Developing Multiplicative Thinking and Algebraic Reasoning by Solving a Practical Problem: The Skyscraper Growing Pattern Problem

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken, where no explicit strategies were modelled by the teacher at the start of the problem-solving process (Hourigan & Leavy 2022). Instead, once the teacher introduced the problem, these Year 3 students solved a range of mini-challenges using their own invented strategies. During the planning phase, the teachers had predicted various ways students may see and understand the characteristics of the growing pattern (Friel & Markworth 2009; Markworth 2012). This paper explores the modifications made to the problem context to promote engagement, the range of approaches adopted by two different classes of Year 3 students in response to the problem challenges, as well as the role of the teacher in guiding students to understand the problem and in orchestrating the sharing of student strategies.