Introduction

Emotions, attitudes, and beliefs are commonly seen as key determinants of the success of a learning process. In general, the school curriculum, teachers, and formal education infrastructure focus only on cognition in relation to problem solving and problem posing, overlooking the affective components of student learning development (Voica et al., 2020). However, recently many researchers have begun to suggest the need for learning that emphasizes affective and motivational variables (Goldin, 2017).

To focus on this concept, this study uses the affective domain definition of Philipp, (2007). The affective domain covers emotions, beliefs, and attitudes. In general terms, emotion or feeling is attached to an idea or object (Philipp, 2007). Emotion refers to feelings or states of consciousness. There is positive (e.g., the feeling of ‘aha’) and negative (e.g., the feeling of panic) emotion. Beliefs manifest propositions, understanding and the premises of the world held by individuals. While emotions and beliefs are both considered to be part of the affective domain, they have distinct definitions. Emotions are conscious experiences such as happiness, panic, and so on, whereas belief is a student’s belief in something deemed true. Furthermore, attitude refers to the way of behaving, thinking or feeling that indicates one’s viewpoint or mentality (Philipp, 2007). More specifically, attitude is the tendency of an individual’s state of mind towards a value, which is manifested through the responsive expression of oneself, person, place, object, or event (object of attitude) which ultimately influences individual thoughts and actions (Sewell, 1989). Attitude is strongly associated with social contexts (Moscovici & Marková, 2006).

The affective domain analyzed in this study is self-efficacy (Bandura, 2010). Self-efficacy can be defined as a person’s belief about their ability to meet the challenges in completing a task successfully (Liu et al., 2008). Bandura argues that students with high self-efficacy aspire more in life, be more flexible in problem-solving, demonstrate higher intellectual skills, and conduct self-evaluations more accurately than those of equal cognitive skills, but lack confidence in their abilities (Bandura, 2010). Self-efficacy contributes to the inconsistencies in people’s conduct caused by emotions and cognition. Poor performance, low self-esteem and negative conceptions of personal achievement and development are associated with lack of self-efficacy. High self-efficacy results in the ability to recognize one’s skills to achieve in particular areas, such as in the academic field. Self-efficacy in the educational field, as a context-related construct, involves individuals’ beliefs about their own competence to fulfil the predetermined goals (Vasile et al., 2011).

Self-efficacy has a strong correlation with motivation (Voica et al., 2020). Social environment plays an important role in extrinsic motivation. Extrinsic motivation originates from outside the individual and motivates him to engage in learning activities. For example, someone will study knowing that an exam will be held the following morning with the goal of receiving a good mark or winning a prize. Furthermore, Voica (2020) explains that the key to motivation is energy and strong goal-directed behavior that motivates an individual to take action. Motivation is influenced by the fulfillment of basic demands for survival, welfare, and growth (Güss & Dörner, 2017). Motivation is an internal process that encourages and directs individuals to engage with the environment and solve a problem in an adaptive and open-minded way (Güss & Dörner, 2017; Rahayuningsih et al., 2021). Motivation levels are reflected in the choice of action as well as the intensity and persistence of the effort (Bandura, 2010). Campbell claims that autonomous motivation is generated from full awareness of the choices made before acting (Campbell, 2008).

Although self-efficacy and motivation are strongly correlated, they differ in some ways. While motivation refers to an individual’s desire to achieve a goal, self-efficacy involves believing in one’s own ability to create achievements (Gao, 2020). The relationship between the two seems to have a reciprocal effect: increased self-efficacy results in high learning motivation (Chan & Lam, 2008). The relationship between self-efficacy and motivation may work in the opposite direction to create a cycle of success; when individuals are highly motivated to learn, they tend to achieve their goals and improve self-efficacy (Menon & Sadler, 2018).

Past studies cover only a small part of mathematical creativity (Bicer et al., 2020), that is creativity in terms of the meaningful insights experienced by students as they learn new concepts (Kaufman & Beghetto, 2009). Creativity in this study focuses on meaningful interpretations of the experiences, actions, and events that learners have in solving mathematical problems (Levenson, 2013 & Runco, 1996). Several instructional interventions (e.g., problem posing, open-ended problems, multi-solution assignments) have been proven effective in increasing students’ mathematical creativity (Bicer et al., 2020; Leikin & Elgrably, 2020; Leikin, 2014).

Most researchers have discussed the cognitive domain of mathematical creativity, namely fluency, flexibility, and originality and ignore affective aspects such as self-efficacy, beliefs, and attitudes (Cai & Leikin, 2020). According to Bandura (2010), the components of creativity in the affective and cognitive domains play an important role in helping students generate new and permanent ideas (Bandura, 2010). Moreover, Gao (2020) argues that creative thinking ability is not sufficient to express one’s creativity (creative expression). Creative expression, like other forms of behavior, is influenced by self-judgments of one’s ability to produce novelty and useful products (Gao, 2020). Self-judgments is also known as creative self-efficacy (Farmer, 2017), which is the extended form of self-efficacy construction (Bandura, 2010). Self-efficacy in relation to creative thinking ability has been studied vastly (Gao, 2020; Choi, 2004; Laws, 2002; Farmer, 2017). Research has conceptually and empirically revealed the correlation between self-efficacy and creative thinking ability to express creative expression (expression of ideas, solutions, processes and results). Recently, there has been an increasing need to investigate the relationship between self-efficacy and creative thinking ability. The importance of examining self-efficacy in students may be useful for educators and researchers in facilitating students’ creativity (Beghetto, 2006; Byrge & Tang, 2015). In particular, it will provide beneficial information on factors affecting motivation and learning experience associated with students’ self-efficacy and creative thinking ability. Besides, the exploration of the correlation between academic beliefs, behaviors, various levels of self-efficacy and creative thinking ability can contribute to the development of student learning outcomes. Therefore, educators and researchers on creativity will be at a better position in understanding and overcoming factors influencing students’ sense of eagerness to develop and express creative potentials in themselves. The objectives of the current study involve: 1) investigating the extent to which self-efficacy affects students’ mathematical creative thinking ability; 2) exploring the characteristics of students who possess high mathematical creative thinking ability and high self-efficacy.

Methodology

The effect of self-efficacy on students’ mathematical creative thinking ability was investigated through a mixed-methods study, which combined semi-structured interview for data collection and correlation statistics for data analysis (Sharma & Gigras, 2017). The mixed-methods strategy used in the study was explanatory strategy where the quantitative data analysis was followed by the qualitative data analysis (Creswell, 2012; Fraenkel, et al. 2011).

Participants

The participants were selected from Junior High Schools in the city of Makassar. They consisted of ninety-six students (42 boys and 54 girls aged around 14 years old). The participants were invited to complete a questionnaire assessing their mathematics self-efficacy. Based on the result of the self-efficacy questionnaire (M = 56.95; SD = 5.97; Mdn = 57.00), creativity test (M = 76.43; SD = 6.076; Mdn = 75.00) and student gender, two boys and two girls were chosen to represent students with high creative thinking ability and high self-efficacy in mathematics. Students with high creative thinking possess a score of 95 (SKBK) in creative thinking test and a score of 74 (SSE) in self-efficacy test.

Materials

Mathematics Self-Efficacy Scale

The mathematics self-efficacy scale was created in Indonesia using Bandura’s (2010) self-efficacy scale construction guidelines. The scale consists of ten items that reflect mathematics tasks of varying degrees of difficulty based on the participants’ current mathematics study status. Participants were asked to rate the degree to which they agreed with the self-efficacy statements. They were required to rate their trust in their ability to complete tasks by selecting a number between SE0 (cannot do at all) and SE10 (highly certain can do). Participants’ mathematics self-efficacy level were determined by the total score of the ten items. The ten items had a reliability score of 0.95 (Cronbach’s α).

Mathematics Creative Thinking Ability Scale

The Mathematics Creative Thinking Ability Scale was developed based on the research instrument of Rahayuningsih et al. (2020). It contains an indicator of creative thinking ability that is cognitive flexibility (Singer et al., 2017 & Rahayuningsih et al. 2020). According to Singer et al., (2017), the context used to examine students’ creativity in mathematics involves mathematics tasks, like problem-solving sheets, that can be used as an instrument to measure students’ mathematical creative thinking ability. In a problem-solving context, Singer considers cognitive flexibility as the ability to pose a new solution to a problem; it offers various problem-solving strategies, generates novelty in solutions and changes the existing thinking framework.

Procedures

The quantitative data analysis involved descriptive and inferential statistics, while the qualitative data analysis was carried out through: 1) Data reduction; 2) Data Display; 3) Conclusion Drawing/Verification (Creswell, 2012; Fraenkel, et al. 2011). Research hypotheses were tested using simple regression analysis. Hypothesis testing was done to investigate the effect of the independent variable (self-efficacy, X) on the dependent variable (mathematical creative thinking ability, Y). The statistical hypotheses used in this study included:

Note:

Participants who represented the highscore category in the creativity test were invited for semi-structured interview. The participants had to conduct face-to-face interviews individually for 30 to 45 minutes. The interview began with exploring the participant’s understanding of confidence in mathematics learning. Each of the participants was asked to reveal what s/he was thinking at the moment and associate it with her/his past experience that is relevant to the interview question on problem-solving self-efficacy. The participants were asked to elaborate on their ideas during the interview to provide insightful information for the researcher and familiarize themselves with all of the survey statements.

Findings and Discussion

To what extent does self-efficacy affect students’ mathematical creative thinking ability?

Since the sample number was less than 100, test of normality was conducted using Shapiro-Wilk. The analysis of results showed a statistical value of 0.975 for self-efficacy or p-value = 0.072 > 0.05, suggesting normal distribution of data. Meanwhile, creative thinking obtained a statistical value of 0.976 and sig. or p-value = 0.078 > 0.05, indicating normal distribution of data.

Test of normality based on the ANOVA table showed a statistical value of 150.716 with p-value = 0.096 > 0.05, therefore H0 was accepted. Thus, it can be said that self-efficacy had a linear correlation with creative thinking ability.

The regression equation obtained based on the coefficients table was =31,341+0.792X, with a statistical value of 11.549 and a significance or p-value = 0.000 < 0.05. These figures indicate that H0 was rejected and H1 was accepted. In conclusion self-efficacy had a positive effect on students’ mathematical creative thinking ability.

Analysis based on the model summary table showed a statistical value of 133.381 and p-value = 0.000 < 0.05, suggesting to reject H0 and accept H1. It also implied that it was worthwhile to use the regression equation of =31.341+0.792X. Meanwhile, the correlation between self-efficacy and creative thinking ability was confirmed by an R value of 0.771 and sig. = 0.000 < 0.05. Furthermore, the R-Square value of 0.594 revealed that self-efficacy accounted for 59.4% of the variance in students’ creative thinking ability, with the remaining variables not included in the regression equation.

Descriptive analysis indicated a significant effect of self-efficacy on students’ creative thinking ability. Despite this, there are other variables contributing to students’ creativity in mathematics, including anxiety, academic ability, learning style and many others.

The characteristics of students with high mathematical creative thinking ability and high self-efficacy

The characteristics of students with high creative thinking ability and high self-efficacy in mathematics are revealed through interview excerpts provided below.

According to the above interview excerpt, the participant seemed to have a lot of confidence in his problem-solving skills. The problem could be solved because he developed the assumption that he was capable of solving it, even though he initially suspected that the problem contained a mistake.

The following interview excerpt proves that when it comes to solving problems, the students can be anxious and cautious.

Interviewer: Why were you so agitated earlier? (while displaying a video recording of the person completing the task) Participant 2: I read the problem many times to ensure that my reading is right.

Interviewer: You’re able to say what you’re thinking at the time?

Participant 2: I assume the question demands more than one answer, and I’m merely checking that the answer in question is of a different shape. That, I assume, is the remedy. But first, I need to check it for myself.

Interviewer: Is it like that when you look at the camera and seem to be dissatisfied with it?

Participant 2: I’m a bit awkward in front of the camera, which irritates me.

According to the interview excerpt above, the participant solved the problem with extreme caution. The student showed anxiety despite having high levels of self-efficacy and creative thinking skills.

Anxiety caused by elements such as fear of being wrong, and constantly convincing himself to answer each question correctly and acting uncomfortably in front of the camera. The anxiety was evident during the problem-solving process; the student appeared to be excessively cautious, fearful of making a mistake when operating numbers. This finding is in line with those of Hulsizer (2016) who suggests that when students are in front of the camera or hear their own voice, they may become anxious. This shows that they tend to be shy, thereby increasing their anxiety (Huang et al., 2020). However, research conducted by Kearney & Schuck (2005) shows that making videos causes less anxiety than delivering an oral presentation in a classroom.

Students’ anxiety is also revealed in other interview excerpts, such as presented below.

Students with high self-efficacy are more likely to be creative when it comes to solving math problems. This point is confirmed by the following interview excerpt.

The above excerpt indicates that besides self-efficacy, metacognitive skills can also affect students’ problem-solving ability. The process of metacognition in question is retrospective metacognition, which is metacognition that allows for self-evaluation. According to Özcan & Eren Gümüş (2019), the only variable which influences mathematical problem-solving efficiency directly was the metacognition experience, which acted as a mediator for the effects of mathematics self-efficacy, mathematics motivation, and mathematics anxiety. A study by Lai et al. (2015) unearthed the fact that metacognition was able to mediate the effect of math anxiety on mathematical problem-solving. However, Zarch & Kadivar (2006) suggest that mathematical self-efficacy entirely mediates the effect of metacognition on mathematical achievements. In fact, this finding suggests that metacognition plays an essential role in solving challenging tasks, such as mathematical problems (Holton & Clarke, 2006; Jaafar & Ayu, 2010; Özsoy, 2011; Rahayuningsih, Sirajuddin, et al., 2021). In addition, it is also believed that metacognition influences performance by controlling behavior using feedback gleaned from student experiences (Moores et al., 2006).

The following section contains a student’s interview relating to key experiences associated with the improvement of an open-minded mindset, ability to generate ideas, thinking ability in general, ability to change perceptions as well as an increased toolbox for creativity, curiosity, awareness, and positive attitude.

Experts and research conclude that the factors affecting a person’s ability to think creatively in mathematics may come from within (internal) and outside (external) students. Internal factors consist of intelligence, talents, interests, attitudes, self-efficacy and motivation; while external factors include environmental conditions, the socioeconomic status of the family and the people around the students such as parents, teachers and peers (Chan & Lam, 2008; Ikram et al., 2020a; 2020b). According to Bandura (2010), people want to be in control of the events that affect their lives and to see themselves as actors. This feeling of being an actor presents itself in deliberate actions, cognitive processes, and affective processes.

In this study, mathematical self-efficacy involves cognitive and affective processes that guide students to perform better mathematical creative thinking ability. The following are the study’s main findings: (1) Most participants became more creative when solving math problems, showing strong self-efficacy; (2) Certain students had relatively high anxiety, but high self-efficacy and mathematical reasoning skills scores; cautious problem-solving allows students to feel anxious; (3) Prior experiences are associated with learning material and an improved way of thought (open mind), the ability to create thoughts, the ability to think in general, the ability to alter attitudes, as well as an expanded creativity toolbox, curiosity, awareness, and a positive mindset.

Conclusions

In conclusion, the study’s findings indicate that students’ mathematical self-efficacy impacts their mathematical creative thinking ability at the junior high school level. Other results in this study also show that when students have high self-efficacy, their creative thinking skills improve, and vice versa. Anxiety, reliance on previous experiences, such as the ability to produce ideas (cognitive novelty), the ability to suggest a range of completion procedures (cognitive variety), and the ability to alter expectations (cognitive framing) are traits of students with high mathematical creative thinking abilities and high self-efficacy

Conflict of Interest

The authors declare no competing interests.

Author contribution statement

The total contribution percentage for the conceptualization, preparation, and correction of this paper was as follows: S.R 60%., M.N 30 % and N.I.10 %.

Data availability statement

The data supporting the results of this study will be made available by the corresponding author, (S.R), upon reasonable request.

References

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