Student Knowledge and Misconceptions

Abstract

ion is frequently mentioned as a core skill developed when learning programming (Ginat & Blau, 2017). This is similar to the ways in which the learning of algebra is described (Sfard, 1995). Research about practices for helping students adapt to the abstraction involved in algebra may be helpful for identifying pedagogical strategies that could be applicable to CS. In particular, here we will focus on a sequence of instruction called concretetorepresentationaltoabstract, or CRA (Witzel et al., 2008), which we argue might be applicable to computing instruction. 3.4.1 Evidence from Outside of Computing To introduce the basics of CRA we will use the example of a classroom where young students are learning addition. CRA begins by introducing a physical (i.e., concrete) object. For example, this could be physical blocks that could be counted to add them together. once students are comfortable adding together sets of physical blocks, the class could advance to solving the same problems given only a picture (i.e., representation) of the blocks, but not the physical blocks. once students are comfortable using only the pictures, the class could advance to solving the same problems using only numbers (i.e., abstraction). If a student has trouble adding together only numbers (i.e., working at the abstract level), they could be encouraged to draw pictures (i.e., returning to the representation level). If a student has trouble adding together numbers using a drawing, they could be encouraged to work with the physical blocks (i.e., returning to the concrete level). As shown in this example, the concrete, representational, and abstract forms of the problem can be used to “promote overall conceptual understanding and procedural accuracy and fluency” (Witzel et al., 2008, p. 271). Witzel et al. (2008, Table 27.2 Overlap between logical operators AND, ifthen, and ifandonlyif. A B ANd ifthen ifandonlyif