{
  "abstract": "This qualitative case study investigated first-year undergraduate students’ challenges with calculus and how those challenges can be addressed with a focus on related rates problems. This study was undertaken at a University of Technology in South Africa, involving two groups: control (n = 145) and experimental (n = 136). In the control group lessons were conducted via the traditional approach. Lessons were conducted in a collaborative classroom setting for the experimental group during which participants’ muddiest points at the end of each lesson were investigated and analysed using thematic content analysis. Action–Process–Object–Schema (APOS) theory was applied as theoretical framework. Newman’s error analysis model and APOS theory were employed as data analysis tools in identifying students’ challenges. Whereas the former was applied in identifying students’ problem-solving challenges, the latter was utilised to monitor and assess students’ mental constructions when solving related rates problems. Group activities, classroom observations and a standardised test were modes for data collection. The researchers established from this study that: (1) participants who encountered comprehension error and transformation error were unable to operate at the Action level; and (2) finding participants’ muddiest points at the end of each lesson is an appropriate intervention strategy for uncovering students’ challenges in solving related rates problems. The researchers, therefore, recommend finding participants’ muddiest points at the end of related rates lessons to identify, address and minimise students’ challenges. Contribution: This study offers practical insights into formative assessment for improving conceptual understanding in undergraduate calculus.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Education, Faculty of Arts and Design, Durban University of Technology, Durban",
    "Department of Mathematics, Faculty of Applied Sciences, Durban University of Technology, Durban"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Fitzgerald Abakah"
    },
    {
      "affs": [
        1
      ],
      "name": "Deonarain Brijlall"
    },
    {
      "affs": [
        0
      ],
      "name": "Pholoho Morojele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9wnb47yybx1b.bib",
  "cited_by": 0,
  "doi": "10.4102/pythagoras.v47i1.872",
  "fulltext_url": "https://pythagoras.org.za/index.php/pythagoras/article/view/872",
  "id": "e9wnb47yybx1b",
  "issns": [
    "1012-2346",
    "2223-7895"
  ],
  "landing_url": "https://doi.org/10.4102/pythagoras.v47i1.872",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "LB5-3640"
    ],
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2611|Mathematics Education and Programs"
    ]
  ],
  "openalex": "W7215118481",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "AOSIS",
  "ris": "https://research.draconitic.com/paper/e9wnb47yybx1b.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T14:21:08Z",
      "native_id": "051506b02f2742b2992a32a410fa08d4",
      "source": "doaj",
      "url": "https://doi.org/10.4102/pythagoras.v47i1.872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Mathematics Education and Programs",
      "subfield": "general"
    }
  ],
  "title": "An Action–Process–Object–Schema study on first-year undergraduate students solving related rates problems",
  "title_text": "An Action–Process–Object–Schema study on first-year undergraduate students solving related rates problems",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T14:20:22Z",
  "url": "https://research.draconitic.com/paper/e9wnb47yybx1b",
  "venue": "Pythagoras",
  "versions": []
}