The Pancake Story and the Epsilon–Delta Definition

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1 Scopus citations


The complexity in understanding the ϵ–δ definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between ϵ and δ that structures the definition. I designed the story from an anti-deficit perspective on students’ mathematical thinking. I leverage students’ intuitions about quality control, and explicitly build on students’ prior knowledge that I gathered from student interviews. I illustrate the utility of the story in supporting students’ sense-making of the formal definition by sharing changes in students’ claims and justifications about the relationship between ϵ and δ. Students' justifications also provide examples of the kind of thinking an instructor might expect to see in the classroom when using the story. I end the paper with some classroom implications and a teaching episode illustrating how students might use the story to make sense of limit more broadly.

Original languageEnglish (US)
Pages (from-to)662-677
Number of pages16
Issue number6
StatePublished - 2021


  • Calculus
  • anti-deficit approach
  • informal knowledge
  • limit

ASJC Scopus subject areas

  • General Mathematics
  • Education


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