My take is that their approach spirals the practice throughout later lessons, both as review problems and as building blocks for other ideas. For example, writing equations for proportional relationships comes up a LOT in later units. They return to it when looking at percent and slope and linear relationships. I'm not saying it's not helpful to have targeted practice right when you're learning a new concept (I supplement with this as well), but I find that retention is only really achieved when students return to a concept a few more times when they need it for future learning. Curious to hear your thoughts on that!
I think the way that IM spirals practice through later lessons is really well done and is one of the things I like best about their curriculum. In lots of cases that's enough. The issue is that here, writing an equation for a proportional relationship is foundational for lots of other important stuff that's coming up pretty quickly.
There's an activity I love in the very next lesson on centimeter/meter conversions. It emphasizes that there are two equations for each relationship -- you can convert m = 0.01cm or cm = 100m, and those numbers are reciprocals. That's a really cool mathematical idea! But if students are having trouble getting the equations right we either spend time discussing both, which dilutes the intended goal of that problem, or we breeze past the equation part, which reduces the value of the extra practice and can lead students feeling frustrated or confused.
A similar skill comes up later when we start graphing, and I would argue the same thing -- students should be focused on the new skill, which is graphing, and not grappling with writing equations while I want them thinking about the new idea.
Something I should have been clearer about in my original post is that this extra practice is mostly true in situations where the skill is a foundational part of future mathematical thinking. Something like the triangle inequality theorem I think we can have a reasonable debate about how much practice is needed, but the stakes aren't very high because it doesn't lead straight toward some of the big meaty mathematical ideas of 7th grade. A lack of practice with these types of equations ends up holding students back in the future, and that's why it felt more urgent to chunk some solid practice and feedback.
To your final point -- I agree about retention only happening when students return to a concept a few more times down the road. But more specifically, I want those encounters in the future to feel successful, not to feel like I'm reteaching something they quickly forgot.
My take is that their approach spirals the practice throughout later lessons, both as review problems and as building blocks for other ideas. For example, writing equations for proportional relationships comes up a LOT in later units. They return to it when looking at percent and slope and linear relationships. I'm not saying it's not helpful to have targeted practice right when you're learning a new concept (I supplement with this as well), but I find that retention is only really achieved when students return to a concept a few more times when they need it for future learning. Curious to hear your thoughts on that!
I think the way that IM spirals practice through later lessons is really well done and is one of the things I like best about their curriculum. In lots of cases that's enough. The issue is that here, writing an equation for a proportional relationship is foundational for lots of other important stuff that's coming up pretty quickly.
There's an activity I love in the very next lesson on centimeter/meter conversions. It emphasizes that there are two equations for each relationship -- you can convert m = 0.01cm or cm = 100m, and those numbers are reciprocals. That's a really cool mathematical idea! But if students are having trouble getting the equations right we either spend time discussing both, which dilutes the intended goal of that problem, or we breeze past the equation part, which reduces the value of the extra practice and can lead students feeling frustrated or confused.
A similar skill comes up later when we start graphing, and I would argue the same thing -- students should be focused on the new skill, which is graphing, and not grappling with writing equations while I want them thinking about the new idea.
Something I should have been clearer about in my original post is that this extra practice is mostly true in situations where the skill is a foundational part of future mathematical thinking. Something like the triangle inequality theorem I think we can have a reasonable debate about how much practice is needed, but the stakes aren't very high because it doesn't lead straight toward some of the big meaty mathematical ideas of 7th grade. A lack of practice with these types of equations ends up holding students back in the future, and that's why it felt more urgent to chunk some solid practice and feedback.
To your final point -- I agree about retention only happening when students return to a concept a few more times down the road. But more specifically, I want those encounters in the future to feel successful, not to feel like I'm reteaching something they quickly forgot.
Yes, this is totally my experience with IM as well!