Agreed, as developing the atom-stringing process is behind the idea of faded worked examples, surely? I'm intrigued by the idea of starting at -3 though: I always start at zero myself, work out the positive substitutions of x first and then do the negative values afterwards. I teach my students to spot the pattern and use it to verify the negative x-subs as that's where mistakes are most likely to occur. Some colleagues have even dispensed with negative values of x altogether, though I'm uncomfortable with that as an end point.
Thank you Craige for highlighting the importance of a thoughtful approach to atomisation, acknowledging the need to balance breaking down complex concepts into manageable parts with allowing students to apply their knowledge independently.
I strongly agree with your insightful observation about the delicate balance in atomisation. Breaking down complex concepts into smaller, more digestible 'atoms' is undoubtedly a powerful pedagogical tool, but it's essential to avoid the pitfall of over-scaffolding.
As you mentioned, gradually increasing the complexity of tasks allows students to develop a deeper understanding and the ability to apply their knowledge to novel problems.
However, I believe there's also value in providing opportunities for students to grapple with challenges and make mistakes. By allowing them to 'fall into the pit,' we can foster resilience, critical thinking, and a growth mindset.
Formative assessment plays a crucial role in this process. By regularly monitoring student progress, we can identify areas of strength and weakness and provide targeted support. This enables us to guide students towards more efficient and effective problem-solving strategies, empowering them to independently chain and bind atoms of knowledge to achieve desired outcomes.
Agreed, as developing the atom-stringing process is behind the idea of faded worked examples, surely? I'm intrigued by the idea of starting at -3 though: I always start at zero myself, work out the positive substitutions of x first and then do the negative values afterwards. I teach my students to spot the pattern and use it to verify the negative x-subs as that's where mistakes are most likely to occur. Some colleagues have even dispensed with negative values of x altogether, though I'm uncomfortable with that as an end point.
Thank you Craige for highlighting the importance of a thoughtful approach to atomisation, acknowledging the need to balance breaking down complex concepts into manageable parts with allowing students to apply their knowledge independently.
I strongly agree with your insightful observation about the delicate balance in atomisation. Breaking down complex concepts into smaller, more digestible 'atoms' is undoubtedly a powerful pedagogical tool, but it's essential to avoid the pitfall of over-scaffolding.
As you mentioned, gradually increasing the complexity of tasks allows students to develop a deeper understanding and the ability to apply their knowledge to novel problems.
However, I believe there's also value in providing opportunities for students to grapple with challenges and make mistakes. By allowing them to 'fall into the pit,' we can foster resilience, critical thinking, and a growth mindset.
Formative assessment plays a crucial role in this process. By regularly monitoring student progress, we can identify areas of strength and weakness and provide targeted support. This enables us to guide students towards more efficient and effective problem-solving strategies, empowering them to independently chain and bind atoms of knowledge to achieve desired outcomes.
Have a great day.