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Nix the Tricks Book Study – Chapter 8: Conclusion

  This post is the last of an ongoing book study series on Nix the Tricks, by Tina Cardone. Over the past several weeks, a group of math teachers has worked through each chapter, reflecting on how shortcuts shape student understanding and how we might replace tricks with sense-making. This final chapter provides space to step back and reflect on the journey as a whole. The conclusion of Nix the Tricks feels less like an ending and more like a challenge. Rather than presenting a resolution, it challenged us to sit with some uncomfortable truths about our instruction and think carefully about what we pass on to students. One idea resonated strongly with our group: students often arrive with a toolbox full of tricks already. Before we can nix them, we need to stop adding more. Acknowledging Our Role Many of us acknowledge that the tricks discussed in this book are not always ones we actively teach. Instead, they are habits students bring with them from previous courses, tutoring se...
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Nix the Tricks Book Study – Chapter 7: Functions

  This post is part of an ongoing book study series on Nix the Tricks, by Tina Cardone. Foe each chapter, a group of math teachers meets to reflect on the book and discuss how we can move away from shortcuts toward true mathematical understanding. You can find our reflections from the earlier chapters and follow along as we continue to explore. Chapter 7, Functions, introduced a part of the curriculum that many students find deceptively simple: input, output, mapping diagrams and function notation. Many elements seem procedural at first glance, which is why function tricks spread quickly. Additionally, as several teachers pointed out, some of these shortcuts are new, having appeared on platforms such as Pinterest and TikTok rather than in traditional textbooks. This chapter challenged us to reflect on the difference between knowing how to do something and knowing what it means. Did We Learn These Tricks Ourselves? We began by reflecting on our experiences as students. Many of us re...
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Nix the Tricks Book Study – Chapter 6: Equations and Inequalities

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...
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Nix the Tricks Book Study - Chapter 5: Number Systems

  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...
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Nix the Tricks Book Study – Chapter 4: Geometry and Measurement

  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...
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