Abstract
Reviewing bodies have shown that a high percentage of SHS students tend to underperform in mathematics examinations. In that respect, we examined the influence of two teaching approaches on Ghanaian public Senior High School students’ mathematical mindsets. A quantitative research design was used, that is, an ex post facto research design was used for this study. A total sample of 366 respondents was involved in this study. Two sets of questionnaires were employed for the study which are the students’ perceptions of teaching approaches and mathematical mindset questionnaires. Descriptive analysis such as means and frequencies were used to analyze the data. The results revealed a possible influence of the teaching approaches students experienced and their mathematical mindset. That is, students taught with a student-centered approach were found to generally possess a growth mindset while those identified as possessing a more fixed mindset were mostly students taught using a more teacher-centered approach. The study recommended that teachers should adopt a student-centered approach to teaching since it has the potential to shape students’ mindset toward a strong growth mindset, as students who have a growth mindset are more likely to succeed in school and beyond.
Plain Language Summary
Introduction
Around the world, success in mathematics has been one of the essential criteria for professional development and academic success in many fields. This is because the mathematics curriculum is planned to equip students with the necessary skills and experiences required to succeed in the evolutional world of technology (Ngussa & Mbuti, 2017). In Ghana, mathematics is a compulsory subject that starts from preschool to the senior high school level. Despite its significance, failure in the final examination paper in mathematics at either the Junior High School or the Senior High School levels denies the individual the opportunity to continue with his or her education (Ntow, 2009). In the Ghanaian settings, studies and observations from reviewing bodies have shown that a high percentage of SHS students tend to underperform in mathematics examinations (Asamoah, 2018) despite various attempts made in providing students with quality teaching-learning in mathematics. For example, the 2021 West African Senior School Certificate Examination (WASSCE) results, an examination conducted at the end of senior high school showed a decline in the results of Core Mathematics (54.11%) from the 65.51% recorded in 2020. Within the period under review, 899,570 students, representing 50.9%, obtained grades D7 to F9, which are failing grades (Abreh et al., 2018; The West African Examinations Council [WAEC], 2007; WAEC, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020). Not only is the low performance of students in mathematics a challenge for Ghana on the WASSCE, but it is also an international issue, as evident in the country’s performance on TIMSS (2015) in the work of Grønmo et al. (2015) and PISA (2003).
The method of teaching and students’ mindsets have been identified as one of the major factors likely to influence students’ mathematics achievement (Zhang et al., 2017) and their persistence in taking advanced mathematics courses (Ntow et al., 2017). Boaler (2016) argues that the mathematical mindset that students acquire regarding learning is likely to determine whether they will be successful in mathematics. In particular, the effort one will require in partaking in a task, the failure, and the success of a student solely depends on the kind of mindset developed by the individual (Dweck, 2006).
Studies that have been undertaken have also indicated that teaching approaches are a major factor influencing students’ learning in mathematics (Ireland et al., 2014). For example, Sun (2018) argues that the mindsets students develop are as a result of the influence of teaching approaches. Teaching approaches include the teachers’ actual classroom activities, which are guided by their aims and beliefs. Hancock et al. (2002) indicated that teaching approaches are grouped into content-centered, teacher-centered, and student-centered. But, teachers whose teaching and learning philosophy falls in line with the teacher-centered approach are believed to produce passive learners and students get to learn in a procedural and structured way (Ellsworth & Buss, 2000). In contrast, Von Glasersfeld (1989) argues that the philosophy of a student-centered approach is centered on the notion of efficiently participating in the instructional process to inspire students to explore, grow, and produce new knowledge. Current studies have identified that for a student to excel academically, it depends on the mindset they develop which in turn is influenced by the predominant teaching approaches they experience. In the Ghanaian context, literature has established the influence of teaching approaches on students’ achievement as Churcher et al. (2016) reported that student’s academic achievement is predicted by teaching approaches. But for students to academically excel, it depends on the type of mindset developed as students with a growth mindset mentality produce higher grades as compared to students with a fixed mindset mentality (Kismiantini et al., 2021).
Several works indicate the influence teaching approaches have on students’ mindsets; for example, Sun (2018) and Yeager and Dweck (2012) discovered teaching approaches as a critical component that influences the development of students’ mindsets. But, among these works, they did not indicate the type of teaching approach (student-centered or teacher-centered) that elicits a particular mindset be it a fixed mindset or a growth mindset. In this study, mindset was used as a moderating factor that could affect students’ achievement as a result of the type of approach used in teaching in the classroom. Hence, this study explores the influence of teachers’ teaching approaches on Ghanaian Senior High School (SHS) year two students’ mathematical mindsets in the learning of Core Mathematics in the Kumasi Metropolis of the Ashanti Region. The research is guided by the following research questions:
What are senior high students’ perceptions of their Core Mathematics teachers’ teaching approaches?
How do teachers’ teaching approaches influence students’ mathematical mindset?
Literature Review
The beliefs students hold about themselves in terms of learning are the result of their own experiences and observations they gain either in school or in their immediate environment. According to Sternberg et al. (1980), the implicit theory of intelligence is about how people perceive themselves, others, and their immediate environment. Within this, two models exist that an individual may espouse: the incremental theory (growth mindset) and the entity theory (fixed mindset).
The Fixed Mindset or an Entity Theory of Intelligence
The intelligence of a fixed-minded person is seen as a rigid and uncontrolled trait (Dweck & Leggett, 1988) which could function as a limitation to the growth of skills and affect students’ achievement negatively (Hochanadel & Finamore, 2015). As a result, Elliott and Dweck (1988) claim that those with a fixed mindset are more prone to dodge difficult tasks, and people feel compelled to prove themselves over and over, regardless of the situation (Dweck, 2006). Dweck and Leggett (1988) reported that individuals with a fixed mentality typically pursue achievement-oriented goals to get positive feedback on their capabilities, or at the very least to avoid bad feedback. They further argued that failure is seen as a sign of weakness, which often leads to a helpless response as outcome and achievement are recognized as primary goals for a person who has a fixed mentality. A fixed-traits mindset assumes that success is found by proving one’s intelligence and seeking validation for it as failure serves as an indication that one is not intelligent.
The Growth Mindset or an Incremental Theory of Intelligence
The subscribers of the growth mindset argue that intellect can be changed, controlled, and improved (Dweck & Leggett, 1988). Because intelligence is regarded as a malleable quality, individuals with a growth mindset are not worried about proving their intelligence but rather in learning more (Dweck, 2006). According to Boaler (2016), not every person is born with the same skills or brain, but everybody can develop their intelligence with guidance and effort. For this reason, learners are passionate about expanding their knowledge and skills, and they are always assessing the best approach to improving their abilities (Dweck & Leggett, 1988). Hence, Elliott and Dweck (1988) established the fact that people with a growth mentality prefer to seek out difficult chances and engage in creative thinking for completing increasingly complex tasks.
Students’ Mathematical Mindset
A mathematical mindset occurs when students perceive mathematics as a collection of ideas and relationships (Boaler, 2016). In all subjects and aspects of life, students’ mindsets are not the same. According to McCutchen et al. (2016), depending on the subject, students are able to adopt different mindsets. Meaning that the student’s mindset toward the subject of History may differ from their mindset toward Mathematics. When students with a growth mindset are confronted with academic difficulties, they perceive them as chances to learn. As a result, students who have a growth mindset are more likely to succeed in school and beyond (Yeager & Dweck, 2012; Yuksel et al., 2021).
Boaler et al. (2021) made mention that a crucial aspect of adopting a growth mindset when it comes to learning involves embracing challenges and recognizing the value of struggle in the learning process. Research conducted on novice college students who were given complex tasks to complete revealed that these students exhibited discomfort when faced with challenges. Their limited understanding of the benefits of struggling led them to actively avoid engaging in complex tasks (Deslauriers et al., 2019). Meaning that some students still embrace a fixed mindset approach to learning. In another context, Campbell et al. (2021) claimed that engineering students were identified as possessing a growth mindset as a result of their mindset intervention (interaction with teachers). This points out that the type of mindset developed by students is a result of the teacher factor. Teachers are doing their students a big disservice when they encourage them to alter their mindset without also changing the way they teach. For instance, if the focus of teachers is solely on students’ results rather than mastery of content, then the mindset of students would likely be changed from a growth mindset (Hargreaves et al., 2021).
Student-Centered Approach
The features of the student-centered teaching and learning approach include encouraging various explanations and forms of learning, motivating students to examine and pose their questions, encouraging students to work together, and using their colleagues as learning resources. To build a sufficient comprehension of each topic and proceed to a higher thinking level, students must be actively involved in the learning process (Abrams & Lockard, 2004) as students that engage in active learning seek meaning and knowledge of the information by developing and modifying it. For a student to be an active learner, he or she needs to undergo the process of understanding the concepts of mathematics through a series of investigations and trial-and-error exercises with little or no assistance from the teacher (Boaler, 2009). A student-centered teaching approach fosters the utmost levels of learning and achievement by providing a learning environment that is favorable to learning for all students (Ahmed, 2013).
Teacher-Centered Approach
A teacher-centered approach is an instructional process in which teachers are the primary source of information. According to Ellsworth and Buss (2000), the teacher-centered teaching and learning approach focuses on students providing the right answers and encourages students to follow the exact processes that will result in the correct responses. Regardless of these advantages, Ellsworth and Buss (2000) reported that the focus on laid down principles and rules only contributes to students engaging passively in lessons and influences their achievement adversely. Teachers commonly utilize instructional approaches (such as the dogmatic method, lecture method, demonstration, and guided discussion) that establish a focus on the instructor to assist them in keeping control over their students.
Hence, if Ghanaian SHS students are not performing at the desired levels, it is imperative to investigate which of the dominant teaching approaches they may be experiencing in their classrooms and its influence on their mathematical mindset. As it is believed that student-centered produces active learners and teacher-centered approach also produces passive learners.
Methodology
Research Design
The ex post facto research design (quantitative research design) was used to explore the possible influence of teachers’ teaching approaches on students’ mathematical mindsets toward the learning of Core Mathematics. This design is very useful in exploring the relationship between independent and dependent variables when the independent variables cannot be randomized or manipulated (Ary et al., 2010).
Sample and Sampling Techniques
The study’s target population was all public Senior High School students in year two in the Kumasi Metropolis of the Ashanti Region of Ghana. In the Kumasi Metropolis, out of twenty-four (24) public SHS in the Kumasi Metropolis, six schools were purposively selected as the accessible population based on the approaches used by the teachers in teaching Core Mathematics in each selected school. Through the use of an observational guide that was adopted from Ampadu (2012), the dominant teaching approach used by Core Mathematics teachers was determined by the first author. Each school was observed on two occasions in different lessons by using the same class before three schools were identified with the student-centered approach, while the other three schools were also identified with the teacher-centered approach. Despite the initial observation, the participating students were also asked to rate their Core Mathematics teachers’ teaching approach to obtain a firsthand account from them. The questionnaire comprised a set of questionnaires that described teacher-centered and student-centered teaching approaches for students to respond to. The total population of SHS year two students in the six selected schools in the Kumasi Metropolis was 6,792. Year two students were regarded as suitable for this study as compared to year one students due to their more than 1 year of familiarity with their teachers’ teaching approaches. Meanwhile, year three students had completed school at the time of data collection and were therefore unavailable to participate in the study. In all, 378 students were selected based on Bartlett et al.’s (2001) sample size determination table. It should be noted that students from the six selected schools were from the same category of schools and also read these academic courses: Business, General Arts, General Science, Home Economics, and Visual Arts. Depending on the research sample size which is 378 students, a proportional sampling was then carried out in order to allocate the respondents according to the chosen schools. The sample size of 378 was divided by the number of schools selected which is 6, giving a value of 63 representing the sample of students. Hence, a sample of 63 students was selected randomly from each school for a fair representation.
Data Collection Instruments and Analyses
Two sets of questionnaires, students’ perceptions of the Core Mathematics teaching approaches and students’ mathematical mindsets questionnaires, were used in soliciting information from respondents which were adapted from Ampadu (2012) and Dweck (2006) respectively. The students’ perceptions of their teachers’ teaching approach questionnaire comprised 27 items of which it was restructured to 18 items based on the research focus (three items elicited information on student’s background and 15 items on how students perceive teachers’ approaches to teaching). The students’ mathematical mindsets questionnaire comprised 20 items which were all scaled on a 4-point Likert scale format. A four-point Likert scale was chosen since it improves the strength and maximizes efficiency in data collection and analysis (Swan, 2006), as Nworgu (1991) claims that a five-point scale allows for indecisive replies. In all, a response rate of 366 (96.83%) was obtained from the sample of 378 students. Out of the 366 respondents, 208 were males, representing 56.83% while 158 were females, representing 43.17%. A reliability coefficient of 0.76 and 0.75 were recorded for the perception and mindset instruments respectively. These reliability estimates were considered acceptable since Pallant (2010) noted that a reliability coefficient of 0.70 for an instrument is desirable for data collection.
The options on the Likert scale were scored as follows; Strongly Disagree − 1, Disagree − 2, Agree − 3, and Strongly Agree − 4. The criterion mean score for the perception of SHS students on teachers teaching approaches was 2.5. Therefore, a mean score of any student’s perception of teaching approaches that is above 2.5 depicts a higher practice of that teaching approach (student
Findings
The study explores the influence of teachers’ teaching approaches on Ghanaian SHS year two students’ mathematical mindsets in the learning of Core Mathematics as this section seeks to address students’ perceptions of their teachers’ approaches to teaching in Core Mathematics and the type of mathematical mindset they develop in the process of learning.
Research Question 1: What Are Students' Perceptions of Their Core Mathematics Teachers’ Teaching Approaches?
This study explores the influence of teachers’ teaching approaches on SHS year two students’ mathematical mindsets in the learning of Core Mathematics as the main goal of this research question was to ascertain how SHS 2 students perceived their Core Mathematics teachers teaching. Before getting the schools for this study, a field observation was conducted to identify the dominant approach used by teachers in teaching Core Mathematics. Based on the findings, the schools identified with a student-centered approach were categorized as Group 1 (three schools), and those with a more dominant teacher-centered approach were categorized as Group 2 (three schools). Table 1 presents the results on students’ perceptions of their Core Mathematics teacher’s teaching approaches.
Students’ Perceptions of Their Core Mathematics Teacher’s Teaching Approaches.
From the results obtained in Table 1, students in Group 1 schools recorded an overall mean score of 2.98 as compared with their colleagues in Group 2 schools who obtained an overall mean score of 2.30. With reference to the criterion mean score of 2.5 for students’ perception of teaching approaches, it can then be concluded that students in Group 1 perceived their teachers to use a more student-centered approach to teaching Core Mathematics in their respective classrooms compared to those in Group 2. In the second part of the questionnaire which described the characteristics of a teacher-centered classroom, the mean of means of Group 2 schools was 2.61 as compared with that of Group 1 schools which was 2.40.
In conclusion, students in Group 1 schools perceived their teachers’ teaching approaches to be more student-centered with the overall mean of 2.98 being greater than the criterion mean score of 2.50. However, students in Group 2 schools perceived the teaching approaches used by their Core Mathematics teachers to be more teacher-centered approach since the overall mean score of 2.61 recorded on the teacher-centered items is higher than the criterion mean of 2.50. As indicated earlier, these conclusions are also consistent with the deductions made prior to the selection of the six schools using the observation guide.
Research Question 2: How Do Teachers’ Teaching Approaches Influence Students’ Mathematics Mindset?
The main goal of this research question was to determine the type of mindset students develop as a result of teachers’ teaching approaches. Results displayed in Table 2 present the findings of students in Groups 1 and 2 schools’ mathematical mindsets. The findings showed that most students in Group 1 schools possessed a growth mindset and Group 2 schools possessed a fixed mindset.
Students’ Mathematical Mindsets Toward Learning Core Mathematics Schools.
From the results obtained in Table 2, it can be concluded that students in Group 1 schools possessed a growth mindset with an overall mean of 2.39 which is greater than the criterion mean score of 1.50 for students’ mathematical mindset. However, students in Group 2 schools possessed fixed mindsets since the overall mean score of 2.12 recorded was higher than the criterion mean of 1.50.
The findings presented in Figures 1 and 2 show the mathematical mindset developed by students in learning Core mathematics from Groups 1 and 2 schools.
Mindset of SHS students in Group 1.
Mindset of SHS students in Group 2.
It was observed from Figure 1 that the majority of the students in Group 1 schools (65.03%) possessed a growth mindset with some fixed ideas while none of the students possessed a strong fixed mindset. Also, from Figure 2, it can be observed that most of the students (54.64%) possessed a fixed mindset with some growth ideas. However, 3.83% held a strong fixed mindset belief.
Hence, it can be inferred that when teaching is more student-centered, the students tend to possess a mathematical mindset which is more of a growth mindset. On the other hand, the majority of the students in Group 2 schools were found to possess a mathematical mindset which is more of a fixed mindset. Therefore, it appears that the more teaching takes the form of a teacher-centered approach, the more students possess a fixed mentality.
Discussions
The results from Table 1 suggest that students in Group 1 schools perceive their Core Mathematics teachers to use a more student-centered approach to teaching with the overall mean of means being 2.98. A student-centered approach is identified as one of the best ways to help students focus on deepening their understanding of a learned concept (Beausaert et al., 2013). In a study conducted by Kang and Keinonen (2018), the authors revealed that a student-centered approach to teaching positively influences students’ learning and academic achievement. This finding supports the assertion made by Briede (2016) that a student-centered approach is the best way of teaching. Hence, this approach produces active learners as students are able to attain a higher thinking level (Abrams & Lockard, 2004).
The overall mean of means for Group 2 schools on how students perceived their teacher’s teaching approaches (M = 2.61) revealed that their teachers tended to adopt a more teacher-centered approach. The finding affirmed that of Kurniati and Surya (2017) who stated that teachers still used the teacher-centered approach. For example, in Ghana, the SHS Core Mathematics curriculum revised in 2010 explicitly called for the use of a student-centered approach to teaching and learning but the findings of this study indicate that some teachers still adopt a more teacher-centered approach. Ellsworth and Buss (2000) argue that the teacher-centered teaching and learning approach focuses on students providing the right answers and encourages students to follow the exact processes that will result in the correct responses. Regardless of these advantages, Ellsworth and Buss (2000) reported that the focus on laid down principles and rules only contributes to students engaging passively in lessons. Hence, students with such a teaching approach become passive learners but not active learners.
With regards to students’ general mathematical mindset, the majority of SHS students in Group 1 were reported to have a more growth mindset with some few possessing fixed ideas while majority of students in Group 2 schools were also identified as having a more fixed mindset with some few possessing growth ideas. In most cases, students tend to favor one theory over the other, however, they may support both growth and fixed mindsets, depending on the context in which they are used (Hwang et al., 2019). The results further support the work of Boaler (2013) who emphasized that students might have a combination of the two mentalities where a growth mentality is held by 40 percent of students, a fixed mindset by 40 percent, and a mixed mindset by 20 percent of students but did not indicate the extent to which growth or fixed mindset surpasses the other.
Additionally, students’ mathematical mindsets suggest that students develop a more growth mindset when they are taught with a student-centered approach while students possess a more fixed mindset when taught with a teacher-centered approach. Sun (2018) argued that teaching approaches are one of the critical elements that influence the development of students’ mindsets. But, Stohlmann (2022, p. 159) reported that “students may have a general growth mindset, but for a specific subject such as mathematics or science, they may hold more fixed mindset beliefs.” This is because students believe that some are naturally good in subjects such as mathematics and science which makes other students who are not good in these fields feel reluctant in learning. However, we argue that the mindset developed by students is not the result of the subject but a result of the dominant teaching approach they experience in mathematics classrooms. This argument is consistent with the findings by Sun (2015) which revealed that teaching mathematics in a student-centered approach that exceeds algorithm and procedural work aids in the formation of a growth mindset on the part of students. Ellsworth and Buss (2000) reported that the teacher-centered teaching and learning approach focuses on students providing the right answers and encourages students to follow the exact processes in order to avoid mistakes that will result in the correct responses. The intelligence of students with a fixed mentality is seen as rigid and cannot be controlled (Dweck, 2006). These students are less willing to try something new in order to avoid making mistakes and failures. Since such students are not willing to accept new challenges to improve their learning skills, this affects their performance in Core Mathematics. Hence, the student-centered approach will elicit a more growth mindset while the teacher-centered approach will elicit a more fixed mindset.
Conclusions and Recommendations
The study reveals possible influences between the teaching approaches and students’ mathematical mindsets, as students in Group 1 schools perceived their Core Mathematics teachers to use a student-centered approach, while students in Group 2 schools perceived their Core Mathematics teachers to use a teacher-centered approach. The study further concludes that a student-centered approach elicits some strong growth mathematical mindset while a teacher-centered teaching and learning approach also elicits some strong fixed mathematical mindset. The study suggests that students who are open to a series of investigations and trial-and-error exercises, engage in higher thinking, and actively engage in learning activities are said to develop a growth mindset as they are willing to embrace challenges and recognize the value of struggles in the learning process. Again, students who are tasked with following instructions and giving out correct answers believe in the fixed-minded approach, as they think that one’s intelligence cannot be controlled.
The study recommends that teachers should adopt a student-centered approach to teaching since it has the potential to shape students’ learning toward a strong growth mindset. Additionally, considering the underachievement in Core Mathematics by the majority of SHS students and the potential negative effects of possessing a fixed mathematical mindset on students’ learning outcomes, it is important that teachers are supported through professional development programs to fully embrace more participatory teaching approaches. Again, teachers and students should be taken through mathematical mindset interventions for them to recognize the importance of developing a growth mindset.
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
Data Availability Statement
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.