Data collection and analysis

We implemented a mixed method approach: both qualitative and quantitative data collection and analysis are presented. This mixed methodology helped us understand PSTs’ experiences and math teaching anxiety in the online environment. For the first, experience study, which employs a qualitative approach, we used a survey called ‘Experience Survey’ at the end of the 8-week experience. The Experience Survey had open-ended questions and one multiple options question. We analyzed the responses using content analysis. For the second, anxiety study, which utilizes a quantitative approach, we adapted a survey called ‘Anxiety Survey’ from the literature (Hadley & Dorward, 2011) to understand their teaching anxiety and PSTs filled out the Anxiety Survey before and after 8-week experience. We analyzed the responses using paired sample t-tests and independent sample t-tests.

To collect data for the experience study that examined PSTs’ experiences related to the OLS, we designed and administrated surveys for all stakeholders: students, parents, PSTs, and university supervisors at the end of the OLS in Fall 2020. There were a total of 43 PSTs including 10 fourth-year, 13 third-year, and 20 first-year PSTs who participated in the OLS. In this study, we report the survey results of 33 PSTs who filled the survey (7 fourth-year, 12 third-year, and 14 first-year PSTs) after the OLS experience. We asked the following five survey questions (one multiple-option and four open-ended) to understand PSTs’ views and experiences about the OLS:

PSTs’ answers to Question a)

In terms of data analysis for the experience study, we analyzed the first two research questions (“How do PSTs view their experiences of internship in the OLS in terms of professional development?” and “How do PSTs’ views of and experiences in the OLS change based on the cohort they belong to [i.e., first-, third-, and fourth-year PSTs]?”) using content analysis (Cohen et al., 2007). Specifically, we identified themes related to PSTs’ responses to the open-ended questions in the Experience Survey (b through d) and investigated patterns of the themes related to their year in the program and their comments. After reviewing PSTs’ responses to the open-ended questions, each of us determined individually what the categories were, including students’ thinking, specific pedagogical content knowledge (e.g., teaching fractions), technology use, teacher’s role, communication with students, lesson planning, and so on. Then, each of us compared these categories using PSTs’ survey open-ended responses. If there were differences in categories, then we discussed them until we achieved consensus on final categories which best reflected PSTs’ responses.

In this section, we report the results of the survey focusing on the five questions of the Experience Survey and discuss the differences among fourth-year, third-year and first-year PSTs regarding their experiences at the OLS.

Professional Development

For Question a) “In what ways have you improved professionally during the OLS experience?”, PSTs reported that they improved their online teaching methods (27 out of 33 PSTs), technology use (26 out of 33 PSTs) and communication with students (24 out of 33 PSTs). These were the three categories in which PSTs thought they had improved themselves most through this experience (see Fig. 2). The less frequently identified categories of professional development were Planning (20 PSTs), Working Cooperatively (20 PSTs), Implementing Supervisor’s Feedback (20 PSTs), and Mathematical Content Knowledge (15 PSTs).

OLS learning experiences

For Question b) “Please provide at least one detailed example that you think helped you improve during the OLS experience”, generally fourth-year PSTs gave examples related to how they improved in anticipating and managing students’ different approaches to specific problems in class as well as using that information in planning lessons to build on students’ thinking (4 out of 7 PSTs). As an example, one PST wrote:

For example, I learned a lot when I planned a lesson related to how to calculate a fractional part of a quantity. It was difficult for me to be prepared for children’s possible incorrect solutions. But when I created a plan where I thought through this situation, I realized that my teaching went well. I used problems where they calculated unit fractional parts of quantities and it went as I planned. So, I think I improved in teaching fractions.

Third-year PSTs mentioned more general aspects of their learning. For instance, they experienced how to communicate with students or manage a classroom (5 out of 12 PSTs), both of which were typically accessible to them in theory only before their OLS experience. Third-year PSTs also mentioned how their lesson planning practice changed with the role of technology use in the OLS (6 out of 12 PSTs). As an example, one PST wrote:

I think I started integrating more technology when I prepared my lesson plans. The most advantageous part of this online experience is that I developed myself in use of technological tools. I can say that I also started to pay attention more to what the lesson plan should contain, the suitability of learning goals and the content of the plan and including more of the possible students thinking in the plan.

First-year PSTs also gave general comments, but the comments focused on the change of perception related to teaching or the teaching profession. They mostly mentioned three specific categories: how to communicate with students, how to manage students’ different thinking during teaching (7 out of 14 PSTs), and how to create lesson plans (2 out of 14 PSTs). As an example, one PST wrote:

I think I developed myself in many areas during OLS. I think I developed myself most in effective communication with students as a teacher. OLS helped me to think, question and reflect about how to give good impressions to my students about mathematics, how to teach the subject in best ways.

Supervisor’s feedback

For Question c) “What approaches of university supervisors helped (or did not help) you? It can be positive or negative contributions, indicate and please give an example (no need to give any supervisors’ name)”. Almost all fourth-year PSTs provided positive comments. Positive ones included supervisors giving motivational feedback and approaches indicating something was problematic (5 out of 7 PSTs). They felt that supervisors also encouraged them to make things better by acknowledging they were just learning how to teach, interact and ask questions as teachers. As an example, one PST wrote:

They gave us feedback every week when we were lesson planning. They gave ideas for making the plans better. They also gave feedback at the end of the lesson implementations for how to develop our teaching or they made motivational comments such as, ‘your voice tone was very good, or interact with each student so they feel present or part of the class.’ I felt supported.

On the other hand, there was a sharp distinction in terms of how third-year PSTs viewed supervisors’ contributions. They briefly mentioned that they appreciated comments but only the ones that were positive and encouraging. They also mentioned that in general they were discouraged with the ones that focused on their weaknesses. As an example, one PST wrote:

While teaching I spent lots of time with one student since I did not know how to handle the misconception. My supervisor who observed me during the teaching did not help me out via moderator chat box in terms of how to guide the student. Later in the general meeting she mentioned that I spent so much time on one student and gave negative comments.

This PST had difficulty in how to approach an individual student’s misconception and continued with whole class discussion. The supervisor was probably unaware that the PST was a third-year who just started teaching and needed more support. The PST found the comments as evaluative and negative feedback. We found that this type of comment was common among the third- year PSTs’ responses (Eight out of 12 PSTs made such comments).

On the other hand, all first-year PSTs were satisfied with the supervisors’ support and stated that supervisors included them to the discussions in the short reflection meetings and in the general meetings. As an example, one PST wrote:

There were some challenging situations in our class observations. Supervisors gave us examples from their own experiences, and it was great to have such contributions from the supervisors.

Differences between OLS and regular internship

For Question d) “How was your OLS experience different than your traditional/normal internship experience at public or private schools?”, all the fourth-year and third-year PSTs (19 PSTs) stated that OLS provided them opportunities to be more active with such experiences as lesson plan preparations and being responsible as a classroom teacher, compared to their experiences at internship schools. For example, one PST wrote:

The biggest difference is that in the regular internship (face-to-face) you are an assistant teacher or candidate teacher, and you are bound to the mentor teacher. However, you are a teacher in the OLS. And we, as pre-service teachers, have the right to make the decisions. We discuss everything from planning to the teaching and we design them. While we teach only once during whole semester in the face-to-face internship, I taught every week in OLS, and I became the teacher.

Similarly, two PSTs wrote that OLS was helpful for receiving feedback from their supervisors during the class and having an opportunity to discuss their observations after the class in a more regular setting, in comparison to their traditional/regular internship experience. For example, one PST wrote:

It was very different in many aspects. For example, the most important difference was that I was able to get feedback (via moderator chat boxes) while I was teaching and on the spot. By this way, I think the lessons were more effective. This was the most positive and enhancing aspect of the OLS setting.

On the other hand, this question did not apply to most first- year PSTs. They were not in a position to make a comparison between OLS and internship schools. First- year PSTs were having one-to-one tutoring experience as part of another project, but they did not have the experience of a regular internship because they were in the first year of their program.

Lastly, 5 PSTs (of 33 PSTs) from all grade levels mentioned that use of technology in the OLS was very advantageous compared to traditional school settings. As one PST wrote:

It was different because of the technology effect. Because of the physical situations in schools, the opportunities are limited. But in the OLS, technology use was very easy. I think we contacted and reached students more easily and we used technology more actively.

Realization of professional growth

For Question e) “Please explain whether you would suggest your OLS experience to other preservice teachers and justify your decision.” All PSTs (except one who would not suggest this experience in terms of heavy workload for lesson planning) reported they would suggest OLS experience to a peer due to the opportunity of having teaching experience. All of the 33 PSTs wrote that OLS provided them with online teaching experience and that it provides opportunities for being like a real classroom teacher. Nine of them commented that online teaching is a different skill than teaching in a physical classroom environment and they should get prepared for this online teaching for the future even after the pandemic ends. Seventeen of the 33 PSTs commented that the OLS makes them feel like a classroom teacher due to a variety of decisions they need to take before, during, and after teaching. For example, one PST wrote:‘…to have the entitlement of decision making lets us develop ourselves better, it makes us to think more and be more active. I think because of these PSTs should definitely live this experience.’

Moreover, fourth- and third-year PSTs’ justifications were mostly based on the experiences which were categorized as ‘understanding student thinking, developing ability to prepare lesson plans, and receiving feedback from supervisors.’ For example, one PST wrote, ‘‘I definitely recommend this experience for others, since it was very effective to experience children’s thinking and prepare lesson plans.’’ Another responded that the OLS was helpful at least for having an opportunity to reflect on her own teaching performance after teaching:

                 Even if we assume that no one is giving feedback after we teach in OLS, we, as PSTs, had the opportunity to reflect on our own teaching (the videos were recorded) and by this way I would learn something. Because it was such an environment…Therefore, I recommend this experience.

On the other hand, first-year PSTs mostly justified their decision for recommending OLS experience by providing general statements such as learning how to communicate with students and how to use technology in a classroom. For example, one first-year PST wrote:

                 I recommend this experience. Even though I am a first-year student, I learned a lot of information, got to know a lot of nice students, and had the opportunity to meet with nice teachers. While many of my friends in other universities learn theoretical knowledge related to teaching, I moved to the ‘communication’ stage with the students. This was a very important opportunity for all of us.

Conclusion for the experience study

In terms of professional development PSTs reported they benefited from learning online teaching methods, improving in technology use, and communicating with students. Third-year PSTs reported professional growth but also seemed to be ‘challenged’ with the experience. There were differences between the third- and fourth-year PSTs that we had not realized in-depth during the OLS experience. Third-year PSTs’ comments revealed that they needed a lot more support and motivation to build their confidence in planning lessons and implementing them. They could be easily discouraged. Therefore, the beginning of third year is an important time for gaining these skills, so supervisors should be more careful and thoughtful while giving feedback.

The sample for the second study during Fall 2020 consists of 43 PSTs (20 first-year, 13 third-year, and 10 fourth-year) for the pre-OLS survey data prior to the eight-weeks of the OLS, and 27 PSTs (7 first-year, 11 third-year, and 9 fourth-year) who completed both pre-OLS survey and post-OLS survey when the OLS had ended. Remember that third- and fourth-year PSTs’ role at the OLS was to plan and teach middle school mathematics lessons under the guidance of supervisors for eight weeks, while first year PSTs’ role was only to conduct observations and discuss their observations in group meetings.

To collect data for the anxiety study to examine math teaching anxiety levels of PSTs, the relationships between math teaching anxiety and several variables, and changes in PSTs’ mathematics teaching anxiety levels during eight-weeks of the OLS, we administered a math teaching anxiety survey and demographic information questionnaire before and after the OLS. First, Hadley and Dorward (2011) developed the Anxiety about Teaching Mathematics scale by adapting from Mathematics Anxiety Rating Scale-Revised (MARS-R; Hopko, 2003) a scale based on teaching situations. The scale has 12 items with five response categories for each item ranging from “not at all,” “a little,” “a moderate amount”, “a lot” to “very much.” The scale has some validity evidence based on expert reviews and the coefficient alpha was 0.90. In this study, we adapted this scale to online teaching situations and added two more items. Thus, the new scale, the Math Teaching Anxiety (MTA) scale, has 14 items with the same five response categories and the coefficient alpha in the present study is 0.93. While a minimum possible score of 14 indicates no math teaching anxiety, a maximum possible score of 70 indicates high math teaching anxiety. PSTs completed the MTA scale during approximately 20 minutes of a class period. The MTA scale items are presented in Table 1. We also administered a demographic information questionnaire to obtain information about various characteristics, such as the number of methods courses completed.

The MTA scale items

I become anxious when looking through the pages in MEB

or similar mathematics books.

I become anxious when teaching students how to use and

interpret tables, graphs, and charts.

I become anxious when preparing students for a math

exam that will take place in their schools.

I become anxious when working out math equations

online in front of a class of students.

I become anxious when preparing a presentation about

a lesson plan for Online Lab School.

I become anxious when preparing to teach students a new

math concept that will be challenging to them in the

Online Lab School.

I become anxious when a parent may be present during my

online teaching.

I become anxious when talking to a student who is eager to

use a different way to solve a math problem than the way

taught in the Online Lab School.

I become anxious when writing a lesson plan for online

teaching of a new math concept.

I become anxious when waiting whether my students will

be able to respond to my questions.

I become anxious when my supervisor or mentor teacher

evaluates my performance during a math lesson I am teaching.

I become anxious when going online and thinking about

teaching a math lesson.

I become anxious when investigating online tools

(or applications) to support my teaching of mathematics.

I become anxious when I assess my students’ learning during

online teaching.

Note: SD indicates standard deviation.

In terms of data analysis for the anxiety study, we responded to the third and fourth research questions (“What are the math teaching anxiety levels of PSTs?” and “Are there significant relationships among math teaching anxiety and their educational backgrounds such as the number of methods courses completed so far?”) by administering the MTA scale to 43 PSTs before the eight-weeks of the OLS during Fall 2020 as pre-OLS survey data. For the third research question asking PSTs’ math teaching anxiety levels, we examined descriptive statistics. For the fourth research question asking the relationships among their educational backgrounds, such as grade levels, we compared correlations among the variables. To answer the fifth and last research question (“Is there a significant relationship regarding PSTs’ math teaching anxiety levels before and after eight-weeks of the OLS?”), we administered the same MTA scale to 27 PSTs after the OLS and compared those 27 PSTs’ math teaching anxiety before and after the eight-weeks of the OLS by applying paired sample t-tests. Moreover, we compared PSTs’ math teaching anxiety across grade levels using independent sample t-tests.

Math teaching anxiety based on pre-OLS survey data.

For the third research question asking PSTs’ math teaching anxiety levels, the mean math teaching anxiety score was 30.91 with standard deviation of 10.25. While the minimum score was 14, the maximum score was 54. Thus, it can be said that on average, PSTs had math teaching anxiety from “a little” to “a moderate amount” before the OLS. In Hadley and Dorward’s (2011) study with 692 in-service elementary teachers, the mean score for the 12-item survey was 21.55 with standard deviation of 7.41, indicating that the PSTs in the present study had higher math teaching anxiety than those teachers. The MTA scale items are presented in Table 1 with item mean and standard deviation.

Based on Table 1, most of the MTA scale items (11 of the 14 items) had item means over 2.00, indicating higher anxiety responses than the teachers in Hadley and Dorward’s (2011) study, which had only four of 12 items with item means over 2.00. The highest anxiety response was 2.79 for the item “I become anxious when my supervisor or mentor teacher evaluates my performance during a math lesson I am teaching.” This indicates that PSTs experienced highest math teaching anxiety when their university supervisors or mentor teachers observed and evaluated their teaching.

Relationships among several variables based on pre- OLS survey data.

To answer the fourth research question, Table 2 presents the relationships among several variables, including the number of whole class teaching hours; the number of online class teaching hours; the number of mathematics courses completed; the number of methods courses completed; the number of general education courses completed; and GPA. Based on Table 2, math teaching anxiety was only significantly correlated with the number of methods courses completed (r = − .34, p < .05). This indicates that PSTs who had completed more methods courses during their teacher preparation program had significantly less math teaching anxiety. However, there was no significant relationship between math teaching anxiety and the number of mathematics courses (e.g., analytical geometry), or the number of general education courses (e.g., classroom management) completed so far. Similarly, there was no significant relationship between PSTs’ internship experience based on the number of whole class or online teaching hours and their math teaching anxiety. This indicates that PSTs’ completing more mathematics courses or general education courses and their having more teaching experience were not significantly related to their math teaching anxiety.

Correlations among several variables based on pre-OLS survey data (N = 43)

Note: MTA = Math Teaching Anxiety; # = number; *p < .05, **p < .01

Math teaching anxiety during eight-weeks of the OLS

For the fifth and last research question asking whether there was a significant relationship regarding PSTs’ math teaching anxiety during eight-weeks of the OLS, we applied paired sample t-tests for the 27 PSTs who completed both pre-OLS and post-OLS surveys. We found that first-, third-, and fourth-year PSTs’ math teaching anxiety did not significantly change during the OLS. This indicates that the OLS did not contribute to a decrease in math teaching anxiety (see Table 3 for means and standard deviations across grade levels).

Paired sample t-tests across grade levels based on pre-OLS survey and post-OLS survey

First year PSTs

Mean

SD

N

23.86

3.58

7

25.29 (p = .62)

5.59

7

Third year PSTs

Mean

SD

N

35.18

8.81

11

37.18 (p = .38)

9.61

11

Fourth year PSTs

Mean

SD

N

28.11

9.98

9

33.33 (p = .09)

12.94

9

All PSTs

Mean

SD

N

29.89

9.28

27

32.82 (p = .053)

10.85

27

Note: PST = preservice teachers; SD = standard deviation; MTA = Math Teaching Anxiety; *p < .05

Finally, we compared PSTs’ math teaching anxiety across grade levels for both pre-OLS and post-OLS survey data using independent sample t-tests (see Table 3 for mean scores). We found that third-year PSTs had significantly higher math teaching anxiety than first-year PSTs based on both pre-OLS (p = .01) and on post-OLS surveys (p = .01). Moreover, no significant difference existed between first- and fourth-year PSTs’ math teaching anxiety based on both pre-OLS (p = .30) and post-OLS (p = .15) results. Similarly, there was no significant difference between third- and fourth-year PSTs’ math teaching anxiety based on both pre-OLS (p = .11) and post-OLS (p = .46) data.