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Secant–tangent transition applet characterized via the conceptual-structure variables

Design · All designs
Evidence · no claims cited

Description

An interactive applet illustrates the metadata characterization: it represents a function graphically with a secant line defined by two points, one varying with a parameter h; as h approaches zero the secant converges to the tangent. It is characterized as derivative at a point (conceptual), with essential prior knowledge of functions, graphical interpretation, and slope, graphical predominant representation with implicit coordination of multiple representations, and process-level conceptual construction.

Design Implications

Context

Requirements

  • The resource must make the secant-to-tangent transition accessible as a process, consistent with the process level in APOS theory

Constraints

Target Learners

  • high school mathematics students learning the derivative

Learning Goals

  • interpreting the derivative as a limiting process

Claims

Examples

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Key Sources

  • Estefany Castillo Ventura, Javier Ulises Solis Lastra, Anarosa Alves Franco Brandão. (2026). WIP: Bridging the Gap Between Instructional Design and Pedagogical Use: A Framework for Mathematics Educators. https://arxiv.org/abs/2606.20934
Page metadata
Field Value
type design
id secant-tangent-transition-applet-example
title Secant–tangent transition applet characterized via the conceptual-structure variables
description An interactive applet illustrates the metadata characterization: it represents a function graphically with a secant line defined by two points, one varying with a parameter h; as h approaches zero the secant converges...
status review
generated by process:settle-candidates on 2026-10-10
trust unverified — no one has confirmed this page's content
sources 1 — estefany-castillo-ventura-2026

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