sample of the desired size has the same chance of 

being selected (Devore, 2005). On the other hand, a convenience sampling is a type of non-probability 

sampling where members of target population that meet certain practical criteria such as easy 

accessibity, geographical proximity, availability at a given time, or the willingness to participate are 

included for the purpose of the study (Dornyei, 2007). Simple random sampling technique was use to 

select 105 students for the study. Simple random sampling was use to select two intact classes, one from 

each school. This technique was used to avoid bias in selecting the classes. School “A” have seven 

classes for the programmes of General Arts, General Science and Home Economics and School “B” 

also have eight classes for the programmes of General Arts, General Science, Home Economics and 

Visual Arts. These classes were also coded according to each selected school. The coded numbers were 

also keyed into the random number generated calculator to select the classes to be used for this study. 

For school “A”, 3F1 (3 General Arts 1) class was selected, the number students in 3F1 class was 53 and 

for school “B”, 3E1A (3 Home economics, 2) class was selected with a total number of 52 students. 

Final year students were selected because they treated circle theorems in form 2 so they are the right 

students to provide vivid responses about their perception on circle theorems. Convenience sampling 

technique was used to select 6 mathematics teachers and 10 students to collect interview data from each 



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group (control and experimental) school. The selection of both the mathematics teachers and students 

was done based on their availability and willingness to participate in the study at the time the interview 

was conducted.  

3.4 Research Instruments  

Based on the nature of the research questions examined in the study, Circle Theorems Achievement 

Test (pre-test and post-test), semi-structured interview and observation were the main instruments used 

to collect data for this study. The Circle Theorems Achievement Test (pre-test and post-test) was used 

to collect quantitative data while semi-structured interview and observation were also used to collect 

qualitative data.  

3.5 Circle Theorems Achievement Test (CTAT)  

Circle Theorems Achievement Test was used as an instrument in collecting quantitative data to assess 

the effectiveness of the experiment on the experimental group. The researcher administered two tests 

(i.e., pre-test and post-test). These items were developed by the researcher based on the research 

questions and theoretical perspective. The content of the test items was taken from a Government 

approved students’ textbooks that are commonly used in teaching geometry in all Senior High Schools 

(SHSs) in Ghana and all the items aligned with the objectives from the core mathematics teaching 

syllabus for SHSs in Ghana.  

The pre-test consisted of 10 major items (see Appendix B). The pre-test was intended to measure 

students’ level of attainment in the concept before treatment. It also helped to unveil students’ areas of 

difficulty in the concept in order to design a treatment that would best suit their level of attainment. The 

post-test contained the same number of items as the pre-test. The difficulty level of the post-test was 

similar to the pre-test. However, the items in the post-test were different from those in the pre-test (see 

Appendix C). According to Creswell (2012), using different test items on pre-test and post-test of a test 

instrument eliminates biasness from the scores. The post-test was intended to measure participants’ 

attainment in circle theorem after the treatment has been implemented. Pre-test and post-test were 

administered to all the 105 students selected for the study, in both experimental group (52 students) and 

control group (53 students). The scores of both pre and post-tests was used to answer research question 

2. 

3.6 Semi-structured Interview 

Semi-structured interviews have the advantage of generating qualitative data through the use of 

open-ended questions which allow the participants have in-depth conversation with the interviewer, 

choosing their own words. Such interviews have increased validity because it gives the interviewer the 

opportunity to probe for a deeper understanding, ask for clarification and allow the interviewee to steer 

the direction of the interview (McLeod, 2014). The researcher therefore used semi- structured interview 

to seek both students’ and teachers’ in-depth knowledge on the causes of poor performance of students 

in circle theorems. 

 



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The students’ semi-structured interview guide contains 2 items, the first item with 1 sub-item which 

was developed by the researcher and it was administered to 10 conveniently selected students. 5 

students from the experimental group and other 5 students from the control groups after the post-test 

(see Appendix D). The mathematics teachers’ semi-structured interview guide also contains 2 items, 

the first item with 1 sub-item which was developed by the researcher and it was administered to 6 

conveniently selected mathematic teachers. 3 mathematics teachers from each experimental and control 

group’s school (see Appendix E). The interview was used to answer research question 1. 

3.7 Observation 

Observation is a systematic data collection approach in which the researchers use all their senses to 

examine people in natural setting or naturally occurring situations (Cohen & Crabtree, 2006). Two 

mathematics teachers were conveniently selected as observers for the study. The observers were 

always present in the experimental group class during the intervention period. The observers were 

directly observing the implementation of the intervention in each period and taking notes quietly on 

the challenges associate with the inquiry-based teaching approach in the classroom without interfering 

with the lessons based on the observation guide (see Appendix F). Observations made based on the 

observation guide was used to answer research question three.  

3.8 Reliability 

William (2006), was of the view that reliability is the consistency or dependability of the measurement; 

or the extent to which an instrument measures the same way each time it is used under the same 

condition with the same subjects. Moreover, Creswell and Clark (2017) stated that reliability implies 

scores received from participants should be consistent and stable over time when the instrument is 

repeatedly administered. Test-retest is one of the ways to conduct reliability test. Test-retest approach 

was employed by the researcher to examine the reliability of the CTAT in this study. According to 

Creswell (2012), the test-retest approach of measuring reliability involves administering the same test 

at two different times to the same participants at a considerable time interval. In this study, the 

researcher administered CTAT to one of the form 2 science class, 2A1 students of the control group 

school and after a month re-administered them to the same students again. The results were used for 

modification of instruments. The modified and improved instruments were then used in this study. The 

data collected was used to determine the reliability of the instruments. The correlation co-efficient of 

reliability of CTAT was calculated using Karl Pearson’s co-efficient of correlation testing in SPSS. The 

correlation coefficients of reliability of CTAT was 0.82. The reliability coefficient was greater than 

0.5, therefore, the CTAT was reliable for having high degrees of reliability and could help in achieving 

research objective for this study. 

3.9 Validity 

According to Field (2013), validity basically means measuring what you think you are measuring. Field 

(2013) stated that content validity was really the degree to which an item can be considered as a 

representative and Cohen, Manion and Morrison (2007) asserted that content validity is concern with 



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how an instrument fairly and comprehensively covers the domains or items that it purports to cover as 

the face validity is where superficially the test appears at face value to test what it is designed to test. 

To attain content and face validity of the instruments, the researcher gave the instruments (interview 

guide, circle theorems achievement test and observation guide) to his Supervisor to examine after which 

all remarks, corrections and comments were made. 

3.10 Data Collection Procedure 

The researcher visited the sample selected Senior High Schools and discuss the purpose of the study 

with the headmasters, and also seek their permission to carry out all exercises of the study that had to 

do with data collection and intervention. 

3.11 Pre-intervention Stage 

The researcher after seeking permission to carry out all exercises of the study in the selected sample 

schools and had the approval, went on and collected his first data on the schedule date. The circle 

theorems achievement test that is pre-test was administered to students in both schools on the same day. 

The researcher collected students work for marking (see Appendix H) and analysis of scores. Four days 

after the pre-test, researcher met the control and experimental group separately and explain the purpose 

of the interview to them. The researcher then granted one-on-one interviews to 10 students and 6 

mathematics teachers selected from both the experimental and control groups, 5 students and 3 teachers 

from each group. Each interview took a minimum duration of 10 minutes and a maximum duration of 

15 minutes. The researcher audiotaped the questions and responses of the interviews. The researcher 

used a total of two days to conduct the interviews. 

3.11.1 Intervention 

Lesson design 

One of the goals of this study was to teach the same concept in two different ways using traditional, 

lecture-based instruction with the control group, and inquiry-based instructional methods with the 

experimental group. These lessons were to be taught over the same timeframe. The control group 

lessons were taught using the traditional approach described by Stonewater (2005) and Goos (2004) 

which involved reviewing the homework assignment from the previous day, followed by a presentation 

of new material, and concluded with a homework assignment. New material was presented using 

lecture-based instruction that included examples of problems that they would see in their homework, 

and the formulas required to solve these problems. Parts necessary for substitution into circle theorem 

formulas were highlighted, and examples included the various theorems. Experimental group lessons 

were inquiry-based and had specific objectives for each day to keep the experimental group on pace 

with the control group. Students in the experimental group solved the same type of circle theorem 

problems but were taught in a very different manner than the control group. Lessons were specifically 

designed practically to meet the criteria of inquiry-based learning environments and are included in 

Appendix G.  

 



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The inquiry lessons were facilitated through individual work and group work with the expectation that 

students would work with their group members to develop methods for solving problems related to 

circle theorem. As the instructor, I closely monitored the process of individuals and groups, and 

required all participants to give justification for their methods. I carefully designed the lessons to allow 

students to move from more simple environments for formulation into more complex problems that 

required usage of a developed method for solving circle theorem problems. As the class progressed 

into considering more complex theorems, students were expected to draw on previous explorations to 

find solution to new problems. The lessons were designed to engage students in developing their own 

strategies for addressing problems on circle theorem, fitting with basic constructivist learning 

principles. At the end of each lesson, students were provided a problem set to take home and complete 

using their newly developed method. These problem sets were short (consisting of two to four problems) 

and only served to solidify developed understandings. 

3.11.2 Procedure 

At the beginning of the study, all members of the control group and the experimental group took a 

pre-test. The purpose of the pre-test was to measure students’ prior knowledge about geometry and 

circle theorems problems. Data from the control group was compared with the experimental group 

using a t-test. Differences were noted and included in the final comparison of the two classes. Once 

the pre-test was completed, the differing lessons began. I, the researcher instructed the experimental 

class while a different mathematics teacher of the same experience took the class that represented the 

control group. Both of us were teaching the topic based on the lesson’s objectives but different 

approaches.  

The inquiry-based lessons were taught over a three weeks periods. Students were encouraged to discuss 

the circle theorems and develop methods through this discourse. Students’ desks were arranged in 

groups of two or three to encourage group discussion. The researcher served as a facilitator of the 

discussion and guided the direction of the discourse in a way that helped students recognize the 

meaningful relationships underlying their mathematical tasks. This included small segments of direct 

instruction as well as extended periods monitoring students’ progress as individual groups developed 

approaches. Researcher closely monitored individual groups’ progress, aiding them in recognizing any 

noticeable misconceptions through question posing. Though direct instruction was sometimes used, it 

was never the primary method of instruction, and every class period began with student investigations 

and discussions of the circle theorems. Students were expected to defend their ideas in circle theorems 

to their groups as well as to the entire class, to support their abilities to explain circle theorems ideas. 

Students were not required to take formal notes. Instead, the hands-on materials and hand-outs that 

students received during lessons became their resource for future use. Daily lessons concluded with 

short take-home assignments to assess the students’ developing understanding of the circle theorems.  

The control group was taught using the government textbook for the selected school district. Their 

lessons followed those from the selected text and were supplemented with worksheets that are 



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generally used in geometry classes to highlight specific concepts of circle theorems. Students were 

taught the formulas in circle theorems and were expected to use those formulas on a variety of 

problems, including problems that do not give all necessary information. All instruction was 

lecture-based and examples were provided to guide the students in using the circle theorems rules. 

Students were also shown the reasoning behind the formulations. Students were expected to participate 

in the lecture by answering questions and by taking formal notes, which were assessed for 

completeness at the end of the unit. To encourage participation and focus on the instructor throughout 

the class period, students’ desks were placed in rows facing forward. Once instruction was completed, 

students were given an assignment out of the book and a small amount of class time to begin work so 

that they could ask questions if necessary. Work not completed during this time should have been taken 

home by the student for completion and inspect it next period. Students should have felt comfortable 

with this progression through the material, as this instructional approach had already been established 

throughout the school year. 

Throughout the course of the study the researcher maintained a journal in which student behaviours 

within the experimental classrooms were documented, as well as the researcher’s own reflections on 

what went well during the instructional periods. Researcher recorded examples of student 

conversations and strategies as they attempted onto use ideals of circle theorems they were learning. 

Through careful observation, researcher hoped to discover if the method of instruction impacted on the 

students’ willingness to attack difficult problems on their own. Researcher was also trying to determine 

if the students in the experimental group adapted and took responsibility for their learning. When 

differences developed in their approaches to the mathematics and problem-solving approaches, then 

the researcher attempted to generalize these differences and included them in his observational data. 

Researcher also tried to find whether the experimental-group students performed better when 

confronted with a real-life situation involving circle theorem and circle geometry in general, observing 

whether they had a better-established ability to convey meaning and understanding through 

mathematical discourse to others. All of this information was important in determining the overall 

success of the instructional approach. 

3.11.3 Post-intervention Stage  

At the end of the three weeks intervention period, both groups of students were given a post-test. The 

post-test contained similar items as the pre-test. The post-test also contained a section of problems that 

required students to apply their problem-solving abilities. Such problems required more analysis on the 

part of the students and a better understanding of the circle theorems relationships that exist among 

circle geometry and geometry as a whole. Students’ post-test scripts were marked (see Appendix H) 

and analyzed the scores. 

3.12 Data Analysis Procedure 

The data obtained through the pre-test and post-test, semi-structured interview and observation guide 

were organized and summarized to obtain sense of information and to reflect on its overall meaning. 



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The data was analyzed quantitatively (descriptive and inferential data analysis) and qualitatively 

(descriptive words). The descriptive statistics such as measure of central tendencies and dispersion 

were used. According to Creswell (2012), descriptive statistics basically helps researchers to 

summarize the overall trends or tendencies in quantitative data, provides an understanding of the 

variability of the data and provides understanding of how one score compares with another. Thus, 

descriptive statistical analysis was used in an attempt to understand, interpret and describe the scores of 

experimental and control groups from the CTAT. 

The inferential statistics, paired sample t-test and independent samples t-test were run to compare for 

any significant difference in the mean scores of the experimental and control groups at 95% confidence 

level was used to an to answer research question 1 quantitatively. Qualitative data generated from 

interviews and observations were used to answer research question 1 and 3 respectively. Recorded data 

generated from the one-on-one interviews were analyzed using thematic analysis. That is recorded 

audio from the interviews granted to participants were transcribed and analyzed based on the topical 

areas contained in the interview guides. The researcher reported all events that emanated from the 

interviews by describing and interpreting the outcomes after reading the transcribed interview. The 

observations made by the mathematics teachers were also compiled. 

3.13 Ethical Consideration 

The study participants were kept anonymous. All the participants were treated with respect. The 

researcher explained the purpose of the sturdy and their rights such as withdrawal from participation if 

they want to do so, without being compelled to give an explanation. 

 

4. Results and Discussions 

4.1 Demographic Information of the Participants 

The demographic information of students was described in detail in the following two tables. Table 1 

presents the demographic background of the students according to their gender and Table 2 deals with 

their age group. This was necessary in order to understand the researcher’s informants used for the 

study. A total of 105 final year students of the two senior high schools in the district participated in this 

study. This was made up of 29 males, representing 28% and 76 females, representing 72%. One of the 

two schools used for the study was mixed whilst the other was single sex (female) school. This 

contributed to the lower number of males as compared to the higher number of females. However, 

gender have no effect on the results of this study. This distribution is presented in Table 1. 

 

 

 

 

 

 



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Table 1. Gender Status of the Students 

School Class Total number Male Female 

A 3F1 53 29 (55% ) 24 (45 %) 

B 3E1A 52 0 (0% ) 52 (100 %) 

Total  105 29 (28%) 76 (72 %) 

Source: Field data, 2020. 

 

Table 2 shows the age distribution of the students. From Table 2, majority 77(73%) of the students 

were between 17-19 years, followed by 20(19%) of them were 20-22 years and only 8(8%) of them 

were between the ages of 14-16 years. This means that none of them was below 14 years and also 

above 22 years. Majority of the students are matured enough to give correct responses needed for the 

study. 

4.2 Findings 

The findings have been categorized and presented in three main themes in accordance with the research 

questions. These were the causes of poor performance of students in circle theorem, the effects of the 

inquiry-based teaching approach on students’ achievement in circle theorems and challenges of 

inquiry-based teaching approach in teaching circle theorems. 

4.2.1 Research Question 1 

What are the causes of poor performance of students’ in circle theorems? 

Research question 1 sought to find out the causes of poor performance of students in circle theorem. In 

answering this research question, semi-structured interview was granted to 10 students and 6 

mathematics teachers conveniently selected from both experimental and control schools. 

The students’ interview data were presented as follows.  

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 1: Hmmm, sir please no. I always score low marks. In fact my performance is 

not good in that topic. 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 1: The way my teacher taught me, I did not understand it at all. The topic itself 

is something complex for me. 

Interviewer: How does your mathematics teacher teach circle theorems in your class? 

Interviewee 1: When the teacher was teaching us this topic, He allow us to write the 

properties or rules one by one as he was dictating. He then solve one example on each 

properties and ask us to solve some from the textbook as class exercise. In fact I was 

confused about these properties. I didn’t get anything that he taught us. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 



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Interviewee 1: I suggest my teacher should take his time and teach us well, so that I can 

also understand it well. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 2: No, I always score no or low marks in circle theorem exercise. I even don’t 

answer questions involving circle theorem in end of semester since I may score no or low 

marks. 

Interviewer: what are the causes of your low (poor) performance in circle theorems 

exercise? 

Interviewee 2: I find it difficult to apply more than two rules or properties to solve question. 

The rules or the properties are confusing to learn and understand and this makes it 

challenging to me. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 2: I think my teacher should help me to know how to use more than two 

properties to solve problem. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 3: No. I find it difficult to score high marks. 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 3: I have idea or mind-set that circle theorems are complicated and difficult so 

I don’t like solving problems on it. I know I will not select questions on the topic even in 

WASSCE. Thus why I score low marks. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 3: I think teachers should help me to change my mind-set that circle theorems 

are complicated and difficult so I may like to solve more problems on it. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 4: No, please sir. 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 4: My teacher did not teach me well to understand. He do not know how to go 

about it. He made it difficult and totally confused me on the topic. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 4: I suggest my teacher should have patience with those of us, slow learners to 

understand the topic since he always move with the fast learners in class. Interviewer: Do you 

score high marks in circle theorems exercise? 

Interviewee 5: No Sir, I score very low marks. 

Interviewer: what are the causes of your low (poor) performance in circle theorems 



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exercise? 

Interviewee 5: I have difficulties to transfer knowledge on triangle and parallel lines 

properties in circle theorems and also I find it difficult to solve problems involving two or 

more properties. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 5: I suggest teachers should teach me triangle and parallel lines properties 

well then followed by circle theorems so that I can easily transfer knowledge. And also 

teachers should help us to solve problems involving two or more properties. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 6: No Sir, 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 6: The topic is too difficult for me, I don’t get the understanding. It’s confusing. 

Interviewer: what do you suggest should be done in order to improve on you performance 

in the topic? 

Interviewee 6: My teacher should make it easy for me by teaching it again. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 7: No please sir, 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 7: The way my teacher taught me, I did not understand it. He was moving very fast 

making everything difficult and confusing. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 7: My teacher should take his time to teach it well for me to understand it. I 

think my teacher should teach it again. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 8: No Sir, 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 

Interviewee 8: I do not practice or solve problems on circle theorems and also the topic is 

complicated and difficult to me. 

Interviewer; what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 8: I think I have to practice or solve problems on the topic by allowing friends 

to teach me and change my mind set that topic is difficult. 

Interviewer; Do you score high marks in circle theorems exercise? 

Interviewee 9: No sir please. 

Interviewer: what are the causes of your low (poor) performance in circle theorems exercise? 



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Interviewee 9: My teacher made it difficult for me to learn since he just use one period to 

teach all the nine principles of circle theorems and ask us to use them to solve problems. I 

did not understand what he taught us. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 9: My teacher should re-teach the topic again and this time each theorem with a 

specific examples and exercises. 

Interviewer: Do you score high marks in circle theorems exercise? 

Interviewee 10: No Sir 

Interviewee: Question; what are the causes of your low (poor) performance in circle theorems 

exercise? 

Interviewee 9: My perception about the topic is that it’s difficult. It has many principles that 

makes it more difficult for me to understand and also my teacher made it more difficult for 

me to understand. 

Interviewer: what do you suggest should be done in order to improve on your performance 

in the topic? 

Interviewee 9: My teacher should take his time and find proper way to teach the topic again 

for me to understand. 

The mathematics teachers’ interview data were also presented as follows. 

Interviewer: Do your students perform well in circle theorems exercise? 

Interviewee 1: No sir please. Almost all my students performed poorly in circle theorem 

questions. 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 1: Most of my students’ have in their mind that it is difficult topic and they 

are lazy, they don’t practice after classroom work. 

Interviewer: What do you suggest should be done in order to improve on your students’ 

performance in the topic? 

Interviewee 1: I think students should change their attitude towards the topic and 

practice more examples after school. 

Interviewer: Do your students perform well in circle theorems exercise? 

Interviewee 2: No, their performance is not good in the topic. 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 2: Students’ inability to apply their knowledge on triangle and parallel lines 

and other properties in solving circle theorem questions. Also students’ cannot apply two or 

more properties to solve problem. 

Interviewer: What do you suggest should be done in order to improve on your students’ 

performance in the topic? 



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Interviewee 2: I suggest teachers should help students to apply the basic principle in plane 

geometry 1 and how to use more than two circle properties solve a problem. 

Interviewer: Do your students perform well in circle theorems exercise? 

Interviewee 3: No, their performance in the topic is very bad. 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 3: Students’ have problem with connecting one property with others in solving 

circle theorems problems. And using basic properties of triangles and parallel lines in 

solving circle theorems problems. Students don’t practice or solve problem on the topic. 

They claim the topic is too difficult for them to learn. 

Interviewer: What do you suggest should be done in order to improve on your students’ 

performance in the topic? 

Interviewee 3: I think, I should form small groups for students’ and encourage them to practice 

more examples on the topic. 

Interviewer: Do your students perform well in circle theorem exercise? 

Interviewee 4: No sir 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 4: Students are lazy to practices on their own or in group. They are not 

serious about the topic. They claim it difficult to understand. 

Interviewer: What do you suggest should be done in order to improve on your students’ 

performance in the topic? 

Interviewee 4: I think they should stop been lazy and be more serious with their studies. 

Also they should change their attitudes towards the topic that it is difficult. 

Interviewer: Do your students perform well in circle theorems exercise? 

Interviewee 5: No 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 5: Students have ideal that circle theorems questions are complicated and confusing 

for that reason they do not pay much attention on the topic. 

Interviewer: What do you suggest should be done in order to improve on your students’ 

performance in the topic? 

Interviewee 5: I think teachers should help to changes students’ attitudes on the topic that it 

is difficult and confusing. 

Interviewer: Do your students perform well in circle theorems exercise? 

Interviewee 6: No 

Interviewer: What are the causes of their poor performance in the topic? 

Interviewee 6: Students find it difficult to apply the theories to solve problem. Especially 

problem involving two or more properties and other geometry problem. 

Interviewer: What do you suggest should be done in order to improve on your 



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students’ performance in the topic? 

Interviewee 6: Geometry at the junior high school level should be well strengthen in order 

to help students to apply geometry concepts at the senior high school level. 

4.2.2 Research Question 2 

What is the effect of using inquiry-based teaching approach on students’ achievement in circle 

theorems? 

To determine the effectiveness of inquiry-base teaching approach on students’ achievement in circle 

theorems, Circle Theorems Achievement Test (CTAT) was administered to students. All the 105 

students selected from the two schools in the District agreed to participate in the study, wrote both the 

pre-test and the post-test of the CTAT. The summary of the scores of CTAT (pre and post) of the 

students is recorded in Table 2, Table 3, Table 4, Table 5, Table 6 and Table 7. 

 

Table 2. Descriptive Statistics of Pre-test Scores of Control and Experimental groups 

Groups N Minimum Maximum Mean 
Std. 

Deviation 

Experimental (B) 52 4.00 23.00 11.88 3.97 

Control(A) 53 3.00 21.00 11.51 4.45 

Source: Field data, 2020. 

 

The pre-test scores of experimental and control groups were compared to determine if there exist any 

significant difference in the mean scores before treatment. In fact, the pre-test results revealed no 

significant difference between the two groups. The result from Table 2 showed a mean score of 11.88 

for the experimental group as compared to a mean score of 11.51 for the control group. The results 

indicated a mean difference of 0.37 between the mean scores of school “B” and “A” with respect to 

performance in the pre-test. 

The following assumptions of independent sample t-test was checked and met (homogeneity of 

variance, the sample of each group was more than 30, samples scores were normally distributed (see 

Appendix I) and two groups were randomly independent samples) before independent sample t-test was 

tested. 

 

Table 3. Independent Samples T-test of Pre-test of Experimental and Control groups 

Groups N Mean Std. Div. t-value df p-value 

Experimental 

(B) 
52 11.88 3.969 0.455 

10

3 
0.650 

Control (A) 53 11.51 4.453    

Source: Field data, 2020. 



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To ascertain whether the difference between the mean scores was statistically significant, independent 

samples t-test was performed at 95% confidence level. The results of the independence samples t-test 

performed on the pre-test scores of school “B” and “A” is illustrated in Table 4. The results from the 

Table 4, the independent samples t-test performed on the pre-test scores of the two independent groups: 

that is experimental and control groups, revealed that there was no statistically significant difference 

between the experimental group and control group. (103)=0.455, 𝑝=0.650>0.05. This result indicates 

that both the experimental and control groups were at the same level in terms of conceptual 

understanding of the concept of circle theorems before the intervention was carried out. 

The following assumptions of paired sample t-test were checked and met (homogeneity of variance, 

sample scores were normally distributed (see Appendix I) the sample of the group was more than 30 

and the samples were randomly selected) before the paired sample t-test was tested. 

 

Table 4. Paired Sample Statistics of Post and Pre-tests of the Experimental Groups 

Groups N Minimum Maximum Mean 
Std. 

Deviation 

Std. 

Erro.Mean 

Post-test 52 17 44 29.827 6.718 0.932 

Pre-test 52 4 23 11.885 3.969 0.550 

Source: Field data, 2020. 

 

Table 5. Paired Sample T-tests of Post and Pre-tests of the Experimental Groups 

Experimental(B) N 
Mean 

Difference 
Std. Div. t-value df p-value 

Cohen’s 

d 

Post-test – 

Pre-test 

52 17.942 4.578 28.263 51 0.000 3.92 

Source: Field data, 2020. 

 

To find out whether the difference in the pre-test and post-test scores of School “B” was statistically 

significant, paired samples t-test was conducted to compare the pre-test and post-test scores at 95% 

confidence interval. Tables 4 and 6 presents sample t-test of the Circle Theorems Achievement Test 

score of the experimental group. From Table 4, the mean and the standard deviation scores of the 

pre-test was (𝑀=11.885 and 𝑆𝐷=3.969) while that of post-test was (𝑀=29.827 and 𝑆𝐷=6.718). The 

results indicated a mean difference of 17.942 which was significant. 

The results of the paired samples t-test (see Table 5) of participants from school B, the experimental 

group who were taught using inquiry-based teaching approach, indicated that there was statistically 

significant difference in their mean scores of the pre-test and the post-test, 𝑡(51)=28.263, 𝑝=0.000<0.05. 



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The effect size the inquiry-based treatment was calculated to determine the extent of the intervention 

(see Table 5). The effect size Cohen’s 𝑑=3.92 which is large effect size was realized. This effect size 

value implies that the inquiry-based teaching approach has made a tremendous impact on students’ 

concepts of circle theorems. 

Research question 2 focused basically on the effectiveness of inquiry-based teaching approach on 

students’ achievement on the concept of circle theorem in contrast to the traditional instruction. The 

independent variable for the test was the teaching method (That is: the inquiry-based or the traditional 

method) and the dependent variable was the achievement in the post-test of the two groups. 

 

Table 6. Independent Sample Statistics of Post-test of Experimental and Control Groups 

Groups N Minimum Maximum Mean 
Std. 

Deviation 

Std. Error 

Mean 

Experimental 52 17 44 29.83 6.718 0.932 

Control 53 10 37 19.74 5.069 0.696 

Source: Field data, 2020. 

 

Table 7. Independent Samples T-test of Post-test of Experimental and Control Groups 

Groups N Mean Std. Div. t-value df p-value Cohen’s 

d 

Experimental 

(B) 

52 29.83 6.718 8.699 103 0.000 1.71 

Control (A) 53 19.74 5.069     

Source: Field data, 2020. 

 

The post-test scores of experimental and control groups were compared to determine if there exist any 

significant difference in the mean scores after treatment. In fact, the post-test results revealed 

significant difference between the two groups. The result from Table 6 showed a mean score of 29.83 

and standard deviation of 6.718 for the experimental group as compared to a mean score of 19.74 and 

standard deviation of 5.069 for the control group. The results indicated a mean difference of 10.09 

between the mean scores of school “B” and “A” with respect to performance in the post-test. 

From Table 7, the results of the independent samples t-test revealed that there was statistically 

significant difference in mean between the experimental group and control group 𝑡(103)=8.699, 

𝑝=0.00<0.05. This result suggests that the experimental group which was taught with inquiry-based 

teaching approach outperformed the control group taught with the traditional method. 



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The effect size the inquiry-based treatment was calculated to determine the extent of the intervention 

(see Table 7). The effect size Cohen’s 𝑑=1.71 which is large effect size was noted. This effect size 

value signifies that the inquiry-based teaching approach has made a great impact on students’ 

acquisition of circle theorems concepts.  

4.3 Discussion of Results 

This part of the study discusses the result of the study. The findings are discussed in view of previous 

related studies and the findings of the results of the research questions. The analysis of the interview 

data collected from both students and mathematics teachers show causes of poor performance of 

students’ in circle theorems and suggested ways to improve upon their performance. Findings from the 

analysis of interview data revealed that students see circle theorems as the most difficult topic and 

developed negative attitudes towards circle theorems and this is one of the causes of their poor 

performance. These findings are consistent with findings of a research made by Mogari (1999) who 

found out that students with negative attitudes toward geometry have problems with understanding 

other concepts in geometry. Also, this findings is in line with the study made by Geddes and Fortunato 

(1993) who noted that students’ attitudes about the value of learning geometry may be considered as 

both an input and outcome variable because their attitudes towards geometry can be related to 

educational achievement in ways that reinforce higher or lower performance. Similar, Pickens (2005) 

linked higher achievement in geometry to positive attitude on the part of the students. Findings 

reveals that, mathematics teachers teaching method also account for students’ poor performance in 

circle theorem. These findings show that teachers use traditional method mostly to teach students’ 

circle theorem which is line with the study made by Akyeampong, Lussier, Pryor, & Westbrook (2013) 

which confirm that mathematics teachers in sub-Saharan Africa use the traditional method of 

teaching in their lessons where concepts are taught by giving a set of rules to students to be followed 

without the students knowing how those concepts came about. The finding also supports the statement 

This style of teaching is what Battista (2009) as cited by Marshal (2006) described as ineffective and 

seriously stunts the growth of students’ reasoning and problem-solving skills. These findings also are in 

support with findings made by Keith (1999) who found out that the methods used in teaching 

Mathematics are instrumental in determining one’s performance. Further findings show that the 

complex and abstract nature of geometry (Circle theorems) itself is also a cause of students’ poor 

performance in the topic. This finding agrees with the research finding made by Akinlade (2004) that 

geometry is one of the topics among the abstract and complex aspects of mathematics that students 

find difficult to learn. 

The finding from the independent samples t-test (see Table 3) analysis, 𝑝=0.650>0.05 showed that 

there was no statistically significant difference in the participants’ achievement levels in plane 

geometry II (circle theorems) between the experimental group (school B) and the control group (school 

A) before the treatment was carried out. This indicated that both groups were on the same level of 

achievement before treatment. Findings from the paired samples t-tests (see Table 5) of participants 



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from school B, the experimental group who were taught using inquiry-based teaching approach, 

indicated that there was statistically significant difference in their mean scores of the pre-test and the 

post-test, 𝑡(51)=28.263, 𝑝=000<0.05. The effect size of the intervention, Cohen’s 𝑑=3.92 (see Table 6) 

was realized, which is large effect size. This effect size value implies that the inquiry-based teaching 

approach has made a tremendous impact on students’ achievement in circle theorems. 

Furthermore, the finding from the independent samples t-test (see Table 7) showed a statistically 

significant difference at 𝑝=0.000<0.05 between the achievement in the post-tests of participants who 

were exposed to inquiry-based teaching approach (Mean=29.83) in the experimental group and those 

exposed to the traditional approach (Mean=19.74) in the control group. The difference in means 

between both groups comparatively was an indicator to the result that the experimental group 

outperformed the control group in the post-test. The effect size Cohen’s 𝑑=1.71 which is large effect 

size was noted (see Table 7). This effect size value signifies that the inquiry-based teaching approach 

has made a great impact on students’ acquisition of circle theorems concepts. These findings revealed 

that when inquiry-based teaching approach is employed, students’ achievement is higher than when the 

traditional method is used. These findings strongly agrees with the studies by Riordan and Noyce 

(2001), Crawford and Snider (2000), Crawford and Snider (2000), Ferguson (2010), Mensah-Wonkyi 

and Adu (2016) and Abdi (2014) who in separate studies found students in the experimental group, 

who were exposed to lesson by enquiry-based teaching strategy, improved significantly in the post-test 

as compared to their counterparts in the control group taught by the traditional method. These results 

also support findings made by Al-Qurashi (2002) on examining inquiry-based instruction in 

mathematics and concluded that inquiry- based instruction promoted student achievement. The 

outcome of this study also confirm what Aktamis, Higde and Ozden (2016) found in their meta-analysis 

study that the inquiry-based learning method used in science education had much more significant 

effects on student achievement rather than on their science process skills and their attitudes towards 

science in contrast to the traditional teaching method. The results of this study agrees with 

theoretical framework of the study by Khalid and Azeem (2012) said constructivist approach 

modifies the role of the teacher to that of a facilitator who helps students to construct knowledge rather 

than to reproduce a series of facts which is the bases of inquiry- based teaching approach which 

promote students achievement. 

Findings from the observation made by the mathematics teachers shows that some students don’t fully 

engage themselves in the classroom activities in their various group work. Students also feel 

embarrassed when they answer questions wrongly. These findings are in conformity with what 

Gutierrez (2018) said that students with learning disabilities feel embarrassing and unwilling to 

participate in small group during inquiry-based learning. Inquiry-based teaching methods require more 

time due to its practical and investigative nature. Students need to spend time to explore and find out the 

truth about each of the theories one after the other without learning them through “chew and pour”. 

This finding agrees with the study conducted by Aulls (2002), who observed several teachers as they 



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implemented inquiry-based activities in their classrooms. He reported that the teacher whose students 

achieved all of their learning goals spent a great deal of time in instructional interactions with students 

by simultaneously teaching content and scaffolding-relevant procedures. The finding also agrees with 

Wei and Li (2017), said schooling and class time are limited, and students are not able to complete 

inquiry experiments in a short period of time. Outcome of the observation also shows that class control 

and management was a bit challenging due to the fact that the classroom was not spacious and the class 

size was large. This finding is in line with study made by Harris and Rooks (2010) and Lawson 

(2000) who in separate studies found that teachers find it challenging to manage an inquiry classroom. 

 

5. Major Findings 

The major findings of the study are classified according to the research questions. They are presented 

under three main sub-headings in accordance with the research questions in this section. 

5.1 Research Question 1: What Are the Causes of Poor Performance of Students in Circle Theorems? 

The findings from interviewees’ responses from both students’ and mathematics teachers’ show that 

poor performance of students are mainly cause by students’ attitude towards circle theorems and 

mathematics teachers’ methods or strategies of teaching. Students’ have in mind that the topic is too 

difficult and confusing and for that matter they don’t worry themselves to practice examples on it. 

Moreover, students said they will not answer any questions on it at the final exam. Teachers teaching 

method (the use of traditional method) in teaching circle theorems. This method makes students aware 

that circle theorem is full of rules that must be chew and pour making it difficult for students to 

remember them and apply. 

5.2 Research Question 2: What Is the Effect of Using Inquiry-based Teaching Approach on Students’ 

Achievement in Circle Theorems? 

Findings from the pre-test analysis showed that students in both the experimental and control groups 

were at the same level in terms of conceptual understanding of the concept of circle theorem before the 

intervention was carried out. Also, findings from the post-test analysis revealed that students in the 

experimental group (school B) outperformed their counterparts in the control group (school A) after 

treatment. The findings also revealed a statistically significant difference in the mean scores between 

the experimental and control groups in the post-test comparison. 

5.3 Conclusions 

Based on the findings from the study, it can be concluded that students’ negative attitude and teachers’ 

teaching methods are the main causes of students’ poor performance in circle theorems. It can also be 

concluded that inquiry-based teaching approach increased students’ conceptual understanding in circle 

theorems and hence increased students’ achievement in circle theorems than the traditional 

instruction. Finally it can be concluded that forming smaller groups in class, control and management 

problem due to large class size and classroom not spacious and inadequate time factor are some of the 

challenges associated with the inquiry-based teaching approach 



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5.4 Recommendations 

From the findings of this study, the following recommendations are offered: 

1) Mathematics teachers in senior high school level should use inquiry-based teaching approach to 

teach geometry (circle theorems) since it increases students’ conceptual understanding and haven 

positive impact in their achievement in geometry (circle theorems). 

2) Mathematics teachers should help students to changes their negative attitudes towards circle 

theorems (that it is difficult and confusing) and other geometry topics in order to sustain their interest 

in the topic. 

 

References 

Abdi, A. (2014). The effect of inquiry-based learning method on students’ academic achievement in 

science course. Universal Journal of Educational Research, 2(1), 37-41. 

https://doi.org/10.13189/ujer.2014.020104 

Abreh, M. K., Owusu, K. A., & Ameadahe, F. K. (2018). Trends in performance of WASSCE 

candidates in science and mathematics in Ghana: Perceived contributing factors and the way 

forward. Journal of Education, 198(1), 113-123. https://doi.org/10.1177/0022057418800950 

Adegun, I. K., & Adegun, B. O. (2013). Students and teachers’ views of difficult areas in 

mathematics syllabus: Basic requirements for Science and Engineering Education. Journal of 

Education and Practice, 4(12), 235-243. 

Adler, J. (1997). A Participatory-Inquiry and the mediation of mathematical knowledge in a 

multilingual classroom. Educational Studies in Mathematics, 33(1), 235-258. 

https://doi.org/10.1023/A:1002976114883 

Ahmed, E. (2005). Identification of the problems of the low achievers in the subject of Mathematics at 

secondary level (Un-published Thesis). IER, Lahore: University of the Punjab. 

Aiken, L. R. (1990). Assessing the relationship between attitude toward mathematics and achievement 

in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28(1), 26-47. 

https://doi.org/10.2307/749662 

Akinlade, C. R. (2004). Mathematics topic that students find it difficult to learn. 

Aktamis, H., Higde, E., & Ozden, B. (2016). Effects of the Inquiry-Based Learning Method on 

Students’ Achievement, Science Process Skills and Attitudes towards Science. Journal of Turkish 

Science Education, 13(4), 248-261. 

Akyeampong, K., Lussier, K., Pryor, J., & Westbrook, J. (2013). Improving teaching and learning of 

basic maths and reading in Africa: Does teacher preparation count? International Journal of 

Educational Development, 272-282. https://doi.org/10.1016/j.ijedudev.2012.09.006 

Al-ebous, T. (2016). Effect of the Van Hiele Model in Geometric Concepts Acquisition: The Attitudes 

towards Geometry and Learning Transfer Effect of the First Three Grades Students in Jordan. 

International Education Studies, 9(4), 87-98. https://doi.org/10.5539/ies.v9n4p87 

https://doi.org/10.13189/ujer.2014.020104
https://doi.org/10.1177/0022057418800950
https://doi.org/10.1023/A:1002976114883
https://doi.org/10.2307/749662
https://doi.org/10.1016/j.ijedudev.2012.09.006
https://doi.org/10.5539/ies.v9n4p87


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

29 
Published by SCHOLINK INC. 

Al-Qurashi, F. (2002). An investigation of the role of inquiry-based instruction in mathematics teacher 

professional development activities and outcomes of an inquiry-based instruction project. (UMI 

No. 3062143) 

Alsup, J. K. (2003). A comparison of traditional and reform mathematics curricula in an eighth-grade 

classroom. Education, 123, 689. 

Arem, C. A. (2010). Conquering math anxiety. Brooks/Cole Cengage Learning.  

Asante, K. O. (2012). Secondary students’ attitudes towards mathematics. IFE Psychologia: An 

International Journal, 20(1), 121-133. 

Asiedu-Addo, S. K., & Yidana I. (2000). Mathematics teachers’ knowledge of the subject. 

Aulls, M. W. (2002). The contributions of co-occurring forms of classroom discourse and academica 

activities to curriculum events and instruction. Journal of Educational Psychology, 94, 520-538. 

https://doi.org/10.1037/0022-0663.94.3.520 

Awanta, E. K. (2004). Helping students overcome mathematics anxiety. Mathematics Connection, 4(1), 

39-43. https://doi.org/10.4314/mc.v4i1.21499 

Ayot, H. O., & Patel, M. M. (1992). Instructional methods. Nairobi: Educational Research and 

Publications LTD. 

Aysen, O. (2012). Misconceptions in geometry and suggested solutions for seventh grade students. 

International Journal of New Trends in Arts, Sports and Science Education, 1(4). 1-13. 

Baffoe, E., & Mereku, D. K. (2010). The Van Hiele levels of understanding of students entering senior 

high school in Ghana. African Journal of Educational Studies in Mathematics and Science, 8, 

51-61. https://doi.org/10.4314/ajesms.v8i1.69103 

Baker, W., Barstack, R., Clark, D., Hull, E., Goodman, B., Kook, J., Kraft, K., Ramakrishna, P., 

Roberts, E., Shaw, J., Weaver, D., & Lang, M. (2008). Writing-to-learn in the inquiry-science 

classroom: Effective strategies from middle school science and writing teachers. Clearing House, 

81(3), 105-108. https://doi.org/10.3200/TCHS.81.3.105-108 

Banchi, H., & Bell, R. (2008). The many level of inquiry. Science and Children, 46(2), 26-29. 

Retrieved from http://login.pallas2.tcl.sc.edu/login? 

Barell, J. (2007). Problem based learning and inquiry approach. New Delhi: Sage Publications India 

Pvt. Ltd. 

Battista, M. (2009). Highlights of research on learning school geometry. In T. V. Craine, & R. 

Rubenstein (Eds.), Understanding Geometry for a Changing World: Seventy-first Yearbook (pp. 

91-108). Reston VA the National Council of Teachers of Mathematics (NCTM). 

Battista, M. T. (2007). Geometry results from the Third International Mathematics and Science study. 

Teaching Children Mathematics, 5(6), 367-373. https://doi.org/10.5951/TCM.5.6.0367 

Behlol, G. (2009). Development and validation of module in English at secondary level in Pakistan 

(Unpublished PhD thesis). Islamabad: International Islamic University. 

https://doi.org/10.30971/pje.v26i2.168 

https://doi.org/10.1037/0022-0663.94.3.520
https://doi.org/10.4314/mc.v4i1.21499
https://doi.org/10.4314/ajesms.v8i1.69103
https://doi.org/10.3200/TCHS.81.3.105-108
http://login.pallas2.tcl.sc.edu/login
https://doi.org/10.5951/TCM.5.6.0367
https://doi.org/10.30971/pje.v26i2.168


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

30 
Published by SCHOLINK INC. 

Betiku, O. F. (2001). Causes of mass failure in Mathematics examinations among students. A 

commissioned paper presented at Government Bloom (1986) Secondary school, Karu, Abuja 

science day, 1st March. 

Booker, G. (1992). Constructing mathematical conventions formed by the abstraction and 

generalization of earlier ideas: The development of initial fraction ideas. Paper presented at the 

Seventh International Congress on Mathematical Education (ICME-7), University Laval, Quebec 

City, Quebec, and Canada. 

Bruce, D. (2016). Mathematics anxiety among Ghanaian students: A case study of students of Kinbu 

Senior High/Technical School, Accra and Hermann-Gmeiner SOS Junior High School, Tema. 

Journal of Education and Practice, 7(15), 75-83. 

Bruner, J. (1986). Actual minds, possible worlds. Cambridge, Mass.: Harvard University Press. 

https://doi.org/10.4159/9780674029019 

Burns, M. (2004). Writing in math. Educational Leadership, 62, 30-33. 

Burton, D. M. (1999). The history of mathematics: An introduction (4th ed.). Boston: WCB 

McGraw-Hill. 

Canada, D., & Blair, S. (2006). Intersections of a circle and a square: An investigation. The 

Mathematics Teacher, 100(5), 324-328. https://doi.org/10.5951/MT.100.5.0324 

Cangelosi. (2003). Quoted by national science foundation. Applications and Applied Mathematics 

(AAM): An International Journal, 1(1), 62-82. 

Chappell, M. F. (2003). Keeping Mathematics front and Centre, Reaction to middle grades Curriculum 

Projects Research 285-298 Mahwah. Erlbaun associates. 

Charles, B., & Lynwood, W. (1990). The teaching of secondary Mathematics (4th ed.). 

Chen, B., & Wei, B. (2015). Investigating the factors that influence chemistry teachers’ use of 

curriculum materials: The case of China. Science Education International, 26(2), 195-216. 

Cheng, V. M. (2004). Progress from traditional to creativity education in Chinese society. Singapore: 

World Scientific Publishing. https://doi.org/10.1142/9789812567192_0007 

Cheng, V. M. (2010). Teaching creative thinking in regular science lessons: Potentials and obstacles of 

three different approaches in an Asian context. Asia-Pacific Forum on Science Learning and 

Teaching, 11(1), 1-21. 

Clement, D. (2003). Teaching and learning geometry. In J. Kilpatrick, W. Martin, & D. Schifter, 

(Eds.), A research companion to principles and standards for school mathematics. Reston, VA: 

NCTM. 

Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning handbook of research on 

mathematics teaching and learning: A project of the National Council of Teachers of Mathematics 

(pp. 420-464). New York, NY, England: Macmillan Publishing Co, Inc. 

Clements, D. H., & Sarama, J. (2000). The earliest geometry. Teaching Children Mathematics, 7(2), 

82-84. https://doi.org/10.5951/TCM.7.2.0082 

https://doi.org/10.4159/9780674029019
https://doi.org/10.5951/MT.100.5.0324
https://doi.org/10.1142/9789812567192_0007
https://doi.org/10.5951/TCM.7.2.0082


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

31 
Published by SCHOLINK INC. 

Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. 

Educational Psychologist, 23(2), 87-103. https://doi.org/10.1207/s15326985ep2302_2 

Cockroft, W. H. (1982). Report of the committee of inquiry into the teaching of Mathematics in schools. 

London: HMSO. 

Cohen, D., & Crabtree, B. (2006). Qualitative research guidelines project. Retrieved from 

http://qualres.org/HomeObse-3594.html 

Cohen, L., Manion, L., & Morrison, K. (2007). Research method in education. New York: Taylor & 

Francis e-Library. https://doi.org/10.4324/9780203029053 

Crawford, D. B., & Snider, E. (2000). Effective mathematics instruction: The importance of 

curriculum. Education and Treatment of Children, 23, 122-142. 

Creswell, J. W. (2009). Research design: Qualitative, quantitative and mixed methods approaches (3rd 

ed.). London: Sage Publications. 

Creswell, J. W. (2012). Educational research: Planning, conducting and evaluating quantitative and 

qualitative research (4th ed.). Boston, MA: Pearson Education, Inc. 

Creswell, J. W., & Clark, P. V. (2011). Designing and conducting mixed methods research (2nd ed.). 

Thousand Oaks, CA: Sage Publications, Inc. 

Creswell, J. W., & Clark, V. L. P. (2017). Designing and conducting mixed methods research. Sage 

Publications. 

Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. In M. M. 

Lindquist (Ed.), Learning and teaching geometry, K-12 (Vol. 1987, Yearbook, pp. 6-13). Reston 

Virginia: The National Council of Teachers of Mathematics. 

Cunningham, D., & Duffy, T. (1996). Constructivism: Implications for the design and delivery of 

instruction. Handbook of research for educational communications and technology (pp. 170-198). 

New York: Simon & Schuster Macmillan. 

Davidson, N. (1990). Cooperative learning in mathematics: Handbook for teachers. Menlo Park, 

California: Addison-Wesley Publishing Company. 

Devore. (2005). Statistics-The exploration and analysis of data. USA: Thomson Learning Inc. 

Dornyei, Z. (2007). Research methods in applied linguistics. New York: Oxford University Press. 

Draper, R. (2002). School mathematics reform, constructivism, and literacy: A case for literacy 

instruction in the reform-oriented math classroom. Journal of Adolescent & Adult Literacy, 45(6), 

520. 

Drickey, N. (2001). A comparison of virtual and physical manipulatives in teaching visualization and 

spatial reasoning to middle school mathematics students. Retrieved from Dissertation Abstracts 

International http://www.lib.umi 

Driscoll, M., Dimatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide 

for teachers, Grade 5-10. Portsmouth, NH: Heinemann. 

 

https://doi.org/10.1207/s15326985ep2302_2
http://qualres.org/HomeObse-3594.html
https://doi.org/10.4324/9780203029053
http://www.lib.umi/


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

32 
Published by SCHOLINK INC. 

Duatepe, A. (2000). Best practices for teaching mathematics to secondary students with special needs. 

Focus on Exceptional Children, 32. https://doi.org/10.17161/foec.v32i5.6919 

Engle, P., Grantham-McGregor, S., Black, M., Walker, S., & Wachs, T. (2007). How to avoid the loss 

of potential in over 200 million young children in the developing world. Child Health and 

Education, 1(2), 15. 

Ernest, P. (1996). Varieties of constructivism: A framework for comparison. In G. A. Golding (Ed.), 

Theories of mathematical learning (Vol. Working Group 4 (WG4) Theories of learning 

mathematics, pp. 335-351). New York: Routledge. 

Fabiyi, T. R. (2017). Geometry concepts in Mathematics perceived difficult to learn by Senior High 

School students. IOSR Journal of Research & Method in Education, 7(1), 84-90. 

https://doi.org/10.9790/7388-0701018390 

Farrant, S. J. (1997). Principles and practice of education. Essex: Singapore: Longman Publishers. 

Ferguson, K. (2010). Inquiry based mathematics instruction versus traditional mathematics instruction: 

The effect on student understanding and comprehension in an eighth grade pre-algebra classroom. 

Cedarville: Cedarville University. https://doi.org/10.15385/tmed.2010.5 

Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage Publications. 

Friesen, S., & Scott, D. (2013). Inquiry-based learning: A review of the research literature. Alberta: 

Alberta Ministry of Education. 

Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among 

adolescents [Research work on adolescents]. Journal for Research in Mathematics Education 

(Monograph # 3), 4-71. https://doi.org/10.2307/749957 

Geddes, D., & Fortunato, I. (1993). Geometry: Research and classroom activities. In D. T. Owens 

(Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 199-225). New York: 

Macmillan Publishing. 

Gerrish, K., & Lacey, A. (2010). The research process in nursing (6th ed., pp. 455-472). 

Wiley-Blackwell, Oxford.  

González, G., & DeJarnette, A. F. (2013). Geometric reasoning about a circle problem. Mathematics 

Teacher, 106(8), 586-591. https://doi.org/10.5951/mathteacher.106.8.0586 

Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for 

Research in Mathematics Education, 35(4), 258-291. https://doi.org/10.2307/30034810 

Gutierrez, D. (2018). Pro and cons of inquiry base learning for college success. Stanford 

University. 

Haghighi, A. M., Vakil, R., & Weitba, J. K. (2005). Reverse-traditional/hands-on: An alternative 

method of teaching statistics. Application and Applied Mathematics (AAM.), 1. 

Halat, E. (2008). In-service middle and high school mathematics teachers: Geometric reasoning stages 

and gender. The Mathematics Educator, 18(1), 8-14. 

 

https://doi.org/10.17161/foec.v32i5.6919
https://doi.org/10.9790/7388-0701018390
https://doi.org/10.15385/tmed.2010.5
https://doi.org/10.2307/749957
https://doi.org/10.5951/mathteacher.106.8.0586
https://doi.org/10.2307/30034810


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

33 
Published by SCHOLINK INC. 

Harris, C., & Rooks, D. (2010). Managing inquiry based science: Challenges in enacting complex 

science instruction in elementary and middle school classroom. Journal of Science Teachers 

Education, 21(2), 227-240. Retrieved May 26, 2011, from Ebscohost database. 

https://doi.org/10.1007/s10972-009-9172-5 

Hesse-Biber, S. N. (2010). Mixed methods research: Merging theory with practice. Guilford Press 

Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in 

problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). 

Educational Psychologist, 42 (2), 99-107. https://doi.org/10.1080/00461520701263368 

Hodge, L. (2008). Student roles and mathematical competence in two contrasting elementary classes. 

Mathematics Education Research Journal, 20(1), 32-50. https://doi.org/10.1007/BF03217468 

Horn, L. R. (1995). Classroom learning & teaching. NY: Longman Publisher. Reading, Mass: 

Addison-Wesley publishing company 

Ibadan: University Press Ltd. 

Idris, N. (2006). Teaching and learning of mathematics: Making sense and developing cognitive ability. 

Kuala Lumpur: Utusan Publication and Distributors. 

Ismail, J. (2008). The effects of a reform curriculum on students’ problem solving abilities 

(Unpublished master’s thesis). Boise State University, Boise, ID. 

Jones, K., & Bills, C. (1998). Visualization, imagery, and the development of geometrical reasoning. 

Paper presented at the British Society for Research into Learning Mathematics, University of 

Birmingham, UK. 

Jones, K., Fujita, T., & Ding, L. (2006). Informing the pedagogy for geometry: Learning from teaching 

approaches in China and Japan. Paper presented at the Proceedings of the British Society for 

research into Learning Mathematics. 

Kalhotra, S. K. (2013). A study of causes of failure in mathematics at high school stage. Academic 

Research International, 4(5), 588-599. 

Kausar, R., & Zaheer, S. (2008). Analysis of grade 4 students’ performance in mathematics 

(Un-published thesis). IER, Lahore: University of the Punjab. 

Keith, J. (1999). Planning for mathematic learning in Johnston-Wilder, S. (Eds.), learning to teach 

Mathematics in secondary schools. London and New York; Rout ledge. 

Khalid, A., & Azeem, M. (2012). Constructivist VS traditional: Effective instructional approach in 

teacher education. International Journal of Humanities and Social Science, 2(5), 170-177. 

Kim, M., & Tan, A. L. (2013). Rethinking difficulties of teaching inquiry-based practical work: Stories 

from elementary pre-service teachers. International Journal of Science Education, 33(4), 465-486. 

https://doi.org/10.1080/09500691003639913 

Kiminza, O. (1999). National study of science and mathematics in primary and secondary schools in 

Kenya. Nairobi: KIE. 

 

https://doi.org/10.1007/s10972-009-9172-5
https://doi.org/10.1080/00461520701263368
https://doi.org/10.1007/BF03217468
https://doi.org/10.1080/09500691003639913


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

34 
Published by SCHOLINK INC. 

Kinyua, M., Maina, L., & Odera, J. (2003). Advancing in mathematics teachers’ guide form 2. Nairobi: 

Longhorn publishers Ltd. 

Knight, K. C. (2006). An investigation into the change in the Van Hiele levels of understanding 

geometry of pre-service elementary and secondary mathematics teachers (Doctoral dissertation). 

The University of Maine. 

Lampert, M. (1990). When the problem is not the question and the solution is not the answer: 

Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63. 

https://doi.org/10.3102/00028312027001029 

Lawson, L. E. (2000). Managing the inquiry classroom: Problems and solutions. The American Biology 

Teacher, 62(9), 641-648. Retrieved June 10, 2010, from Ebschost database. 

https://doi.org/10.2307/4451002 

Lemlech, J. K. (1998). Curriculum and instruction methods for elementary and middle school. Upper 

Saddle River: Prentice-Hall, Inc. 

Levasseur, K., & Cuoco, A. (2003). Mathematical habits of mind. In H. L. Schoen (Ed.), Teaching 

mathematics through problem solving (pp. 27-37). Reston: The National Council of Teachers of 

Mathematics Inc. 

Li, J. J. (2015). Research on the inquiry teaching of mathematics in high grade of primary school-A 

case of Shijazhuang city elementary school (Master’s Thesis). Hebei Normal University. 

Lie, K. M., & Hafizah, H. (2008). Malaysian students’ achievement in solid geometry. Recent 

Researches in Education, 141-147. 

Longo, C. (2010). Fostering creativity or teaching to the test? Implications of state testing on the 

delivery of science instruction. The Clearing House, 83(2), 54-57. 

https://doi.org/10.1080/00098650903505399 

Mammana, C., & Villani, V. (1998). Geometry and geometry-teaching through the ages. NEW ICMI 

STUDIES SERIES, 5, 1-3. https://doi.org/10.1007/978-94-011-5226-6_1 

Marcus, R., & Fey, J. T. (2003). Selecting quality tasks for problem-based teaching. In H. L. Schoen 

(Ed.), Teaching mathematics through problem solving (pp. 55-67). Reston: The National Council 

of Teachers of Mathematics, Inc. 

Marshal, J. (2006). Math wars 2: It’s the teaching, stupid! Phi Delta Kappan, 87, 356-363. 

https://doi.org/10.1177/003172170608700506 

Martins, R. C., Sexton, Franklin, T. J., & Gerlovich. (2005). Teaching Science for All Children: An 

Inquiry Approach (4th ed.). Allyn & Bacon. 

Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate pre- service teachers. 

Journal for Research in Mathematics Education, 14, 58-69. https://doi.org/10.2307/748797 

Mayer, R. E. (1992). Thinking problem solving and cognition (2nd ed.). NY; Preeman press. 

McLeod, S. (2014). Simply psychology. Retrieved from Simply Psychology website: 

www.simplypsychology.org/interviews.html 

https://doi.org/10.3102/00028312027001029
https://doi.org/10.2307/4451002
https://doi.org/10.1080/00098650903505399
https://doi.org/10.1007/978-94-011-5226-6_1
https://doi.org/10.1177/003172170608700506
https://doi.org/10.2307/748797
http://www.simplypsychology.org/interviews.html


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

35 
Published by SCHOLINK INC. 

Mensah-Wonkyi, T., & Adu, E. (2016). Effect of the inquiry-based teaching approach on students’ 

understanding of circle theorems in plane geometry. African Journal of Educational Studies in 

Mathematics and Sciences, 12, 61-74. 

Mereku, D. K. (2010). Five decades of school mathematics in Ghana. Mathematics Connections, 9(8), 

73-86. https://doi.org/10.4314/mc.v9i1.61558 

Mestre, J. (1989). Hispanic and Anglo students’ misconceptions in mathematics. Retrieved from ERIC 

Digests website: http://www.ericdigests.org/pre- 9213/hispanic.htm 

Michalopoulou, A. (2014). Inquiry-based learning through the creative thinking and expression in early 

years education. Creative Education, 5(6), 377. https://doi.org/10.4236/ce.2014.56047 

Ministry of Education. (2010). National syllabus for senior high school mathematics. Accra: Ministry 

of Education. 

Minner, D. D., Levy, A. J., & Century, J. (2010). Inquiry- based science instruction-What is it and does 

it matter? Results from a research synthesis years 1984 to 2002. Journal of Research in Science 

Teaching, 47(4), 474-496. https://doi.org/10.1002/tea.20347 

Mogari, D. (1999). Attitude and achievement in Euclidean geometry. Proceedings of the International 

Conference on Mathematics Education into the 21st Century, Cairo. New York: Macmillan 

Publishing. NCTM (2000). Principles and Standards for School Mathematics. Reston: NCTM. 

Morris, R. V. (2001). Drama and authentic assessment in a social study classroom. Journal of Social 

Studies, 92(1), 41-45. https://doi.org/10.1080/00377990109603974 

Mulwa, E. C. (2014). The role of the language of mathematics in students’ understanding of number 

concepts in Eldoret Municipality, Kenya. International Journal of Humanities and Social 

Science, 4(3), 264-274. 

Muschla, J. A., & Muschla, G. R. (2000). Geometry teacher’s activities kit: Ready-to-use lessons & 

worksheets for grades 6-12. Jossey-Bass. 

National Board for Professional Teaching Standards. (2009). Profiles in excellence. Chicago, Illinois. 

National Council of Teachers of Mathematics. (2000). Principles and standards for school 

mathematics. Reston, VA: Author. 

National Council of Teachers of Mathematics. (2003). Principles and standards for school 

Mathematics. Reston, V. A: NCTM. 

NCTM. (2009). Guiding principles for mathematics curriculum and assessment. Retrieved October 14, 

2009, from National Council for Teachers of Mathematics: 

http://www.nctm.org/standards/content.aspx?id=23273 

Ndinda, M. D. (2016). An analysis of the factors influencing achievement in mathematics geometry 

among secondary school students in Makadara sub- county, Nairobi County (Doctoral 

dissertation). Kenyatta University. 

 

 

https://doi.org/10.4314/mc.v9i1.61558
http://www.ericdigests.org/pre-%209213/hispanic.htm
http://www.ericdigests.org/pre-%209213/hispanic.htm
https://doi.org/10.4236/ce.2014.56047
https://doi.org/10.1002/tea.20347
https://doi.org/10.1080/00377990109603974
http://www.nctm.org/standards/content.aspx?id=23273


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

36 
Published by SCHOLINK INC. 

Neel-Romine, L. E., Paul, S., & Shafer, K. G. (2012). Get to know a circle. Mathematics 

Teaching in the Middle School, 18(4), 222-227. 

https://doi.org/10.5951/mathteacmiddscho.18.4.0222 

Noraini, I. (2006). Teaching and learning of mathematics: Making sense and developing cognitive 

abilities. Perak: Utusan Publication Sdn. Bhd. Nigeria. 

Nworgu, B. G. (2006). Educational research: Basic issues and methodology. Nsukka: University Trust 

Publishers, 45-49. 

Olatoye, R. A., & Agbatogun, A. O. (2009). Parental involvement as a correlate of pupils’ achievement 

in mathematics and science in Ogun State, Nigeria. Educational Research and Reviews, 4(10), 

457. 

Pappas, C. (2014). Instructional design models and theories: Inquiry-based learning model. 

Parr, R. (2007). Improving science instruction through effective group interactions. Science Scope, 

21-23. Retrieved June 10, 2010, from Ebschost database. 

Pesek, D. D., & Kirshner, D. (2000). Interference of instrumental instruction in subsequent relational 

learning. Journal for Research in Mathematics Education, 31(5), 524-540. 

https://doi.org/10.2307/749885 

Pickens, J. (2005). Attitudes and perceptions. Organizational Behaviour in Health Care, 4(7), 43-76. 

Polit, D. F., & Hungler, B. P. (1999). Nursing research: Principles and methods (6th ed.). Philadelphia: 

J. B. Lippincot. 

Rafiq, M. T., & Ansari, Z. (2012). Mathematics-7. Lahore: Punjab Text Book board. 

Rao, D. (2001). Science education in developing countries (pp. 124-126). New Delhi; Discovery 

Publishing House. 

Riordan, J. E., & Noyce, P. E. (2001). The impact of two standards based mathematics curricula on 

student achievement in Massachusetts. Journal for Research in Mathematics Education, 32, 

368-398. https://doi.org/10.2307/749700 

Rose, C. M., & Arline, C. B. (2009). Uncovering student thinking in mathematics, Grades 6-12: 30 

Formative Assessment probes for the Secondary Classroom. USA: Corwin Press. 

Rukangu, S. M. (2000). Pupils’ development of spatial ability in Mathematics: An issue of learning 

environment in selected secondary schools in Kenya. Nairobi (Unpublished Ph.D thesis). 

Kenyatta University, Kenya. 

Sa’ad, T. U., Adamu, A., & Sadiq, A. M. (2014). The causes of poor performance in mathematics 

among public senior secondary school students in Azare Metropolis of Bauchi State, Nigeria. 

IOSR Journal of Research & Method in Education (IOSR-JRME), 4(6), 32-40. 

https://doi.org/10.9790/7388-04633240 

Santrock, J. W. (2001). Educational psychology. United States of America: McGraw- Hill Companies, 

Inc. 

 

https://doi.org/10.5951/mathteacmiddscho.18.4.0222
https://doi.org/10.2307/749885
https://doi.org/10.2307/749700
https://doi.org/10.9790/7388-04633240


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

37 
Published by SCHOLINK INC. 

Scopes, P. G. (1973). Mathematics in secondary schools: A teaching approach. London: 

Cambridge University Press. 

Sdrolias, K. A., & Triandafillidis, T. A. (2008). The transition to secondary school geometry: Can there 

be a “chain of school mathematics”? Educational Studies in Mathematics, 67(2), 159-169. 

https://doi.org/10.1007/s10649-007-9093-1 

Singh, M. (2004). Modern teaching of mathematics. New Delhi: Anmol publications PVT. LTD. 

Slavin, R. E. (2006). Educational psychology: Theory and practice (8th ed.). Boston: Pearson 

Education, Inc. 

Sofowora, S. O. (2014). Anxiety and lack of motivation as factors affecting success rates in bridging 

mathematics (Doctoral dissertation). University of South Africa, South Africa. 

Sproken-Smith, R. (2007). Experiencing the process of knowledge creation: The nature and use of 

inquiry-based learning in higher education. Journal of Educational Research. 

Stonewater, J. K. (2005). Inquiry teaching and learning: the best maths class inquiry teaching and 

learning: The best maths class study. Chicago: School Science and Mathematics. 

https://doi.org/10.1111/j.1949-8594.2005.tb18034.x 

Telima, A. (2011). Problems of teaching and learning of geometry in secondary schools in River State, 

Nigeria. International Journal of Emerging Science, 1(2), 143-152. 

Uys, H. H. M., & Basson, A. A. (1991). Research methodology in nursing. Pretoria: Haum (pp. 

59-80). 

Wartonic, D. (2005). A comprehensive assessment of CMP (Connected Math Program): Deficiencies 

leading to supplementation that meets key traditional educational needs (Unpublished Master’s 

Thesis). Cambridge College, Cambridge, Massachusetts. 

Weber, E. (2006). Brain based business. Retrieved December 23, 2007, from 

http://brainbasedbusiness.com  

Wei, B., & Li, X. (2017). Exploring science teachers’ perceptions of experimentation: implications for 

restructuring school practical work. International Journal of Science Education, 39(13), 

1775-1794. https://doi.org/10.1080/09500693.2017.1351650 

West African Examinations Council. (2006). West African Senior School Certificate Examination. In 

Chief Examiner’s Report. Accra: West African Examinations Council. 

West African Examinations Council. (2017). West African Senior School Certificate Examination. In 

Chief Examiner’s Report. Accra: West African Examinations Council. 

Wiggins, G. (2016). Conceptual understanding in mathematics. Retrieved from 

https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding- inmathematics/ 

Wiggins, G., & McTighe, J. (2008). Put understanding first. Educational Leadership, 65(8), 36-41. 

William, M. K. (2006). The Research Methods Knowledge Base. Cornell University. Retrieved on July 

12, 2017 from http://www.socialresearchmethods.net/kb/order.htm 

 

https://doi.org/10.1007/s10649-007-9093-1
https://doi.org/10.1111/j.1949-8594.2005.tb18034.x
http://brainbasedbusiness.com/
https://doi.org/10.1080/09500693.2017.1351650
https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-inmathematics/
https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-inmathematics/
http://www.socialresearchmethods.net/kb/order.htm


www.scholink.org/ojs/index.php/fce           Frontiers of Contemporary Education             Vol. 3, No. 3, 2022 

38 
Published by SCHOLINK INC. 

Wood, W. B., & Gentile, J. M. (2003). Teaching in a research context. Science, 30(2), 15-10. 

https://doi.org/10.1126/science.1091803 

Wu, Z. (2003). The discussion of difficulties and solution in inquiry-based science classes. Yan Jiu 

Xue Xi Zhuan Ti, 35. 

Xue, H. N., & Chen, X. (2012). A national survey on the quality of present teacher training programs. 

Educational Science, 28(6), 53. 

 

 

https://doi.org/10.1126/science.1091803

