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1. Understanding Preservice Teachers’ Noticing of Online Teaching.

   Liu, J.; Buchbinder, O.; Weingarden, M. (January 2022, The 44th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   The rapid move to online teaching brought about by the global pandemic highlighted the need for the educational research community to develop new conceptual tools for characterizing these environments. In this paper, we propose a conceptual framework Instructional Technology Triangle (ITT) which extends the instructional triangle of teachers, students, and content to include technology as a mediating mechanism. We use the ITT framework to analyze noticing patterns in the written reflection of a prospective secondary teacher, Nancy, who, over the course of one semester taught online four lessons integrating reasoning and proof . The fluctuations in Nancy’s noticing patterns, in particular, with respect to technology, shed light on her trajectory of learning to teach online and the role of reflective noticing in this process. We discuss implications for teacher preparation and professional development. 

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2. Exploring the noticing of science teachers: What teachers' notice and using video to capture teacher knowledge

   https://doi.org/10.1111/ssm.12623  

   Luft, Julie_A; Huang, Yuxi; Singh, Harleen; Ozen‐Tasdemir, Hatice; DeLuca, Joe; Watson, Shelby; Ayano, Elizabeth; Whitworth, Brooke_A (November 2023, School Science and Mathematics)

   Abstract Knowing how science teachers develop their professional knowledge has been a challenge. One potential way to determine the professional knowledge of teachers is through videos. In the study described here, the authors recruited 60 elementary and secondary science teachers, showed them one of two 10‐min videos, and recorded and analyzed their comments when watching the videos. The coding focused on their noticing of student learning, teacher's teaching, types of teaching practices, and the use of interpretative frames. The noticing data were collected and analyzed to determine the differences between groups of teachers. The findings from the analysis indicated that most science teachers noticed the instruction of teachers rather than the learning of students, and these noticing events were often focused on general instructional practices as opposed to the science practices emphasized in theNext Generation Science Standards(National Research Council, 2013). The only difference between the teachers was in the area of evaluating the videos. Secondary science teachers and experienced elementary teachers were more likely to evaluate the videos than were novice elementary teachers. This may be a result of the knowledge base of the teachers. These results suggest a need for explicit reform‐based instruction and a revision of this research process. 

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3. Exploring Free Digital Tools in Education

   Mucundanyi, G.; Woodley, X. (January 2021, International journal of education and development using information and communication technology)

   Technology can assist instructional designers and teachers in meeting the needs of learners in traditional classrooms and virtual course environments. During the COVID-19 pandemic, many teachers and instructional designers began looking for resources they could use for hybrid and online course delivery. Many found that the cost of some technology tools was well outside of their financial means to assist them in meeting student learning outcomes. However, some digital tools provide free access for educators and are beneficial to students. In this article, the authors shared five tools they have used in developing and teaching online and traditional technology courses at the college level. They share how they used a learning management system tool, a collaboration tool, a search engine tool, a content creation tool, and a content sharing tool to engage students in their courses. As teachers look for alternatives to use as they move content from classroom teaching to online instruction, this article can help them consider the recommended tools for instruction. Teachers, instructors, and instructional designers may explore the free digital tools in this article and do further research on other digital tools to support student learning in their disciplines. 

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4. A framework to support teacher noticing of students' mathematical thinking in technology‐mediated environments

   https://doi.org/10.1111/ssm.12601  

   McCulloch, Allison W.; Dick, Lara K.; Lovett, Jennifer N. (October 2023, School Science and Mathematics)

   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. 

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5. Pre-service Teachers' Learning from Significant Opportunities for Improvement in a Positive Error Culture

   Groth, R.; Bergner, J. (January 2021, Mathematics teacher education and development)

   Many teacher education models involve reflecting on teaching practice for the sake of improving it. Such reflection must be carefully structured to help practitioners identify and act upon significant opportunities for improvement (SOIs). Learning from SOIs requires the cognitive activities of noticing students’ mathematical thinking and its connection to instructional practice, along with an affective disposition to view sub-optimal teaching practices as learning opportunities. We draw upon existing literature and theory related to the notion of developing positive error cultures to identify design principles for helping teachers learn from their own sub-optimal practices rather than becoming discouraged by them. The design principles include experience-based learning, low-stakes settings, collaboration, process reflection, and exploration of disagreements. We then describe a mathematics teacher education environment incorporating the design principles. Examples of pre-service teachers’ work within the environment are analysed for possible patterns of learning from SOIs within a positive error culture. Based on these examples, a four-quadrant model to characterise teachers’ learning from SOIs is proposed. The four quadrants describe various outcomes related to recognising and resolving SOIs. 

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