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 earlier chapters and follow along as we continue exploring. Chapter 6, “Equations and Inequalities,” took us into one of the most common danger zones for student misconceptions. This is the chapter where many of the “classic” algebra tricks show up: move the 3 to the other side and “change the sign,” “cross off” matching terms, or use the “log circle” as a shortcut to solving exponential equations. Our discussion centered around whether the fixes offered in this chapter are realistic for our students, and how our own language and instructional habits can inadvertently cement tricks instead of understanding. Thoughts on the Fixes While many of us agreed with the fixes presented, especially the emphasi...

  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 earlier chapters in previous posts and follow along as we continue exploring. Chapter 5, “Number Systems,” pushed us to think deeply about how students build meaning around integers, rational numbers, and exponents, and how quickly shortcuts can derail that sense-making. While earlier chapters focused on specific tricks, this one made us reflect on the foundation of number itself and how our instruction shapes students’ long-term understanding. Rethinking Our Past Practices As we reflected on our own teaching, a few themes came up repeatedly, especially around integer multiplication and rational exponents. Most of us admitted that at some point in our careers, we’ve leaned on oversimplified rul...

  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 prior chapters in previous posts, and follow along as we continue through the book. Chapter 4, “Geometry and Measurement,” took us into one of the most visual and language-rich areas of mathematics. For many of us, geometry is where we first learned to “see” math, but it’s also a place where shortcuts and memorized formulas can overshadow the reasoning behind them. Our discussion this week revolved around three major themes: definitions, sense-making, and vocabulary. Rethinking Tricks and Formulas When reflecting on the “tricks” in this chapter, several teachers admitted they’ve used them in the past, especially when teaching CP (College Prep) Geometry classes. It’s easy to fall back on formul...

  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...