TY - CONF

T1 - SORTING ALGORITHMS FOR 5TH AND 6TH GRADE STUDENTS: GREEDY OR COOPERATIVE?

AU - Di Paola, Benedetto

PY - 2016

Y1 - 2016

N2 - Our main research goal lies in a proposal to discuss the lack of, and improve, activities in the Italian school curriculum about discrete mathematics, computer algorithms and cryptography, especially for 3rd to 8th grade students. Activities of this kind are missing almost entirely, both in the school programs and in textbooks, despite many agree that they can be really useful to improve both general skills, such as reasoning and modeling, and skills particular to discrete mathematics, such as algorithmic and recursive thinking. A survey among various grades teachers confirmed this.The activity we are going to describe fits into a wider research project. Design research, chosen as the methodology to use, feels quite appropriate, as we are facing a brand new experience in an environment that we need to analyze carefully, i.e. on a local scale, considering all the different elements in the learning environment.The activity exposed in our paper is part of some lessons about sorting algorithms for 5th and 6th graders. From simple ordering to more efficient algorithms (quicksort as an example), we get to sorting networks and other variants.We focus on one single activity which is presented to students as a group task, giving them the rules, but with the goal that they find themselves the algorithm for the solution. The methodology used follows the principles of the Guided Reinvention of Mathematics and of RME (Freudenthal, 1973) and allowed us to highlight one particular and very important aspect discussed with the student: the relation between algorithms called greedy and others which are more group-oriented.A qualitative analysis of the results, through some videos recorded in the classroom, shows, according to Vygotsky’s perspective on the zone of proximal development (Vygotsky, 1981), how children, playing together, realize that some greedy algorithms might never work, if we want to achieve the group success. Some dynamics in which the game cannot finish if they seek to optimize their own result over the group result are shown.

AB - Our main research goal lies in a proposal to discuss the lack of, and improve, activities in the Italian school curriculum about discrete mathematics, computer algorithms and cryptography, especially for 3rd to 8th grade students. Activities of this kind are missing almost entirely, both in the school programs and in textbooks, despite many agree that they can be really useful to improve both general skills, such as reasoning and modeling, and skills particular to discrete mathematics, such as algorithmic and recursive thinking. A survey among various grades teachers confirmed this.The activity we are going to describe fits into a wider research project. Design research, chosen as the methodology to use, feels quite appropriate, as we are facing a brand new experience in an environment that we need to analyze carefully, i.e. on a local scale, considering all the different elements in the learning environment.The activity exposed in our paper is part of some lessons about sorting algorithms for 5th and 6th graders. From simple ordering to more efficient algorithms (quicksort as an example), we get to sorting networks and other variants.We focus on one single activity which is presented to students as a group task, giving them the rules, but with the goal that they find themselves the algorithm for the solution. The methodology used follows the principles of the Guided Reinvention of Mathematics and of RME (Freudenthal, 1973) and allowed us to highlight one particular and very important aspect discussed with the student: the relation between algorithms called greedy and others which are more group-oriented.A qualitative analysis of the results, through some videos recorded in the classroom, shows, according to Vygotsky’s perspective on the zone of proximal development (Vygotsky, 1981), how children, playing together, realize that some greedy algorithms might never work, if we want to achieve the group success. Some dynamics in which the game cannot finish if they seek to optimize their own result over the group result are shown.

KW - Math Education

KW - algorithm

KW - didactical transposition

KW - Math Education

KW - algorithm

KW - didactical transposition

UR - http://hdl.handle.net/10447/201911

M3 - Other

SP - 162

EP - 162

ER -