Making sense of math grades
Guided Practice versus Independent Practice
We so often hear from students that they "get it" when the teacher shows it to them, but they can't do it on their own.
When a student struggles in math class, it is usually a product of a disconnect between "being shown how" by the teacher and "doing it yourself" by the student. "Guided Practice" is where a teacher demonstrates a lesson and the students follow along. "Independent Practice" is where the student engages the material alone.
So when a student "gets it" when shown but can't "do it" alone, there is a disconnect between the Guided and Independent Practice.
The Connector: Feedback
What connects -- or in its absence, disconnects -- Guided and Independent Practice is feedback. When a teacher provides feedback by showing the answers to an entire class, students may not be getting any real feedback because the teacher is not addressing that student's own process directly, or, worse, the teacher assumes the student knows something that he or she does not, which renders the entire lesson meaningless.
Math lessons accumulate vertically
The same process of Guided practice, Independent practice and feedback applies to all classes, but it usually shows up in math class first. The reason for it is that math lessons build vertically whereas in other courses they accumulate laterally. In other words, in math, each lesson tends to be a required element for success in the next, so if the student misses something from the first he or she will not follow the next. In other classes, the basic skill sets are usually repeated within distinct units so there is great opportunity to figure it out along the way, whereas in math the student just gets lost.
Guided v. Independent Practice - and Feedback
Please see this short video for a demonstration of how it works:
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