The development of simulation technologies has made it possible for the implementation of alternative tools to enhance early field experiences of preservice teachers in preparation for clinical practice. One type of simulation is the use of Mixedreality software like TLE TeachLive^{TM}/Mursion^{TM} (Andreasen & Haciomeroglu, 2009). Mixedreality Simulations (MRSs) allow preservice teachers to experience and develop teaching skills, in particular, those related to eliciting students’ thinking (Hatton, Birchfield, & MegowanRomanowicz, 2008).
This report presents results of an ongoing study that examines the effectiveness of using MRSs environments to develop preservice elementary mathematics teachers’ ability to incorporate dialogue between teacher and students in an elementary classroom. Specifically, the simulation was used as a way to enhance their ability to elicit evidence of students’ mathematical knowledge and understanding through the use of productive mathematical talk moves (Chapin, O’Connor, & Anderson, 2009). To this end, the researchers sought to answer the following questions: (i) To what extent do preservice elementary mathematics teachers, trained in the use of Productive Mathematical Talk moves (PMTM) through MRSs, elicit student's thinking through a clinical interview compared to elementary preservice mathematics teachers who were not exposed to the virtual simulation? (ii) To what extent does the exposure to MRSs help elementary preservice mathematics teachers build confidence in eliciting students’ thinking?
Theoretical Framework
Mathematics teachers must determine the most effective way to provide their students with opportunities to reason, discuss, and develop conceptual understanding (National Council of Teachers of Mathematics [NCTM], 2014). This is accomplished when teachers observe their students’ work and listen to their comments while they solve a problem, in order to make effective instructional changes (Stuhlman, Hamre, Downer, & Pianta, 2009). One way to reveal their thinking is through individual and group discussions using productive talk moves (Kazemi, 1998; Chapin et al., 2009). Through this process, the teacher develops “insights that not only are about what students know, but also about the approaches they use, how–and how well–they understand the ideas, and the ways they present their knowledge” (Kersaint, 2015, p.10).
The National Research Council (NRC, 2002), reported that teaching mathematics for understanding that includes dialogue requires experience and practice. The NRC offered guidelines when conducting classroom discussions such as, considering different ideas among students and their prior knowledge, increasing motivation through the implementation of meaningful activities, and developing learning communities. However, future teachers have limited opportunities to develop their skills in how to elicit students’ understanding before they have their own classrooms. Preservice teachers also have few opportunities to develop expertise in eliciting students’ thinking by asking high order questions. Straub, Dieker, Hynes, & Huges (2014) defined high order questioning as “openended questions [starting with how, what, or why] that allow students to use past experiences, prior knowledge, and previously learned content and relate it to newly learned content in order to create a well thoughtout answer” (p. 3). Time constraints often limit elementary mathematics preservice teachers’ opportunities to practice and refine their questioning strategies before they engage in the practice of teaching (Moyer & Milewicz, 2002).
One way to address this concern is to include in their coursework related MRSs. These environments can be used to provide preservice teachers with practice sessions where they learn how to unfold productive talk. Mixedreality has been defined as a “computergenerated display that allows [participants] to have a sense of being present in an environment other than the one they are actually in [with the benefit of being able to] interact with that environment” (Schroeder, 2008, p. 1). The use of MRSs would allow preservice teachers to experience the interaction with virtual students–prior to being with real students–for which mistakes do not have any other consequence other than the learning that could emerge as result of the intervention.
Simulations used in conjunction with cognitively guided instruction [CGI] (Carpenter, Fennema, Franke, Levi, & Empson, 1999) provides a framework for preservice teachers to engage in practicing productive mathematical talk moves (Chapin et al., 2009) in wholegroup discussions, or individual interviews. CGI is a studentcentered approach to teaching mathematics, for which word problems are designed to allow students to use their own knowledge and understanding to solve a problem. In the current study, CGI was used as a foundation for preservice elementary mathematics teachers to engage in productive mathematics talk.
Methods and Data Collection
The study was designed to examine preservice teachers’ productive mathematical talk moves when conducting a clinical interview in which teaching mathematics with understanding is fostered. The participants were preservice teachers taking an elementary mathematics methods course during the spring 2018 semester. There were two sections: one section (i.e., the treatment group) was asked to practice using productive talk moves through the use of virtual simulation software, and the second section (i.e., the comparison group) experienced coursework through lectures in a regular classroom setting. Students in the treatment group engaged with virtual simulation one time for ten minutes. In total, 50 preservice teachers agreed to participated in the study, in which 94 percent were females and six percent were males. The use of virtual simulation to foster productive mathematical talk moves was a technique never used before in the program.
Every preservice teacher was required––as part of the course assignment––to conduct a clinical interview with an elementary student. The purpose of the assignment was threefold: (i) allow preservice teachers to deepen their knowledge on how elementary students solve problemsolving activities, (ii) gain an understanding of how elementary students reason when solving a problem, and (iii) to practice the use of productive mathematical talk moves.
Qualitative data were collected to document the interaction between the preservice teacher and the elementary student, which included interaction logs, notes, transcriptions, and written reflections. The data were analyzed using the productive mathematical talk moves as a guide. The coding was intended to reveal aspects of productive talk moves that the preservice teachers used during their clinical interviews to elicit the elementary student's conceptual understanding, problem solving strategies, and procedural knowledge. The productive talks moves from both sections were compared. Note that both sections were exposed to the same set of instructional materials (i.e., readings, videos, cases, and classroom activities).
Results and Conclusions
For the purpose of this report, seven students’ transcripts from both sections were randomly selected for analysis using productive talk codes adapted from Moyer and Milewicz (2002), Ginsburg (1997), and Chapin, O’Connor, and Anderson (2009). Table 1 presents the codes.
Table 1. TalkMoves Coding Scheme
Code 
Move Type 
Characteristic 
R_{V} 
Revoicing 
Paraphrasing to verify an statement 
R_{E} 
Repeating 
A repetition on the original question 
E 
Elaborating 
Request to add or elaborate a response 
E_{F} 
ElaboratingFollowup 
Following up a previous response 
L 
Leading 
Instructing, no eliciting 
W 
Waiting 
Allowing time in silence 
N 
No question 
No question or move at all 
LOQ 
LoworderQuestions 
No reasoning is encouraged, simple questions, or comments. 
NC 
No Category 
others 
Table 2 presents preliminary results of the transcripts’ analysis for both the treatment and comparison group. The frequency for each code was determined. Interrater reliability was found to be 82 percent agreement then it rose to 91 percent after discussing differences.
Table 2. Preliminary Frequencies of Productive Talk Moves Codes
Code 
Move Type 
Comparison Group (No MRS training) 
Treatment Group 
R_{V} 
Revoicing 
2 
7 
R_{E} 
Repeating 
3 
2 
E 
Elaborating 
12 
12 
E_{F} 
ElaboratingFollowup 
6 
4 
L 
Leading 
2 
12 
W 
Waiting 
0 
2 
N 
No question 
1 
0 
LOQ 
LoworderQuestions 
8 
15 
NC 
No Category 
1 
2 

TOTAL 
34 
56 
Preliminary results showed a large difference in the number of productive talk moves between the comparison and treatment group. However, the number of moves in the group exposed to the Mixreality simulation were not all productive. It appears that there were more leading moves, in which preservice teachers guided their students instead of eliciting their understanding. Apparently, preservice teachers exposed to the MRSs may have developed more confidence in interacting with an elementary student, something that was not observed in the transcripts of the control group (i.e., preservice teachers not exposed to MRSs), but this does not represent an indication of mastering the skills of productive mathematical talk. The data does not show a difference between the control and treatment group in the number of elaborating questions asked, which might be an indication that rehearsing with the MRSs does not make a difference in how preservice teachers elicit their students’ thoughts. In any case, this is a question that needs to be explored in more detail.
Both groups had the same number of elaborating statements. This indicated that regardless of the setting, elementary preservice teachers developed an ability to ask a student to elaborate on their responses during a clinical interview. Revoicing occurred more frequently in the treatment group than in the comparison group. This suggests that those in the treatment group may have developed a greater propensity to listen to students’ responses during the interview. A surprising result was that the treatment group’s frequency in asking higherorder questions was less than the comparison group’s frequency. This finding needs to be further explored to determine the reason behind the virtual simulation group asking fewer higherorder questions. This may be due to the situation in which a clinical interview was being conducted rather than a teaching episode.
Since preservice teachers were only exposed to the simulation one time and although feedback was provided in class, more time and practice would be needed in the use of productive mathematical talk moves. Previous research has indicated that participants in virtual simulation training would need to be exposed to MRSs between three to five times in sessions ranging from 5 to 10 minutes to acquire and master a skill (Straub et al., 2014). Following Straub et al., the researchers are in the process of collecting a new set of data for which the treatment group is exposed to at least three to four MRSs sessions in a semester. In addition, the coding process for the rest of the preservice teacher’s transcripts is a work in progress, for which another report will be reported including all the collected data.
The current study contributes to the research in the preparation of preservice teachers to develop discussion skills. The findings provide evidence that the use of MRSs as part elementary mathematics teacher preparation programs can offer opportunities for them to have meaningful experiences and interactions prior to actually engaging in realworld field experiences. This is not to say that virtual reality simulations should replace real experiences, rather they offer preservice elementary teachers a chance to hone teaching skills, in this case, productive talk moves, in a simulated and safe environment.
References
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Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K6. Sausalito, CA: Math Solutions.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Postmourth, NH: Heinemann.
Kersaint, G. (2015). Orchestrating mathematical discourse to enhance student learning. North Billerica, MA: Curriculum Associates, LLC.
Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4(7), 410.
Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5(4), 293315.
National Research Council. (2002). Learning and understanding: Improving advanced study of mathematics and science in U.S. high schools. Washington, D.C.: National Academies Press.
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Straub, C., Dieker, L., Hynes, M., & Huges, C. (2014). Using virtual rehearsal in TLE TeachLivE™ mixed reality classroom simulator to determine the effects on the performance of mathematics teachers. 2014 TeachLivE™ National Research Project: Year 1 Findings. Orlando, FL: University of Central Florida.
Stuhlman, M. W., Hamre, B. K., Downer, J. T., & Pianta, R. C. (2009). How classroom observations can support systematic improvement in teacher effectiveness (pp. 34). Charlottesville, VA: University of Virginia Curry School of Education.