The role of porridge words in students’ mathematical thinking

Abstract Mathematical thinking can reveal growth and insights into conceptual understanding and mathematical processes and procedures. It is widely recognised that mathematical thinking is a multi-faceted, multi-modal, and complex process. In communicating mathematical thinking, students can use both specific mathematical terms and language or generic language. The use of generic language can facilitate mathematical thinking. However, there is little known about the processes that primary-aged students use in communicating their mathematical thinking to others. To address this, Edward de Bono’s (1971) practical thinking was used to identify specifically the use of ambivalent or vague terms or what de Bono refers to as porridge words that children use to facilitate the communication of their mathematical thinking. To identify the occurrence and frequency of porridge words, qualitative data in the form of children’s drawings, descriptions of their drawings, and responses were analysed using a retroductive process. Employing discourse analysis uncovered patterns in how students used porridge words to communicate their mathematical thinking. Discourse analysis identified four categories of porridge words: (1) generic porridge words; (2) conceptual use; (3) process or procedural use; and (4) invisible thinking. An aim of applying porridge words to students’ mathematical thinking was to make an ambiguous aspect of mathematical practice transparent and relatable. Encouraging students to clarify vague terms, or porridge words, explain their reasoning, and reflect on their word choices can support deeper understanding and promote more accurate communication of mathematical thinking.