Examining reasoning-and-proving in the treatment of complex numbers in Irish secondary mathematics textbooks

This study examined student tasks in the area of complex number operations in six Irish secondary mathematics textbooks and a Project Maths teaching and learning plan for reasoningand-proving (RP) opportunities. At the ordinary level, 9.1% of 1274 student tasks were coded as RP. At the higher level, 13.3% of 1373 tasks were coded as RP. The majority of argument opportunities in ordinary level materials were the lowest form of argument -proofwriting exercises. At the higher level, the majority of argument opportunities were within argument-specific or argument-general categories. Less than 2% of the tasks at the ordinary or higher level involved pattern identification or conjecture development. Students were not asked to test conjectures, construct counterexamples, develop proof subcomponents, or formulate RP objects in any of the seven sets of materials. Only one RP task appearing across all seven sets of materials involved the use of technology. The implication of these results as well as how textbook materials could be redesigned using the RP framework are discussed.