---
title: "Teaching and learning strategies for the derivative in engineering education: scoping review proto"
id: "plos-one-23-teaching-and-learning-strategies-for-the-derivative-in-engineering-education-a"
canonical_url: "https://medichelpline.com/clinical-feed/plos-one-23-teaching-and-learning-strategies-for-the-derivative-in-engineering-education-a"
content_type: "clinical_feed_article"
specialty: "General"
source_name: "PLOS ONE (Medicine)"
source_url: "https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0360253"
published_at: "2026-10-22T14:00:00.000Z"
evidence_level: "Journal Feed"
license: "CC-BY-NC-4.0 / Informational Use"
---
# Teaching and learning strategies for the derivative in engineering education: scoping review proto
## Provenance & Clinical Metadata
- **Canonical URL:** https://medichelpline.com/clinical-feed/plos-one-23-teaching-and-learning-strategies-for-the-derivative-in-engineering-education-a
- **Specialty:** [General](https://medichelpline.com/clinical-feed/general.md)
- **Primary Source:** PLOS ONE (Medicine)
- **Source URL:** [Original Journal Publication](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0360253)
- **Published At:** 2026-10-22T14:00:00.000Z
- **Evidence Rating:** Journal Feed
## Executive GIST (TL;DR)
- The protocol maps evidence on didactic strategies for teaching the **derivative** to undergraduate **engineering education** students, centering on the use of authentic engineering problems with or without **digital technologies**. - The review follows the JBI Manual for Evidence Synthesis and PRISMA-ScR reporting standards, with the PCC framework guiding inclusion: Population (undergraduate engineering students), Concept (didactic strategies grounded in authentic engineering problems), Context (higher education engineering programs). - Databases to be searched include Scopus, Web of Science, ERIC, and SciELO; languages limited to English, Spanish, and Portuguese; publication years 2000–2026. - Two independent reviewers will screen records using Rayyan; disagreements resolved by consensus. - Data extraction will use a pilot-tested form; synthesis will combine descriptive statistics, thematic categorization, and narrative summary of didactic strategies, problem types, and reported learning difficulties. - The protocol notes common student difficulties documented in the literature: reliance on symbolic procedures, weak limit concept understanding, and challenges with covariational reasoning required to interpret coordinated variation in dynamic contexts. - The literature describes instructional supports such as interactive tools (GeoGebra, simulators, visualization tools) and active-learning formats (problem- and project-based learning, flipped classrooms, interactive simulations). - The authors reported that the specific intersection—derivative, authentic engineering problems, and undergraduate engineering students—has not been previously synthesized in existing review literature, motivating the scoping review. - Scoping review limits are acknowledged: the approach maps evidence without conducting critical appraisal of methodological quality. - Funding and administrative details were disclosed; no competing interests were declared by the authors.
## Clinical Analysis & Structured Key Points
Teaching and learning strategies for the derivative in engineering education: A scoping review protocol | PLOS One Browse Subject Areas ? Click through the PLOS taxonomy to find articles in your field. For more information about PLOS Subject Areas, click here . Article Authors Metrics Comments Media Coverage Reader Comments Abstract The derivative is a fundamental concept in engineering education, as it enables students to model and interpret phenomena related to rates of change, optimization, and the analysis of physical processes. However, its teaching in higher education often emphasizes decontextualized algebraic procedures, with limited integration of authentic engineering problems and interactive digital technologies. This protocol outlines a scoping review aimed at mapping the available evidence on teaching and learning strategies for the derivative in undergraduate engineering education that incorporate authentic engineering problems, with or without the support of digital technologies. The review will follow the methodological framework proposed by the JBI Manual for Evidence Synthesis and the reporting guidelines of PRISMA-ScR. The review is guided by the PCC framework: (P) undergraduate engineering students; (C) didactic strategies for teaching and learning the derivative grounded in authentic engineering problems, with or without the support of digital technologies; and (C) higher education engineering programs. Searches will be conducted in Scopus, Web of Science, ERIC, and SciELO for peer-reviewed publications published between 2000 and 2026 in English, Spanish, and Portuguese. Two reviewers will independently screen and select studies using Rayyan, and disagreements will be resolved by consensus. Data will be extracted using a pilot-tested data extraction form and synthesized through descriptive statistics, thematic categorization, and narrative synthesis. The review will provide a comprehensive mapping of didactic strategies, types of authentic problems, and reported learning difficulties related to the derivative in engineering education. The findings are expected to inform instructional design and support the development of evidence-based teaching practices in calculus courses for engineering students. Citation: Galindo Illanes MK, Chamorro Manríquez DD, Herrera Valdés C (2026) Teaching and learning strategies for the derivative in engineering education: A scoping review protocol. PLoS One 21(10): e0360253. https://doi.org/10.1371/journal.pone.0360253 Editor: Manuela Mendonça Figueirêdo Coelho, Federal University of Ceara, BRAZIL Received: April 21, 2026; Accepted: September 24, 2026; Published: October 22, 2026 Copyright: © 2026 Galindo Illanes et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: No datasets were generated or analysed during the current study. All relevant data from this study will be made available upon study completion. Funding: Funding: This study was supported by Vicerrectoría Académica and Centro de Investigación para la Educación Superior – Fondo USS-FIN-2026_APC_VRA-014. The institutional support included participation in a research training program focused on the development of systematic and scoping review protocols, as well as funding for the Article Processing Charge (APC) associated with the publication of the final review. The funder had no role in the design of the protocol, preparation of the manuscript, or decision to submit it for publication. Competing interests: The authors have declared that they have no conflicts of interest. 1. Introduction The derivative plays a fundamental role in engineering education, providing a key mathematical tool for modeling rates of change, analyzing physical phenomena, and solving optimization problems [ 1 ]. Its application through authentic engineering problems has been recognized as an effective way to strengthen the connection between calculus instruction and engineering practice [ 2 ]. This mathematical concept connects mathematical reasoning with authentic engineering problems, where understanding it is essential for interpreting technical phenomena and making decisions based on quantitative models [ 3 ]. The ability to apply the derivative in real contexts enables future engineers to design efficient and sustainable solutions, thereby improving the quality and effectiveness of engineering projects. Despite its central role in engineering education, several studies [ 1 , 3 , 4 ] have documented persistent difficulties in teaching and learning the derivative in higher education. In particular, the predominance of operational conceptions and the use of symbolic procedures have been observed, together with limited integration of graphical, algebraic, and verbal representations within instructional tasks and explanations [ 1 , 4 , 5 ]. There is also evidence of limited understanding of the limit concept as the foundation of the derivative, as well as difficulties with covariational reasoning required to interpret the coordinated variation of quantities in dynamic situations [ 3 , 6 , 7 ]. These difficulties hinder the transfer of knowledge to authentic or plausible engineering situations, such as resource optimization and the interpretation of dynamic phenomena. To address these challenges, recent studies have proposed didactic strategies that promote conceptual understanding of the derivative [ 8 , 9 ]. Among the most prominent approaches are the use of interactive digital technologies —such as GeoGebra, process simulators, and graphic visualization tools [ 10 , 11 ]— and the incorporation of authentic engineering problems that support the representation, exploration, and integration of multiple meanings of the derivative as a mathematical object. Digital technologies have been shown to support the visualization, manipulation, and dynamic exploration of mathematical phenomena within contextualized learning environments. Similarly, authentic problems situated in real or plausible professional contexts support the interpretation and solution of complex engineering situations. For example, the literature describes tasks focused on resource optimization (cost-benefit), the analysis of variations in water flow, and the interpretation of rates of change in physical processes using realistic data drawn from engineering contexts [ 5 , 10 ]. In engineering education, differential calculus courses are implemented across heterogeneous curricular contexts, including variations in program duration, course sequencing, competency-based approaches, and instructional modalities [ 12 , 13 ]. This diversity reinforces the need to map how the derivative is taught and learned across different undergraduate programs and disciplinary contexts. Furthermore, a substantial body of evidence from engineering education supports the use of active learning approaches grounded in authentic and contextualized problem-solving, including problem-based learning, project-based learning, flipped classrooms, and interactive simulations. These approaches have been associated with improved academic performance and significant reductions in failure rates compared with traditional lecture-based instruction [ 14 – 18 ]. However, important gaps remain regarding how these approaches have been implemented specifically for teaching the derivative, the types of authentic engineering problems used in calculus instruction, and the role that digital technologies play in these instructional approaches. Despite these advances, the evidence on teaching and learning strategies for the derivative in engineering education that integrate authentic engineering problems, with or without digital technologies remains fragmented and heterogeneous. As a result, it is difficult to develop a comprehensive understanding of the current state of the evidence and to identify research trends, knowledge gaps, and opportunities for instructional design and instructional practice. Accordingly, conducting a scoping review was considered appropriate to map the available literature, characterize its main features, and clarify concepts and practices across diverse educational contexts. Scoping reviews are designed to map the scope, nature, and characteristics of the available evidence without critically appraising the methodological quality of the included studies [ 19 – 21 ]. A preliminary examination of review studies identified during the development of this protocol, complemented by exploratory searches of review literature indexed in Scopus and Web of Science during manuscript revision using combinations of the terms “derivative,” “differential calculus,” “engineering education,” “teaching,” “learning,” and “review,” suggests that the specific intersection addressed by the present scoping review—namely, didactic strategies for teaching the derivative through authentic engineering problems in undergraduate engineering education—has not been systematically synthesized in the existing review literature. Several reviews have examined active learning across science, technology, engineering, and mathematics (STEM) higher education. Freeman et al. [ 15 ] conducted a meta-analysis demonstrating that active learning increases student performance across STEM disciplines; however, their review was not restricted to engineering programs, did not focus on a specific mathematical concept, and did not examine authentic engineering problems as a distinct instructional approach. Similarly, Prince [ 16 ] reviewed active learning in engineering education and discussed general pedagogical approaches such as cooperative learning, problem-based learning, and project-based learning, without addressing the teaching of differential calculus or the derivative specifically. Reviews focused on technology-enhanced learning have likewise remained at a broader level. Reis et al. [ 22 ] synthesized evidence regarding immersive technologies in engineering education, while Sailer et al. [ 23 ] conducted a second-order meta-analysis of learning activities in technology-enhanced higher education. Although both reviews provide valuable insights into educational innovation, neither focuses on the derivative as a mathematical object nor on authentic engineering problems as a pedagogical context for calculus instruction. Similarly, Sukackė et al. [ 24 ] systematically reviewed active learning approaches in engineering education, including problem-based, project-based, and challenge-based learning, without focusing specifically on the derivative. Within mathematics education, research concerning the derivative has mainly focused on conceptual understanding, students’ difficulties, representations, and instructional processes [ 1 , 3 – 5 , 10 , 25 , 26 ]. To the best of our knowledge, no review was identified that simultaneously addressed (a) the derivative as the focal mathematical concept, (b) authentic engineering problems as the instructional context, and (c) undergraduate engineering students as the target population. Consequently, the present scoping review addresses a unique combination of three dimensions: the mathematical object (the derivative), the instructional vehicle (authentic engineering problems, with or without digital technologies), and the educational population (undergraduate engineering students). Mapping this evidence is a necessary first step toward understanding the current state of knowledge, identifying research gaps, and informing future instructional design and research in engineering mathematics education. The aim of this study is to map the available evidence on didactic strategies for teaching and learning the derivative in engineering education through authentic engineering problems and to identify the types of authentic engineering problems used and the main difficulties reported in students’ understanding and application of the derivative. Research question: What evidence does the academic literature provide on didactic strategies that use authentic engineering problems, with or without the support of digital technologies, for teaching and learning the derivative among engineering students in higher education? To address the study objective more precisely, the following sub-research questions are proposed: What types of authentic engineering problems are used in the teaching and learning of the derivative in higher education engineering programs? What didactic strategies have been implemented to teach the derivative through authentic problems in engineering education? What difficulties are reported in students’ understanding and application of the derivative in these contexts? What role do digital technologies play in didactic strategies based on authentic problems for teaching the derivative? 2. Methodology The review will follow a systematic sequence of stages: (i) formulation of the research question and eligibility criteria using the Population–Concept–Context (PCC) framework; (ii) development and implementation of the search strategy; (iii) reference management and deduplication; (iv) independent screening of studies by two reviewers; (v) systematic data extraction (charting); and (vi) narrative and thematic synthesis of the evidence. Each stage will be documented using the corresponding instruments, including the data-charting form, the PRISMA-ScR flow diagram, and the completed PRISMA-ScR checklist. 2.1 PCC framework The review is guided by the Population–Concept–Context (PCC) framework, which is recommended for scoping reviews. Population (P): undergraduate students enrolled in engineering programs in higher education. Concept (C): didactic strategies for teaching and learning the derivative or differential calculus based on authentic engineering problems, with or without digital technologies. Context (C): higher education engineering programs. This framework will guide the development of the eligibility criteria and the search, study selection, and analysis processes throughout the review. 2.2 Eligibility criteria Studies will be included if they involve undergraduate students enrolled in engineering programs and focus on teaching and learning the derivative or differential calculus in higher education through at least one authentic engineering problem, as operationally defined below by criteria A–D. The presence of an authentic engineering problem is therefore a mandatory inclusion criterion, whereas the use of digital technologies is optional and will be treated as a characteristic of the didactic strategy rather than as an eligibility requirement. Eligible sources will include peer-reviewed journal articles, academic book chapters, and full papers published in peer-reviewed conference proceedings. Eligible study types will include empirical studies, instructional experiences, intervention proposals, theoretical studies, and review studies, provided that they meet the Population, Concept, and Context eligibility criteria described above. The review will include studies published between 2000 and 2026, a period characterized by sustained transformation in higher education and, particularly, in engineering education. These decades have witnessed the incorporation of active learning approaches, digital technologies for learning, competency-based instructional design, and an increasing emphasis on flexible and innovative education [ 27 , 28 ]. These developments have fostered teaching approaches that reconsider the role of differential calculus and the derivative in engineering education while promoting learning experiences more closely connected to professional practice. Works published in English, Spanish, and Portuguese will be considered, as these languages account for a substantial proportion of the published research in mathematics education and engineering education in Europe and Latin America. Definition of didactic strategy For the purposes of this review, a didactic strategy refers to any planned instructional approach, pedagogical intervention, teaching sequence, learning activity, digital technology, or instructional design intentionally used to support students’ understanding and application of the derivative. Examples may include problem-based learning, project-based learning, inquiry-oriented activities, modeling tasks, technology-enhanced instruction, simulations, visualization tools, or instructional sequences specifically designed for differential calculus. The didactic strategy constitutes the pedagogical approach adopted by the study, whereas authentic engineering problems represent the contextualized tasks through which the strategy may be implemented. Definition and operationalization of authentic engineering problems For the purposes of this review, authentic engineering problems are conceptualized as tasks situated in realistic engineering contexts that require students to engage with mathematical ideas in ways that resemble professional engineering practice. Authenticity is understood not merely as the presence of a real-world context [ 29 ], but as the meaningful integration of disciplinary knowledge, decision-making, and interpretation within an engineering situation [ 30 , 31 ]. To ensure consistent identification of authentic engineering problems during study selection and data extraction, the following operational definition was developed for this review. A task will be classified as an authentic engineering problem when it simultaneously satisfies the following four criteria: A. Mathematical centrality. The derivative—understood as a function, a rate of change, a linear approximation, or a tool for optimization—is the primary mathematical object that the task requires students to calculate, construct, interpret, or apply. Tasks in which the derivative appears only incidentally, as a by-product of another procedure, or is provided as a given result without student engagement in its use will not satisfy this criterion. B. Engineering situatedness. The context of the task corresponds to a phenomenon, system, process, or decision recognizable as belonging to at least one engineering discipline (e.g., civil, mechanical, electrical, chemical, industrial, or systems engineering). This criterion is satisfied when the engineering context is necessary for understanding the task and cannot be replaced by an abstract mathematical setting without altering its meaning. C. Empirical grounding of data. The numerical values used in the task are drawn from real measurements, technical standards, empirical records, or are explicitly described as representative of plausible engineering conditions. Tasks based on arbitrary numerical values whose representativeness is neither stated nor reasonably inferable from the disciplinary context will not satisfy this criterion. D. Functional use of the derivative. The application of the derivative produces a result that is meaningful within the engineering context described, such as identifying an optimal design parameter, quantifying the rate of a physical process, predicting system behavior, or supporting a technical decision. Tasks in which the derivative is used solely to practice differentiation procedures without interpretation of the result within the engineering situation will not satisfy this criterion. A study will be considered to contain authentic engineering problems when it reports at least one task satisfying criteria A–D simultaneously. Studies that refer to authentic, contextualized, or real-world problems only in general terms, without providing sufficient information to assess these criteria, will not be classified as involving authentic engineering problems. Exclusion criteria specific to authenticity A task or study will be excluded on the basis of insufficient authenticity when any of the following conditions appl
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