Keywords

9.1 Introduction

Collaborative problem-solving (CPS) has become a critical competency for teenagers’ future lives (OECD, 2017). Currently, K-12 mathematics education attaches more importance to cultivating students’ CPS skills through group teaching. However, some teachers do not know how to guide the collaborative process and facilitate student interaction (Le et al., 2018), especially in developing countries that rarely adopt group teaching methods. Inefficient collaboration places greater demands on mathematics teachers’ professional group teaching abilities. Many previous studies have shown that teachers’ effective guidance can promote the development of group activities (Van Leeuwen & Janssen, 2019). There is a close connection between teachers’ noticing and classroom teaching behaviors (Blömeke et al., 2022). To respond to students’ performance appropriately, teachers should attend to their behavior first and then interpret the meaning based on prior experiences (Jacobs et al., 2010).

Teachers’ noticing, a critical component of teaching expertise, is the process of how teachers manage the vast amounts of sensory information they face in the classroom (Sherin et al., 2011). The prior educational studies show that teachers’ noticing involves two main facets: attending to important classroom events and making sense of these events in an instructional setting (Santagata et al., 2021). In teacher education, teachers’ noticing ability plays an important mediating role between teachers’ resources (such as their knowledge and beliefs) and their teaching performance (Blömeke et al., 2015). Early research on teachers’ noticing suggests that experienced teachers have stronger perceptions of classroom activities and can selectively allocate attentional resources to important events (König et al., 2022). However, to our knowledge, the informative results of past studies mainly focus on the traditional teaching classroom; teachers’ noticing of students’ group collaboration in China remains unexplored. Studying what they notice during students’ collaborative process helps uncover the cognitive processes behind teachers’ instructional strategies and behaviors. Thus, this study aims to investigate what teachers tend to notice during students’ CPS processes and further  explore the differences between what experienced and preservice teachers notice.

One of the most common methods of studying teachers’ noticing is the video-based interview, which asks participants to describe and explain what they noticed after viewing their own or other teachers’ instruction videos. It is well known that one’s fixation is closely related to their cognitive process (Just & Carpenter, 1980). Using eye-tracking technology, we can obtain precise information on moment-by-moment teachers’ visual fixation (i.e., where and when they fixed their eyes) and further explore their cognitive processes without interrupting their activities. Therefore, this study adopts both eye-tracking technology and video-based interviews to investigate the noticing differences between experienced and preservice teachers when viewing CPS processes. The research questions are as follows: What do teachers notice in collaborative problem-solving processes? What are the differences in teachers’ noticing between experienced and preservice teachers?

Next, we review existing eye-tracking studies on collaborative problem-solving and summarize some key conclusions regarding the characteristics of teachers’ noticing.

9.1.1 Factors Influencing the Quality of Collaboration

The collaborative problem-solving process involves two important elements requiring team members’ attention: collaboration and problem-solving. The former emphasizes social interactions between group members; the latter highlights the cognitive interactions in the task itself, including extracting information, exploring strategies, and executing plans. During the collaborative process, group members must establish mutual understanding, maintain team organization, and reach a consensus by communicating with others. We can see that people’s gaze plays a central role in the CPS process. Eye-tracking technology provides researchers with an unprecedented opportunity to obtain participants’ eye-movement information in their natural environment, including where they focus and for how long.

Many researchers have used eye-tracking technology to study the key factors in collaboration quality. In addition to group relationships and prior knowledge of other group members (Sangin et al., 2008; Villamor & Rodrigo, 2017), the visual synchronization of participants is also critical to collaborate effectively (Salminen-Saari et al., 2021). Cherubini et al. (2008) found that students tend to point to an object when discussing it, to draw their partners’ attention at the same time. If group members’ gaze points draw closer, misunderstandings will be decreased, and collaborative activity will be more efficient. Thus, team members need to achieve joint attention through collaboration, and there is a close relationship between the fixation overlap rate and the quality of interactions (Jermann & Nüssli, 2012; Jermann et al., 2011). Some studies have even found that higher levels of visual synchronization are positively associated with students’ collaboration quality (Cakir & Uzunosmanoğlu, 2014; Schneider & Pea, 2013; Uzunosmanoğlu & Çakir, 2014).

Accordingly, researchers have tried to promote group members’ joint attention and mutual understanding by altering their noticing, such as by sharing text selections, providing partners’ real-time gaze behaviors, and designing an online collaborative environment called the Virtual Math Team (Jermann & Nüssli, 2012; Schneider & Pea, 2013; Uzunosmanoğlu & Çakir, 2014). In addition to offering visual information on members, teachers’ guidance could also facilitate members’ joint attention externally and improve group collaboration quality. However, the studies applying eye trackers to the CPS process have mainly focused on problem solvers and rarely focused on teachers. Researchers have also focused on teachers’ roles in supporting group problem-solving. For instance, Haataja et al. (2019) found that teachers’ scaffolding intentions significantly affect their gaze behaviors; specifically, gazing at students’ faces tends to be normal, regardless of what kind of scaffolding intentions. This impressive finding inspired us to further study teachers’ cognitive focus with eye-tracking technology.

Teachers play an important role in group collaboration, as their guidance can promote the development of group activities. Van Leeuwen and Janssen (2019) synthesized 66 quantitative and qualitative studies on collaborative learning and found that teachers paid careful attention to giving feedback on students’ problem-solving strategies, helping students organize tasks, and coordinating group participation, which positively influenced students’ collaboration. To provide practical guidance, teachers should pay attention to students’ performance. Wells (2017) explored how focusing on students’ conversations and gestures affects teachers’ interventions during the group problem-solving process, and found that dialogues emerged as students progressed on a problem and students’ gestures became more pronounced with increased confidence. In addition, students participating in discussions often unconsciously imitated other group members’ body postures. Teachers can better understand students’ performance and make more meaningful decisions by focusing on these behaviors. Therefore, it is necessary to study teachers’ noticing in the collaborative problem-solving process to improve their professional noticing skills.

9.1.2 Characteristics of Teachers’ Noticing in Classroom Settings

Teachers’ noticing plays a crucial role in classroom teaching, and a better understanding of teachers’ noticing can thus help to improve mathematics teaching and learning. In the classroom, teachers often need to distribute many cognitive resources to process different kinds of behavioral information, adjust teaching schedules and achieve effective classroom management (Berliner, 1986; Hogan et al., 2003). Two definitions of teachers’ noticing have been most frequently used in previous studies. In the first, Van Es and Sherin’s (2002) learning to notice framework, noticing has three components, including “(a) identifying what is important or noteworthy about a classroom situation; (b) making connections between the specifics of classroom interactions and the broader teaching principles; and (c) using what one knows about the context to reason about classroom interactions.” The second definition concerns the professional noticing of children’s mathematical thinking, which involves “attending to children’s strategies, interpreting children’s understandings, and deciding how to respond on the basis of children’s understandings” (Jacobs et al., 2010). Combining these two definitions, this study defines teachers’ noticing as identifying classroom activities and then understanding or interpreting these activities.

Many recent studies have suggested that noticing patterns are highly influenced by teachers’ prior teaching experience. There are considerable differences between what experienced and novice teachers notice (Erickson, 2011). For example, experienced teachers distribute their attention more evenly across the classroom than preservice teachers (Van den Bogert et al., 2013). Experienced teachers’ attention to critical objects occurs earlier and lasts longer (Miller, 2011). Thus, experienced teachers make more comprehensive observations and are skilled at distinguishing between important and unimportant information in complex situations. In addition, teachers with different levels of teaching experience also differ in how they interpret what they notice. In contrast to the simple descriptions provided by novice teachers, experienced teachers can better monitor, understand, and interpret events in more detail and make inferences or provide suggestions about what they see (Carter et al., 1988; Sabers et al., 1991).

Experienced and preservice teachers also differ in their reactions to students with problematic behaviors, with more experienced teachers using more modes to handle misbehaviors. Sabers et al. (1991) explored the noticing differences between seven experienced, four novice, and five preservice teachers while observing teaching videos presented on three computers simultaneously. The participants were asked to pay attention to specific facets of classroom management. The results showed that the experienced teachers paid attention to the inappropriate behaviors of some students, objectively inferred the possible reasons for those behaviors, and put forward specific ways to correct them. In contrast, the novice and preservice teachers only expressed their dissatisfaction and criticized the students’ problematic behavior. Similarly, other studies have reported that experienced teachers can address such situations properly without dedicating too much attention to them in some cases (Ding et al., 2008; Wang et al., 2013). Learning to distinguish between important and unimportant information is thus a critical professional teaching skill in complex teaching situations (Berliner, 2001).

In summary, the rapid development of science and technology has given researchers more reliable and accurate tools to deeply analyze the collaboration process. It is essential to investigate what teachers tend to notice during CPS processes and determine the differences between what experienced and preservice teachers notice to help preservice teachers better understand classroom information and facilitate group collaboration.

9.2 Method

9.2.1 Data Collection

9.2.1.1 Participants

We hypothesize that teachers’ ability to notice is closely related to their teaching experience and that experienced teachers could recognize important information under complex circumstances. We recruited 18 experienced teachers (77.78% female) with more than 15 years of secondary school mathematics teaching experience and 28 preservice teachers (67.86% female) who specialized in mathematics education but had no mathematics classroom teaching experience in China. All teachers participated in this study voluntarily. Finally, 13 experienced and 15 preservice teachers were selected for eye-tracking data analysis, who met the requirements that the eye-movement data had an accuracy or precision level of less than 0.5° and a sampling rate of more than 70%.

9.2.1.2 Materials

The research materials used include a video of the students’ group collaboration and an outline of the structured interviews. This video was selected from the data from the project, “The Social Essentials of Learning: An experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China.” The short video (10 min and 30 s) features four students collaborating on a mathematical task titled “The Tower Problem,” which explicitly uses graphical elements (see Appendix (Task 3) for detailed information). As the students had just finished primary school and most had difficulties drawing solid figures individually, group collaboration was an appropriate way to solve the problem by providing the students with six blocks to imagine potential answers. The efficacy of such a task in stimulating student collaborative work has been tested by Clarke and Chan (2015).

It is essential to illustrate why we chose this group in this study. The group was heterogeneous, including two boys and two girls, and showed great individual differences between group members, including their mathematics performance and participation in group activities. While the students did not find the right answer, they had clear ways of thinking about the solution. In addition, the group collaboration video recording was of high quality, with clear imagery and audio and no one obstructing the camera. Therefore, this video met the research requirements.

To understand the participants’ feelings after watching the video, they were asked four questions: (1) What do you think of the group collaboration in the video? (2) Did you see any inattentive or distracted students during the discussion? If so, what is your opinion about this? (3) Were you impressed by someone or something? Why? 4) Do you have any other thoughts or personal feelings about this group?

9.2.1.3 Apparatus and Procedure

A Tobii Pro X3-120 eye tracker with a sample rate of 120 Hz was used to record participants’ eye-movement information as they watched the video. The eye tracker is compact and light (324 mm long and 118 g) and uses pupil-centered corneal reflection, a technique combining dark and bright pupil tracking. It was installed at the bottom of the 15.6-inch screen on the laptop used to play the video. Tobii Pro Lab was used as supporting data analysis software. In addition, a digital voice recorder was used to record the interviews. This study chose the “Tobii I-VT (Fixation)” option and kept the default 30°/s threshold. Data points with angular velocity below this threshold value are classified as part of a fixation; data points above are classified as part of a saccade.

Data were collected from each participant for approximately 30 min. Before starting, the participants were informed of the experimental process. First, each participant completed the group task individually to become familiar with it. Then, the participants were asked to sit on a chair positioned approximately 60 cm from the recording laptop, and the eye tracker was calibrated to their eyes. Once calibration was complete, the participants watched the video and then were interviewed. The participants were allowed to turn their heads freely while watching and were encouraged to share their thoughts during the interviews. In addition, to ensure the participants were not misled or interrupted, the interviewer did not express any views or opinions. Instead, the interviewer asked them repeatedly if they had any thoughts on the question posed.

9.2.2 Data Analysis

9.2.2.1 Analysis of Eye-Tracking Data

The CPS process was divided into two stages—a task-analyzing process (where all members identified the problem) and a problem-solving process (where all members focused on solving it). Due to considerable differences in the students’ performance during collaboration, we selected three different group types (four students, three students, and two students) to identify the subtle differences between experienced and preservice teachers as they faced students of varied performance. Nonattentive or uncollaborative students, such as those joking with others or playing with personal belongings, were recognized as not involved in the group activity. Hence, there were four video segments in total, including one segment analyzing the task and three segments solving the problem, as shown in Table 9.1. For our analysis, each student in the segment was coded according to their participation based on the following three roles: speaking student (S), listening student (L), and misbehaving student (M). While each student could play different roles in different segments, the sequence number remained unchanged.

Table 9.1 Four segments
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Before analyzing the eye-movement data from the different segments, four areas of interest of the same oval size were defined; each area represented a different student in the group, as shown in Fig. 9.1. We applied an index of the total fixation duration of the four areas of interest, namely the sum of all durations of the fixation points. The standard deviation of the fixation duration was used to evaluate uniformity in the distribution of visual attention; a higher value indicated less uniformity. Statistical significance was tested by using an independent sample t-test of the uniform distribution of attention between two types of teachers and applying a variance analysis of the fixation durations of different areas of interest. Due to our small sample size, we also applied the effect size. Cohen’s d was selected to measure actual differences between the two types of teachers (Coe, 2002).

Fig. 9.1
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Division of four interest areas

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9.2.2.2 Analysis of Interview Data

To study teachers’ noticing of students’ mathematical thinking, Van Es and Sherin (2008) asked teachers to watch three video clips of mathematics classroom teaching and comment on what they noticed before and after receiving video training. They used the following codes to analyze the interview data: actor, topic, stance, level of specificity, and video focus. Two of these dimensions, topic and stance, were used to analyze our data and examine what the teachers attended to and how they analyzed this information. According to previous research, teachers focus on the fundamental elements of the mathematics teaching process, such as pedagogy, mathematical content, management, classroom environment, etc. (Frederiksen et al., 1998; Star & Strickland, 2008; Van Es & Sherin, 2008).

However, group teaching involves a more complex teaching process, with some unique features relative to traditional mathematics teaching. Teachers need to do more to prepare for group teaching activities, such as setting group teaching goals, establishing appropriate groups based on students’ characteristics, designing tasks for group collaboration, etc. During group collaboration, teachers must support the problem-solving process and serve as facilitators by, for example, dealing with conflicts between group members and helping students who are not participating to focus on the group activity. In addition, there are more opportunities for students to express their opinions; in addition to cognitive engagement, students can be involved in social interactions with other members. Hence, we divided the topic of teachers’ noticing into three categories: preparation for the group activity, support for collaborative learning, and group members’ performance. Each category covers specific facets, as shown in Table 9.2.

Table 9.2 Three categories of teachers’ noticing
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Furthermore, regarding teachers’ comments on the presented video, some research has focused on the level of description, interpretation, evaluation, etc. (Sabers et al., 1991; Seidel & Stürmer, 2014; Van Es & Sherin, 2008). We added two levels based on our interview results: prediction and suggestion. All levels of teachers’ noticing examined are detailed in Table 9.3.

Table 9.3 Five levels of topic analysis
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Therefore, we analyzed the interview data from two dimensions: what teachers noticed and how they commented on what they noticed. The analysis proceeded by recording the stance each teacher adopted when referring to the given topic and then measuring the corresponding percentage. Teachers using multiple stances to analyze the same topic were assigned the highest values. The transcripts were coded blindly, and any differences were discussed until the two coders reached a consensus.

9.3 Results

We recruited 18 experienced teachers and 28 preservice teachers to watch a video of four students collaborating on a task, and then interviewed them individually. Eye-movement data with an accuracy or precision level of more than 0.5° and a sampling rate of less than 70% were eliminated to ensure data quality. Then 13 experienced teachers (ETs) and 15 preservice teachers (PTs) were selected for analysis. The main results are shown below.

9.3.1 Differences in the Distribution of Visual Attention

Based on the mean standard deviation of fixation duration, shown in Table 9.4, the degree of uniformity in the distribution of visual attention of experienced teachers was smaller than that of the preservice teachers in all four segments.

Table 9.4 Degree of uniformity in the distribution of visual attention
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The t-test statistical results revealed a significant marginal difference in attention distribution between experienced and preservice teachers (p = 0.096) for segment 1 (four students’ task analysis stage). The d value indicated a relatively large difference (d = −0.685), meaning experienced teachers’ attention was more evenly distributed than preservice teachers’ attention. No statistically significant difference was found between the two groups in segments 2 and 3 (four and three students participating in problem-solving, respectively). However, when only two students participated, experienced teachers distributed their attention significantly more evenly than preservice teachers (p = 0.002, d = −1.269).

Variance analysis comparing these two groups’ fixation duration for the four students in each segment showed a significant main effect between the subjects (F (1, 26) = 3.783, p = 0.063), and longer fixation durations for preservice than experienced teachers. The fixation durations of ETs and PTs for the four areas of interest in each segment are shown in Fig. 9.2. The differences between them are discussed below.

Fig. 9.2
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Fixation durations of ETs and PTs for four areas of interest

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In segment 1, speakers 1, 2, and 4 gladly expressed their personal views and participated actively in the group discussion, while listener 3 mainly read the questions by herself or listened to others’ ideas. We find a marginally significant difference between experienced and preservice teachers in noticing speaker 1 (p = 0.078, d = −0.721), with preservice teachers paying more attention than experienced teachers, as shown in Fig. 9.2. While there was no significant difference regarding the others, the difference in fixation duration between speakers 2 and 4 was still large (d = −0.569, d = −0.639). A larger sample should be used to test these statistical results further. In sum, it appears the preservice teachers paid more attention to speakers than experienced teachers.

In segment 2, speaker 3 suddenly said, “If there are more than three sides of the cubes painted, four sides are painted,” then immediately noted, “The cubes at the top are impossible.” Before this, she had hardly said a word. No significant differences in noticing for each student were found, but the difference for speaker 3 was larger, d = −0.530. The preservice teachers showed longer fixation durations for speaker 3 than the experienced teachers. Preservice teachers seemed more likely to view the students’ discussions as a series of unrelated events occurring in chronological order. Therefore, when one student suddenly engaged in abnormal behaviors, the preservice teachers quickly focused on her. In contrast, the experienced teachers observed more systematically and were not distracted by speaker 3’s new behavior.

In segment 3, speakers 1 and 4 had a heated discussion; listener 3 focused on them but said little. However, student 2, who was misbehaving, began to play with the calculator on the desk and paid no attention to the group activity. The results showed no significant differences between experienced and preservice teachers; still, the actual difference found for misbehaving student 2 was large (d = −0.531), showing that the preservice teachers paid more attention to misbehaving students. Moreover, the difference for listener 3 was also large (d = 0.532), indicating that experienced teachers looked at listener 3 longer than preservice teachers. In other words, the preservice teachers paid more attention to students with problematic behaviors for longer periods, and less attention to students who did not speak.

In segment 4, two students exhibited obvious problematic behaviors while the others focused on problem-solving. The misbehaving students played with the microphone on the desk, with student 1 mumbling some strange, amusing words into the equipment. The results showed that the preservice teachers focused significantly longer on misbehaving student 1 than the experienced teachers (p < 0.05, d = −0.806), and the two groups of teachers differed considerably in how long they watched misbehaving student 2 (d = −0.596). Specifically, the preservice teachers paid more attention to students exhibiting inappropriate behaviors than the experienced teachers.

9.3.2 Differences in the Features of Collaborative Problem-Solving Noticed

As shown in Table 9.5, almost all experienced teachers paid attention to all three categories, including preparation for the group activity, support for collaborative learning, and group member performance. They were more inclined to put forward suggestions than preservice teachers. However, preservice teachers focused primarily on group member performance, and many made evaluations or gave advice. Only half of the preservice teachers focused on preparation for the group activity, and nearly one-third made recommendations regarding teacher support for the collaborative problem-solving process. Thus, the more experienced teachers made more comprehensive observations and offered more practical suggestions. In addition, preservice teachers paid less attention to teaching support and were more likely to comment on participating members’ performance. The specific content noticed in each category was analyzed next; the main results are below, with specific examples for the comment level in each category.

Table 9.5 Percentage levels for teachers during topic analysis
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Table 9.6 Five levels of teachers’ comments on the preparation for group activity
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Table 9.7 Focuses in preparation for group activity
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Table 9.8 Five commenting levels of support for collaborative learning
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For the first focus (group activity preparation) with examples in Table 9.6, a higher percentage of experienced teachers than preservice teachers focused on the three sub-themes, as shown in Table 9.7. Preservice teachers tended to evaluate and offer suggestions about group construction and rarely thought about teaching goals. Only one preservice teacher made a judgment regarding teaching goals; he thought the group collaboration had low inefficiency and students failed to achieve the goal of collaboration. While problems were generally solved faster when addressed collaboratively, the group could not identify the correct answer. In contrast, half of the experienced teachers mentioned teaching goals, including short-term course goals and long-term mathematics teaching goals. Nearly 80% of the experienced teachers made suggestions about grouping or dividing work among members, such as the factors to be considered, whether to assign group leaders, etc. Furthermore, experienced teachers tended to provide ideas on designing appropriate tasks to promote group collaboration, while preservice teachers tended only to evaluate whether the designed task was reasonable.

In terms of support for collaborative learning with examples in Table 9.8, the results show that more experienced teachers than preservice teachers noticed learning materials and teaching guidance, while preservice teachers were more concerned with disciplinary management (see Table 9.9). Regarding learning resources, preservice teachers were inclined to simply state that there were six blocks on the table or evaluate whether the blocks provided were appropriate; fewer of these teachers provided suggestions. Regarding teaching guidance, Approximately 70% of experienced teachers provided specific teaching methods or strategies, while a few preservice teachers only briefly described the classroom teachers’ specific behaviors. In addition, 32.14% of the preservice teachers proposed possible solutions. Thus, compared to experienced teachers, preservice teachers paid less attention to learning materials and teacher guidance and were more concerned with discipline management. They tended to make superficial narratives or rough evaluations and could give some suggestions about instructional strategies.

Table 9.9 Focuses of support for collaborative learning
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Table 9.10 Five commenting levels of performance of group members
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Table 9.11 Focuses on group member performance
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Finally, regarding group member performance (see examples in Table 9.10), preservice teachers paid more attention to possible problem-solving approaches than mathematical thinking, such as spatial imagination and abstract reasoning. More than twice as many experienced teachers were concerned with mathematical thinking, and most offered remarks provided suggestions on cultivating students’ mathematical thinking. As shown in Table 9.11, approximately 90% of preservice teachers mentioned problem-solving approaches, and 57.14% evaluated idea clarity. All teachers mentioned group interactions, but the experienced teachers were more skilled at making suggestions to improve students’ collaboration skills and provide students equal opportunities to participate. Nearly 40% of preservice teachers only evaluated group collaboration, and some explained some students’ lack of participation from various perspectives (e.g., students’ personalities, interests, or mathematical abilities).

9.4 Discussion

This study has explored the differences between experienced and preservice teachers in noticing the collaborative problem-solving process, based mainly on teachers’ visual attention distribution and specific CPS content. Unlike many previous studies on teachers’ noticing, this study combined eye-tracking and interviews to collect data from several teachers watching a group problem-solving video. It used eye-tracking technology to obtain moment-to-moment gaze information and traditional structured interviews for supplementary explanations of teachers’ thought processes. The results suggest that teachers with different teaching experience levels have different focuses when viewing group work videos. Experienced teachers distributed their attention more evenly than preservice teachers and noticed more important features of the CPS process. Next, we conduct a detailed discussion of three categories of group collaboration noticed by experienced and preservice teachers—group performance, support for collaborative learning, and preparation for group activity. For each facet, we summarize one bullet point.

9.4.1 Preservice Teachers Attend to More Superficial Information

First, regarding group member performance, preservice teachers focused significantly more on students who spoke frequently, such as speaker 1 in the segment where four students analyzed the task. These teachers paid less attention to students who spoke little, such as listener 3 in the segment where three students participated in problem-solving. Preservice teachers appeared more interested in speakers with salient behavioral features, ignoring those who, while not exhibiting explicit behaviors, might be involved in implicit thinking activities. This suggests preservice teachers’ attention was easily drawn to students who spoke, and they paid more attention to the superficial and formal aspects of the discussion process (Star & Strickland, 2008). The preservice teachers lacked the requisite classroom experience to realize there was much to notice in the classroom and could not use other key information to understand the students synthetically.

Further analysis of this segment revealed that the preservice teachers spent significantly more looking at the four students than the experienced teachers, p = 0.037, while the experienced teachers spent more time observing the students placing the blocks (M = 13.615) than preservice teachers (M = 11.582). Teachers could clearly hear what students were saying when watching the group collaboration video. Experienced teachers focused more on substantively problem-solving rather than simply watching whoever spoke, showing that teachers’ expertise in explaining students’ understanding grows as their teaching experience increases (Jacobs et al., 2010). Thus, compared to preservice teachers, experienced teachers have a more detailed, comprehensive, and richer understanding of students’ mathematical thinking.

The interviews also showed that preservice teachers were more concerned with superficial information. Preservice teachers tended to describe or evaluate specific problem-solving approaches, and the percentage of experienced teachers mentioning profound mathematical thinking was far greater than that of preservice teachers. Moreover, some experienced teachers even proposed specific means to cultivate students’ mathematical skills. For example, one experienced teacher said, “We could try to use all 48 blocks first to help students whose spatial imagination abilities are poor and make them experience the mathematical process from the concrete to the abstract.” In contrast, most preservice teachers were inclined to recall detailed solutions (e.g., “They discussed the blocks painted on more than three sides first and then discussed the others”) or simply repeat what the students said. Some tended to comment only on whether the group understood the problem or solution (Carter et al., 1988).

Experienced teachers reflected on the students’ overall performance rather than simply criticizing them based on what happened; they acknowledged that the group’s idea, while slightly confusing, was common, and the right answer gradually emerged through heated discussion and repeated correction. As Sabers et al. (1991) noted, experienced teachers will provide strategies to increase student engagement and help students solve problems efficiently based on their performance, such as analyzing the problems slowly, thinking independently before discussing, and drawing diagrams to solve mathematical problems.

In addition, almost all teachers noticed considerable differences in the students’ participation, with some students hardly participating in the group discussion. In response, some experienced teachers predicted the whole class’ learning results based on this one group’s collaboration and offered many impressive ways to encourage students to participate, such as by reminding students that they could use drawings to facilitate communication and asking group members to speak in turn. However, nearly half of the preservice teachers only complained about the students’ poor participation and explained the group’s performance based on their experiences with similar situations.

This may have occurred because preservice teachers are used to acting as students being taught rather than as mathematics teachers. Limited by this perspective, they try to understand student performance as much as possible but cannot think deeply about the teaching and learning process. Specifically, preservice teachers relate group performance to their own learning experiences and focus more on salient features that people easily attend to. In this study, when teachers watched the group collaboration video, they should have been more concerned with the collaborative process’ implicit and substantive features and discussed important things like mathematical thinking, student participation, and teaching strategies.

9.4.2 Preservice Teachers Are More Concerned with Students’ Misbehaviors

Second, preservice teachers with no teaching experience were inclined to be distracted by students’ exhibiting problematic behaviors, such as the misbehaving students in the segments involving three and two students participating in problem-solving. This echoes existing studies on preservice teachers’ noticing, which found they focus more on students’ classroom misbehavior in traditional classrooms (Erickson, 1984; Sabers et al., 1991; Star & Strickland, 2008). It means preservice teachers are more concerned with disciplinary management and regard classroom management as their primary task.

Shen et al. (2009) investigated 527 elementary school teachers’ perceptions of classroom problem behaviors in five provinces in China and found significant differences in the amount of time spent on classroom management and that the time spent decreased as teaching experience increased, indicating that more classroom experience broadens teachers’ possible solutions to students’ behavioral problems. Preservice teachers, lacking classroom teaching experience, find it harder to deal with classroom behavior problems, are unable to find appropriate ways to deal with them quickly, and may even worry about losing control of the classroom. As such, preservice teachers spend more time focusing on students’ problematic classroom behaviors. Experienced teachers, on the other hand, are more concerned about students’ mathematical thinking when group members discuss problems, and do not disrupt the group’s problem-solving because of individual students’ misbehaviors. They are more conscious of what to pay attention to and what to ignore in specific situations (Erickson, 1984). This echoes Miller’s (2011) observation that experienced teachers do not pay attention to everything they see; instead, they quickly adapt their attention to suit the situation and actively ignore, to a certain extent, less important things.

Notably, the interview results showed that a higher proportion of preservice than experienced teachers mentioned disciplinary management, which is consistent with the results of our eye-tracking data analysis. We therefore conducted a supplementary analysis to investigate the misbehaviors recalled by the two types of teachers. Nearly 43% of the preservice teachers talked at length about how student 1 had said strange, funny words into the recording equipment, while only one experienced teacher mentioned it. This suggests that preservice teachers’ inexperience leads them to be distracted by problematic student behaviors and more sensitive to classroom discipline.

In addition to classroom management, providing useful learning materials and teaching guidance is essential for supporting collaborative learning. Interestingly, fewer preservice teachers focused on learning resources and teaching guidance. Only half paid some attention to the teacher, who barely instructed the students beyond reminding them to write down their group numbers. Most instead tended to describe or evaluate the blocks on the desk; for example, “Not all 48 wooden blocks were given, and the rest should be imagined by themselves, so that students’ geometric intuition could be developed” and “The blocks are rather strange and will interfere with the students’ thinking, because they will keep placing the blocks instead of thinking about drawing.”

The experienced teachers’ perceptions were more comprehensive. They made specific recommendations on how many blocks to provide to improve the students’ involvement and remarked on the advantages of using white paper for drawing. This corresponds to Star’s (2008) finding that only 44% of preservice teachers correctly answered questions about the classroom environment before training, and generally did not notice important classroom environment features or feel these features were worth attention. This shows that preservice teachers do not pay enough attention to key details that facilitate collaborative group learning.

In addition, approximately three-quarters of the experienced teachers offered suggestions based on their teaching experience, such as teaching strategies for group collaboration. Greatly influenced by their accumulated classroom teaching experience, they could associate the group’s performance with relevant general teaching principles or strategies.

9.4.3 Preservice Teachers Focus Little on the Teaching Goal of Group Collaboration

Third, among the three categories noticed by teachers, preservice teachers gave the least attention to preparing for the group activity and only one mentioned the teaching goal. In contrast, some experienced teachers provided advice on collaborative learning and mathematics activity goals. For example, one experienced teacher said, “If I were the teacher in the class, I would reflect on what I really wanted. If I wanted this group to give the right answer quickly, my attention would be on the most active students; but if I wanted to make all students improve, I would focus more on low-involvement students.” This reflects this experienced teacher’s in-depth thinking about effective teaching. Another ET noted, “Our students should be able to face their future life and interact positively with society, not only by solving problems but also by knowing how to communicate with others.” This reflects the PISA 2021 mathematics framework, which identifies communication as one of eight important twenty-first-century skills (OECD, 2018).

Preservice teachers mentioned task design and group construction more often than teaching goals. They pointed out whether the group task was reasonable and provided specific advice, such as “When creating groups, it is important for the groups to be equal in terms of students’ mathematical skills and personalities.” However, the experienced teachers put forward more impressive and practical suggestions: “I prefer grouping students with various skill levels so they can help each other. However, if they need to solve problems, students with similar skills should be in the same group to easily exchange their thoughts and ideas. Therefore, I design tasks with different levels of difficulty for different groups, according to each group’s skill level.”

As we can see from the results, preservice teachers with a collaborative learning experience in middle schools could evaluate whether the task designed was appropriate for the seventh-grade students and roughly suggest how to effectively construct groups. However, it was difficult for them to determine the lesson’s teaching goal from a teaching perspective. The experienced teachers not only offered specific advice based on their teaching experience, but they also provided ideas on mathematics teaching that were consistent with modern educational ideas. While the preservice teachers may have had some professional knowledge about teaching, they did not yet know how to apply abstract theories to actual teaching skills and effectively practice them. Therefore, when watching the video, the preservice teachers could not connect specific events to broader teaching principles; instead, they only attended to what was occurring on the surface.

Doyle (1986) noted that classrooms have three main properties: simultaneity, multidimensionality, and immediacy. Based on our analysis of a four-student collaborative activity, we can see that the students’ participation varied greatly, and key changes occurred at the same time. Therefore, it is necessary for teachers to continually monitor several simultaneous events. Teachers must not only listen to speakers; they must also pay close attention to whether other students are understanding or keeping up with the activity. However, preservice teachers, who lack teaching experience, may focus primarily on more salient behaviors and ignore other implicit features of CPS, as they are used to observing the teaching process as learners. Teachers should give students showing little or no participation extra attention when teaching. Moreover, they must selectively perceive more significant features of specific situations and constantly strive to understand or analyze them. They should consider what is happening as a continuous whole and quickly make important decisions to respond to patterns that need to be changed.

9.5 Conclusions and Implications

Based on the discussion above, teachers’ noticing ability is closely related to their classroom teaching experience. As shown by prior studies, experienced teachers’ perceptions of group collaboration are more detailed, systematic, and comprehensive. Experienced teachers think more deeply about what they attend to and more often propose practical teaching strategies than preservice teachers. Although it is difficult to precisely describe what is noteworthy during CPS activities, it is appropriate to notice important objects and logically and reasonably observe the fundamental elements of the CPS teaching process, such as teaching goals, group construction, problem-solving, group interaction, and teachers’ guidance. The experienced teachers in our study showed roughly these characteristics.

This study also presents some limitations. First, some relevant factors that may affect teachers’ noticing were not considered in this study, such as teachers’ beliefs and educational backgrounds (Jacobs et al., 2010). Second, as with many other studies, the sample size in this study was small, with no significant differences in participant characteristics. Increasing the number of participants could further verify the results. In addition, viewing a video of group collaboration in a laboratory setting differs from facilitating multiple groups in an authentic classroom context, which may limit our conclusions’ generalizability. Next, we will investigate the differences in professional noticing between teachers with different experience levels in an authentic group teaching classroom situation and further analyze the possible reasons underlying their behaviors. We also intend to determine whether teachers’ noticing changes group members’ visual attention, leads to students’ joint attention, or improves students’ collaborative quality in other ways, as described in the literature. Such areas remain unexplored and require more in-depth exploration. Reflecting on teachers’ noticing about group collaboration using innovative technology can help improve teachers’ classroom practices and students’ collaborative learning.