A STUDY OF WHAT STUDENTS FOCUS ON AND NOTICE ABOUT QUADRATIC FUNCTIONS REPRESENTATIONS DURING INSTRUCTION

Oct 15, 2026

Study examines how students focus on and notice during quadratic functions instruction and how these patterns relate to a teacher’s stated goals. Qualitative analysis compares teacher goals for students’ focusing and noticing with students’ actual attention and noticed features. Findings show partial alignment alongside clear cases of mismatch, informing understanding of learning mechanisms for quadratic functions and suggesting implications for focusing and noticing in other mathematics topics.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Theoretical orientation toward student focusing and noticing

Student focusing and noticing

Theoretical orientation toward learning of quadratic functions

Quadratic functions

A STUDY OF WHAT STUDENTS FOCUS ON AND NOTICE ABOUT QUADRATIC FUNCTIONS REPRESENTATIONS DURING INSTRUCTION Charles Hohensee University of Delaware [hohensee@udel.edu](hohensee@udel.edu) Yue Ma University of Delaware [yuemajoy@udel.edu](yuemajoy@udel.edu) Sara Gartland National University of Ireland Galway [sara.gartland@nuigalway.ie](sara.gartland@nuigalway.ie) Srujana Acharya University of Delaware [srujana@udel.edu](srujana@udel.edu) 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. Keywords: Algebra and Algebraic Thinking, Cognition, Learning Theory. This study is about what students focus on and notice during quadratic functions instruction. The topic of student focusing and noticing is a vitally important consideration for the field of mathematics education because (a) focusing and noticing are crucial processes for any and all reasoning (i.e., what remains unnoticed cannot be reasoned with or about; Bransford & Schwartz, 1999), and (b) what students focus on and notice might not always align with what their teachers want students to focus on and notice (Mason, 1999). Although teacher noticing has become a thriving area of research among teacher education researchers, student focusing and noticing has yet to garner the same kind of attention among student learning researchers. Our research sets out to help address that imbalance. Foremost, our research sets out to produce insights about how students learn about quadratic functions. However, we also view our findings as having potential relevance for the learning of other topics as well. Theoretical Orientation Towards Student Noticing and the Learning of Quadratic Functions In this section, we first present our theoretical orientation toward student focusing and noticing. We then present our theoretical orientation toward the learning of quadratic functions. Student Focusing and Noticing We conceive of student focusing and noticing as the last two parts of a three-part process involving attending, focusing, and noticing. All three are needed for student noticing to occur (i.e., attending and focusing are precursors to noticing) . To conceptualize these processes, we turn to von Glasersfeld (1995). We conceptualize attending as “pick[ing] a chunk of experience, isolate[ing] it from what came before and from what follows, and treat[ing] it as a closed entity,”(p. 91). In other words, to attend to an object in a complex perceptual or conceptual context requires that the object be mentally isolated or foregrounded. While driving, for example, someone could foreground traffic signals against a background of other aspects of the Lamberg, T., & Moss, D. (2023). Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2). University of Nevada, Reno. 15 Articles published in the Proceedings are copyrighted by the authors. environment. Next, we conceptualize focusing on an object as “the mind, then,‘to posit it as object against itself’. . . to re-present it,”(von Glasersfeld, 1995, p. 91). In other words, focusing on an object ina complex perceptual and/or conceptual field goes beyond simply attending to the object, and requires the creation

FAQs

What is the study trying to understand about quadratic functions instruction?

It investigates what students focus on and notice while learning quadratic functions representations, and how these outcomes relate to teacher goals.

How did the researchers analyze student focusing and noticing?

They conducted a qualitative comparison between what teachers aimed for students to focus on and notice and what students actually focused on and noticed.

What did the study find about alignment between teacher goals and student outcomes?

Results indicated some alignment, but also informative ways in which teacher goals and student outcomes for focusing and noticing were misaligned.

Oct 15, 2026

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