The Compass math curriculum was designed using a constructivist approach to mathematics. Tasks and lessons are designed to give children space to create, invent, experiment with, and make sense of mathematical ideas and truths through exploration, collaboration with others, and reflection on their own practices. The intention of constructivist mathematics is to help children see the math period as a time to make sense of and communicate about math rather than finish a set of tasks.
Content Spiral: Our math curricular scope and sequence is carefully designed to be a coherent spiral. Throughout the K-5 progression, there are many opportunities to return to specific mathematical content areas and concepts in order to have multiple chances to master strategies, make connections, and support students in building upon their schema for numbers and space.
Common Core State Standards for Mathematical Practice: We incorporate the Common Core State Standards for Mathematical Practice into our curriculum. These practices emphasize critical methods and strategies for effectively communicating and logically solving math problems.
Mathematical Literacy: We strive to make our students literate in the language of mathematics. Compass students are given experience in dissecting the language of word problems and are prompted to explain their mathematical thinking in written response. Our end of workshop discussions provide many opportunities for students to verbally explain their problem solving methods and receive constructive critique about their clarity.
Computational Fluency: While implementing a constructivist curriculum we also emphasize the importance of computational fluency. After proving that they have conceptually mastered specific areas of mathematics, we encourage students to adopt efficient knowledge and practices for problem solving. Examples of this include having automaticity in combinations of 10 or multiplication combinations of numbers up to 12, as well as specific efficient algorithms or procedures.
Reasoning and Logical Problem Solving: Our math block provides students and teachers time to explore complex problems as a class. Teachers select or write problems with rich, engaging contexts, multiple entry points for the range of students in the class, and enough difficulty to make students grapple with disequilibrium without becoming discouraged. In each classroom, educators place emphasis on the problem solving process.
Daily Structure of Math Workshop
Math Workshop is comprised of the following elements. These elements aren’t stagnant and may or may not be completed in this order each day.
Setting up the Activity: At the beginning of the workshop, the teachers set up the situation or activity in which students will explore. This may include discussing specific learning benchmarks and goals for the day, posing a problem or a task, discussing past work, or modeling an activity. This element may happen once in the lesson or multiple times depending on the length of each exploration.
Exploration and Work Time: Students work within the context of the activity that was set up. This may include exploration of a topic or problem, small group or partner work, playing games, or doing individual work. During this time, teachers are conducting guided math groups or rotating throughout the room to support or assess individual students or groups.
Discussion/Share: At the end of each math workshop, there is a discussion or share. This is a forum for students to be exposed to new strategies and ways of thinking about math. Students spend time explaining, defending, and justifying their own work to other class members. Students also evaluate, critique, and question the work that others did during the work time. Together as a group, the students make new assumptions and create new rules surrounding mathematical topics. They also evaluate how the work they did during the exploration time aligned with the learning benchmarks or solved the problem that was posed at the beginning of the math workshop.
We believe that no one math curriculum is perfect for fitting the needs of a diverse range of learners. We use resources and lessons from a variety of curricular sources that emphasize a constructivist, problem-based approach to mathematics to piece together engaging units of study that meet the benchmarks, skills, and practices detailed in the New York State and Common Core State Standards. Our main curricular resources will be comprised of TERC Investigations, Contexts for Learning, and Marilyn Burn’s Math Solutions materials