Acutely Curious
Framework Guide

The 3R
Framework

A clear, repeatable process for designing learning experiences where technology and math thinking work together — so you can build, adapt, and evaluate with confidence.

The Framework
The 3R Method works whether you're in Desmos, GeoGebra, Edulastic, or anything new. The framework is the constant.
Recognize
What does quality look like?
Reverse-Engineer
Why does it work?
Reimagine
How can I build something better?
Cutting through the obtuse.
For K–12 Math Educators & Instructional Coaches
acutelycurious.com
Introduction

Why we need a framework

Technology in math classrooms is everywhere. But access to tools is not the same as knowing how to use them well. The 3R Framework exists to close that gap.

Most educators have experienced the digital activity that looks great on a screen but asks students to do nothing more than click the right answer. The interactivity is cosmetic. The math thinking is shallow. And the teacher, pressed for time and trusting the platform, doesn't have a reliable way to know the difference before they assign it.

The 3R Framework gives you that reliable way. It's built on 30+ years of K–12 math classroom and district experience — work as a classroom teacher, curriculum specialist, instructional coach, and state-level math assessment specialist. It's the framework that grew out of asking, repeatedly: what actually makes a digital math activity good?

The answer, it turns out, is the same as what makes any math activity good: mathematical depth, visible student thinking, productive struggle, and feedback that moves learning forward. What changes with technology is the opportunity — and the responsibility — to design for those qualities intentionally.

Platform-agnostic by design. The 3R Framework works whether you're in Desmos, GeoGebra, Edulastic, Google Forms, or anything new. Platforms change. The framework is the constant. That's intentional.


The Framework at a Glance

Three steps. One clear process.

The 3R Framework is a three-stage thinking process for working with digital math activities — as an evaluator, a designer, or both.

R
Recognize
R
Reverse-Engineer
R
Reimagine

Each stage builds on the last. You start by developing a clear lens for what quality looks like. Then you use that lens to understand why existing activities work or don't. Then you put that understanding to work — building, adapting, or transforming activities with intention.

You can enter the framework at any stage depending on your goal. But the sequence matters: the quality of your Reimagine work depends on how well you've done the Recognize work.

The Three Steps

The framework, in depth

Step 01

Recognize

Identify what makes a digital math activity genuinely effective.

Most educators can tell when something feels "off" about a digital activity. The Recognize step turns that instinct into a framework. You learn to name what you're seeing — and more importantly, what you're not seeing.

Quality digital math activities share a set of defining characteristics: they require mathematical thinking, not just input; they make student reasoning visible; they include feedback that informs instruction; and the technology does something that paper cannot. Recognizing these qualities — and their absence — is the first professional skill this framework develops.

Key questions at this stage:

  • Does this activity require mathematical thinking, or just answer-clicking?
  • Is student reasoning visible — to the student and to the teacher?
  • What does the technology make possible that paper cannot?
  • Does the feedback in this activity move learning forward?
  • What's the cognitive demand? Is it maintained through the digital format?

✦ 5Q Digital Activity Audit — the free tool that makes the Recognize step practical. Five questions. Any digital activity. Under five minutes. Get it free →

Step 02

Reverse-Engineer

Deconstruct activities you admire to understand the design decisions behind them.

Once you can recognize quality, the next step is understanding why it works. This means looking beneath the surface of an activity you admire — or one that puzzles you — and asking: what choices did the designer make? What constraints did they work within? Where does the productive struggle live, and how was it engineered?

Reverse-engineering is how expert teachers think. It's the move from "this works" to "I understand why this works" — and that understanding is what makes you a designer, not just a user.

Key questions at this stage:

  • What mathematical goal is this activity actually serving?
  • What design decisions created the productive struggle here?
  • Where does the technology serve the math — and where is it decorative?
  • What constraints did the designer work within, and how did they navigate them?
  • What would a teacher need to do before, during, and after this activity for it to work?
Step 03

Reimagine

Build your own — or transform existing activities — with intention.

Reimagine is where the framework becomes creative work. You take what you've learned — the quality indicators from Recognize, the design principles from Reverse-Engineer — and you apply them. You might transform a worksheet into a richer digital experience. You might redesign an existing activity that falls short. You might build something new entirely.

The key word is intention. You're not just digitizing content. You're making deliberate design decisions about mathematical depth, student thinking, feedback, and the role of technology — and you can articulate why you made them.

Key questions at this stage:

  • What mathematical thinking do I want this activity to produce?
  • Which tool is the right fit for this goal — and why this one?
  • Where is the productive struggle, and how am I engineering it?
  • What will student work look like, and what will I do with it?
  • What does the technology make possible here that paper cannot?

◈ 3R Lesson Builder — the interactive tool that walks you through all three stages and generates a complete, ready-to-teach lesson plan from your thinking. Try it free →

In Practice

What this looks like in real classrooms

The 3R Framework isn't abstract theory. It's a thinking process built for real educators working in real classrooms — across grade levels, subject areas, and platforms.

The Activity Makeover

One of the most powerful applications of the 3R Framework is what we call the Activity Makeover: taking a traditional math activity — a worksheet, a warm-up, a card sort — and reimagining it as a richer digital experience.

A Makeover isn't digitization. Scanning a worksheet and putting it in a Google Form is not a Makeover. A Makeover applies Reverse-Engineer thinking to the original activity (what mathematical work is this actually asking for?) and then uses Reimagine thinking to redesign it in a way that the technology genuinely serves the math.

Before: The traditional version

A worksheet asks students to solve 12 equations and circle the correct operation. Students work individually and silently. The teacher collects papers at the end of class.

After: The reimagined version

Students work through a Desmos activity that surfaces their reasoning. Mistakes are visible. The teacher pauses the class when the dashboard shows a productive misconception worth discussing together.

The mathematical goal is the same. The learning experience is fundamentally different — because the design was intentional.


Using the framework for coaching

Instructional coaches find the 3R Framework particularly valuable as a shared language with their teachers. When a teacher and coach both have the same vocabulary for quality — when they can both ask "what's the cognitive demand here?" and "where is student thinking visible?" — coaching conversations become more productive and less subjective.

The Recognize step is especially powerful as a coaching entry point. Instead of telling a teacher that an activity isn't working, you can use the 5Q Digital Activity Audit together, let the framework surface the gaps, and move the conversation from evaluation to design.


Using the framework for curriculum work

Curriculum specialists and district leaders use the 3R Framework to create platform-agnostic guidelines that don't lock schools into any single tool. Because the framework focuses on design principles rather than specific platforms, it holds up as tools change — which they always do.

A curriculum guide built on 3R principles doesn't say "use Desmos for this unit." It says "here's what a high-quality digital experience looks like for this mathematical concept, and here's how to evaluate whether any platform you're using is delivering it."

The framework as a virtual coach

The 3R Lesson Builder is an AI-powered tool that walks you through the full Recognize → Reverse-Engineer → Reimagine process for any lesson or activity you're working on — and generates a complete, ready-to-teach lesson plan from your thinking at the end.

It's not an activity generator. It's a thinking tool. The AI asks you the right questions at each stage of the framework, pushes back on vague answers, and helps you articulate design decisions you might otherwise leave implicit. The lesson plan it produces at the end reflects your thinking — structured, refined, and ready to use or share.

Available at: acutely-curious-3r-builder.vercel.app

Framework Principles

What makes this framework different

There is no shortage of frameworks for evaluating instructional technology. What distinguishes the 3R Framework:

It's grounded in math-specific design principles

Generic "good tech" frameworks evaluate technology on engagement, accessibility, or ease of use. The 3R Framework evaluates it on mathematical depth, visible reasoning, productive struggle, and instructional feedback. These are different questions, and they produce different answers.

It's generative, not just evaluative

Most frameworks help you decide whether something is good or bad. The 3R Framework also helps you make things better. The Reimagine step is where the framework becomes a creative tool — and where educators go from consumers of curriculum to designers of learning experiences.

It's platform-agnostic

The framework does not depend on any particular tool, platform, or subscription. It works with whatever you have access to — and it works equally well when that changes.

It respects educator expertise

The 3R Framework doesn't hand teachers a script. It develops the professional judgment to make their own decisions — and to explain those decisions to coaches, administrators, and students.

"The goal is not to teach educators to use specific tools.
It's to develop the design thinking that transfers across all of them."

Getting Started

Your next steps

Start with the 5Q Audit

Download the free 5Q Digital Activity Audit and use it on the next digital activity you assign. It takes less than five minutes and puts the Recognize step immediately into practice.

Get the free 5Q Audit →

Try the Lesson Builder

Bring a lesson you're working on to the 3R Lesson Builder. Go through all three stages and see what the full framework produces when you apply it to something real.

Launch the Lesson Builder →

Do a Makeover

Pick one traditional activity from your current unit. Run it through the Activity Makeover Tool to get three distinct ideas for reimagining it as a richer digital experience.

Try the Activity Makeover →

Bring it to your team

Use the 5Q Audit in your next coaching conversation or PLC. Let the framework create the shared language for evaluating and designing digital math activities together.

Get the free 5Q Audit →