{"title":"Using algorithmic thinking to design algorithms: The case of critical path analysis","authors":"Timothy H. Lehmann","doi":"10.1016/j.jmathb.2023.101079","DOIUrl":null,"url":null,"abstract":"<div><p>Algorithmic thinking is emerging as an important competence in mathematics education, yet research appears to be lagging this shift in curricular focus. The aim of this generative study is to examine how students use the cognitive skills of algorithmic thinking to design algorithms. Task-based interviews were conducted with four pairs of Year 12 students (n = 8) to analyze how they used decomposition and abstraction to specify the projects, designed algorithms to solve scheduling problems by first devising fundamental operations and then using algorithmic concepts to account for complex and special cases of the problems, and tested and debugged their algorithms. A deductive-inductive analytical process was used to classify students’ responses according to the four cognitive skills to develop sets of subskills to describe how the students engaged these cognitive skills.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Behavior","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0732312323000494","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
Algorithmic thinking is emerging as an important competence in mathematics education, yet research appears to be lagging this shift in curricular focus. The aim of this generative study is to examine how students use the cognitive skills of algorithmic thinking to design algorithms. Task-based interviews were conducted with four pairs of Year 12 students (n = 8) to analyze how they used decomposition and abstraction to specify the projects, designed algorithms to solve scheduling problems by first devising fundamental operations and then using algorithmic concepts to account for complex and special cases of the problems, and tested and debugged their algorithms. A deductive-inductive analytical process was used to classify students’ responses according to the four cognitive skills to develop sets of subskills to describe how the students engaged these cognitive skills.
期刊介绍：
The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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