## Characteristics of Students with High or Low Self-Efficacy

The students mainly assessed their self-efficacy as rather high; most respondents assessed it as 8 or 9 on the scale from 1 to 10. In particular, students #1, #2 and #3 gave themselves the mark of 8 on a 10-point scale, student #4 gave themselves a 9, and student #7 ranked themselves as being between 8 and 9.

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Most of the students who gave themselves a mark between 8 and 9 claimed that they had not felt very confident prior to taking the courses. This was due to a number of reasons. For instance, one of the participants noted that they had known mathematics rather well, but it had been hard for them to return to the most basic concepts and explain them to children.

The importance and difficulty of using only precise vocabulary while teaching mathematics was also pointed out. A number of respondents stressed that they had lacked the experience of teaching and, because of this, had not been confident about their ability to conduct the teaching activities in the classroom. However, the participants emphasized that the courses provided them with the knowledge of techniques which may be used to teach mats, as well as with some practical experience of teaching, even if they only practiced with colleagues. It should be stressed that these students perceived the peer interaction during the classes as very useful. On the whole, it is possible to summarize that the students with high levels of self-efficacy appeared rather confident in their knowledge, and also felt prepared to using their new skills of teaching in the real classroom.

On the other hand, students #5 and #6 gave themselves 7 points on the scale from 1 to 10 while assessing their self-efficacy. These students were less confident about their abilities not only after taking the courses but also prior to them. For instance, student 5 stated that they had forgotten most of the material that they had to teach even at the level of the elementary school.

However, they stressed that the courses helped them to remember the basic concepts and gain some practice in teaching. Even though practically all respondents stated that mood affected their self-efficacy, it seemed that the students who gave themselves a 7 perceived themselves as more affected by mood changes than those who gave themselves 8 or 9.

## Mathematical Content Knowledge

It was apparent that many of the students had not been confident in their knowledge of mathematics prior to taking the courses. Most of the students stated that they knew mathematics well, but were not prepared to explain the very basic concepts of this science to young learners. One of the respondents pointed out that they had been very good at mathematics, but that their communication skills had been insufficient.

Simultaneously, certain students (for instance, student #5) noted that they were certain that they had forgotten most of the materials that they had been supposed to teach at school. On the whole, it might be summarized that the students with higher levels of self-efficacy mostly had been confident in their knowledge of mathematical content prior to taking the courses, whereas those with lower levels of self-efficacy had not been confident in their knowledge.

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On the other hand, after taking the courses, the students became significantly more confident when it came to assessing their knowledge of mathematics. The respondents stated that the courses allowed them to remember not only the basic but also more advanced concepts and notions of mathematics, and that explaining them allowed for a better understanding of these concepts, being very beneficial to those who did the explaining. In particular, it was pointed out that peer interaction allowed for developing a better understanding of the notions that the participants explained to one another, as well as for becoming familiar with multiple techniques which can be utilized in order to elaborate these concepts.

Therefore, most students believed that they had known mathematics rather well prior to taking the courses; however, a number of students denied that confidence. Simultaneously, after taking the courses, students became rather confident of their knowledge of mathematical content.

## Beliefs in Students’ Ability to Teach

The survey allowed for uncovering the fact that taking the courses permitted the students to enhance their beliefs in their ability to teach mathematics. On the whole, practically all the members of the sample stated that they had initially perceived themselves as unable of teaching even the most basic concepts of mathematics to school pupils. In a number of cases, this was explained as resulting from the fact that the respondents had not dealt with these basic notions for such a long time that they had forgotten everything.

However, many participants believed that they had had the necessary knowledge of mathematics, but had significantly lacked the ability to explain the materials to the school pupils. This, according to their responses, had been the result of the fact that they had only studied mathematics, but had not studied or practiced teaching mathematics; consequently, they had known the material, but had not been familiar with the ways to explain them.

In particular, one of the respondents emphasized that they had not known how many ways there may exist to explain a particular concept. Another participant pointed out that an explanation that had appeared clear to them was not perceived as such by their peers and professor to whom that participant had attempted to elaborate some materials during the practice. It was also noted by some respondents that they had expected difficulties while interacting with their future learners due to the dearth of communication skills, even though they had good knowledge of mathematics.

On the other hand, taking the courses in mathematics allowed for improving the participant’s perceptions pertaining to their ability to teach. After having explained a number of mathematical notions either to their peers or to their instructors, the participants obtained a certain amount of experience of teaching, and realized what it should “look like.” Consequently, the respondents’ beliefs in their ability to teach improved significantly as a result of taking the courses.

## Summary

Therefore, it might be summed up that most of the future pre-service teachers who took part in the current survey had perceived themselves as not very skillful teachers of mathematics prior to taking the courses. It should be pointed out that even those respondents who were confident in their content knowledge of mathematics had not thought of themselves as of highly competent educators. On the other hand, it is apparent that after taking the courses, the participants of the survey became significantly more confident in their skills and ability to teach school pupils.

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It is also very important to point out the fact that event those respondents who stated that they had forgotten most of the basic notions and mathematics, and, consequently, had been in doubts regarding their ability to properly teach them, were much more confident in their content knowledge of mathematics after taking the courses. Thus, it is possible to summarize that students had had varying perceptions of their skills, competence, and ability to teach prior to taking the courses, but practically all of them achieved significantly higher levels of these after taking the courses.