This paper contributes to current discussions about supporting prospective teachers (PSTs) in developing skills of noticing students’ mathematical thinking. We draw attention to PSTs’ initial noticing skills (prior to instruction focused on supporting noticing) as PSTs engage in analyzing written artifacts of student work and video-records. We examined and compared PSTs’ noticing skills as they analyzed how students reason about, generalize, and justify generalizations of figural patterns given student written work and video records. We identified aspects of student thinking about generalizations and justifications, which PSTs addressed and interpreted. We also examined how PSTs respond to students as they analyze student thinking given written artifacts of student work or video-records of small group discussions, and we identified the foci of PSTs’ responding practice.
Our data revealed that PSTs’ initial noticing skills of student generalizations and justifications differed while accounting for ways in which student thinking was externalized (written work or video-records). PSTs’ attending-
Our results document that without providing any intentional support for PSTs’ noticing skills, PSTs are more deliberate to focus on mathematically significant aspects of student thinking while analyzing written artifacts of student work compared to video-records. We believe that the analysis of student written work might demand from PSTs to be more analytical. While examining written representations, PSTs have to reconstruct students’ reasoning. Unlike the videos where the students tell or use gestures to express their thinking, written work provides fewer clues about student thinking. Thus, written work demands a deeper level of engagement from PSTs as they strive to understand student reasoning. Our study extends research on PSTs’ noticing skills by documenting differences in PSTs’ noticing in relation to the nature of artifacts of student work that PSTs analyze. Our work also adds to prior research on PSTs’ noticing by characterizing specific aspects of students’ thinking about pattern generalizations and justifications that PSTs address as they analyze student thinking and respond to students.
- NSF-PAR ID:
- 10212540
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- International Journal of STEM Education
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2196-7822
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This work-in-progress paper describes a collaborative effort between engineering education and machine learning researchers to automate analysis of written responses to conceptually challenging questions in mechanics. These qualitative questions are often used in large STEM classes to support active learning pedagogies; they require minimum calculations and focus on the application of underlying physical phenomena to various situations. Active learning pedagogies using this type of questions has been demonstrated to increase student achievement (Freeman et al., 2014; Hake, 1998) and engagement (Deslauriers, et al., 2011) of all students (Haak et al., 2011). To emphasize reasoning and sense-making, we use the Concept Warehouse (Koretsky et al., 2014), an audience response system where students provide written justifications to concept questions. Written justifications better prepare students for discussions with peers and in the whole class and can also improve students’ answer choices (Koretsky et al., 2016a, 2016b). In addition to their use as a tool to foster learning, written explanations can also provide valuable information to concurrently assess that learning (Koretsky and Magana, 2019). However, in practice, there has been limited deployment of written justifications with concept questions, in part, because they provide a daunting amount of information for instructors to process and for researchers to analyze. In this study, we describe the initial evaluation of large pre-trained generative sequence-to-sequence language models (Raffel et al., 2019; Brown et al., 2020) to automate the laborious coding process of student written responses. Adaptation of machine learning algorithms in this context is challenging since each question targets specific concepts which elicit their own unique reasoning processes. This exploratory project seeks to utilize responses collected through the Concept Warehouse to identify viable strategies for adapting machine learning to support instructors and researchers in identifying salient aspects of student thinking and understanding with these conceptually challenging questions.more » « less
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Teacher education has begun to embrace the use of 360 videos to improve preservice teachers' (PSTs) engagement and immersion. While recent research on such use is promising overall, there are specific questions that have been left unanswered about the construct of presence in 360 videos. More specifically, research has yet to fully explore how video delivery devices and PST characteristics may impact presence. The purpose of this study was to respond to this gap in the literature by examining PST major, delivery device (ie, head mounted display vs. flat screen), and the interaction between the two in informing presence. A total of 93 PSTs watched 360 videos and then completed a questionnaire. Findings indicated that presence in head‐mounted displays was related to emotions and agency. Conversely, presence with flat screens meant familiarity and control. Moreover, PST major was a predictor of presence, suggesting that 360 videos should be personalized according to PST career and professional goals. Finally, the interaction effect of preparing to teach K‐12 mathematics and wearing a head‐mounted display had a negative and statistically significant effect on participants' perceived presence, thus indicating a non‐cumulative effect.
Practitioner notes What is already known about this topic
360 videos are increasingly used to support preservice teacher training.
360 videos for teacher education foster immersion, presence, and noticing skills.
What this paper adds
Empirical evidence that 360 videos experienced with head‐mounted display facilitate agency and emotional involvement.
Empirical evidence that 360 videos experienced with flat screens facilitate feelings of control.
Data showed that preservice teachers' content area (math) was a positive predictor of presence in 360 videos.
Implications for practice and/or policy
Head‐mounted displays show promise as a delivery mode for 360 videos in teacher education.
360 videos should be personalized according to PST career and professional goals.
The eXtended Reality Presence Scale is confirmed as a robust instrument to measure presence in immersive environments.
More research is needed to evaluate the scalability of this approach in other contexts.
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Abstract The practice of teacher noticing students' mathematical thinking often includes three interrelated components: attending to students' strategies, interpreting students' understandings, and deciding how to respond on the basis of students' understanding. This practice gains complexity in technology‐mediated environments (i.e., using technology‐enhanced math tasks) because it requires attending to and interpreting students' engagement with technology. Current frameworks implicitly assume the practice includes noticing the ways students use tools (including technology tools) in their work, but do not explicitly highlight the role of the tool. While research has shown that using these frameworks supports preservice secondary mathematics teachers (PSTs) developing noticing practices, it has also shown that PSTs largely overlook students' technology engagement when they are working on technology‐enhanced tasks (
Journal for Research in Mathematics Education , 2010; 41(2):169–202). In this article, we describe our adaptation of Jacobs et al.'s framework for teacher noticing student mathematical thinking to include a focus on making students' technology‐tool engagement explicit when noticing in technology‐mediated environments, the Noticing in Technology‐Mediated Environments (NITE) framework. We describe the theoretical foundations of the framework, provide a video case example, and then illustrate how the framework can be used by mathematics teacher educators to support PSTs' noticing when students are working in technology‐mediated environments.