Pedagogical Content Knowledge

The Value of Video Annotations: Noticing Different Modes and Aspects of Student Thinking

Cadre-Admin — Tue, 27 Jan 2026 22:30:50 +0000

The Value of Video Annotations: Noticing Different Modes and Aspects of Student Thinking

The purpose of this study is to explore if and how different types of video annotations support pre-service teachers (PSTs) in learning how to notice student multimodal, or verbal and non-verbal, mathematical thinking. We implemented a video club intervention in a middle grades mathematics methods class. We asked PSTs to annotate classroom videos using two types of annotations. The first type was a pinning tool, which allowed the PSTs to mark video timestamps. The second type was a drawing tool, which allowed PSTs to draw directly on the video. We found that when PSTs used the pin tool, they largely attended to students' verbal thinking. In contrast, with the draw tool, PSTs began to attend to more of students' non-verbal thinking. When PSTs attended to verbal student thinking, they mostly interpreted it in terms of students' disciplinary understanding. When PSTs attended to non-verbal thinking, they reasoned about additional aspects of student thinking including affect, communication goals, and students' processes for learning the content. These findings have implications for PD design that supports teachers in expanding their multimodal noticing.

Walton, M., Moon, P., & Walkoe, J. (2026). The value of video annotations: Noticing different modes and aspects of student thinking. School Science and Mathematics. https://doi.org/10.1111/ssm.70009

Cadre-Admin Tue, 01/27/2026 - 17:30

https://onlinelibrary.wiley.com/doi/10.1111/ssm.70009

Learning by Evaluating in Engineering Design Classrooms: A 5E Instructional Model Perspective from Teachers

Cadre-Admin — Mon, 15 Dec 2025 23:02:00 +0000

Learning by Evaluating in Engineering Design Classrooms: A 5E Instructional Model Perspective from Teachers

This study explores how Learning by Evaluating (LbE) can be integrated into the 5E instructional model to support technology and engineering education. LbE, influenced by comparative judgment, engages students in analyzing peer work to foster reflection, design reasoning, and iterative thinking. Using qualitative content analysis of teacher interviews, this research investigates how LbE can contribute to each phase of the 5E model: Engage, Explore, Explain, Elaborate, and Evaluate.

Findings suggest that LbE enhances engagement during the Engage phase by leveraging real-world examples and peer comparisons to activate interest and prior knowledge. In the Explore phase, it aids design ideation and constraint recognition, though students often need structure to express their insights. During the Explain phase, LbE supports analytical thinking by helping students distinguish strong and weak designs, yet misconceptions may persist without debriefing. In the Elaborate phase, LbE reinforces the value of feedback and supports refinement of criteria and constraints, serving as a primer for redesign. In the Evaluate phase, it promotes reflection and group communication, though many students struggle to articulate evaluative reasoning without scaffolding.

Overall, LbE offers a flexible and impactful way to deepen learning when intentionally embedded across the 5E framework. However, its success depends on thoughtful implementation and alignment with broader design thinking goals. The study recommends future research to explore how LbE supports long-term learning outcomes and how it may be adapted for diverse classroom settings.

Lee, W., Mentzer, N., Jackson, A., Bartholomew, S. R., & Clevenger, A. B. (2025). Learning by evaluating in engineering design classrooms: A 5E instructional model perspective from teachers. Journal of Technology Education, 37(1), 94–129. DOI: 10.21061/jte.v37i1.a.5

Cadre-Admin Mon, 12/15/2025 - 18:02

https://jte-journal.org/articles/10.21061/jte.v37i1.a.5

Effects of Perceptual and Cognitive Factors on Preservice Teachers’ Professional Noticing: A Grounded Cognitive Perspective of Professional Noticing

Cadre-Admin — Mon, 22 Sep 2025 14:36:28 +0000

Effects of Perceptual and Cognitive Factors on Preservice Teachers’ Professional Noticing: A Grounded Cognitive Perspective of Professional Noticing

Professional noticing is a critical skill for teachers, enabling them to interpret and respond to significant moments in the classroom to support student learning. While recent theoretical papers have broadened the conceptualization of noticing to include social, embodied, and environmental factors, empirical research exploring the interaction of such domains is limited. To address this gap, the current study investigated the effects of perceptual (eye-tracking and presence) and cognitive (pedagogical content knowledge) factors on preservice teachers’ professional noticing within a 360 video. By integrating data across these domains, this paper provides empirical evidence for conceptualizing noticing through a grounded cognitive perspective. Results indicated that factors influencing professional noticing operate independently rather than as components of a single overarching construct. Among these, PCK emerged as a strong predictor of effective noticing, while excessive focus on the teacher negatively impacted the ability to attend to students’ thinking. Additional results and their implications for teacher education and future research are discussed.

Kosko, K. W., Zolfaghari, M., Ferdig, R. E., Gandolfi, E., Austin, C. K., Pavlic, C., & Guan, Q. (2025). Effects of perceptual and cognitive factors on preservice teachers’ professional noticing: A grounded cognitive perspective of professional noticing. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-025-01734-8

Cadre-Admin Mon, 09/22/2025 - 10:36

https://link.springer.com/article/10.1007/s11858-025-01734-8

Discursive Differences in Written Feedback of Individuals with Varied Teaching Experiences: Towards Validating Knowledge of Content and Teaching Specific to Proof

Cadre-Admin — Tue, 29 Jul 2025 19:28:57 +0000

Discursive Differences in Written Feedback of Individuals with Varied Teaching Experiences: Towards Validating Knowledge of Content and Teaching Specific to Proof

Fostering student engagement with mathematical reasoning and proving requires a special kind of teacher knowledge – Mathematical Knowledge for Teaching Proof (MKT-P). One important component of MKT-P is Knowledge of Content and Teaching specific to Proof (KCT-P), which is knowledge of pedagogical practices for supporting student learning of proof. Providing effective feedback on students' mathematical arguments is one of the key aspects of KCT-P. This study examined the qualitative differences in written feedback of secondary teachers, undergraduate mathematics and computer science majors, and pre-service teachers participating in a capstone course focused on mathematical reasoning and proving. The discursive distinctions in the groups’ feedback, along with changes in the feedback of prospective teachers, provide empirical support for the construct of KCT-P as knowledge unique to teachers, which develops with experience.

Buchbinder, O., Butler, R., & McCrone, S. (2025). Discursive differences in written feedback of individuals with varied teaching experiences: Towards validating knowledge of content and teaching specific to proof. The Journal of Mathematical Behavior, 80. https://doi.org/10.1016/j.jmathb.2025.101272

Cadre-Admin Tue, 07/29/2025 - 15:28

https://www.sciencedirect.com/science/article/pii/S0732312325000367

Connecting Expertise in Noticing Children’s Mathematical Thinking and Conducting Whole-Class Discussions

Cadre-Admin — Tue, 29 Jul 2025 18:36:54 +0000

Connecting Expertise in Noticing Children’s Mathematical Thinking and Conducting Whole-Class Discussions

We extend research that connects teacher noticing expertise and instructional quality by providing rich illustrations of these connections at three levels of noticing expertise. Grounded in a vision of teaching that is responsive to children’s mathematical thinking, we investigated connections between teachers’ expertise in noticing children’s thinking and their centering of children’s thinking in whole-class discussions. We showcase three upper elementary school teachers as focal teachers, each with a different level of noticing expertise. Data were drawn from a large design study and included teachers’ written responses to an artifact-based noticing assessment and video of their whole-class discussions focused on children’s strategies for fraction story problems. We found that increased expertise in noticing was associated with increased centering of children’s thinking in whole-class discussions. As noticing expertise increased across our focal teachers, their primary uses of strategy details in whole-class discussions shifted from only making details visible; to visible and highlighted; to visible, highlighted, and collectively explored. Furthermore, increased noticing expertise was associated with increased use of visual and verbal supports to foreground strategy details, increased engagement of children with strategy details, and increased opportunities to link strategy details to broader mathematical ideas. This study provides insight into the importance of expertise in teacher noticing for whole-class discussions while also illustrating the mathematical and pedagogical richness of the details of children’s mathematical thinking.

Jacobs, V. R. & Empson, S. B. (2025). Connecting expertise in noticing children’s mathematical thinking and conducting whole-class discussions. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-025-01713-z

Cadre-Admin Tue, 07/29/2025 - 14:36

https://link.springer.com/article/10.1007/s11858-025-01713-z

Toward a Framework of Culturally Relevant Science and Mathematics Pedagogy: A Pedagogical and Analytical Tool for Teacher Education

Cadre-Admin — Mon, 30 Jun 2025 16:02:17 +0000

Toward a Framework of Culturally Relevant Science and Mathematics Pedagogy: A Pedagogical and Analytical Tool for Teacher Education

In this article, we present a framework of culturally relevant science and mathematics pedagogy (CRSMP), which is grounded in the tenets of culturally relevant pedagogy. It delineates practices ranging from the most accessible and easy-to-implement, to the most challenging and often contentious ways to teach mathematics and science. We provide examples of CRSMP that re-position marginalized learners in relation to science and mathematics. We discuss the ways in which this framework can disrupt dominant, inequitable systems of instruction and preview ways of working with teachers to support their efforts to provide meaningful science and mathematics learning experiences for youth.

Magee, P. A. & Willey, C. (2024). Toward a framework of culturally relevant science and mathematics pedagogy: A pedagogical and analytical tool for teacher education. Cultural Studies of Science Education, 19, 753–778 https://doi.org/10.1007/s11422-024-10235-1

Cadre-Admin Mon, 06/30/2025 - 12:02

https://link.springer.com/article/10.1007/s11422-024-10235-1

Mathematics Teacher Educators’ Navigational Expertise When Designing Multimodal Representations of Practice: A Semiotic Analysis

Cadre-Admin — Sun, 29 Jun 2025 18:01:18 +0000

Mathematics Teacher Educators’ Navigational Expertise When Designing Multimodal Representations of Practice: A Semiotic Analysis

Critical elements of the expertise of mathematics teacher educators (MTE) can be identified in the artifacts they design for working with prospective teachers (PT), specifically for engaging PT in the double role of practitioners and students of practice. While MTE are increasingly utilizing designed multimodal representations of practice (such as storyboards), theoretical frameworks and methods for analyzing these pedagogical artifacts and the meanings they support are still in early development. We utilize a semiotic framework, expanding systemic functional linguistics to encompass non-linguistic elements, to identify aspects of what we call navigational expertise—which supports PTs in engaging both as practitioners and students of the practice. We view this expertise as tacit knowledge-in-use, enacted through artifact production. The paper demonstrates MTE’s navigational expertise by showing how MTE design storyboards of practice to engage PT as fellow teachers experiencing the lesson taught by a peer and as university students who consider the artifact (including the represented lesson) as an object of study. The framework allows us to identify how MTE’s navigational expertise lies in seamlessly interweaving these two purposes and navigating between them, knowing when, how, and for what purposes to invoke each. Through analysis of storyboards from four MTE in diverse US settings, we uncover some of the nuanced tacit components of navigational expertise, highlighting linguistic and non-linguistic design choices and their potential meanings for transactions with PT.

Schwarts, G., Herbst, P., Chazan, D. Buchbinder, O., Clark, L. M., Wieman, R., Zahner, W. (2025). Mathematics teacher educators’ navigational expertise when designing multimodal representations of practice: a semiotic analysis. Journal of Mathematics Teacher Education, 28, 341–368. https://doi.org/10.1007/s10857-024-09658-y

Cadre-Admin Sun, 06/29/2025 - 14:01

https://link.springer.com/article/10.1007/s10857-024-09658-y

Variation in the Implementation of Educative Curriculum Materials for Elementary Science Teacher Educators in Two Course Contexts: An Exploratory Case Study

Cadre-Admin — Fri, 11 Apr 2025 03:33:47 +0000

Variation in the Implementation of Educative Curriculum Materials for Elementary Science Teacher Educators in Two Course Contexts: An Exploratory Case Study

Educative curriculum materials (ECM) have been shown to support K-12 teacher learning, but little is known about teacher educators’ use of ECM. In this study, we report on enactments of ECM designed to support the development of preservice elementary teachers’ content knowledge for teaching about matter in two different courses to understand how teacher educators use ECM. Participants were two full professors teaching science content and science methods courses for elementary preservice teachers at a public university in the Pacific Northwest. While both instructors had similar years of experience teaching science education courses and used the same ECM, they implemented them differently. Substituting different activities or resources provided by the ECM or supplementing the ECM with alternate activities are examples of adaptations leveraged by the instructors. Decision-making around implementation was guided primarily by the instructors’ pedagogical approaches, the fit of the ECM with existing course content and goals, and alignment with problems of practice facing their elementary preservice teachers.

Melton, J. C. & Mikeska, J. N. (2025). Variation in the implementation of educative curriculum materials for elementary science teacher educators in two course contexts: An exploratory case study. Journal of Science Teacher Education, 1–22. https://doi.org/10.1080/1046560X.2025.2467469

Cadre-Admin Thu, 04/10/2025 - 23:33

https://www.tandfonline.com/doi/full/10.1080/1046560X.2025.2467469

Variation in the Implementation of Educative Curriculum Materials for Elementary Science Teacher Educators in Two Course Contexts: An Exploratory Case Study

Cadre-Admin — Fri, 11 Apr 2025 03:33:47 +0000

Variation in the Implementation of Educative Curriculum Materials for Elementary Science Teacher Educators in Two Course Contexts: An Exploratory Case Study

Cadre-Admin Thu, 04/10/2025 - 23:33

https://www.tandfonline.com/doi/full/10.1080/1046560X.2025.2467469

Middle School Mathematics Teachers’ Proportional Reasoning and Its Relation to Their Content and Pedagogical Content Knowledge

Cadre-Admin — Fri, 11 Apr 2025 03:17:17 +0000

Middle School Mathematics Teachers’ Proportional Reasoning and Its Relation to Their Content and Pedagogical Content Knowledge

Proportional reasoning is an important but challenging skill for students and teachers. This article, presents findings from two studies investigating whether four categories of reasoning identified by Copur-Gencturk et al. (2022, A Closer Look at Teachers’ Proportional Reasoning. International Journal of Science and Mathematics Education, 21(1), 113–129) apply to a national sample of U.S. middle school mathematics teachers (N = 1,320) and can be captured consistently by similar tasks. We explored the meaningfulness of these reasoning categories with a new sample of middle school mathematics teachers (N = 224) investigating the role of reasoning categories in teachers’ content and pedagogical content knowledge. Both studies suggest that teachers’ proportional reasoning could be grouped into four categories: incorrect, additive, relative, and proportional. Additionally, the way teachers reason in novel proportional situations provides insights into their overall understanding of the content and their pedagogical content knowledge of ratios and proportional relationships.

Copur-Gencturk, Y. & Ezaki, J. (2025). Middle school mathematics teachers’ proportional reasoning and its relation to their content and pedagogical content knowledge. Research in Mathematics Education, 1–21. https://doi.org/10.1080/14794802.2025.2462930

Cadre-Admin Thu, 04/10/2025 - 23:17

https://www.tandfonline.com/doi/full/10.1080/14794802.2025.2462930