Cameron Setter

The following is a slide taken from NCETM Checkpoints. I was happy with the fraction pair on the right but the left stumped me! Then I had that 'aha' moment!  What I used to do I never used to teach equivalent fractions like the one on the left to my classes. I would just use arrows to multiply both numerator and denominator to find an equivalent fraction, very similar to the fractions on the right.  The issue with this though is, like me, students don't necessarily see all of the multiplicative relationships between the fractions as well as within the fraction. They are missing that key knowledge to support them answering the first pair of fractions.   What I do now Ratio tables allow students to see those multiplicative links. By doing this it makes questions like the checkpoints task much easier for students to do.  Disclaimer: this isn't the only way I teach equivalent fractions. I also show students how prime factors can also help us. There will be a future...

One of our department focusses for this year has been around encouraging students to talk like Mathematicians. Previously there was an issue with too much talk happening and not enough students engaged in the work. As a school we went the opposite way and pushed for silence during the time students were working. Now we are at a stage where behaviour and off task talking is no longer an issue so we want to look at the next step. We initially focussed on our questioning and ensuring students are giving full answers and using correct mathematical terminology. (We have had a real drive on literacy and ensuring students clearly understand what different words mean and how they can be used etc.) However we have noticed that this means only a select minority actually get the chance to use these words and talk about the maths that they are doing.  This week we spoke about introducing some of the Kagan structures in lessons, when appropriate, to encourage that discussion. I used some of the...

How would you answer the question above? How would you teach students to answer it? What I used to do When introducing Speed, I previously used a formula triangle much like the one below. Explained what S, D and T stand for. Completed a few examples on the board before setting some questions for students to complete themselves. As I wander around the room, I notice lots of students have done 72 x 20 (this is incorrect). I pause the class and go through this particular question showing students that minutes and hours are different and how they should have done 72 x 1/3 = 24 miles. Very quickly, I have hands up. Students haven't fully understood what to do. Where did 1/3 come from Sir? - Not understanding converting time Why is it multiply when they are next to each other? What does it mean with the D on top of S? - remembering how to use the triangle effectively Where does the S go? - forgetting the formula Teaching using a formula triangle is ineffective. Students aren't being ...

As part of my NCETM course we had the opportunity to watch some videos of teachers from Shanghai teaching some concepts.  It struck me the language they were using even for topics such as introducing what an angle is. New words would be introduced early on, clearly defined, backed up with examples and reinforced with students applying the word in context. Consistent high level language that is built on as the topic deepens can then be used to avoid misconceptions and gives students and teachers a common language to be able to communicate effectively.  🔊 Listen:  Becoming educated speaking to Michael Child's about his book The Sweet Spot. In the podcast the underlying focus was on optimizing teaching whether through improving your classroom layout or ensuring time is better spent on improving explanations than peeling displays for your classroom. Listen here .  📚 Read: My blog on the benefits of using Ratio tables in the classroom. Over the next few weeks I will be ...

Only 36% of students were able to answer the question on the right. Whereas 75% of students were able to correctly answer the problem on the left. (7) Why? What's the big difference?  Students are more likely to relate values between objects (left question) than within an object (right question). (7) A similar issue comes up in the questions below. 91% getting the bottom question correct, relating 11 people to 33 people. Whereas only 51% answered the top question correctly.  Students often struggle to see all of the multiplicative links between and within values. One of the misconceptions my own students had with the right 'L' question was that the answer was 45. They had added 13cm because 8 + 13 = 21 on the base of the 'L'. "Young children tend to see multiplication additively" Dietmar Kuchemann   DfE suggests teaching multiplication as repeated addition, with arrays, in Yr2. Yr3 scaling is introduced but after that isn't mentioned again. It is as...

My trainee and I have been discussing the importance of transitions in a lesson. One of his work ons has been to make them 'snappier' so students are focussed and on task quickly after explaining what to do.  Good transitions start with clarity in instructions. By clearly stating what you expect to see students doing there is no grey area and students know the expectations. Non compliance can then be followed up according to the behaviour pathway. E.g. "On the board is 5 questions, I'd like you to write down the answers with workings into your book. This is to be done by yourself, in silence. You have 5 minutes, off you go."  Next is to make use of the word 'go' to help create a sense of urgency. Go is associated with racing and so it encourages students to get on with the work straightaway. Following this, for the first 30s of setting students off on a task, the teacher just stands and observes. The first 30s is where students will fall into bad habits, t...

I have been utilising ratio tables more and more in my lessons at the moment and it has given me a bit of a realisation.  If I am teaching a topic where I want to show students and additive relationship between values e.g. how adding 10% and 5% gives 15% then I will use bar modelling to show this. If I want to show a multiplicative relationship then I will use ratio tables. E.g. 10% X 1.5 = 15%.  Obviously there are certain scenarios where one would be more beneficial than the other. But if I strip my teaching right down to the essentials I feel that these two representations allow me to demonstrate to students most concepts they will come across in Secondary School I am in the process of writing a series of posts in how I use ratio tables so keep an eye out for it. In the mean time, the following thread is a great start from Sam Blatherwick.  🔊 Listen: High performance podcast with Scotland Football Manager Steve Clarke. One quote in particular stood out for me "don't ...