Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between teaching for understanding and procedural teaching is highlighted. An analogy is drawn with Charles Dickens' character, Mr Thomas Gradgrind, who would have endorsed procedural teaching and abhorred teaching that encouraged understanding. The work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between teaching for understanding and procedural teaching is highlighted.