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.

Transformations, including symmetry and rotations, are important in solving mathematical problems. Meta-cognitive functions are considered critical in solving mathematical problems. In the current study, we examined prospective teachers’ use of meta-cognitive functions while solving mathematical-based programming problems in the Scratch environment. The study was conducted among 18 prospective teachers, who engaged in a sequence of mathematical problems that utilize Scratch. The data sources included video recordings and solution reports while they performed mathematical problems. The findings indicated that the participants developed their meta-cognitive functions as problem solvers related to both mathematics and programming aspects. The findings also indicated that the participants developed regulation meta-cognitive functions more than awareness and evaluation ones in mathematical and programming aspects.

Task design, in general, and task design in a technological environment, is attracting the attention of educational researchers. The present research investigates task design of prospective teachers in the Scratch programming environment. A total of twenty-three female prospective teachers participated in a professional development program. They were in their third academic year majoring in teaching mathematics and computer science in the middle school. The prospective teachers attempted to design mathematics-based programming problems. The present research utilizes the theory of didactical situations in mathematics, specifically the situation types, the paradoxes of the didactical contract and the situation components, to study the task design of the prospective teachers. It does that by focusing on one group of prospective teachers. The research results indicated that the prospective teachers were concerned mainly with the situation of information, situation of reference and situation of action. Doing so, they were concerned with the paradox of the said and the unsaid, the paradox of uncertainty, and the paradox of devolution. In addition, they took care of both algorithmic and creative reasoning. They also took care of students′ devolution, where this devolution was conditioned with following an institutionalization. They were also concerned with giving students autonomy and encouraging decision making regarding the solution of the problem. Furthermore, they planned to enable students′ control over their learning.

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