According to Mark McCourt (@EmathsUK), 320 ideas, or leaps, are what students are expected to process in order to understand the entirety of our Mathematics Curriculum in the UK. In order to achieve an A* (or a soon to be level 9) at GCSE , a student, in 11 years of schooling, needs to take on board something entirely new 320 times. It was really interesting to have a figure placed on this, and really demonstrated how narrow our curriculum is. What is further demonstrated was how we excuse a lack of achievement when we really should not.
Mark described the UK teaching system as one of a conveyor belt, where students are sorted into those who learn enough to achieve the very highest grades, and we accept that others do not as we progress through the course material. Teaching for Mastery does not allow this to happen however.
Whilst regularly touted as a new approach to education, Mark points out that Mastery has it’s roots as far back as Aristotle’s dialogues with his students, and the key to Aristotle’s one-to-one approach was his constant building on prior knowledge, and ensuring that misunderstandings were dealt with as soon as they arose, before moving on.
Carelton Washburne, in the early 20th century, was a pioneer of taking these approaches, and beginning to develop methods for implementing this in a whole-class setting – retaining the features of immediate feedback and intervention in order to identify and correct misconceptions as quickly as possible. Carelton took a position working alongside Frederic Burk, who was working as superintendent of Winnetka School District, and it was here that he used a method of teaching that ensured that students were only able to progress through a carefully consider subject route if all of students had shown themselves to have understood all of the class content.
According to McCourt, “It was clear to Carleton that, rather than accelerating a small group of so-called gifted children, the purpose of schooling should be to ensure that every child is extended and successful.”
So teaching for Mastery is not something that involves “teaching Mastery Lessons on a Thursday,” or “spending a whole term on place value.” Mastery is a method of teaching that carefully considers the questions that are asked and the learning that they demonstrate has taken place. Mastery is about ensuring that all students are expected to retain all of the material that they are taught. Those that demonstrate that they have not, are given immediate support and correctional instruction in order to bring them up to pace, whilst those that achieve understanding are provided with resources and tasks that develop their depth of understanding of each topic. Pre-assessment of knowledge and understanding takes place through pre-testing of material, and only when the building blocks, or Jenga blocks as Mark refers to them, in a metaphor for knowledge acting as a support at each level, are secure, is another layer added.
In trying to précis Mark’s talk to our department on Monday, it became clear how complex and abstract this all becomes when comparing it to our current system of teaching, where we move our way through the Scheme of Learning Calendar, and move on from topics once their allocated time is up, regardless of whether the material has been truly and deeply understood. Of course as we teach the material, we are constantly asking probing questions, and planning tasks that both develop and demonstrate understanding, whilst intervening and supporting those that struggle. However, the difference with Mastery is that we do not move on until almost all (Mark sets his threshold at 80%, as an almost historical compromise between a number of educators and researchers) are at the required level of understanding. Furthermore it is a model of constant research, testing, adapting and working out what a group or cohort of students needs to really develop new knowledge. There is a need to develop carefully considered questions and testing that ensure that content has been grasped fully.
As previously mentioned, Mark told us that if we really consider that only 320 new ideas are required to grasp the entirety of our UK Mathematics curriculum, then our focus for effective teacher training should be to equip every teacher with 5 ways of explaining each of those 320 ideas. That equates to a toolbox of 1600 explanations that would allow a Maths teacher to be able to use a range of means by which to impart the understanding of the entire curriculum, over the course of 11 years. The use of a range of interconnected explanations ensures that a depth of understanding is achieved.
I’ve spent a lot of time over the last couple of days considering what I can do within my department to help to develop something that can at least start us on a journey toward something like this. I find myself fluctuating between a feeling of helplessness in the scale and level of change this would require, and a belief that it would be possible to begin a journey toward developing this, especially in conjunction with schools within a MAT. I have the feeling that it is something that is going to occupy my mind for a while, and probably lead to me boring my colleagues with “what if’s” and “how can we…?” I’m very much looking forward to the next parts of Mark’s blog, and considering whether this is a path that is viable in ensuring that we deliver the best chance for our students to get to grips with the Curriculum that we teach, and having an attitude that every student can achieve at the highest level. Whilst it may feel incredibly slow to start with, the hope is that this leads to such an improved level of understanding at the very basic level, that it becomes increasingly easier for students to make the links and leaps that they are required to make, and the levels of achievement seen in Winnetka during Burk’s time in charge of the District in the 1920s can be replicated as a result.