Evidence & Research

The Research Behind Our Approach

The CTC methodology draws from decades of research on effective mathematics instruction and the world's highest-performing math education systems.

Programs That Inform Our Methodology

Singapore Mathematics

Singapore consistently ranks #1 or #2 in international mathematics assessments (TIMSS, PISA). Their approach emphasizes mastery over speed, conceptual understanding before procedural fluency, and a systematic Concrete-Pictorial-Abstract (CPA) progression that ensures every student builds deep understanding.

CTC Integration: We adopt Singapore's mastery-based progression and CPA methodology, combined with our historical approach to provide the "why" behind each mathematical concept.

NCTM's Principles to Actions (2014)

The National Council of Teachers of Mathematics identified eight effective teaching practices supported by extensive research: establishing clear goals, promoting reasoning, connecting representations, facilitating discourse, posing purposeful questions, building fluency from understanding, supporting productive struggle, and using evidence of student thinking.

CTC Integration: All eight practices are woven throughout our workshop. Teachers experience each practice as learners, then plan lessons implementing them.

Japanese Lesson Study

Japan's Lesson Study model — where teachers collaboratively plan, observe, and refine lessons — is widely regarded as one of the most effective forms of professional development ever developed. Research shows it builds deep pedagogical content knowledge and creates lasting professional learning communities.

CTC Integration: Our workshop includes collaborative lesson planning sessions modeled on Lesson Study. Teachers leave with both a completed lesson and the skills to continue this practice at their schools.

Classical Education & ACCS Tradition

The classical education tradition — rooted in the trivium and quadrivium — has taught mathematics through original sources for centuries. The Association of Classical Christian Schools (ACCS) emphasizes logic, proof, and the integration of mathematics with broader liberal arts education. Students trained in this tradition develop exceptional reasoning abilities.

CTC Integration: Our "From Euler" methodology is deeply rooted in the classical tradition of teaching from primary sources, emphasizing proof, logical reasoning, and the philosophical foundations of mathematics.

Illustrative Mathematics & Eureka Math

These programs demonstrate the power of coherent mathematical storylines — where each lesson connects to the next in a logical progression. Their professional learning models emphasize teachers doing the math themselves before teaching it, understanding the mathematical landscape across grade levels.

CTC Integration: Our counting-to-calculus progression provides the ultimate coherent storyline — the historical development of mathematics itself — giving teachers a complete picture of how mathematical ideas connect.

What Research Says About Effective Math PD

The Institute of Education Sciences (IES) and leading researchers have identified key characteristics of professional development that actually changes teaching practice.

"Content-focused PD is significantly more effective than generic pedagogical training."

IES, 2016

"Teachers who experience math as learners first implement new methods more effectively."

Hill, 2004

"Collaborative participation (teams from same school) dramatically increases implementation rates."

Cajkler et al., 2014

"Sustained, intensive PD (14+ hours) produces measurable changes in teaching practice."

Desimone, 2009

"Active learning approaches in PD are more effective than passive lecture formats."

Givvin & Santagata, 2011

"PD that models effective teaching practices leads to higher adoption rates."

Sims & Fletcher-Wood, 2021

Experience Evidence-Based Training

Our workshop is built on what the research says works. Come experience it yourself.