Yesterday I stumbled across this paper by Jo Boaler, a professor of mathematics education at Stanford University, and it made my day. In her paper, Dr. Boaler describes a series of strategies used to address the strengths and weaknesses of all students in a diverse classroom. This is something that is often on my mind and has occupied a lot of my recent thinking. The challenge of meeting a wide variety of needs within a single math class is a hot topic at my school. While we are fully committed to differentiating instruction so that all students can be successful in a diverse classroom, there is a recurring pressure from families to stream math classes and accelerate gifted students.
All the strategies described in the paper have merit, which is demonstrated in the empirical results of her study, but the one that stood out to me was what she called the “multidimensionality” of the classroom. This is something I have tried (to varying degrees of success) to describe to parents who are eager to see their children accelerated through the math curriculum. Too often, mathematics and computation are seen as one and the same. Thus, students who are good at computation are often accelerated, regardless of whether they are good at other math skills like identifying patterns, formulating a question, selecting an appropriate skill or operation, communicating their reasoning and reflecting on whether their answer is reasonable.
Teaching math at an IB school, I have seen the benefits of a multidimensional math curriculum first-hand. The framework of math in the Middle Years Program requires that I assess students on their knowledge and understanding (computation), their ability to investigate patterns, communicate their reasoning using multiple forms of representation, and apply math in real-life situations. In doing this, I have found that all students experience success in at least one of the objectives and all students have room for improvement in at least one of the objectives. In general, the students who have an intuitive grasp of math tend to excel in knowledge and understanding assessment (like unit tests), but often struggle to articulate their reasoning. Conversely, students who struggle with the knowledge and understanding tend to articulate their reasoning very well because they have learned to work through problems one step at a time.
Meeting the needs of a diverse group of learners in one classroom is no easy task; however, by measuring success using a variety of objectives, even the most gifted math students will find an appropriate challenge.