Mathsational

  This post is part of an ongoing book study series on Nix the Tricks by Tina Cardone. Each week, a group of math teachers meets to reflect on one chapter of the book and discuss how we can move away from shortcuts and toward true mathematical understanding. You can find our reflections from Chapter 1: Introduction and Chapter 2: Operations in previous posts and follow along as we continue through the book. Chapter 3, “Proportional Reasoning,” was one of the heaviest sections we’ve read so far. It’s packed with tricks that almost every math teacher has encountered at some point: Butterfly Method , Flip and Multiply , Cross Multiply , and the Formula Triangle , to name a few. These are the kinds of tricks that often sneak into students’ repertoires long before they truly understand what a proportion or ratio represents. As we discussed this chapter, one central question emerged: “Do students ever really understand the math behind these shortcuts, or do they lose the reasoning once ...

This post is part of an ongoing book study series on Nix the Tricks by Tina Cardone. Each week, a group of math teachers has been meeting to reflect on one chapter of the book and discuss how we can move away from shortcuts and toward a deeper understanding of mathematics. You can find our reflections from Chapter 1: Introduction in the previous post and follow along as we continue through the book. Our second week of the Nix the Tricks book study focused on Chapter 2, “Operations.” This chapter took us into some of the earliest habits students develop around computation, key words, order of operations, and the tricks we’ve all seen (and maybe even taught) that make math seem like a list of steps rather than something that makes sense. As we worked through the examples, one big question kept surfacing: Are students relying on tricks because they lack mathematical understanding, or because they struggle with literacy? Key Words and Context The chapter opens with a discussion on “Total...

  I used to declare that I hated synthetic division. It always felt like a jumble of steps with no real meaning behind them, and my students never seemed to remember the process anyway. For years, I told my Algebra 2 classes that long division made more sense because it connected to what they already knew about dividing numbers. I also believed that synthetic division only worked when the divisor was a linear expression. Recently I came across a blog post explaining that synthetic division can, in fact, be used in all cases. I was skeptical at first, but after reading and experimenting, I realized I had been wrong. I immediately shared the post with my department, confessing my mistake and sparking an unexpectedly lively discussion about math instruction, “tricks,” and conceptual understanding. That conversation prompted us to revisit Nix the Tricks by Tina Cardone , a book that challenges educators to think critically about the shortcuts we teach and why. One simple email turned ...

  Too often, the powerful ideas of equity and cultural responsiveness seem abstract, leaving teachers unsure of how to translate them into concrete math-class practices. This post offers practical moves to make those principles visible and actionable. Why Vocabulary Matters Our goal isn’t just learning vocabulary; it’s building strong academic communication skills. Purposeful math talk enhances achievement and broadens students’ ability for deep, conceptual thinking. Overcoming Reluctance: Structured Talk Moves Many students hesitate to explain their reasoning because thinking and speaking at the same time are cognitively demanding. Structured talks provide a clear framework that allows everyone to participate in meaningful mathematical discussions. Equity and Agency: Key Ideas Equity : what is fair and just Agency : the power and capacity to act When equity is used to foster agency, students build confidence, independence, and perseverance; skills directly aligned with the Standar...