Norms/Expectations
"Teachers' beliefs influence the decisions that they make about the manner in which they teach mathematics. Students' beliefs influence their perception of what it means to learn mathematics and their dispositions toward the subject" (National Council of Teachers of Mathematics, 10).
The quote above puts into perspective the importance of the Norms/Expectations component of my vision. The beliefs and attitudes our students have about themselves and mathematics will shape their behaviors in the math classroom. This component sets the expectation for the beliefs and actions of students and teachers within this flipped instructional model.
If students have had previous years of math experiences under a GRR model they may get the idea that:
If we are to eliminate the achievement gap in math and ensure mathematical success for all students, it is vital that students understand the beautiful, creative, multidimensional subject that math is, as opposed to the dry, rigid subject that they are led to believe math is. We help students come to understand this in part through the norms and expectations that we communicate to students about what good mathematicians do and what it means to be "good" at math. This step what I would consider Step 0. It lays the groundwork for the other components of the flipped model.
The following are a set of expectations about math, outlined in Mathematical Mindsets, that students should be made aware of :
Additionally, I communicate to students what types of actions good mathematicians take part in when working with math:
This relates back to my You-do We-do I-do vision because it communicates to students that they are active participants in their own learning, rather than passive observers expected to absorb the information from the teacher (which is an implicit message students get from the GRR model). Simply communicating these expectations for students does not ensure equitable instruction or mathematical success for all. Our actions as teachers must actively support these norms. "Research tells us that students learn when they are encouraged to become the authors of their own ideas and when they are held accountable for reasoning about and understanding key ideas" (Smith & Stein, 2). Students experience roles as active participants in their own learning during the You-do and We-do portions of the flipped model because, unlike the GRR model, the teacher provides no demonstration of how to do a similar problem prior to students' independent and group work time on a problem/task. Thus, students must use their own problem solving and critical thinking skills to work through the task.
Throughout this site it will be made clear how the remaining components of my vision (learning goals, tasks, and student voice) support and reinforce these expectations.
The following links will take you to a page with artifacts which exhibit how I enacted this component of my vision during my student teaching: Norms/Expectations Artifacts
If students have had previous years of math experiences under a GRR model they may get the idea that:
- math is "a subject of calculations, procedures, or rules" (Boaler, 22)
- "their role in the math classroom... is to get questions right" (Boaler, 21)
If we are to eliminate the achievement gap in math and ensure mathematical success for all students, it is vital that students understand the beautiful, creative, multidimensional subject that math is, as opposed to the dry, rigid subject that they are led to believe math is. We help students come to understand this in part through the norms and expectations that we communicate to students about what good mathematicians do and what it means to be "good" at math. This step what I would consider Step 0. It lays the groundwork for the other components of the flipped model.
The following are a set of expectations about math, outlined in Mathematical Mindsets, that students should be made aware of :
- Math is a subject focused on learning, not performing
- We are responsible for each other's learning, in addition to our own
- Mistakes are valuable for learning
- Everyone can do well at math
- Getting the correct answer is not enough, one must be able to clearly explain their reasoning.
- Depth is more important than speed
Additionally, I communicate to students what types of actions good mathematicians take part in when working with math:
- Good mathematicians (1) revise their thinking, (2) ask questions, (3) clearly communicate their ideas, (4) make connections among mathematical ideas, (5) make sense of problems, (6) are creative, and (7) use mathematical reasoning to make predictions.
This relates back to my You-do We-do I-do vision because it communicates to students that they are active participants in their own learning, rather than passive observers expected to absorb the information from the teacher (which is an implicit message students get from the GRR model). Simply communicating these expectations for students does not ensure equitable instruction or mathematical success for all. Our actions as teachers must actively support these norms. "Research tells us that students learn when they are encouraged to become the authors of their own ideas and when they are held accountable for reasoning about and understanding key ideas" (Smith & Stein, 2). Students experience roles as active participants in their own learning during the You-do and We-do portions of the flipped model because, unlike the GRR model, the teacher provides no demonstration of how to do a similar problem prior to students' independent and group work time on a problem/task. Thus, students must use their own problem solving and critical thinking skills to work through the task.
Throughout this site it will be made clear how the remaining components of my vision (learning goals, tasks, and student voice) support and reinforce these expectations.
The following links will take you to a page with artifacts which exhibit how I enacted this component of my vision during my student teaching: Norms/Expectations Artifacts