Curriculum Guide: Mathematics
The PBS Approach
At the Phillips Brooks School, we strive to inspire all students to see themselves as mathematicians. There is a common misconception that some people are born “math people,” and we are working with our students to combat this myth. Math is not just memorization of steps to solve a problem, but requires deep thinking about why these steps work. In order to foster a deep conceptual understanding of foundational math concepts, students receive a rich, differentiated curriculum.
Bridges in Mathematics
We utilize Bridges in Mathematics, published by the Math Learning Center, as the foundation of our K–5 math curriculum. Class time includes a balance of teacher-guided instruction and student-directed inquiry. Mini-lessons pose problems and teach strategies.
Students then apply these skills: small groups participate in structured investigations, manipulatives and math tools support open-ended explorations, and workplace activities allow for practice and reinforcement of skills. Throughout the year, families receive unit overviews to stay abreast of the skills and understandings that students are developing.
Bridges offers a wealth of resources for families, with overviews summarizing each unit of instruction and optional enrichment and extension activities and games for use at home. In addition, PBS’s math enrichment coordinator maintains a Family Math Portal with even more resources for parents to learn more about math instruction. A Community Portal login is required to access the Family Math Portal.
Partnering with Stanford Researchers
Teachers also supplement with a variety of additional resources to extend student learning. Since 2015, PBS has maintained a strong relationship with Dr. Jo Boaler and has been inspired by her Stanford-based math education organization, youcubed.
Like the youcubed team, we believe that struggle is an important component of learning math, and speed is not an indication of skill. Children should not and are not labeled as “good at math” or “bad at math;" to the contrary, all students can grow and change their math mindsets through concentrated effort.
PBS students start each school year with the Week of Inspirational Math by youcubed, and Jo Boaler and her colleagues have led faculty professional development, parent education sessions, and curriculum assessments at PBS.
- Intentional Exploration: Teachers use open-ended investigations throughout units to help students see patterns, raise questions, and make discoveries.
- Differentiation: Teachers offer choices, provide manipulatives, and present students with a variety of ways to approach a problem. They add scaffolds or increase rigor to meet students at their individual learning edge.
- Ownership: Children are given choices about how to approach their work, opportunities to share their thinking, and real-world situations in which to apply their knowledge. Students come to see themselves as mathematicians.
- Communication: Students often work in partnerships and groups, learning from each other and growing as mathematicians.
- Flexibility: Children are encouraged to find multiple approaches and ultimately the most efficientl strategies to solve problems.
- Justification: Teachers require students to explain orally and in writing how they solved a problem and to support their thinking with sound mathematical reasoning and relevant examples.
- Reflection: Students are given opportunities to reflect on their development and work habits in relation to the learning goals set forth by their teachers.
Habits of Mind
- Makes sense of problems and perseveres in solving them
- Attends to precision
Reasoning and Explaining
- Reasons abstractly and quantitatively
- Constructs viable arguments and critiques the reasoning of others
Modeling and Using Tools
- Models with mathematics
- Uses appropriate tools strategically
Structure and Generalizing
- Looks for and makes use of structure
- Looks for and expresses regularity in repeating reasoning