Peter Sullivan

Emeritus Professor, Monash University

April 2025

One of the alarming features of the current emphasis on explicit teaching is the production of scripted resources for teachers to use in their mathematics classes. Of course, teachers can benefit by access to ideas suggesting engaging ways of teaching. But this is quite different from materials that are intended to be reproduced by the teacher and delivered verbatim.

My main concern is the message this sends to teachers. I want teachers to be career-long learners about the science and the art of teaching mathematics. This is partly about the ways mathematical ideas connect and develop, but it is also related to engaging students in thinking about such ideas for themselves. It would be preferable for teachers to wonder how particular ideas might be applied and managed, and to become a better teacher through a process of enacting, reflecting, evaluating and revising those ideas.

Another concern about such lock-step resources such as scripted slide shows, is the expectation that teachers follow the script, irrespective of different ways students may respond. Every teacher knows the students in their classroom reflect a diversity of prior experience, motivation, confidence, concentration and attention. For any given experiences on any given day, there will be students who are confused by the pace or who lack relevant prior experience, and others who are bored, since they have mastered the content already. One of the most important qualities teachers need to develop is to be responsive and adaptable to the differing needs of their students.

Even worse, is that many of such resources are of extremely doubtful validity, both mathematically and pedagogically. They seem not to have been even trialled in classrooms.

Many resources propose a daily review consisting of a set of slides to which students respond perhaps by writing on mini whiteboards or maybe chorusing answers. In nearly of all of the examples I have seen, some questions are not suited for this format and others are trivial. A particular concern is that none of the questions in this scripted review phase anticipate or connect to the lesson to come. Not only does this increase the cognitive load during the subsequent learning, but there also seems no chance for teachers to remediate misconceptions exposed during the review phase, even if the majority of students’ responses are incorrect or confused.

It is hard to image ANY experienced teacher not being able to develop better lessons than the scripted ones I have seen. Mathematics is about connections, intuition and application. The scripted lessons I have seen are not connected to the curriculum and achievement standards, they seem deliberately designed to minimise other connections to the specific idea that is the focus of the lesson, teachers are instructed to forbid intuitive approaches, and applications and connections to reality are minimised because allegedly they exacerbate cognitive load. But it is critical that students build connections between ideas in more or less every lesson, they are encouraged to use their own intuitive thinking processes and to experience mathematics as useful.

In other words, not only will teachers not increase their skills and confidence from using scripted lessons, but also it is highly likely they would be de-skilled by the process. The best way for teachers to respond would be to create their own daily reviews connected to the upcoming lesson content and to plan and sequence their own lessons based on the various resources to which they have access.