It is very frustrating to me that many students (and an apparently-increasing number of administrators, politicians, text book authors, and even teachers) seem to think that the most effective way to learn math is to have students practice problems that are the same as problems that the teacher has already shown the class how to do (just with different numbers).
My school’s current algebra 1 textbook takes this to a whole new level. For many of the problems for students to work on, there is a box in the margin that lists the exact page number and example number for a worked-out problem which is structurally identical to what is being asked (just with different numbers).
This explicit encouragement to just plug new numbers into a worked-out problem is pretty disappointing. This kind of thing doesn’t encourage students to actually understand what they’re doing.
Even when trying an “I do, we do, you do,” there has got to be some novelty in the later problems that students will be working through. Students need to learn to expect that in EVERY LESSON they will need to apply the procedures they are learning in a NEW way in order to solve deeper questions. Thinking they understand the material when they are just able to replace the old numbers in the problem with new numbers is NOT a good sign. This particular textbook worsens this issue!
Here’s my rant: http://havingneweyes.com/2012/11/29/just-mimic-the-example-in-the-book-thats-learning-right/
Unfortunately, making the We Do and You Do structurally identical to the I Do is precisely what math CMs are taught at Institute. I still remember listening to my CMA tell me to copy/paste problems from my INM into my GP/IP (with different numbers) and thinking, “That can’t be right…” It’s a start, but math instruction needs to move past that.