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The Jets won Super Bowl 3

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Cédric Villani on the 7 Ingredients of Creativity

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What does it take to come up with a new idea? In this beautifully illustrated RSA Short, award-winning mathematician Cédric Villani reveals the seven key ingredients that come together to create breakthrough moments in human knowledge and innovation. Watch the full talk (RSA Replay): https://youtu.be/iEWvTt1EFWs.

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When teachers take a step back from center stage, they create space for students to collaborate as active math learners.

Over the past five years, I have slowly relinquished my classroom position as "sage on the stage" to become instead a "guide on the side." Before, I saw myself as a dispenser of information in my role as a mathematics teacher, but now I embrace being a facilitator of mathematics learning. It's been my experience that students are more actively involved in their learning as a result of this approach.

Shifting my position this way has created space for students to develop the confidence to learn to reason and prove their solution paths, a key expectation articulated by the National Council of Teachers of Mathematics (NCTM) process standards. Here are three teacher moves I use that promote active learning by positioning students to be doers-rather than recipients-of mathematics.

3 Strategies to Facilitate Active Learning

1. Dim your light: After an online graduate school experience during which my classmates and I spoke for nearly 90 percent of the class, I had an epiphany. I was learning so much by talking about, questioning, exploring, failing, and experimenting with the math tasks I was assigned that I longed to re-create an experience like that for my students.

What I had to reckon with was shifting my role from teacher to facilitator. What did that look like? How would my students learn if I didn't tell them everything? I had to become comfortable with presenting tasks in a way that would require and encourage my students to explore them and extract the mathematical ideas for themselves.

The tasks had to generate thinking through analytical questioning and comprehension activities, and they needed to align with NCTM's Standards for Mathematical Practice. Because discourse between the learners is a recurring theme throughout the standards, I knew I had to limit the amount of time that I spoke in class and create opportunities for the students to speak, think, debate, question, and justify regularly.

This shift eventually caused the students to leave class discussing the topic of the lesson, rather than grumbling over note-taking or inquiring about which part of the lesson would be on the next quiz. Dimming the light on my ego brightened the opportunity for my students to become active participants in their learning.

2. Stand back: A second, seemingly trivial, teacher move presents space, figuratively and literally, for students to consider conceptual ideas and make decisions independent of teacher influence. This positioning is even more powerful after you've created a safe learning environment where student agency carries significant value.

During activities which probe the class as a collective, we should position ourselves out of the sightline of students. One smile, nod, or slight twitch of the head can change the trajectory of a student's strategy and can negatively affect a student's self-esteem. Placing the decision of confirming or denying solutions on the students has the potential to engage all students and provide agency and voice to each one.

During a recent warm-up about negative inequalities in my pre-algebra class, a student offered an incorrect inequality as the solution; he hadn't realized that he needed to change the sign from "greater than or equal to" to its opposite. As I stood off to the side, several voices from the class gently discouraged the student's answer, offered the correct solution, and supported their reasoning by referring to the number line provided on the board.

The high level of engagement by multiple students would not have happened if I had stepped in and corrected the student. The moment was a strong example of collaborative active learning and how students can take ownership of their understanding.

Standing behind students during a discussion about a task or during a warm-up activity also encourages the students to focus more on the question or task at hand, rather than wait for the teacher to tell them what to do or think. It suggests to the students that the solution paths are accessible for all of them. It also deepens the shift for the teacher by strengthening the facilitator role.

3. Design opportunities for discourse: Specialized lessons with both guiding and extension questions create opportunities for rich mathematical discourse. Pages of naked-number problems, or exercises without any context, will not encourage discussion, and dense word problems could ignite frustration. There has to be a balance of equations infused with real-world contexts, which generate conversations and provide depictions of math that allow students to see themselves.

Comprehension activities such as comparing and contrasting, restating, and debating ideas have to be included in the task work. We have to invest time in learning our lessons' nuances, misconceptions, and, if applicable, multiple solutions or solution paths in order to field potential questions and maintain analytical conversation.

As teachers we must also become comfortable with the students' initial discomfort and not jump in to "save the day." The energy previously devoted to lecturing must shift toward facilitation of learning and become questions, words of encouragement, and clarification statements.

Additionally, teachers and students will need to become used to the beneficial awkwardness of productive struggle. We must allow ourselves to be pursued by students rather than step in and problem-solve for them.

This method can be more challenging than reading from a teachers' edition workbook or handing out a predetermined worksheet because of the level of preparation required, but it will generate student thinking in the classroom in a way that lecturing cannot. It may feel like a relinquishing of power, but it actually allows us to utilize our power in a more effective and relevant way.

The shift from teacher to facilitator is multifaceted, yet can be initiated by implementing these teacher moves as preliminary steps toward the transition. Recognizing that student voice is a necessity for meaningful understanding to develop, standing behind the students during discussions, and providing cognitively demanding tasks are three teacher moves that can promote active student development of conceptual knowledge.

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A Shift From Lecturing to Facilitating Learning in Math

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When teachers take a step back from center stage, they create space for students to collaborate as active math learners.