Appendix. Interview guide

The purpose of this interview is to gain insight into your experience as a high school teacher.

SECTION I: Knowledge of policy

The Obligatory Education Model (MEO), which serves as a foundation for the high school curriculum where you work, includes the following statements:

• “A key component of lifelong education is reflecting on the ways in which one learns, and on some skills, like memory or attention, that can be used to fine-tune and improve learning.”
• As part of the teaching principles, “school accommodates cognitive self-regulation… to promote the development of knowledge.”

With respect to these statements:

1. What does the model mean when it says that students should reflect on the way they learn and on their difficulties, and what is the purpose of this?
2. What are the characteristics of this type of reflection, and under what conditions does the model expect this reflection to take place in mathematics?
3. What actions or strategies does the model expect of mathematics teachers in order for reflection and cognitive self-regulation to occur in students?
4. Based on this educational model, how can cognitive self-regulation serve as a basis to promote the development of mathematical knowledge in students?
5. What teaching tools or suggestions does this model provide to mathematics teachers in order to achieve this reflection and cognitive self-regulation in their students?

The school’s curriculum states that “teaching is centered on student learning. This means that students should learn to learn.” In this regard:

6. What does the curriculum mean when it says that teaching means students should learn to learn?
7. What is the purpose of students learning to learn, in mathematics for example?
8. What is required of mathematics teachers by the curriculum in order for such learning to occur in students?
9. What teaching tools or suggestions does the curriculum provide to mathematics teachers in order to achieve this learning?

SECTION II: Conceptual knowledge

1. The MEO makes reference to the concept of “cognitive self-regulation.” What does this concept mean to you?
2. What are the characteristics of cognitive self-regulation in the context of teaching mathematics?
3. What student actions or strategies demonstrate that self-regulation is taking place?
4. What is the purpose of students learning to learn?

The MEO and the school’s curriculum mention the following concepts: a) reflection on one’s own learning, b) cognitive self-regulation, c) learning to learn, and d) control of learning. With respect to this:

5. Do you believe there are any differences or similarities between these concepts? Please justify your answer.
6. What conditions are required in order for students to learn to learn, and to achieve cognitive self-regulation, reflection on learning, and control of learning?

SECTION III: Procedural knowledge

1. What do you do when students make conceptual or procedural mistakes during a mathematics class?
2. In your class, are students given an opportunity to defend, justify or explain the procedures or answers they arrive at for a given problem? Why? How does this happen?
3. When you set a mathematical problem, are students told how to solve it or do they have to come up with their own proposal? What is the purpose of this?
4. How can students be made aware that what they have learned in class is applicable to other similar mathematical problems?
5. In your classes, are there times when students are asked to review (evaluate), either individually, in groups or with the whole class, the contributions they make or their procedures or answers to a given problem? What is the purpose of this?