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Royalmont Prepares Students for Real-World Problem Solving

Building Thinking Classrooms in Math: Preparing Students for Real-World Problem Solving and Success

At Royalmont Academy, we believe math is more than just numbers—it’s a tool for critical thinking and real-world problem solving. This is why we’ve implemented the Building Thinking Classrooms (BTC) pedagogy in high school, a research-backed approach that encourages students to think critically, work collaboratively, and connect math to everyday life. BTC is specifically designed to prepare students for success on college readiness exams like the ACT and SAT, equipping them with the problem-solving skills necessary for higher-level education and life beyond the classroom.

What is the Building Thinking Classrooms Approach?

Building Thinking Classrooms shifts the focus from rote memorization and passive learning to active problem-solving. This method transforms the typical classroom dynamic, emphasizing students’ role as active participants who work together to solve challenging problems right from the start.

BTC vs. Traditional “I Do, We Do, You Do” Method

In many math classrooms, the “I Do, We Do, You Do” approach dominates. Here’s how it works:

  • The teacher demonstrates a problem (I Do).
  • The teacher and students solve a similar problem together (We Do).
  • Students then practice independently (You Do).

While this method provides structured support, it often limits students’ opportunity to engage deeply with problems on their own terms. The focus on memorization and procedural steps can lead students to rely heavily on the teacher for direction, rather than encouraging them to think independently.

In contrast, Building Thinking Classrooms emphasizes:

  • Active participation: Students are immediately given complex problems to solve in small groups without prior explanation.
  • Exploration and reasoning: Students engage in discussion and exploration, approaching problems from various angles rather than following step-by-step instructions.
  • Deeper understanding: By reasoning through problems, students gain a better understanding of math concepts, leading to stronger long-term retention.

Comparison: What This Means for Students

Aspect Traditional Learning in Math Problem-Based Learning (BTC) What This Means for Students
Structure & Delivery Teacher-led, focusing on note-taking and procedural steps. Student-led, emphasizing tasks, discussions, and exploration of concepts. Encourages deeper reasoning and active participation in their learning.
Certainty & Confidence Students receive immediate, concrete answers. Students may explore multiple strategies before arriving at a solution. Working through uncertainty builds persistence and stronger problem-solving skills.
Effort & Outcomes Students aim for quick, correct answers, providing a sense of accomplishment. Effort focuses on process and reasoning, even if the correct answer isn’t immediate. It can feel challenging, but this approach fosters resilience and critical thinking.
Articulation of Learning Students can describe what they learned in procedural terms. Learning involves reasoning, collaboration, and exploration, which can be harder to explain. Struggling to explain concepts may mean deeper thinking is occurring.
Approach to Complexity Problems are broken down into simpler steps. Problems are more complex, requiring different perspectives and approaches. Tackling complexity helps students build confidence and resilience.

How Regnum Christi Integral Formation Sets Royalmont Academy Apart

At Royalmont Academy, math education doesn’t stand alone—it’s embedded within a comprehensive approach to formation that develops the whole person: intellectually, humanly, spiritually, and apostolically. This is what makes us different from other schools, both public and Catholic. Our commitment to Regnum Christi Integral Formation ensures that students don’t just learn facts and figures but are transformed in mind, heart, and spirit.

The image below provides a visual representation of how RC Integral Formation works across the four pillars:

Key Differences in the RC Integral Formation Approach:

  • Intellectual Formation: While traditional education focuses on information and technique, Royalmont Academy goes deeper by teaching the causes and reasons behind what is being learned. The RC approach further develops students’ ability to communicate and convince—skills critical for success on the ACT and SAT, and for leadership roles in life.
  • Human Formation: Rather than just focusing on external compliance with rules, our goal is to help students internalize these virtues through fortitude and perseverance. BTC helps cultivate these skills by pushing students to work through problems, even when solutions aren’t immediately clear.
  • Spiritual Formation: At Royalmont, we don’t stop at external religious practices. Our students are led into a personal relationship with Christ, deepened through discernment and humility. This kind of spiritual formation supports intellectual growth, as students are encouraged to use their God-given talents for a higher purpose.
  • Apostolic Formation: BTC, and education at Royalmont overall, is aimed at preparing students to give of themselves in service to others. Our apostolic formation teaches students that their learning should radiate outward, making them radiant and enlivening leaders in their communities and beyond.

How BTC Prepares Students for the ACT and SAT

The ACT and SAT require more than just a mastery of mathematical formulas—they test a student’s ability to think critically and apply knowledge to real-world situations. The Building Thinking Classrooms approach mirrors this by presenting students with non-routine problems that require more than simple computations. It teaches students to break down problems, think creatively, and work through challenges logically, all of which are crucial skills for success on these exams.

For example, in our Algebra I classes, students are tasked with solving equations that simulate real-life financial decisions, such as calculating interest rates or understanding the relationship between time and distance in travel scenarios.


Real-World Examples from Royalmont Academy’s BTC Program

To give you a better sense of how BTC works in practice, here are a few examples from our classrooms:

Example 1: Algebra 1, Unit 1, Lesson 1

In this lesson, students explored basic algebraic concepts through a problem involving car rentals. They had to calculate which car rental company offered the best deal based on daily rates and mileage, making the math immediately relevant to everyday decisions.

Link to Algebra 1, Unit 1, Lesson 1 Slides and Teacher Plan

Example 2: Geometry, Unit 1, Lesson 19

This lesson challenged students to apply geometric principles to design a city park. By integrating geometry into urban planning, students learned how math is used in professions like architecture and engineering, demonstrating the real-world application of their learning.

Link to Geometry, Unit 1, Lesson 19 Slides and Teacher Plan


The Goals of Building Thinking Classrooms at Royalmont Academy

At Royalmont Academy, our goal is to develop students who are not only proficient in math but are also capable thinkers. Through BTC, we aim to:

  • Foster a growth mindset where mistakes are seen as learning opportunities.
  • Encourage deep understanding rather than surface-level memorization.
  • Prepare students for real-world problems and challenges.
  • Equip students with the skills to excel in standardized tests such as the ACT and SAT.

Our approach also aligns with our broader mission of integral formation, helping students develop in mind, body, and spirit.


Experience the Difference of RC Integral Formation and BTC

At Royalmont Academy, education is about more than learning facts—it’s about forming the whole person. We invite you to explore how our unique combination of Building Thinking Classrooms and Regnum Christi Integral Formation can benefit your child, preparing them for both academic success and a life of purpose, faith, and leadership.

Schedule a visit to Royalmont Academy to learn more about how our formation model transforms lives.

Join Our Royalmont Family

Are you ready to give your child the gift of a lifelong love of learning and faith? Request information, schedule a visit, or begin the application process for the coming school year. Be part of a community that has been forming Christian leaders for over 29 years.