The present study examined the influence of mathematics methodology courses on pre-service early childhood education teachers’ sense of self-efficacy. Seven specific areas were targeted to develop an adequate understanding of how courses in mathematics methods affect the development of self-efficacy among pre-service early childhood teachers.

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The first two areas aimed at evaluating the differences in self-efficacy between pre-service teachers exposed to (1) content pedagogy courses versus one or two mathematics methods course, and (2) one content pedagogy mathematics course versus two content pedagogy mathematics courses. The third area aimed at evaluating how self-efficacy varies among pre-service teachers exposed to one methods course versus those exposed to two methods courses, while the fourth area assessed the impact of mathematics methodology courses on pre-service teachers’ sense of self-efficacy.

Other important areas targeted in the study include understanding if there any gender-based differences in the self-efficacy of pre-service teachers; identifying pre-service teachers’ perceptions of their skills, competence, and ability to teach mathematics; and developing an adequate understanding of the aspects of mathematics methods courses that are instrumental in influencing the development of self-efficacy beliefs of future teachers of mathematics. The main findings of the study are discussed in the described areas of interest.

## Differences in Self-Efficacy: Content Pedagogy Courses versus Methods Courses

In response to the first research question that assessed the differences in self-efficacy between content pedagogy courses and mathematics methods courses, the study found a significant difference in self-efficacy beliefs between pre-service teachers exposed to content pedagogy courses and those exposed to one or two mathematics methods courses.

The mean self-efficacy score of pre-service teachers exposed to content pedagogy courses was low (77.53) compared with those exposed to mathematics methods courses (84.83). This particular finding is a good indicator of the fact that mathematics methods courses may have more beneficial effects in developing the self-efficacy of pre-service teachers than general content pedagogy courses.

Although to the best of our knowledge no study has specifically evaluated how content pedagogy courses and mathematics methods courses compare in developing the self-efficacy of pre-service teachers, Lancaster and Bain (2010) found statistically significant gains in self-efficacy among pre-service elementary education teachers exposed to a 13-week compulsory undergraduate inclusive education course. On their own, content pedagogy courses may be unable to increase the self-efficacy beliefs of elementary pre-service teachers due to their inability to provide demonstrations, hands-on activities, and enactive masterly experiences (Velthuis, Fisser, & Pieters, 2014).

Although the two groups (pre-service teachers exposed to content pedagogy courses and those exposed to mathematics methods courses) had equal variances according to the results from the Levene’s test for equality of the variances (F=1.061, with *p*-value =.305), a test of between-subjects effects showed that the null hypothesis showing no difference between the two groups of pre-service teachers could be rejected at the 5% significance level (F=29.878 with *p *<.001).

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This finding reinforces the fact that targeted mathematics methods courses are more effective than generalized pedagogy courses in developing the self-efficacy beliefs of elementary pre-service mathematics teachers. In their study, Wilkins and Brand (2004) found “a positive relationship between participating in the mathematics methods course and changes in teacher beliefs and attitudes” (p. 226). In another related study, Easterly (2003) found that mathematics self-efficacy, teacher efficacy, and mathematics teaching efficacy increased substantially among pre-service and novice elementary teachers exposed to a mathematics methods course over a fixed period.

Overall, with regards to the first research question, the present study showed a consistent positive increase in self-efficacy that covaried with exposure to either one or two mathematics methods courses compared with exposure to content pedagogy courses. As such, it can be argued that participation in mathematics methods courses can be perceived as a potential source of increased self-efficacy among pre-service early childhood education teachers.

This is consistent with the observation made by Cone (2009) that targeted mathematics methods courses act as sources of masterly and vicarious experiences that reinforce the self-efficacy beliefs of elementary pre-service teachers. Additionally, mathematics methods courses may be more effective than content pedagogy courses in developing an enabling environment for the exhibition of self-efficacy mediating aspects, such as positive attitude, task engagement, as well as feedback (Wilkins & Brand, 2004).

## Differences in Self-Efficacy: One Course versus Two Content Pedagogy Courses

The second research question addressed the differences in self-efficacy between pre-service teachers exposed to one content pedagogy mathematics course and pre-service teachers exposed to two content pedagogy mathematics courses. Although ANCOVA tests showed that pre-service teachers exposed to one content pedagogy course had a lower self-efficacy mean score (74.94) than those exposed to two content pedagogy courses (78.12), the test of between-subject effects demonstrated that the null hypothesis that there is no difference between the two groups of teachers could not be rejected at the 5% significance level (t = -.868, with *p* =.460).

This finding implies that no significant differences in self-efficacy were noted between pre-service teachers who participated in one content pedagogy course and those who took part in two content pedagogy courses. This finding shows that the number of content pedagogy courses does not affect the pre-service teachers’ viewpoints, perceptions, or judgments of their capabilities to succeed in teaching mathematics in the future.

The finding contrasts the results of a previous study that found that the “differences at the university level in courses taken during the first year between science content courses and science methods courses…influenced the pre-service teacher’s development of science teaching self-efficacy” (Velthuis et al., 2014, p. 445).

However, the finding is consistent with the argument made by several scholars that content pedagogy courses cannot often increase the self-efficacy of elementary pre-service teachers as they are unable to not only emphasize constructivist experiences but also to accentuate a problem-solving conception of mathematics that is inherent in a methods course (Briley, 2012; Ford & Strawhecker, 2011).

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This particular finding underscores the importance of blending content pedagogy courses with mathematics methods courses, rather than offering them in isolation. In their study, Ford and Strawhecker (2011) found that a blended course of math content and math methods not only enhanced the connections between content and methods but also developed the confidence, mathematical aptitude, and self-efficacy beliefs of pre-service teachers beyond their preferred teaching level.

Since pre-service teachers’ beliefs, teaching efficacy, and sense of self-efficacy can be influenced by teacher education programs (Briley, 2012), it is important to blend content pedagogy courses with mathematics methods courses to ensure optimal benefits in terms of developing and reinforcing self-efficacy beliefs.

Overall, the finding that no significant differences in self-efficacy exist between pre-service teachers exposed to one pedagogy course and those exposed to two content pedagogy courses reinforces the conclusion made by Woodcock (2011) that the structure of preparation programs might indeed affect how teachers develop their self-efficacy beliefs.

## Variations in Self-Efficacy: One Methods Course versus Two Methods Courses

The third research question addressed the variations in self-efficacy between pre-service teachers exposed to one mathematics methods course and those exposed to two methods courses. Here, the study found no significant difference in self-efficacy between teachers who participated in one methods course and those who participated in two methods courses.

Although ANCOVA results showed that the mean self-efficacy score for pre-service teachers exposed to one methods course was lower compared to the score for teachers exposed to two methods courses (82.64 and 85.95 respectively), the test of between-subjects effects was unable to reject the null hypothesis that there is no significant difference between the two groups of teachers at the 5% significance level (t = -.868 with *p* =.460).

This finding could be explained in the context of the existing disconnect between training programs for elementary pre-service teachers and accrued self-efficacy gains, with Charalambous and Phillipou (2003) arguing that training programs are at risk of becoming a “sink and swim experience” for pre-service teachers due to their incapacity to influence the development of teacher efficacy beliefs.

Available literature demonstrates that “the assumed benefits of positive teacher self-efficacies are believed to derive from the effects of teacher self-efficacy on teacher cognition and motivation” (Chan, 2005, p. 155). Research is also consistent that self-efficacy beliefs relate to the capacity of teachers to not only develop high confidence in their teaching abilities (Charalambous & Phillipou, 2003; Palmer, 2006) but also to realize specific outcome expectancies and efficacy expectancies (Chan, 2005).

Drawing from these statements, it is clear that there were no significant gains in teacher cognition and motivation that could be associated with exposure to two mathematics methods courses, meaning that participation in two mathematics courses was not effective in increasing the beliefs of pre-service teachers about their own ability to successfully execute specific teaching actions. However, this explanation addresses variations in self-efficacy between the two groups, and it does not mean that mathematics methods courses are not effective in increasing self-efficacy gains among elementary pre-service teachers.

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This finding is consistent with the observation made by Cone (2009) that, “despite the number of science and multicultural education courses taken, pre-service teachers continue to enter their student teaching semesters and professional careers with low science teaching efficacy beliefs and with beliefs about diversity that undermine the equality principle articulated in science reform initiatives” (p. 25). However, the finding contrasts the results of other studies showing that improved teaching methods would foster greater self-efficacy among pre-service teachers (Chan, 2005; Ford & Strawhecker, 2011).

## Impact of Mathematics Methodology Courses on Self-Efficacy

The main purpose of the present study was to examine the impact of mathematics methodology courses on pre-service early childhood and special educators’ self-efficacy and beliefs. In response to the fourth research question that assessed the impact of mathematics methodology courses on pre-service teachers’ sense of self-efficacy, the study found significant raises in teachers’ self-efficacy upon exposure to mathematics methodology courses.

Specifically, statistical tests showed that the impact of mathematics methods courses on pre-service teachers’ self-efficacy was significant at the 5% confidence level (t=5.427 with *p*-value <.001), with the estimated regression coefficient for mathematics showing that the self-efficacy of the teachers increased by 7.293 when they participated in the mathematics methodology courses. This finding is consistent with previous research studies documenting the positive effects of mathematics methodology courses on pre-service teachers’ self-efficacy (Cone, 2009), teacher efficacy beliefs and mathematics teaching efficacy (Esterly, 2003), and motivational orientation (Stevens, Olivarez, Lan, & Tallent-Runnels, 2004).

Several researchers have attempted to explain why participation in mathematics or science methods courses leads to positive gains in pre-service teacher’s sense of self-efficacy and beliefs. For example, Turner, Cruz, and Papakonstantinou (2004) argue that such courses not only argument teachers’ feelings of confidence for teaching mathematics but also expose them to many opportunities for masterly experiences as well as verbal and social persuasion.

On their part, Velthuis et al. (2014) argue that methods courses are more effective than content courses in reinforcing the self-efficacy and teaching efficacy of elementary pre-service teachers as they aspire to instruct teachers on the skills and competencies needed to teach the particular subject, “such as relevant teaching strategies, assessment of students’ science [or mathematics] knowledge and application of classroom management techniques” (p. 447). Bleicher (2004) found that professional methods courses are more practical in the application of masterly experiences, leading to significant gains in teacher’s self-efficacy beliefs.

Overall, the finding that mathematics methods courses impact positively on elementary pre-service teachers’ self-efficacy is welcome based on the available evidence showing that teachers’ with high self-efficacy beliefs “are more capable of using instructional strategies effectively, more capable of ensuring student participation, and more successful in classroom management skills” (Ozder, 2011, p. 1). However, a study by Palmer (2006) found that pre-service teachers can gain confidence directly from success in understanding content and pedagogy, meaning that significant increases in self-efficacy could still be attained through cognitive content masterly as well as cognitive pedagogical masterly.

## Differences in Self-Efficacy based on Gender

The fifth research question assessed if there are significant differences in the self-efficacy of pre-service teachers based on their gender. Although the ANCOVA test found that the self-efficacy score for female teachers was slightly lower compared to the score for male teachers (80.90 and 85.14 respectively), the between-subjects effects test failed to reject the null hypothesis that there is no difference in self-efficacy between the two groups at the 5% confidence level (t=.078 with p=.780). This finding can be interpreted to mean that gender does not mediate the difference in self-efficacy beliefs among elementary pre-service teachers. The finding is consistent with previous research studies documenting that gender has no significant effect on personal mathematics teaching efficacy and science teaching efficacy beliefs (Bursal, 2010), teacher self-efficacy beliefs (Senemoglu & Demirel, 2009), and confidence to teach mathematics or science (Ford & Strawhecker, 2011; Palmer, 2006; Tenaw, 2013).

It is important to note that the ANCOVA test revealed significant differences in self-efficacy between pre-intervention and post-intervention results using gender as a covariance (F=5.691 with p-value = 0.019). This finding could be interpreted to mean that most female teachers have low self-efficacy beliefs than their male counterparts before enrolling in training programs, but bolster their self-efficacy beliefs to be at par with male teachers once they participate in the training courses.

This view is supported in the literature, as Albayrak and Unal (2011), Briley (2012), and Woodcock (2011) have documented several studies that found a positive relationship between exposure to mathematics methods courses and significant gains in pre-service teachers’ self-efficacy beliefs. Similarly, other researchers (e.g., Cone, 2009; Charalambous & Phillipou, 2003) found that pre-service teachers exposed to methods and special teacher education courses reported high self-efficacy beliefs after attending the courses.

Since self-efficacy beliefs are easy to change or manipulate in the presence of favorable conditions (Woodcock, 2011), it could be that the self-efficacy beliefs of female pre-service teachers increased and averaged that of male pre-service teachers once they were exposed to one mathematics methods course or two mathematics methods courses.

The main finding, however, is that post-intervention scores showed no significant difference in self-efficacy beliefs of pre-service teachers based on the gender variable. This particular finding shows that female pre-service teachers are as good as their male counterparts in developing self-efficacy beliefs upon exposure to the necessary conditions.

## Perceptions of Pre-Service Teachers

The sixth research question assessed the perceptions of pre-service teachers about their skills, competence, and ability to teach mathematics. The themes that were used to analyze the qualitative data included “mastery experiences, vicarious experiences, social persuasions, and sociological factors.” In mastery experiences, the interviewed pre-service teachers agreed that they can develop the skills, competence, and ability to teach mathematics through exposure to hands-on activities, modeling/simulating real-life classroom contexts, watching videos of real-life classroom situations, and participating in creating and presenting lesson plans.

One pre-service teacher noted that participating in all those activities helped her to “feel more confident and more prepared to teach those subjects in the future”, while another pre-service teacher acknowledged that these activities enabled her to “learn how to teach math rather than learning how to do the math.” These results are consistent with previous research studies documenting that training and hands-on activities provide the necessary enactive mastery (Bray-Clark & Bates, 2003; Turner et al., 2004), which in turn acts as an important source of self-efficacy beliefs for pre-service teachers (Cone, 2009, Tenaw, 2013).

The value of enactive mastery is embedded in the fact that “when faced with similar situations, individuals rely on perceptions of past mastery to produce information that is used to make judgments about present capabilities” (Bray-Clark & Bates, 2003, p. 16). In line with the results of other researchers (Charalambous & Phillipou, 2003; Esterly, 2003; Palmer, 2006), the present study also found that teachers were able to feel more confident and comfortable to teach mathematics once they participated in these activities.

In vicarious experiences, the participants said that modeling, use of physical tools, use of manipulations, peer observations, and group collaborations were particularly useful in developing their skills, competence, and ability to teach mathematics. Research is consistent that “vicarious experience capitalizes on the notion that an individual’s efficacy beliefs can be enhanced through the observation of a significant model engaged in an activity that they perceive as being well aligned with their needs and capabilities” (Bray-Clark & Bates, 2003, p. 17).

Although one participant felt “nervous” watching other students perform various tasks, it is evident from the responses that these observations were critical in enhancing their self-efficacy beliefs through social comparisons made with other students (Albayrak & Unal, 2011), observations of successful and unsuccessful teaching behaviors with the view to enhancing their ability to engage in analysis and self-correcting patterns of behavior (Bray-Clark & Bates, 2003), and small group interactions (Esterly, 2003).

The theme of verbal or social persuasion showed that the participants were able to improve their skills and competence to teach mathematics through feedback from the instructor, learning in small groups, and adopting a brainstorming strategy with the view to promoting varied thought processes. The notion of social persuasion is nested on the fact that “the communication of verbal judgments from respected or influential others can affect an individual’s self-efficacy beliefs” (Bray-Clark & Bates, 2003, p. 18).

This assertion is well depicted in the present study, as most participants reported that instructor feedback and brainstorming issues with peers and their instructor helped them to build math vocabulary, internalize confidence in teaching mathematics, and develop their self-efficacy and self-awareness beliefs. Furthermore, the participants reported that they felt more confident from both positive and negative feedback and that the instructor underscores the need for providing balanced feedback depending on context or issue.

This finding confirms the assertion made by several researchers that superficial or hollow feedback is unlikely to bolster the self-efficacy beliefs of individuals (Chan, 2005; Ediger, 2012), and that verbal persuasion can change the self-efficacy beliefs of elementary pre-service teachers only when the behavior-related information is not only convincing but is also conveyed in a way that interrupts the pre-existing distrust in own capabilities (Bray-Clark & Bates, 2003).

Lastly, in the theme of psychological factors, most participants agreed that confidence, good attitude, and an open environment are important in developing the skills and competence to teach mathematics. It is clear from the responses that most participants believed in sharing ideas and experiences at the beginning of the teaching session to set the proper mood for classroom engagement and also encourage the reinforcement of a mathematics mindset.

Such engagement coupled with a relaxed environment for cooperative learning, according to Ediger (2012), encourages individuals to contribute in problem-solving situations, build on the thinking of others, develop connections in ongoing lessons and units of study, and encourage creativity in finding own best way to solve problems. Bray-Clark and Bates (2003) argue that “because self-efficacy beliefs are intertwined with psychological states (each is highly dependent on one another), physiological states such as anxiety, stress, and fatigue provide other potentially important sources of efficacy information” (p. 18).

To put this argument into context, two participants noted that the long class hours and heavy workload distracted their concentration to learn. This finding underscores the need to pace mathematics lessons with the view to ensuring that the pre-service teachers succeed in mastering the content presented (Bates, Latham, & Kim, 2013; Charalambous & Phillipou, 2003; Ediger, 2012; Ford & Strawhecker, 2011). Overall, the implication of these findings for pre-service training is the noticeable need to pace mathematics lessons, express positive and compelling feedback, and provide a favorable environment in which elementary pre-service teachers feel they may engage in learning processes in a non-intimidating, cooperative manner.

## Aspects of Mathematics Methods Courses

The seventh research question assessed the specific aspects of the mathematics methods courses that influence the self-efficacy beliefs of future teachers of mathematics. Responses from the qualitative interviews show that pre-service teachers benefited more from the mathematics methods courses due to their ability to provide hands-on use of manipulatives and other activity-based lessons that increase their confidence and self-efficacy beliefs.

It is also clear from the responses that that practical nature of the mathematics methods courses positively influenced the beliefs of pre-service teachers in their ability to teach mathematics, though their self-rating scores on teaching efficacy showed that majority of the teachers are yet to achieve full confidence to teach mathematics due to lack of actual field experience.

These findings underscore the argument made by Wilkins and Brand (2004) that “An important goal of teacher education programs should be to help pre-service teachers develop beliefs and dispositions that are consistent with current educational reform” (p. 226). Additionally, most pre-service teachers agreed that small-group instruction strategy, peer interaction, modeling/simulations, and use of videos were particularly useful in assisting them to gain the confidence and self-efficacy beliefs needed to teach mathematics in the future.

Several researchers have documented the efficacy of mathematics methods courses in changing teacher self-efficacy beliefs and confidence levels. For example, Wilkins and Brand (2004) found that pre-service teachers who participated in mathematics methods course “changed their beliefs in a way that was more consistent with current mathematics education reform and also changed their sense of self-efficacy in a positive way” (p. 231).

Lancaster and Bain (2010) found that participation in an inclusive education course covaried with enhanced perceptions of self-efficacy, though they were unable to find any relationship between self-efficacy beliefs and the type of course design experienced by pre-service teacher education students. Similarly, Velthuis et al. (2013) found that “differences at the university level in courses taken during the first year between science content and science methods courses influenced the pre-service teachers’ development of teaching self-efficacy.

The present study goes beyond describing the association between mathematics methods courses and self-gains to identifying the specific aspects of mathematics methods courses that lead to gains in self-efficacy beliefs. Overall, the findings of this research question provide an example of how instructors can assess and modify their mathematics methods courses in terms of teacher self-efficacy beliefs by ensuring that the courses cannot only provide hands-on use of manipulatives and activity-based lesson but also employ small-group dynamics, peer interactions, and modeling during instruction.

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