Any suggestion (books, references, etc.) would be greatly appreciated.
I have seen 5E's used for math and have used it myself when I wished to take a more constructivist approach.
In terms of which models I've also seen used for math, I'd say that the Madeline Hunter model was most suggested by my education professors and other math teachers.
The Madeline Hunter model has 7 basic steps that essentially follow the order of "getting students ready to learn, instruction and checking for understanding, and independent practice."
This model can be effective if you want students to develop a specific skill, but is less effective for developing deep understanding of the topic. I tend to use it when I wish for my students to have a rote ability to do something automatically. (Such as, for instance, simplifying square root expressions. The understanding is helpful and I include it, but unless they become fluent in the skill it won't help them).
This model is more effective with struggling students, and (by personal experience / distaste) very ineffective with gifted students.
As a second response, I have found decent success using Dan Meyer's Three Acts lesson plan. I don't know if this falls quite into the realm of a teaching model, particularly since I don't believe it has any supporting research, but I have managed to have several very successful lessons following this lesson plan format. I've summarized the Acts how I personally have used the lesson plan. It fits well into an 80-minute block, with time left over for independent practice.
Act one: Set the stage. A strong visual piques interest and students pose mathematical questions about the scenario. The scenario can be carefully selected so that some of the questions that arrive naturally are those that require the mathematics you plan on teaching.
Act two: Help students develop the mathematical tools they need to answer the question. Ask them what information they would look for, and teach them the new mathematics they need to finish the job. Direct instruction is fine here. You could even fit a mini-Madeline Hunter plan in here.
Act three: "Resolve the conflict and set up the sequel/extension." Once the concept has been taught, ask the students to solve the problem posed in act 1, guiding them through it and encouraging them to work together. Encourage them to ask and answer more advanced questions if there is time.
I hope that these fit some of what you are looking for. For the record, I have only just finished my first year of teaching high school math, so who knows -- in 3 years I may look back at this post and cringe.
The source is provided in the picture and there is a vast body of literature on modelling. You might want to specifiy your question:
- Which institution / age?
- Is your interest on how to model modelling or on how to teach modelling or on specific examples of modelling sessions in school?
Let me know, maybe I can add some ressources.