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Publication# A Comparative Analysis of Tools & Task Types for Measuring Computational Problem-Solving

Abstract

How to measure students' Computational Problem-Solving (CPS) competencies is an ongoing research topic. Prevalent approaches vary by measurement tools (e.g., interactive programming, multiple-choice tests, or programming-independent tests) and task types (e.g., debugging problems or Parson problems). However, few studies have examined the measurement tools of CPS competencies themselves: affordances and limitations of the measurement tools and how they compare, or whether different task types might elicit CPS competencies differently. Research needs to address these questions in order to better understand how to design robust, generalizable, and effective measurement tools for CPS competencies. This paper presents an exploratory study that contributes to this research direction. It is part of a larger international project to develop an open-access formative assessment platform for CPS, which includes a novel authoring tool for a wide range of task types for interactive block-based programming. We used the tool to create an interactive programming experience with multiple task types and gave it to more than 300 secondary school students from different countries. We also administered a validated multiple-choice measurement of Computational Thinking with block-based programs. We focused on task complexity as a characteristic of task type, using a classification scheme based on task design features. Comparing students' performances on tasks of different complexity and using two distinct measurement tools, we found that the multiple-choice measurement only partially predicts performance in the interactive programming task. Additionally, its predictive capacity varies significantly between task types of differing complexity.

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Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Decision problem

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.

Average-case complexity

In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the algorithm, averaged over all possible inputs. It is frequently contrasted with worst-case complexity which considers the maximal complexity of the algorithm over all possible inputs. There are three primary motivations for studying average-case complexity.

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