What is Mathematical Beauty? Teaching through Big Ideas and Connections

Mathematics is a beautiful subject. Ask mathematicians and others what they love about the subject and they will talk about the amazing connections that thread through the terrain, unifying the different ideas. There are not many facts or methods to remember in mathematics but there are a few really big and important ideas that are connected to each other and that infuse the subject. Yet when we ask students what they think math is, most will say that it is a lot of different rules and methods. This is really unfortunate as students who believe mathematics is a set of methods to be remembered are the lowest achieving students, worldwide, as revealed by PISA data (Boaler & Zoido, 2016). So, why do so few students, or teachers, see mathematics as a set of rich ideas and connections? One of the reasons is that teachers are given sets of standards to teach and no matter how good the standard writers are, they all cut mathematics up into small pieces and give teachers small atomized content areas – usually a set of methods – to teach. The connections disappear – teachers cannot see them and they are lost from students’ learning pathways. Instead, teachers see the lists of content – often 100 or more methods in a year – and work systematically through them. This often leads teachers to skim through content quickly as when mathematics is disconnected and offered in small sections there is a lot to get through in any year. The connections between ideas are invisible and students do not develop one of the most important insights into mathematics that they can develop – that mathematics is a set of connected, big ideas.