More MATH - CGI

I'm currently attending a 3 day CGI {Cognitively Guided Instruction} training (with 2 additional days later in the year). I signed up for the training so that I had a better understanding of what my students were coming to me with... I had always thought that CGI was ONLY for the lower grades (our 1st/2nd grade use CGI) - After today, I'm realizing that I can easily apply this philosophy to my math instruction. The basis of CGI is that students are allowed to investigate and discover their own methods to solve problems. They extend their strategy database though the modeling of other students {not the teachers}. I'm not going to lie....as a 3rd grade teacher - this FREAKS me out! Problem solving is so crucial in 3rd grade and this is a HUGE adjustment to how I currently teach problem solving. This book will definitely take me out of my comfort zone. I am going to try it and see how it works in my classroom. On another note....our instructor is very knowledgeable and has so many wonderful math resources. You can see her teacher store and wonderful math activities! She has great center activities and they are very inexpensive - go check her out! Here is her website with more freebies and resources.

Along with the training, we're also doing a book study with the above book. I would love to bounce ideas off of anyone who has read or who implements CGI in their classroom - especially in the upper grades! Here are my thoughts & questions so far with the first few chapters of this book:

Chapter 1:

• Students don't naturally solve problems the way that we do. They follow the action of the problems, similar to a recipe to solve the problem. For example Alyssa has 5 erasers. How many more erasers does she need to have 11? We would solve this problem by subtracting 5 from 11. However kids would take the 5 and count up till they got to 11. 
• Kids already have a knowledge base for mathematics, we need to tap into this background knowledge.
• Students should be allowed to discover their own strategies to solve problems. They will learn different ways to solve by sharing with their peers. Teachers should not model and impose our thinking on the students.
• Children don't have to be taught specific strategies to solve particular problems.

My questions:

• Where should we start with upper students? The instruction videos show that you allow students to use manipulatives and it seems they start very small. Should we revert to the basics with older students as well?

Chapter 2: Here is a organizer that explains the different types of problems.

• Problems are classified based on the way children think about the problem.
• Addition/Subtraction are separated into result unknown (most common), change unknown, and start unknown (hardest type of problem). The problems all have an action that happens in the problem (something is added or taken away)
• Part-Part-Whole & Compare problems have no actions, and instead are based on relationships.
• Problems can be more challenging or rigorous by changing the wording to past tense or numbers within the problem that don't represent a set number of objects (such as weight)

My questions:

Should the structures of the different types of problems be explicitly taught to students? How would this be accomplished if the teacher shouldn't be modeling problems?