skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 10:00 PM to 12:00 PM ET on Tuesday, March 25 due to maintenance. We apologize for the inconvenience.


Title: A STUDY OF WHAT STUDENTS FOCUS ON AND NOTICE ABOUT QUADRATIC FUNCTIONS REPRESENTATIONS DURING INSTRUCTION
Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher’s goals for student focusing and noticing during quadratic functions instruction with what students actually focused on and noticed. Qualitative analysis revealed some alignment but also informative ways that the teacher’s goals and student outcomes for focusing and noticing were misaligned. These results will further the field’s understanding of how students learn about quadratic functions and may have implications for student focusing and noticing of other mathematics topics as well.  more » « less
Award ID(s):
1651571
PAR ID:
10503457
Author(s) / Creator(s):
; ;
Editor(s):
Lamberg, T; Moss, D.
Publisher / Repository:
PMENA
Date Published:
Journal Name:
Proceedings of the 45th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
Volume:
2
Page Range / eLocation ID:
16–24
Format(s):
Medium: X
Location:
Reno, NV
Sponsoring Org:
National Science Foundation
More Like this
  1. Ayalon, M.; Koichu, B.; Leikin, R.; Rubel, L.; Tabach, M. (Ed.)
    The topic of study in this report is student focusing and noticing. Specifically, we examined a teacher’s goals for student focusing and noticing and the student outcomes for focusing and noticing. The mathematics context for this research was quadratic functions and covariational reasoning. Two whole-class discussion episodes were analyzed. Results showed ways that the teacher’s goals and student outcomes were aligned and three ways that they were misaligned. These results could inform how quadratic functions are taught and how teachers can improve the alignment between their goals for student focusing and noticing and student outcomes for focusing and noticing. 
    more » « less
  2. Lamberg, T. (Ed.)
    This brief research report examines the discursive shifts of a secondary mathematics teacher participating in a collaborative learning community centered on culturally responsive mathematics teaching. We draw on two frameworks to analyze the teacher’s discursive moves. The first framework comes from Lefstein et al., (2020) on generative discourse practices in learning communities. The second framework — FAIR (Louie et al., 2021) — offers noticing practices for deficit versus anti-oppressive mathematics teaching. Through these lenses, we found that the teacher’s initial discourse practices were marked by deficit framing and noticing. The teacher’s discourse practices begin to shift towards a culturally responsive pedagogy in response to a particular artifact that captured student noticing and reframed the teacher’s problem of practice. 
    more » « less
  3. As a core practice, teacher noticing of students' mathematical thinking is foundational to other teaching practices. Yet, this practice is difficult for preservice teachers (PSTs), particularly the component of interpreting students' thinking (e.g., Teuscher et al., 2017). We report on a study of our design of a specific approximation of teacher noticing task with the overarching goal of conceptualizing how to design approximations of practice that support PSTs' learning to notice student thinking in technology-mediated environments with a specific focus on interpreting students' mathematical thinking. Drawing on Grossman et al.'s (2009) Framework for Teaching Practice (i.e., pedagogies of practice), we provided decomposed opportunities for PSTs to engage with the practice of teacher noticing. We analyzed how our design choices led to different evidence of the PSTs' interpretations through professional development design study methods. Findings indicate that the PSTs frequently interpret what students understood. Yet, they were more challenged by interpreting what students did not yet understand. Furthermore, we found that providing lesson goals and asking the PSTs to respond to a prompt of deciding how to respond had the potential to elicit PSTs' interpretations of what the students did not yet understand. The study highlights the interplay between task design, prompt wording, and PSTs' interpretations, which emphasizes the complexity of developing teacher noticing 
    more » « less
  4. 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. 
    more » « less
  5. A teacher’s noticing or their ability to see and interpret classroom events is an important component of their expertise. Examination of these noticings is a way to understand changes in their learning over time. In this research, we examine changes in teacher noticing of classroom instruction for two groups that participated in slightly different professional development experiences to understand how this PD shaped their personal domain of learning. Findings suggest that both programs shaped teacher noticing and learning but in different ways. 
    more » « less