A Trajectory for Advancing the Meta-Cognitive Solving of Mathematics-Based Programming Problems with Scratch

Wajeeh Daher,Otman Jaber,Nimer Baya’a,Juhaina Awawdeh Shahbari

doi:10.3390/sym12101627

Wajeeh Daher, Otman Jaber + Show 2 more

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https://doi.org/10.3390/sym12101627

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Abstract

It is the intention of the current study to suggest a trajectory for the advancement of prospective mathematics teachers’ use of meta-cognitive skills in solving mathematics-based programming problems with Scratch. Scratch is a code-based program that can be utilized in teaching various disciplines, especially geometry and its rich range of subjects such as the topic of symmetry. The present study suggests that advancing prospective teachers’ meta-cognitive skills in the Scratch environment could be done through problem solving and negotiations. The present paper analyzed the implementation of the trajectory by two pedagogic supervisors who attempted, in the frame of one-year preparation (2018–2019), to educate 18 prospective teachers to use meta-cognitive skills in mathematics-based programming activities, where this attempt was based on problem solving and negotiation processes. Data were collected through videoing and recording the learning sessions of the prospective teachers and was analyzed using deductive and inductive constant comparison methods. The deductive analysis utilized theoretical models of meta-cognitive processes and negotiation processes. The research results indicated that the negotiation processes supported the development of the prospective teachers’ meta-cognitive processes in solving mathematics-based programming problems with Scratch.

Highlights

Tools and strategies are suggested as means that empower students in their mathematics problem solving activity
Development in using meta-cognitive skills in their solving of mathematics-based programming problems: (1) negotiating the skills needed for solving the programming problems: programming skills and meta-cognitive skills; (2) problem solving for developing the prospective teachers’ knowledge of Scratch programming; (3) negotiating the meta-cognitive processes with Scratch programming when the prospective teachers solve programming problems individually; (4) negotiating, in groups, the meta-cognitive skills with Scratch; and (5) negotiating, independently, the use of meta-cognitive skills in programming with Scratch
We describe each of the trajectory processes, but first we describe the initial awareness of the prospective teachers regarding using meta-cognitive skills in programming

Summary

Introduction

Tools and strategies are suggested as means that empower students in their mathematics problem solving activity Two such tools and strategies are technology (e.g., [1,2]), especially programming (e.g., [3]), and meta-cognition (e.g., [4,5,6]). Scratch utilization in mathematics has been considered a factor that assists students’ and prospective teachers’ learning of mathematical concepts and relations, on the topic of symmetry (e.g., [8]). This is especially important as symmetry is one of the main concepts in mathematics. Yanofsky and Zelcer [9] argue that considering mathematics on the basis of symmetry can help in answering important questions as to what mathematics is, why we are certain of mathematics, and why we see the semantics of mathematics in line with the semantics of scientific discourse (p. 495)

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