A Detailed Look at Trinity's Approach to Mathematics

A Detailed Look at Trinity's Approach to Mathematics

Trinity utilizes a constructivism model for mathematics as developed by Dr. Catherine Fosnot, author of over 70 books on math and Professor Emerita of Education at the City College of New York. Constructivism helps students go beyond memorizing math facts (e.g., multiplication table) or procedures (e.g., long division). With constructivist mathematics, kids develop a deep understanding of the numerical relationships that the facts and procedures represent. Students progress from counting strategies to additive thinking to multiplicative reasoning to proportional reasoning, and finally, to functional reasoning.

Traditional math and constructivist math actually start in the same place. In kindergarten, students begin by literally counting objects. They progress to group adding (5+5+5+5) or skip counting (5, 10, 15, 20), which dovetails into concepts like multiplication and division. This is the point where traditional math starts to become overly dependent on memorization.

With constructivism, students continue to develop their conceptual thinking in a way that leads to a deep and intuitive understanding of numerical relationships. This is crucial for higher-level math courses that rely on proportional reasoning and functional reasoning.

"When students start relying on memorized procedures too early, their thinking gets more and more hollowed out as they progress to higher levels of math. When we confront them with brand new situations they've never seen before, they are much more likely to get stuck."

Mark Pietka
Middle School Math Specialist

Compared to a more traditional model, the teacher demonstrates how to solve a problem, and then the students practice with and without the teacher's help. Students can learn this way, but when they see a path to the solution at the front end, they are much more likely to memorize the steps, regurgitate it for the test, and not truly absorb and retain those problem-solving skills.

At Trinity, teachers establish some basic principles, and then students lead the discussions and do the heavy lifting. We trust kids to confront problems head on and give them room to work through things independently. That "productive struggle" unveils insights to students in a very personalized way, which builds a love of learning and leads to a deep understanding. True comprehension is much more elusive without this struggle.

"The students have to do the hard work of learning themselves. At my best, I facilitate that learning and get out of the way, so they can do what they need to do."

Andy Petusky
Middle School Math Teacher (Geometry, Algebra II, Programming)

Trinity's approach is not only about developing a rich conceptual framework. We also prioritize meeting every student where they are. Students are not in the exact same place in terms of how they are thinking about a particular mathematical concept. There's a range, and that's completely normal. Our teachers account for this range, nudging students at a pace that works best for them. We ensure the material is accessible to kids who need a little more guidance while challenging those who are on their way to mastery.

Check out the video below to learn more about Trinity's philosophy and approach to mathematics. You'll see teachers and learning specialists give concrete examples of our constructivist approach and how it evolves through grades K–8. Please feel free to reach out if you have any questions!


Parent Meeting: Our Meaningful Approach to Mathematics

Get even more details by watching this parent meeting recorded Oct. 26, 2022.

In this video, you will get an overview of constructivist mathematics, walk through a "problem string" exercise, and learn how Trinity holistically and intentionally plans for the entire student journey, from kindergarten through 8th grade. There are time-stamp links in the video description, so you can quickly see an outline of the discussion and jump to topics.

0:00 Our Approach at a Glance
Head of Lower School Shanna Prewitt-Hines, Head of Middle School Shanna Weiss, and Middle School Math Specialist Mark Pietka introduce Trinity's approach and philosophy for teaching mathematics

04:52 "Problem String" Exercise
Third Grade Teacher Marisa Brody walks through a "problem string," a common exercise we use to develop creativity and problem-solving strategies.

14:55 Development of Mathematical Thinking
Ms. Brody explains where traditional math instruction goes wrong and explains how Trinity helps students progress from counting strategies to additive thinking to multiplicative reasoning to proportional reasoning to functional reasoning.

21:00 The Landscape of Learning
Ms. Brody outlines how we meet students where they are and help them progress at level that's right for them.

23:29 Memorizing vs. Constructing
Instructional Support Specialist Delane Weber explains that kids need to know "math facts," but first we want them to construct their own understanding of the numerical relationships that those facts represent.

26:25 Grades K–2
Second Grade Teacher Elizabeth Trull uses one mathematical concept (i.e. measurement) to show the progression from kindergarten through 2nd grade.

32:14 Grades 3–4
Ms. Brody continues looking at the concept of measurement for third and fourth grade

35:13 Grades 5–8
Mr. Pietka shows how middle schoolers start applying proportional reasoning.

37:51 Prepared for the Next Level
Middle School Teacher Andy Petusky shows how Trinity's approach prepares students for functional reasoning, which they will use in high school and beyond.

47:35 Course Trajectory
Ms. Weiss explains how grades K–6 lay the foundation for more advanced pathways beginning in 7th grade.

50:20 Measuring Success
One qualitative measurement of success is comments from high school faculty and staff, who tell us that Trinity students are often leaders in their high school math classes. We also track quantitative metrics and national benchmarks.

53:34 Summary & Conclusion
Ms. Weiss and Ms. Prewitt-Hines explain why we use an integrated, constructivist approach and how it helps kids develop a deep understanding of mathematical concepts, which leads to success in high school and beyond.