Yes that is definitely an option! I think Brendan would agree that eventually moving to flexible pictorial and then abstract representations are always the goal, so when you can have concrete as optional it’s best to move students along towards the more pictorial and abstract
Great demonstration, thank you. Something I’ve been grappling with is how to prevent expertise reversal effect for the high ability students in a mixed ability class. I love the clarity of explicit instruction but wonder whether some students will feel like they are sitting there waiting for other students to catch up. Does it make sense to move some students more quickly to the independent practice phase rather than expecting the whole class to sit through the explanations. I think high ability students do still need explicit teaching (when they are introduced to new concepts or content), but at a much more challenging level (where you would lose the other students). It’s the tricky hinge point of fluency vs challenge to maintain motivation. Are you able to address expertise reversal effect in one of your future episodes please? I’d love to hear your thoughts - particularly in the secondary context.
Great point! I like to have more independent practice activities prepared than I think anyone will be able to complete. Generally, I will still have the whole class start with me, even if I suspect some students may already know what I'm about to teach. The main reasons for this is because I don't know if they've picked up bad habits and also want to ensure that they use the same language as me. Once they've shown competence, I can release them for independent practice.
We can also play around with the types of questions. This way, you present the same task, but differentiate it based on your questioning. e.g. What’s the same and what’s different about these two problems? How do you know your answer is correct? Can you draw this? Anne Watson and John Mason have done some great work on this.
The other way to tackle this issue is by having a gradient of challenge available in the CFU questions and independent task so there is always more challenging examples and problems for students to solve once they complete the base and medium level ones designed for all or most students.
Hi Alex, I think it’s ok to move students on, but explicit sequences tend to be over quite quickly because of their efficiency. We try to find other ways to meet the needs of gifted learners like workshop style lessons that are streamed, once a cycle. Great suggestion re expertise reversal and differentiation to the top. Thank you.
Great episode. Re Concrete-pictorial-abstract, would you agree it can also be useful for some students to use counters as a quick way to show commutative property? Especially for students who may readily move counters into position but take longer to complete the task if they had to draw the dots.
Getting students to use manipulatives is actually a great way to assess conceptual understanding.
Keep coming back to the purpose. The reason why we want to move to the abstract representation is because it allows them to access higher levels of mathematics, but if they don't understand what the abtract symbol/concept represents, then they probably need time with manipulatives.
Yes that is definitely an option! I think Brendan would agree that eventually moving to flexible pictorial and then abstract representations are always the goal, so when you can have concrete as optional it’s best to move students along towards the more pictorial and abstract
Great demonstration, thank you. Something I’ve been grappling with is how to prevent expertise reversal effect for the high ability students in a mixed ability class. I love the clarity of explicit instruction but wonder whether some students will feel like they are sitting there waiting for other students to catch up. Does it make sense to move some students more quickly to the independent practice phase rather than expecting the whole class to sit through the explanations. I think high ability students do still need explicit teaching (when they are introduced to new concepts or content), but at a much more challenging level (where you would lose the other students). It’s the tricky hinge point of fluency vs challenge to maintain motivation. Are you able to address expertise reversal effect in one of your future episodes please? I’d love to hear your thoughts - particularly in the secondary context.
Great point! I like to have more independent practice activities prepared than I think anyone will be able to complete. Generally, I will still have the whole class start with me, even if I suspect some students may already know what I'm about to teach. The main reasons for this is because I don't know if they've picked up bad habits and also want to ensure that they use the same language as me. Once they've shown competence, I can release them for independent practice.
We can also play around with the types of questions. This way, you present the same task, but differentiate it based on your questioning. e.g. What’s the same and what’s different about these two problems? How do you know your answer is correct? Can you draw this? Anne Watson and John Mason have done some great work on this.
The other way to tackle this issue is by having a gradient of challenge available in the CFU questions and independent task so there is always more challenging examples and problems for students to solve once they complete the base and medium level ones designed for all or most students.
Hi Alex, I think it’s ok to move students on, but explicit sequences tend to be over quite quickly because of their efficiency. We try to find other ways to meet the needs of gifted learners like workshop style lessons that are streamed, once a cycle. Great suggestion re expertise reversal and differentiation to the top. Thank you.
Great episode. Re Concrete-pictorial-abstract, would you agree it can also be useful for some students to use counters as a quick way to show commutative property? Especially for students who may readily move counters into position but take longer to complete the task if they had to draw the dots.
Getting students to use manipulatives is actually a great way to assess conceptual understanding.
Keep coming back to the purpose. The reason why we want to move to the abstract representation is because it allows them to access higher levels of mathematics, but if they don't understand what the abtract symbol/concept represents, then they probably need time with manipulatives.
By the way here is the video of Brendan’s teaching in full: https://youtu.be/UvnkX-7BTGY?si=gT0Aevi6TweuEBc5