Today I had the enormous privilege to visit St Martin's Voluntary Academy in Stoke Golding. A colleague and I were there to see the use of Connecting Maths Concepts, a Direct Instruction Program that was developed in the United States. I am looking to use these materials to support some pupils who have struggled with maths in the past, and if successful to integrate them into the small group intervention work we do with pupils at my school.
I suspect some will be surprised to hear that from me, particularly after my recent podcast with Craig Barton so allow me to clarify. I am 100% of the opinion that developing understanding of mathematical concepts slowly and carefully is the best way to teach maths, both from a pupil outcome point of view and from a "this is what maths is" point of view. For me, this is what maths teaching should like, and this is what the experience of learning maths should be. So why then would I be looking at a program that (at least on the surface) seems to be entirely about developing "procedural fluency" in isolation? Well for two reasons:
1) I believe that developing understanding carefully and slowly is the best way of going about teaching maths, and that most pupils will develop a strong and flexible understanding of maths by working in this way. But I am not naive enough to think that this will work 100% of the time for 100% of the pupils. It would always be my start point, but for some this will not be enough. We already know that understanding on its own is not enough for retention- pupils forget even those things that in the moment they appear to understand. This is why it is important, even when building understanding of concepts, to plan in opportunities to revisit and re-use ideas. I often refer to this as "picking up an idea", pupils need to pick up ideas they have seen before, play with them for a bit, and then put them down again. And some need a lot more of this revisiting than others. The benefit of this program is that it is at least 80% revisiting previous ideas. And they are built on directly. The links between (for example) adding and subtracting decimals and comparing the sizes of decimals are explicitly made. Couple this with the fact that kids were getting stuff right. Lots of stuff. By some estimates kids in these programs answer up to 500 questions in an hour. And they get the vast majority right. Now I know that maths is not about just "getting it right", but imagine being that kid that only ever got things wrong. That barely even did anything compared to their peers and then mostly got it wrong. Perhaps the only time they got it right was when they had an adult supporting them. Would you be minded to explore the depths of that subject? I know I wouldn't. What I saw today was pupils having the opportunity to be successful in what they saw as maths, something they probably hadn't experienced for the first 6 or 7 years of their education, and then being shown how this can lead them to getting other things right. And I definitely don't think that is a bad thing for eventually supporting pupils to have the productive disposition to explore maths further. Coupled with this is the simple lack of mathematics these pupils have encountered relative to their peers. Whilst the value of "30 million" has been challenged in recent years, it is clear that there is a word gap between disadvantaged pupils and their peers when they start school, and this often widens to the detriment of the eventual outcomes of these pupils. I suspect that part of the power of DI programs is simply the amount of mathematics questions that pupils have to engage with, which will seek to redress any gap in the amount of exposure these pupils have had in relation to their peers.
2) I am far from convinced that these programs have to focus on procedural fluency in isolation. Having worked with Rosenshine's principles of instruction, cognitive science and teaching for mastery principles, I have seen how there is much more to connect them than separate them. Infact this will be part of the subject of my talk at ResearchEd Rugby. It may be that some DI programs do focus exclusively on procedural fluency, but that is not what I saw today. I saw pupils using images of tens frames and larger grids to support their making sense of addition. I saw them making sense of what it means to be a quadrilateral, a triangle, a rectangle, through being exposed to and identifying examples and non-examples. I saw pupils being forced to develop their thinking and language through intelligent questioning, both verbally in the display materials. I saw pupils being expertly guided by their teacher, the fantastic Chloe Sanders who took great care of both myself and my colleague all afternoon.
I would have been happy for the visit to have stopped there, as I had everything I wanted at that point. Instead we were treated to what can only be described as a visit fit for royalty. Firstly treated to lunch with the head, Clive Wright where we had the chance to talk about their journey with DI, discuss the progress of the Knowledge Schools Hub and Chloe's exciting upcoming visit to America to the National Institute for Direct Instruction to talk with (among others) Kurt Engelmann, son of the legendary late Siegfried Engelmann. Then whisked on a tour of the school and seeing the fantastic culture that the team at St Martin's have developed. Every lesson had pupils working with expertly designed materials, taught well by teachers whose expertise were recognised and celebrated, and in classrooms where behaviour was utterly impeccable. A big part of this was the utterly ruthless consistency of application in every classroom. All pupils have access to the same material and challenge, with those who need it supported to achieve as well as others. Every classroom has the same routines, but rather than being stifling to pupils these allow pupils a sense of ease - they know what is expected of them and what they can expect from their teachers. This allows for a relaxed atmosphere where pupils and teachers work together seamlessly for the benefit of all. Everything is thought of and planned, from the lesson materials (not all scripted for DI, but all explicitly taught) to the resealable cans of still water that are available that cut down on plastic waste.
I am honestly not sure I can adequately put into words just how impressive our visit was. My heartfelt thanks have to go to Clive and particularly Chloe who took such good care of us, as well as to all the pupils and staff at St Martin's who accommodated us. I would heartily recommend you visit for yourself if you can and see the incredible work going on at this school - make contact with the Direct Instruction Hub and see it for yourself!
I suspect some will be surprised to hear that from me, particularly after my recent podcast with Craig Barton so allow me to clarify. I am 100% of the opinion that developing understanding of mathematical concepts slowly and carefully is the best way to teach maths, both from a pupil outcome point of view and from a "this is what maths is" point of view. For me, this is what maths teaching should like, and this is what the experience of learning maths should be. So why then would I be looking at a program that (at least on the surface) seems to be entirely about developing "procedural fluency" in isolation? Well for two reasons:
1) I believe that developing understanding carefully and slowly is the best way of going about teaching maths, and that most pupils will develop a strong and flexible understanding of maths by working in this way. But I am not naive enough to think that this will work 100% of the time for 100% of the pupils. It would always be my start point, but for some this will not be enough. We already know that understanding on its own is not enough for retention- pupils forget even those things that in the moment they appear to understand. This is why it is important, even when building understanding of concepts, to plan in opportunities to revisit and re-use ideas. I often refer to this as "picking up an idea", pupils need to pick up ideas they have seen before, play with them for a bit, and then put them down again. And some need a lot more of this revisiting than others. The benefit of this program is that it is at least 80% revisiting previous ideas. And they are built on directly. The links between (for example) adding and subtracting decimals and comparing the sizes of decimals are explicitly made. Couple this with the fact that kids were getting stuff right. Lots of stuff. By some estimates kids in these programs answer up to 500 questions in an hour. And they get the vast majority right. Now I know that maths is not about just "getting it right", but imagine being that kid that only ever got things wrong. That barely even did anything compared to their peers and then mostly got it wrong. Perhaps the only time they got it right was when they had an adult supporting them. Would you be minded to explore the depths of that subject? I know I wouldn't. What I saw today was pupils having the opportunity to be successful in what they saw as maths, something they probably hadn't experienced for the first 6 or 7 years of their education, and then being shown how this can lead them to getting other things right. And I definitely don't think that is a bad thing for eventually supporting pupils to have the productive disposition to explore maths further. Coupled with this is the simple lack of mathematics these pupils have encountered relative to their peers. Whilst the value of "30 million" has been challenged in recent years, it is clear that there is a word gap between disadvantaged pupils and their peers when they start school, and this often widens to the detriment of the eventual outcomes of these pupils. I suspect that part of the power of DI programs is simply the amount of mathematics questions that pupils have to engage with, which will seek to redress any gap in the amount of exposure these pupils have had in relation to their peers.
2) I am far from convinced that these programs have to focus on procedural fluency in isolation. Having worked with Rosenshine's principles of instruction, cognitive science and teaching for mastery principles, I have seen how there is much more to connect them than separate them. Infact this will be part of the subject of my talk at ResearchEd Rugby. It may be that some DI programs do focus exclusively on procedural fluency, but that is not what I saw today. I saw pupils using images of tens frames and larger grids to support their making sense of addition. I saw them making sense of what it means to be a quadrilateral, a triangle, a rectangle, through being exposed to and identifying examples and non-examples. I saw pupils being forced to develop their thinking and language through intelligent questioning, both verbally in the display materials. I saw pupils being expertly guided by their teacher, the fantastic Chloe Sanders who took great care of both myself and my colleague all afternoon.
I would have been happy for the visit to have stopped there, as I had everything I wanted at that point. Instead we were treated to what can only be described as a visit fit for royalty. Firstly treated to lunch with the head, Clive Wright where we had the chance to talk about their journey with DI, discuss the progress of the Knowledge Schools Hub and Chloe's exciting upcoming visit to America to the National Institute for Direct Instruction to talk with (among others) Kurt Engelmann, son of the legendary late Siegfried Engelmann. Then whisked on a tour of the school and seeing the fantastic culture that the team at St Martin's have developed. Every lesson had pupils working with expertly designed materials, taught well by teachers whose expertise were recognised and celebrated, and in classrooms where behaviour was utterly impeccable. A big part of this was the utterly ruthless consistency of application in every classroom. All pupils have access to the same material and challenge, with those who need it supported to achieve as well as others. Every classroom has the same routines, but rather than being stifling to pupils these allow pupils a sense of ease - they know what is expected of them and what they can expect from their teachers. This allows for a relaxed atmosphere where pupils and teachers work together seamlessly for the benefit of all. Everything is thought of and planned, from the lesson materials (not all scripted for DI, but all explicitly taught) to the resealable cans of still water that are available that cut down on plastic waste.
I am honestly not sure I can adequately put into words just how impressive our visit was. My heartfelt thanks have to go to Clive and particularly Chloe who took such good care of us, as well as to all the pupils and staff at St Martin's who accommodated us. I would heartily recommend you visit for yourself if you can and see the incredible work going on at this school - make contact with the Direct Instruction Hub and see it for yourself!
