The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have difficulty with basic multiplication table fact retrieval. Difficulty retrieving multiplication facts directly influences students' ability to engage effectively in factorisation of quadratics, since factorisation is a process of finding products within the multiplication table. Students also find it challenging to recognise and understand varied representations of the same quadratic relationship. In her own classroom, she has explored various pedagogical strategies in order to mediate for the challenges that she has outlined--everything from rehearsal to real world applications. However, she felt that her pedagogical efforts lacked the necessary insight on how the brain creates memory and felt that her pedagogical directions might be enhanced with this knowledge. Therefore, in order to construct her own classroom solutions, she turned to cognitive science to assist her in better understanding the mechanisms of fact retrieval. She surmised that problems with quadratic relations might potentially be linked to the ways in which the brain constructs cognitive representations and this knowledge might in turn inform her pedagogical decision-making as a classroom teacher. This article is a sharing of her investigation, discussing the linking of cognitive science to pedagogy, as well as making the right kind of mathematical memories. She also discusses long-term semantic memory together with varied representations and classroom implications. (Contains 1 table.)