Mathematics at Blue School
Mathematics at Blue School is about collaboration and investigation that leads to abundant, confident, and creative problem solving. Blue School believes that the crux of mathematics is reasoning. Through a balance of inquiry, numeracy and skill development, children learn to make sense of problems, think deeply about mathematical relationships, and effectively communicate their strategies for solving problems.
Our inquiry-based approach to math involves a variety of classroom experiences that prioritize the development of flexible mathematical thinkers. Students engage in mathematical investigations where they first explore ideas or materials, and then are invited to ask questions, make predictions, and work together to model their thinking. In addition to these inquiry-based learning experiences, teachers use classroom numeracy routines to support children’s number sense and skill development. Numeracy routines such as number strings, number talks, and quick images build fluency through the examination and use of relationships rather than rote memorization. At different stages of both inquiry and numeracy activities, students work independently, with partners, and in small groups.
Our teachers expose students to question-provoking scenarios that encourage them to see the world through a mathematical lens. By teaching math through contexts that are interesting and relevant to children, we develop excitement around mathematics as a tool to explore the world. In the younger grades, natural curiosity about patterns and relationships between numbers leads to numeracy development which builds a foundation for algebraic thinking in later grades.
We believe that creating confidence around mathematical skills and reasoning is important in creating lifelong mathematical thinkers. Rather than focusing exclusively on speed and a specific process or predetermined algorithm, we encourage students to construct mathematical meaning and solve problems using strategies that make the most sense to them. Teachers carefully choose questions and investigations for students and represent mathematical relationships both visually and numerically, ensuring that all students have a way to access the problem and explore a solution, regardless of current skill level and learning style. Providing all students with an entry point and fostering mathematical learning will lead to both growth and confidence in mathematics.
At Blue School, we want students to understand mathematics as it exists in the world, and consider multiple options for tackling problems effectively. To this end, we promote flexibility, efficiency and creativity in problem solving, asking students to consider which strategies lend themselves best to a situation. We encourage multiple approaches to any given problem and the development of creative strategies to tackle new, unknown scenarios.
Mathematical discussions are a key element in promoting flexibility and creativity. We provide students with opportunities to share their various methods for solving problems and reflect and revise these strategies in order to become more efficient mathematicians. Discussions take many forms and are designed with a purpose in mind. They may range from an open-strategy share to a more targeted discussion that invites students to compare and connect ideas.
Inquiry-based learning, numeracy and skill development play an integral role in developing the curiosity, confidence, and creativity of mathematicians. After students engage with a mathematical idea through investigation, teachers formalize these concepts by introducing mathematical language, skills, and opportunities for practice.
Blue School’s math frameworks are aligned with the Common Core State Standards. In grades K-5, teachers use TERC Investigations and Math in the City’s Contexts for Learning as resources for designing lessons, investigations, and skill practice. The main resources used in grades 6-8 are Connected Math and Contexts for Learning. These are resources to inform and support teachers’ planning, and are not necessarily followed in a linear order or used every day. Additional resources include Dreambox, a digital resource that shifts its content depending on a student’s progress through a series of games and concept building activities. Teachers also draw influence from various mathematical theorists such as Jo Boaler and Marilyn Burns, using textbooks and digital publications to support daily practice.
Number talks and number strings are routines that take place in every classroom at Blue School and support the development of number sense. A number talk is classroom practice where students mentally solve computation problems and talk about their strategies. A number string is a series of related problems designed to help students develop big ideas about mathematics and build their own strategies.
Skill development, number sense, and mathematical reasoning are also developed through games. Mathematical games are appropriate for students of all ages to develop fluency, solve problems and practice logical reasoning.
In kindergarten and first grade, the focus of mathematics is on representation, relation and understanding of number sense, addition and subtraction. Students focus on developing an understanding of strategies for counting and cardinality, place value, whole number relationships, addition and subtraction within 20, and reasoning with shapes and numbers.
In the second and third grade, the focus of math becomes extending students’ understanding of base-ten notation, increasing fluency with addition and subtraction, and developing efficient strategies for adding and subtracting larger numbers. These skills form the foundation of multiplication and division with the intention of developing skills around fractions, arrays and more complex two-dimensional geometry.
Fourth and fifth graders grow in their understanding and fluency with multi-digit multiplication and division with multi-digit dividends. Students clarify strategies and skills around equivalence, addition, subtraction and multiplication of fractions. Decimals, fractions and place value are also included in the students’ work as they develop greater fluency around decimal and whole number operations. Their geometric thinking evolves to incorporate concepts of parallel and perpendicular sides as well as angle measurement and symmetry.