Learning to solve more challenging mathematics problems using multiple strategies has been promoted by research and is a feature of numerous curricula. Yet teachers have been found to be reluctant to incorporate these tasks into their lessons predicting resistance from students. This study examined 87 senior secondary students' reactions to a challenging quadratics task as part of their teachers' participation in a design-based research project. It sought insights into students' own perspectives on challenge and multiple strategies in mathematics teaching and learning, with the intent of understanding more about the cognitive, affective, and motivational aspects of this teaching approach. In responding to open-ended prompts, the students reported diverse but generally positive reactions related to their interest in the task and its relevance for their learning. Two thirds reported that they liked learning strategies from peers, and two thirds liked learning multiple strategies from their teacher. Implications for considering secondary students' preferences for learning, engagement, and motivation in mathematics lessons are discussed.