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 remember seeing several of these tricks in high school, especially shortcuts for evaluating functions, identifying domain and range, or quickly checking whether a relation was a function.

However, we also noticed something.

  • Some of today’s tricks were not available when we were students.

  • Some seem to come from Pinterest, social media, or cheat sheet graphics that circulate online.

  • Students often encounter these outside of class, meaning that many walk in with procedural habits before they have built conceptual understanding.

This insight helped us realize that in the age of social media, un-teaching tricks is becoming just as important as teaching strategies that build meaning.

How Tricks Affect Later Understanding

Our discussion next moved to the long-term impact of teaching tricks for functions, especially as students move into Algebra 2, Precalculus, and further.

We agreed on several key ideas.

  • Tricks often reduce functions to isolated procedures rather than relationships. Students might memorize how to find f(3) but not understand what a function represents or how outputs depend on inputs.

  • Students need multiple exposures to understand something, often two or three times, and tricks can short-circuit that productive struggle.

  • Teaching something helps you learn it more deeply, which reminded us to create opportunities where students explain their reasoning, not just perform steps.

Our group also explored the question: Is it helpful to use rules or tricks for fluency?

Our consensus: When rules are grounded in a structure, they can support fluency. Tricks that bypass meaning slow students down in the long run.

For example:

  • Understanding function notation builds a foundation for composition, inverse, and transformation.

  • Understanding the significance of domain restrictions prepares students for rational functions and logarithms.

  • Seeing functions as relationships supports later work with modeling, data, and calculus.

When shortcuts are introduced too early, students may get correct answers without understanding, which can make higher-level work feel abstract.

Big Takeaways

  • Many function tricks are new, coming from social media rather than traditional classrooms.

  • Students often need multiple exposures to build a real understanding.

  • Peer teaching or explaining concepts strengthens comprehension more than memorizing steps.

  • Procedural fluency should stem from conceptual understanding, not replace it.

  • Functions are the backbone of secondary mathematics.

Next time, we’ll wrap up the series with Chapter 8: Probability and Statistics, where we’ll explore how shortcuts can obscure randomness, structure, and reasoning, and what we can do instead to support deeper thinking.

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