This post was written by Rosalind Walker (@Rosalindphys) in preparation for the Cognition in Science meeting in July.

Below are some of the key points from the articles listed on the “Mastery links” page. As with the “Memory and Retrieval” summary, this is not intended to be a comprehensive review but rather a starting point for discussion and further work.

History and key points of the Mastery model

Mark McCourt tells the story of mastery in early 20th century America, as pioneered by Carleton Washburne, Henry Clinton Morrison, and later Benjamin Bloom. The model was founded on a belief that “every single child could be successful in the “common essentials”.

The program would present learning material in a logical and tested sequence, with the course broken down into small steps. After each step, the student is given carefully designed questions, which test their understanding and knowledge. The materials are designed with complementary solutions and explanations so that the student receives immediate feedback, allowing both the student and teacher to act in real time”.

Later, Henry Clinton Morrison “further developed the idea of immediate intervention, formulating a ‘variety of correctives’ which included ‘re-teaching, tutoring, restructuring the original learning activities, and redirecting student study habits.

What’s being done already

This quote from the EEF prompts Dan Williams to ask whether mastery is really all that different from “just good teaching”: “Typically, mastery approaches involve breaking down subject matter and learning content into discrete units with clear objectives and pursuing these objectives until they are achieved before moving on to the next unit. Students are generally required to show high levels of achievement before progressing to master new content. This approach differs from conventional approaches, which often cover a specified curriculum at a particular pre-determined pace”

Jemma Sherwood describes how her maths department is applying the mastery model:I start a unit with a list of its objectives, then drill down into what I want students to think about most, what I want them to practise most… Examples need to be extensive so that students have seen lots modelled by the teacher. They need to be sufficiently varied to allow students access to as many different thought processes as possible.  My planning becomes identifying these examples and the best source of practice for students… and lessons flow one to the next rather than being standalone”. Jemma adds that while this may seem like “just good teaching” to some, the atmosphere has changed from producing standalone lessons with things to match Ofsted checklists to taking as long as is needed, not being bound by hour-long lessons, and to teach for the learning rather than an observer.

In science, several people have written about equations, drill and automaticity. Pritesh Raichura blogged about using cognitive science to inform his approach to equations:

  • getting pupils to follow a defined method. whatever the content or equation
  • drilling pupils on equations, symbols for each variable, and units
  • interleaving examples during practice so pupils have to select the correct equation
  • modelling thought processes, layout, and checking using a visualiser
  • learning only one version of a formula (and NO formula triangles)

Eric Nelson blogged about the need for automaticity in procedures, to free up working memory, and Kristy Turner suggests a list of chemistry knowledge desirable for automaticity, including:

  • recalling the formulae of common substances
  • recalling with reasonable accuracy which are the metallic and non-metallic elements
  • balancing symbol equations
  • common sense checking of the magnitude answer in relation to the question
  • checking units

Things to think about

David Didau sounds some cautionary notes. Student performance is not the same as long-term learning, so we need to continually revisit previously mastered areas in order to fight the “forgetting curve”. Furthermore, describing an area as “mastered” may foster overconfidence in our pupils and lead them to in fact think about the area less and therefore forget what they have learned. Didau also points out that  At any one time, students think and believe more than one thing. These ideas compete with the older, more established idea usually winning out over the new idea. When we teach, students’ performance improves; the new idea comes to the fore. They seem like they’ve mastered it, but this is, as often as not, mere mimicry. Conceptual change, the pressure to transform or revise misconceptions as new understandings are learned is tricky. The old idea re-emerges and the new fades into the background. When we refuse to take students’ current performance as evidence of mastery, we acknowledge the difficulty of battling misconceptions. Change is gradual. It takes time and continual reintroductions of new ways of thinking for the change to stick and become permanent. My fear is that many mastery programmes miss this important truth and run the risk of making false and potentially damaging assumptions.”

Niki Kaiser blogged many interesting points raised in Twitter discussions around mastery in science including whether we can actually apply mastery to Science. The nature of scientific knowledge is important here. If mastery depends on a gateway/progression structure, this does not match all of science. For example, pupils need to master particle theory before they can explain the gas laws, but it is less clear that they need to master, for example, the wave equation before doing uses of the electromagnetic spectrum. These ideas link to the work Niki Kaiser has done on hurdles and bottlenecks. Science has a lot of depth in terms of explanation in some areas but also a great width in that there is a lot of description of phenomena, and there is often not a singular route from one area of knowledge to another.

Furthermore, in many cases the underlying principles that explain groups of phenomena are often highly abstract and challenging, and arguably are learned better later, rather than first as a gateway to the phenomena they explain. The concept of “potential”, for example, explains electric circuits, latent heat and gravitational potential energy, but few would argue that potential should be mastered before we can study any of these manifestations. So how does the structure and relations of concepts in science relate to the order we should put them in a mastery model?

There is a third aspect to the structure of scientific knowledge that must be considered, and that is the difficulty of questions we can ask. Some areas have an almost infinite number of levels of difficulty of questions it is possible to ask, and therefore it is clear which types of question need to be mastered first. Pupils must master interpreting chemical formulae before they can balance equations, for example, and we can introduce more complexity in the formulae in the equations. By contrast, selective breeding might have two or three possible levels of difficulty of questions, but after a point it becomes impossible to increase the difficulty of the question without introducing new content.

 What activities from mastery can we use?

Questions can be used for both practice and diagnosis, so question banks would be very useful. Teaching in response to diagnosed problems is a key feature of the Mastery approach, so Adam Boxer and I (see here) have developed what we now refer to as “Shed Loads Of Practice” or “SLOP” resources. Feedback is also very important.

However, a recurring obstacle that teachers raise when discussing Mastery, as with many things in Education, is that of time. How can we balance the demands of an increased curriculum load with the goal of “taking as long as it takes”?

Some questions to consider:

  1. What is mastery? Are we in danger of applying the term to too many things? Is it just “good teaching”?
  2. Can (and should) the Mastery approach be used in Science? If so, how and for which aspects of the curriculum? Which areas of the Science curriculum really lend themselves to being deconstructed, practised and then re-combined?
  3. What are the key difficulties with applying a Mastery approach to Science teaching?
  4. What resources are needed?




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