Table 4 Summary of computational concepts and how they are applied in CT-based mathematics context
CT concepts | CT concepts as defined in the reviewed literature | CT concepts as applied in CT-based mathematics context | Additional references from the reviewed literature |
|---|---|---|---|
Variable | An entity that can “store, retrieve, and update values” (Ng & Cui, 2021, p. 6) | A numerical (e.g., number of times to carry out a specific mathematical procedure; Ng & Cui, 2021), algebraic (e.g., result of operating with two or more variables; Dickes et al., 2020; Kaufmann & Stenseth, 2021; Ng & Cui, 2021), or geometric (e.g., movement of a point having a variable location on a circle; Sinclair & Patterson, 2018) representation of an entity whose values can be stored, retrieved and operated on | None |
Conditionals | “Instructions that either perform an action or not, according to a given condition” (Rodríguez-Martínez et al., 2020, p. 319) | A set of decisions, actions, statements executed based on numerical (e.g., when a number equals a certain value; Ng & Cui, 2021), algebraic (e.g., when a parametric equation determines the amount of rotation of the wheels; Ng & Cui, 2021; Sinclair & Patterson, 2018) or geometric properties (e.g., when a draggable point determines how much a given shape is scaled by; Sinclair & Patterson, 2018) | Jurado et al. (2020); Rodríguez-Martínez et al. (2020); Sáez-López et al. (2019) |
Loops | “The control structure that makes it possible to repeat one or more sequences multiple times” (Rodríguez-Martínez et al., 2020, p. 319) | Repeatedly carry out a mathematical procedure, e.g., a numerical calculation (Cui & Ng, 2021), or geometric construction (Dickes et al., 2020; Jurado et al., 2020; Miller, 2019; Sinclair & Patterson, 2018) | |
Sequences | “The sequence or structure of instructions that should be followed to complete a goal” (Rodríguez-Martínez et al., 2020, p. 319); or “a series of individual steps or instructions to be executed by the computer” (Ng & Cui, 2021, p. 6) | A sequence of steps set up according to mathematical rules or logic to perform a particular instruction for solving a mathematical task, e.g., to program a sequence of codes for testing prime number and then illuminating the LED lights accordingly (Ng & Cui, 2021); to move the robot based on a target geometric pattern (Jurado et al., 2020; Muñoz et al., 2020) | |
Events (handling) | “Handle one thing that causes another to happen” (Brennan & Resnick, 2012, as cited in Ng & Cui, 2021, p. 6); and “Instructions that make it possible to interact with objects in the programming environment” (Rodríguez-Martínez et al., 2020, p.319) | When an instruction that can be converted into mathematical information is executed, another instruction related to it with numerical (e.g., as pressing a button the variable “day” increases by 1, and another variable “the balance” will increase by 222; Ng & Cui, 2021) is executed | |
Subroutines | “A procedure that can be called within another procedure” (Sinclair & Patterson, 2018, p. 68) | A set of instructions designed to perform a specific mathematical procedure or task (e.g., geometric construction; Sinclair & Patterson, 2018) that can be used repeatedly within a program | None |
Operators | “Provide support for mathematical, logical, and string expressions” (Brennan & Resnick, 2012, as cited in Ng & Cui, 2021, p. 6) | The of use of symbols or functions to denote or perform a mathematical (e.g., > , < , mod, ceiling, floor) or logical operation (e.g., AND, OR; Ng & Cui, 2021) | None |