The keys to this method: 1) Pre-assessment. I need to know exactly where everyone is, not because they're labeled gifted or LD but because I've seen them work on this type of problem and I've taken notes about what they're doing and how they can progress. 2) The opportunity to work through problems without being shown how to do it; I want them to build on their prior knowledge and use it as the basis for the skills they're developing. It's very, very easy to short-circuit this process, and this is the biggest pitfall that most teachers make when they think they're using constructivist teaching methods: instead of letting kids figure out the next level on their own, they try to jump them two or three levels at once by explaining. It doesn't work. 3) No marks. They are not graded on any of this until they've been working on it for several days, and even then, if I discover that they're not getting it, I'll turn the evaluation into a practice activity and we'll work on it some more. Nobody is well-served if I jump the gun and evaluate them before they've consolidated their learning. 4) Flexible groups based on observation, with plenty of opportunity to try problems that other groups are tackling. I'll generally have a series of problems available so that if a kid gets to the end of a problem before their group, I've got something just slightly harder for them to do. As often as possible, this involves a different way of looking at their work rather than just harder numbers. 5) Clear expectations. I want to be able to tell the lowest group when they've met the grade five expectations (which gets them a B) and I want to be able to tell the highest group that they're doing grade seven work. It's all laid out somewhere and I know exactly where I'd like to steer them next, no matter what level they started at. 6) A wide variety of manipulatives. In your pill box example, I'd be taking that group aside for practice with arrays and basic multiplication, but if another kid wanted to horn in on that lesson and proved they were ready for it, well, the more the merrier. Kids can use whichever manipulatives or resources they want to best model the problem for themselves. 7) Flexible assessments - some kids will be asked to write out an explanation, some will be asked to make connections, some will be asked to create a similar problem for someone else, some will be asked to find the patterns. If possible, they get a choice in how they show their learning. Often, if they can explain it to me out loud, I'll write down a mark without making them write it down.
Congratulations! You just got a crash course in constructivist mathematics at the junior level!
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1) Pre-assessment. I need to know exactly where everyone is, not because they're labeled gifted or LD but because I've seen them work on this type of problem and I've taken notes about what they're doing and how they can progress.
2) The opportunity to work through problems without being shown how to do it; I want them to build on their prior knowledge and use it as the basis for the skills they're developing. It's very, very easy to short-circuit this process, and this is the biggest pitfall that most teachers make when they think they're using constructivist teaching methods: instead of letting kids figure out the next level on their own, they try to jump them two or three levels at once by explaining. It doesn't work.
3) No marks. They are not graded on any of this until they've been working on it for several days, and even then, if I discover that they're not getting it, I'll turn the evaluation into a practice activity and we'll work on it some more. Nobody is well-served if I jump the gun and evaluate them before they've consolidated their learning.
4) Flexible groups based on observation, with plenty of opportunity to try problems that other groups are tackling. I'll generally have a series of problems available so that if a kid gets to the end of a problem before their group, I've got something just slightly harder for them to do. As often as possible, this involves a different way of looking at their work rather than just harder numbers.
5) Clear expectations. I want to be able to tell the lowest group when they've met the grade five expectations (which gets them a B) and I want to be able to tell the highest group that they're doing grade seven work. It's all laid out somewhere and I know exactly where I'd like to steer them next, no matter what level they started at.
6) A wide variety of manipulatives. In your pill box example, I'd be taking that group aside for practice with arrays and basic multiplication, but if another kid wanted to horn in on that lesson and proved they were ready for it, well, the more the merrier. Kids can use whichever manipulatives or resources they want to best model the problem for themselves.
7) Flexible assessments - some kids will be asked to write out an explanation, some will be asked to make connections, some will be asked to create a similar problem for someone else, some will be asked to find the patterns. If possible, they get a choice in how they show their learning. Often, if they can explain it to me out loud, I'll write down a mark without making them write it down.
Congratulations! You just got a crash course in constructivist mathematics at the junior level!