## Shifting STEM culture

January 24, 2022

*This post is republished from* *Into Practice*, *a biweekly communication of Harvard’s Office of the Vice Provost for Advances in Learning*

**Robin Gottlieb, Professor of the Practice of Teaching Mathematics**, aims to make mathematics accessible and exciting to all students in each of her courses. “When students come to Harvard, they have very different but set ideas of what happens in the classroom,” Gottlieb explains. “In many high school math classrooms, the dominant cultural norm is an ‘I do, you do, we do’ model. The teacher is expected to tell you what to do. One of my main objectives is to shift the culture of the classroom so that students become mathematical thinkers.” Gottlieb works alongside colleagues on the preceptor team to construct classrooms in which students actively participate in the development of ideas. Inspired by colleagues’ such as Eric Mazur’s active learning and John Asher Johnson’s Tao of TALC, Gottlieb has students spend more time working on problems together in groups at the blackboard, reflect actively on questions and lessons from daily problem sets, and co-build community norms around supportive teamwork. Through group work, Gottlieb has developed mathematics classrooms that are more welcoming, active, and empowering places of learning.

**The benefits: **Students can construct, incorporate, and apply concepts much better through an active learning process. Rather than memorizing formulas and mimicking procedures, students explore, discover connections, and engage in applying their knowledge. Gottlieb’s students reported transformational experiences where they fully understand the material, are excited by it, and see its utility, often for the first time. Some have moved on to become mathematics teachers themselves, and utilize Gottlieb’s strategies in their classrooms, producing ripple effects beyond Harvard.

“Being seen helps empower students. Empowering them helps them become better problem-solvers. Being better problem-solvers helps them do math.”

**The challenges: **While most students welcome this format once they understand it creates deeper and more portable learning, Gottlieb notes that a few occasionally have trouble adjusting from the rote style of high school to an active learning environment. “The biggest challenge is students who say, ‘I need to know how to do what we’re doing before we do it,’” she explains. “Sometimes there is a fear that they can’t think through something without a model.” Gottlieb addresses this through scaffolding material, creating opportunities for successes, normalizing mistakes as a step in learning, building upon the strengths of each student and meeting individual students both to do mathematics and to get to know them so they understand they are not being defined solely by their work.

**Takeaways and best practices**

**Model group work inside the classroom.**“Often on the very first day of class I break students into groups and send the groups up to the board to make a list of the kinds of behaviors that makes group work a successful learning experience for all group members and the kinds of behaviors that should be avoided,” Gottlieb notes. “By pooling their ideas, we come up with a robust set of class norms. I want students to be participants, questioners, and active listeners. Group work has the potential to break down people’s images both of themselves and their classmates as to ‘who knows what.’ They realize that it is the wrong question to be asking—that the ‘mathematical power’ is distributed around, and they have some of the mathematical power.”**Frame being wrong as a step to being right.**“Progress is not always made linearly,” Gottlieb explains. “Math is a process of questioning, exploring, experimenting, and sensemaking.” “The more you problem-solve, the better your problem-solving abilities,” Gottlieb says. “Making mistakes and learning from them is a part of it.” She builds in low-stakes opportunities to self-test, such as optional mini-quizzes that are done individually and then discussed as a group and practice exams that encourage students to synthesize material. Students are asked to organize material for themselves by constructing concept maps and study guides.**Reflect on learning.**Gottlieb encourages student reflection after each homework assignment to deepen their learning. Part of learning from mistakes involves reflection on what went well and what didn’t. In some courses, she offers the opportunity for pre-midterms and pre-finals, where students can return to the teaching team, learn about problems they got wrong, and then complete a harder problem and present it back to them for additional points. “Asking students to stand up and talk about their solution to a challenging problem, allows students to take pride in their mastery and realize that mistakes aren’t final,” she describes. “If there’s something you don’t understand, you can ask questions and work on it. What you understand and don’t understand isn’t static.”

**Bottom line: **Active learning—whether at the blackboard, in groups, or in one-on-one meetings—allows the instructor to be more responsive to student needs and to open space for non-linear, experimental learning. Both deepen students’ confidence with and understanding of the material. As Gottlieb summarizes, “Make sure your students are *seen*, and *feel seen*. Being seen helps empower them and empowering them helps them become better problem-solvers and being better problem-solvers helps them do math.”