4 minute read
Trinity mathematicians are grounded in conceptual understanding
By Jill Gough, Director of Teaching and Learning
All too often, children see mathematics as isolated facts and rules to be memorized and recalled quickly. Far too many people decide that they are not a math person based on these poor criteria. At Trinity, students are expected to develop deep and connected knowledge of mathematics and are engaged in learning environments rich in the use of multiple representations. Just as we “make a movie in our mind” when we read, we must see mathematics in words, pictures, numbers, and symbols. We want all students to know that they are capable of learning math at a high level and that being fi rst and fast is not what makes them good at math. Our broadened, more inclusive defi nition of success encourages students to take the time needed to develop deep mathematical understanding and enjoy learning mathematics. We host Embolden Your Inner Mathematician sessions for parents because we want our pedagogy, practices, and tools to make sense to our community. We appreciate the trust our families place in us as we grow our students’ mathematical profi ciency by building procedural fl uency grounded in conceptual understanding. We intend for all our students to see themselves as capable, confi dent mathematicians. We know that not everyone learns the same way and that mathematical fl exibility increases understanding and off ers multiple pathways to success. When we make sense of another’s reasoning and problem solving, we strengthen our own fl exibility and deepen an important life skill: the ability to think deeply about another’s thinking, seeking fi rst to understand and learn. At Trinity, we demonstrate a commitment to high-quality math instruction and professional development. With our two math specialists, we have ongoing job-embedded professional development in which we study and implement known, researched best practices. In our course Embolden Your Inner Mathematician, we study the National Council of Teachers of Mathematics’ Taking Action: Implementing Effective Mathematics Teaching Practices series, during which we learn, “Equitable teaching of mathematics includes a focus on multiple representations. This includes giving students choice in selecting representations and allocating substantial instructional time and space for students to explore, construct, and discuss external representations of mathematical ideas.”1 At Trinity, learning is our focus. Trinity Teachers and faculty leaders invest in research and best practices to make a diff erence for every student. We have learned that math is not and should not be taught as it was taught in the past. We know that automaticity is important, though it is not most important. We want more, so much more, for our students. Our emphasis on understanding, problem solving, and critical reasoning is paramount to growing their deep, rich mathematical ability. At Trinity, collaboration is our culture. Using the research from NCTM’s 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Schwan Smith and Mary Kay Stein, we plan as a teaching team to anticipate and makes sense of multiple strategies, pathways, and procedures to foster a sense of creativity and curiosity so that students engage, understand, and contribute to a culture of learning. We invite diverse, creative thinkers to share and learn together to broaden and deepen what we know and need to know.
At Trinity, results guide our decisions. Our high standardized test scores show that our students are strong mathematicians and fl ourishing under our math instruction. In addition, our daily, ongoing assessments allow us to know our students individually and motivate us to do more for each student. While our students are learning and their standardized test scores are strong, the results we are seeing cause us to crave more success for our students. Alongside our ethos of learning, collaboration, and results, Trinity’s program and pedagogy focus on inclusion and equity. Possessing a deep conceptual understanding of mathematics not only propels students to learn more, but also opens future pathways that may otherwise be limited. As stated by Smith and Stein, “Equitable teaching of mathematics focuses on going deep with mathematics, including developing a deep understanding of computational procedures and other mathematical rules, formulas, and facts. When students learn procedures with understanding, they are then able to use and apply those procedures in solving problems. When students learn procedures as steps to be memorized without strong links to conceptual understanding, they are limited in their ability to use the procedure.”2 We are dedicated to meaningful educational experiences in which conceptual understanding opens doors for our students rather than limits them. As a community, we are focused on high-quality diff erentiated instruction that leads to deep understanding. We are motivated and driven to learn more so that we continue to serve our young learners in the spirit of our mission, “Serving children age three through Sixth Grade, Trinity School creates a community of learners in a diverse and distinctly elementary-only environment, in which each child develops the knowledge, skills, and character to achieve his or her unique potential as a responsible, productive, and compassionate member of the School and greater community.”
Confident and curious, Kindergartner Riley identifies patterns found in choral counting and demonstrates strong algebraic reasoning.
1Victoria Bill and DeAnn Huinker, Taking Action: Implementing Effective Mathematics Teaching Practices in K–Grade 5, ed. Margaret S. Smith (Reston, VA: National Council of Teachers of Mathematics, 2017), 140. 2Margaret Schwan Smith and Mary Kay Stein, 5 Practices for Orchestrating Productive Mathematics Discussions (Reston, VA: National Council of Teachers of Mathematics, 2011), 93.
