Because math can be so broad, I viewed the Problems of Practice through the lens of the the Standards of Mathematical Practice. Whether I am teaching Algebra 1, Practical Geometry, Algebra 2 Honors, or College Prep, these problems appear in each class. When thinking about directive vs. constructive pedagogical strategies, I often found myself reflecting on how although I want students to get to the constructive place for all problems, I also recognize that in order to do so, some directive strategies are necessary to get there.
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As someone who struggled with math in school, these sound like great ideas for helping support students and their math skills! I've helped with summer school math these last couple of weeks and am seeing many of the same things you see. Like Nigel said below, If it doesn't look exactly the same as the example they struggle with application. These strategies can be used across multiple grade levels.
Lots of good examples here! My students are the same when it comes to connecting past material to new situations as well as the process to application relationship. I find myself covering the same general concepts over and over because they only remember and apply it to the exact scenario (piece of music) that it was discussed with. Sometimes it just feels like I'm going in circles.
I too focused of the Problems within the Practice standards. I was trying to decided what standards to focus on, (fifth) since I am very familiar with those standards after teaching them for the last six years, or (kindergarten) since in my new position those will be the mathematics standards I will be working with most. However, in brainstorming common problems that came up during instruction I realized that many of the kinds of issues would be the same across the grade levels. The mathematical practices that students needed to focus on were quite similar.
By aligning the process to the standards, you have created opportunities for students to incorporate technology tools to meet the challenges they face across the math discipline. I can see how constructivist strategies would be the primary method of instruction for the discipline. It is nice to see how many of the technology tools you have found can help students build those skills!