FRAMING INSTRUCTIONAL TASKS FOR INTERACTION WITH CONTENT - INTRODUCING DERIVATIVES GRAPHICALLY WITH INQUIRY

Oct 15, 2026

Study examines how eight U.S. college calculus instructors used inquiry-oriented instructional situations to frame tasks for introducing derivatives graphically. Across four interviews, instructors proposed tasks involving physical, graphical, verbal, and symbolic representations. Results emphasize two graphical task types: derivative at a point as the slope of a tangent line, and derivative as a function presented by its graph. Although instructional situations varied across instructors, they commonly relied on graphing, conjecturing, and calculating to operationalize inquiry teaching around these derivative concepts.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Literature Review

Graphical representations of derivatives

Theoretical Framework

Inquiry and instructional task framing

FRAMING INSTRUCTIONAL TASKS FOR INTERACTION WITH CONTENT: INTRODUCING DERIVATIVES GRAPHICALLY WITH INQUIRY Saba Gerami University of Michigan [sgerami@umich.edu](sgerami@umich.edu) In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically, verbally, and symbolically (Zandieh, 2000). The findings focus on the two tasks proposed by each instructor that centered the graphical representation of the derivative: derivative at a point as the slope of a tangent line, and derivative as a function presented by its graph. While no two instructors proposed the same tasks with the same instructional situations for teaching these concepts, they relied on graphing, conjecturing, and calculating situations to frame their tasks. Keywords: Undergraduate Education, Calculus, Instructional Activities and Practices, Mathematical Representations This study contributes to our understanding of teaching of calculus and implementing inquiry in undergraduate mathematics classrooms by investigating the ways calculus instructors frame instructional tasks in relation to the content to teach a fundamental calculus concept—derivatives—with inquiry. There is still very little basic research on the instruction of calculus and even less on those that promote ‘active learning’(Larsen et al., 2017) . The existing research has mainly attended to the learning of calculus ideas and the content and cognitive orientation of non-instructional tasks (e.g., exams and textbooks; Tallman et al., 2016; White & Mesa, 2014) . This scarcity of knowledge about what happens in calculus classrooms is discouraging, given that the course has been notorious for being a gateway for many students to follow a STEM pipeline or graduate from college (Blair et al., 2018; Bressoud, 2012) . While lecture still dominates calculus lessons (Laursen, 2019), implementing more inquiry has been promoted to make calculus more accessible. However, research on inquiry teaching in undergraduate mathematics, which has mainly focused on pedagogical variables rather than the content, does not always suggest positive student outcomes (e.g., Johnson et al., 2020) . Alternatively, I attend to the content instructors and students interact with in these classrooms to operationalize inquiry teaching in relation to the content. Using inquiry as the context to study calculus tasks is valuable, as it allows uncovering a wide range of calculus-specific instructional tasks, given that inquiry in undergraduate mathematics education is often characterized by students’ discovery of mathematical ideas through engagement with sequences of mathematical tasks (Laursen & Rasmussen, 2019) . Here, I specifically focus on the tasks that instructors proposed for teaching the graphical representations of derivatives: slope of tangent line, as derivative at a point; and the derivative function, as a graph. More precisely, I address the following research question: How do college Calculus I instructors, who teach with various inquiry approaches, frame instructional tasks to introduce the graphical representations ofthe derivative? 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. 864 Articles published in the Proceedings are copyrighted by the authors. Literature Review The ample research on the learning of derivatives graphically suggests its importance for students’ understanding of derivatives (e.g., García-García & Dolores-Flores, 2021; Ubuz, 2007) . Borji et al. (2018) and Hähkiöniemi (2006) confirmed the importance of the graphical representations of

FAQs

What is the main focus of the study?

The study investigates how calculus instructors frame instructional tasks, using inquiry practices, to introduce derivatives graphically to students.

Which two graphical tasks are emphasized in the findings?

The findings focus on (1) derivative at a point as the slope of a tangent line, and (2) derivative as a function presented by its graph.

How do instructors characterize their task-framing approach in inquiry?

Instructors frame tasks through situations involving graphing, conjecturing, and calculating, even though the exact tasks and situations differ across instructors.

Oct 15, 2026

Uploaded by Jordan Avery