The professional practice of designing tasks: how do pre-service early childhood teachers promote mathematical processes in early algebra?

Abstract Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers’ professional practice of designing tasks. According to this, our aim is to analyze the ways in which pre-service early childhood teachers understand the mathematical processes in the professional practice of designing early algebra tasks and to identify how they intend to promote these processes through the tasks. Content analysis techniques were used to examine the designed tasks. To illustrate the data analysis and results, six tasks are presented. As a result, pre-service early childhood teachers associate problem solving with challenges and questions. They understand problems as unfamiliar situations but ignore the relationships between students and tasks. Moreover, they do not encourage exploration of phases of problem solving and tend to use strategies more suitable for routine tasks. Communication is identified in all the tasks designed, encouraging interaction and discussion. However, only one task explicitly promotes mathematical language. For reasoning and proof, pre-service teachers begin to use questions to elicit explanations and justifications, but do not encourage verification strategies and various modes of reasoning. The process of connections is only present in one task, reflecting the fragmented nature of mathematics teaching. We conclude that the professional practice of designing mathematical tasks is a powerful in teacher education. However, training programs should place greater emphasis on the meaningful use of mathematical processes.