What if the biggest mistake we make in math education is confusing symbols with thinking? What if multiplication, proof, and even zero are not primarily about notation, but about reasoning, argument, and meaning? And what happens to a child’s identity when we teach math as speed and memorization instead of curiosity and sense-making?

Janine Remillard is a Professor at the University of Pennsylvania’s Graduate School of Education and a national leader in mathematics education. Her work focuses on curriculum design, teacher learning, and how educators interpret and enact math instruction in real classrooms. She studies how curriculum materials shape teaching and how teachers can create more conceptually rich, equitable mathematics learning environments.

In this episode, we explore how math became overly procedural and what it would mean to redesign it around reasoning instead. Janine reflects on her early years as an elementary teacher, when she struggled with traditional textbook-driven instruction and eventually discovered a curriculum that led with ideas rather than exercises. Instead of demonstrating steps and assigning repetitive problems, this approach centered visual representations, discussion, and multiple solution strategies. That shift transformed her understanding of mathematics from a set of rules into a language for making sense of the world.

We discuss research showing that children can solve contextual math problems long before they can manipulate formal symbolic notation. When students are given meaningful situations rather than abstract boxes to fill in, they rely on their own reasoning and informal knowledge. Janine explains why accessible, problem-based curriculum allows students to see themselves as mathematically capable, and how multiple strategies in a classroom discussion reveal the underlying structure of mathematical ideas.

A major theme of our conversation is identity. Janine argues that one of the deepest cultural problems in math education is that it is socially acceptable to say, “I’m not a math person,” in a way that would be unthinkable for reading. We examine how timed tests, procedural drills, and speed-based assessments generate anxiety and shape long-term self-perceptions. In contrast, her work in teacher education focuses on helping future educators develop positive mathematical identities by engaging them in collaborative problem solving and discussion.

Ultimately, this episode is about reclaiming mathematics as a human endeavor. From the history of zero to the question of whether math is invented or discovered, we consider what it would mean to teach mathematics as a way of reasoning about the world rather than a set of rules to memorize. In a data-driven society where numbers shape public discourse, Janine makes the case that mathematical confidence is not optional. It is essential for participation, agency, and equity.