What would it take to change your mind?
A question I ask, and consider, regularly
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An important question to ask yourself
This is my third and final newsletter reflecting on what I learned from my recent trip to Sweden.
Judging by the emails and messages I have received, my last two newsletters - one on vertical non-permanent surfaces and the other on an approach to teaching polygons - caused a bit of a stir. Many people told me in no uncertain terms that I was wrong. This is not a bad thing. As the economist Paul Krugman wrote recently: I used to say, only half-jokingly, that if a column didn’t generate a large amount of hate mail, that meant that I had wasted the space.
The ferocity of some of the responses made me think about one of my favourite questions: What would it take to change your mind?
Mini-whiteboards
Let’s take mini-whiteboards. I love them. In all the school support work I have done over the last five years, I have advocated using them throughout each phase of a maths lesson.
So, what would it take for me to change my mind?
In short, I would need evidence.
Last month, I observed a teacher as part of a coaching programme. This was the third time I had worked with the teacher, and she had agreed in advance that I could interrupt her lesson at any point. During her We Do - the topic was expanding double brackets - she Cold-Called five students to help construct the solution and then asked if anyone was stuck or had any questions. There was silence, so she set the students off on consolidation work.
At this stage, I went over and asked her: How many of your students got the We Do question correct?
She thought for a moment and replied: I have no idea.
She then spent the next six minutes circulating the room, dealing with students who had not understood the We Do and so could not start the consolidation exercise.
Long-time readers will know that I use the hypothesis model when coaching. I form a hypothesis and then gather evidence to support or refute it.
My hypothesis in this lesson was: Because the teacher has not seen all the students' responses to the We Do question, she will not know who answered correctly.
The evidence I gathered in the lesson supported my hypothesis.
In the coaching session that followed, we discussed this and together arrived at a new strategy: Using mini-whiteboards during the We Do - specifically, asking students to break down their solution into several steps, with a whole-class check for understanding after each step. This is a process I call Step-by-Step.
The following week, I was back in school and had an opportunity to see this strategy in action. This time, the lesson was on standard form. After the I Do, the teacher embarked on a We Do using mini-whiteboards and the Step-by-Step approach. After she finished and set the kids off on their consolidation work, I asked her the same question again: How many of your students can do the We Do?
This time, she replied: All of them except James, Emma, and Mo, who each went wrong in Step 2.
She then went straight over to them and tackled their misunderstanding in a small group.
This is great. But what would have happened if the teacher had been able to tell me exactly which students could not do the We Do when I asked the question the first time around?
The first difference is that I would not have suggested Step-by-Step in the coaching session, as the evidence I collected did not support it. Instead, I would have focussed on a hypothesis about another aspect of the lesson.
Longer-term, if I observed more teachers who did not use mini-whiteboards during the We Do and yet had a good sense of their students’ understanding, I would change my mind. I would no longer see them as an essential tool during this phase of a lesson and instead seek to learn how these teachers were gathering such information.
Mixed-attainment classes
Let’s take something more controversial. With the huge proviso that weaker, less-experienced teachers are not given the lower sets (as, unfortunately, they often are), I prefer and advocate for students being taught mathematics in sets rather than in mixed-attainment classes.
My hypothesis is as follows:
Because the range in attainment for any given class is smaller when students are taught in sets than in mixed-attainment classes, teaching can be more accurately tailored to students’ needs, so students perform better academically on average.
I could test this hypothesis by choosing two schools with similar demographics (the proportion of students with English as an additional language, those receiving Pupil Premium, etc.), one that teaches maths in sets, and the other that teaches maths in mixed-attainment classes (ideally up to GCSE, although most schools stop at Year 10). I would then compare their Progress 8 scores for maths, drilling down into the scores of both higher and lower prior attaining students. If mixed-attainment schools consistently outperformed schools that teach in sets, I would change my mind.
Why this question matters
I discussed mixed-attainment with an American colleague on my trip to Sweden. I asked if she would change her mind if the results demonstrated that students taught in sets have better academic outcomes. She said no, because she doesn’t believe that exam results wholly capture the benefits of mixed-attainment teaching. She mentioned things like social equity, self-esteem, empathy, and teamwork.
So, I asked her what would make her change her mind.
She said that nothing would. She believed with all her heart in mixed-attainment teaching, and for her, that was all that mattered.
I think that is a problem.
How can we know if our beliefs are correct if they are not refutable?
Sure, my ways of testing the efficacy of mini-whiteboards and mixed-attainment teaching are far from perfect. And if there are better experiments, then I will run those instead. However, I am prepared to change my deep-rooted beliefs based on evidence. I am not sure that is true of some of the teachers I meet (or who email me in response to my newsletters).
A challenge
So, dear reader, I have a challenge for you.
I would like you to choose something you believe deeply related to education. It could be a practice or technique (such as using mini-whiteboards) or something more philosophical (like mixed-attainment). In the comments, please tell me what that thing is, why you believe in it, and what it would take to change your mind.
What do you agree with, and what have I missed?
Let me know in the comments below!
🏃🏻♂️ Before you go, have you…🏃🏻♂️
… checked out our incredible, brand-new, free resources from Eedi?
… read my latest Tips for Teachers newsletter about seductive details?
… listened to my most recent podcast about the Do Now?
… read my write-ups of everything I have learned from watching 1000s of lessons?
… considered purchasing one of my new 90-minute online CPD courses?
… got your tickets for my Australian tour with Ollie Lovell?
Thanks so much for reading and have a great week!
Craig
Thanks for another though-provoking article, Craig!
What is the purpose of school?
I love Maths, and I love imparting knowledge to other people. Being a teacher is a no-brainer for me. But I have a love/hate relationship with schools. On the one hand, I think schools should stick to education and not be so focused on other things. For example, I want to teach mathematics. I don't want to be explaining to a teenager why throwing scissors across the classroom is bad (and then having to write a report about it too). I'm not their parent. I get that school have rules - uniform, mobile phones, etc. But if my students are engaged with my teaching, I don't want to have to send a student out of my class because they are wearing the wrong footwear.
So, on the one hand, I'm not too bothered about the things like "social equity" or things that can be learned from a mixed-attainment class (most of which can be learned in sets).
On the other hand, I want to get to know my students. Obviously, I want to know how they learn, so that my teaching will have the greatest impact. But I also want to know what their aims are in life. What level of Maths do they actually need to achieve those aims?
I am still in contact with many students who have now left school. I see some working at the local supermarket. I see some students mountainbiking trails I use. I see some students at local sporting events I'm involved in. One student (who would listen to music on her phone through headphones when completing her work, not disturbing anyone else, and I would check on her to make sure she understood) now runs the best pizza shop in my area. They are happy to talk to me because I took an interest in their lives.
But the purpose of school is not for me to be able to chat with students when they leave.
I believe that if schools (i.e. the leadership) encouraged teachers to ask the question "What level of [my subject] does each student need to achieve their aims in life?" then the quality of teaching would be better and student perception of school would improve. A lot of what schools do doesn't particularly benefit students later in life. I once wrote a list of nine things schools do where the reality is different. I showed it to a class and said, "I understand you. I understand why you get frustrated."
I honestly don't know what it would take to "change my mind", but my thoughts do definitely evolve over time.
I believe math is worth learning even if students won't use it beyond their schooling. For instance, I think learning the rules of solving multistep equations are worth learning. It's reasonable to me that a significant number of students won't need to solve multistep equations after they leave school. To me, it's worth learning because it is challenging, and learning challenging, abstract concepts is a chance to show students what they are capable of, to show them that they can learn hard things, which helps them develop valuable beliefs about their ability as learners in the future.
This would be a hard hypothesis to gather evidence on, because the outcome is far in the future. I wonder if there is an impact of effective intervention on students' future self-efficacy or growth mindset beliefs? I'd be curious what evidence could address this, it's just a hard thing to test directly.