Common Core Learning Standards for Mathematics
In the Mamaroneck School District we teach the Common Core Learning Standards for Mathematics. "They build on the best of existing standards and reflect the skills and knowledge students will need to succeed in college, career, and life. Understanding how the standards differ from previous standards—and the necessary shifts they call for—is essential to implementing them."
The three major shifts in the standards are: greater focus on fewer topics, coherence, and rigor. By focusing on fewer concepts, students get the opportunity to dig deeper and master the concepts needed to solidify their mathematical foundation. Students apply and extend previous understandings to create a coherent body of knowledge made up of interconnected concepts across the grades. Rigor does not mean making math harder or introducing topics at earlier grades, however it refers to deep, authentic command of mathematical concepts. The three aspects of rigor in the major work of each grade are: conceptual understanding, procedural skills and fluency, and application.
Our Math Curriculum
The Mamaroneck School District uses a mapping process to plan out our math curriculum. Over the last several years, the math coach and the teachers have taken part in mapping sessions, which provide a forum for teachers to plan collaboratively with their grade-level colleagues from the four elementary schools. This allows teachers to look closely at lesson objectives, have reflective conversations about the content, share best practices, and gather resources. The maps are available to the staff on the district website along with an abundance of additional resources.
The Engage NY Math Curriculum is the elementary mathematics program that the Mamaroneck District chose to implement to teach the Common Core Learning Standards. The Curriculum Modules were written over a two-year span to meet the Common Core Standards. Ongoing revisions are being made to the Modules based on teacher feedback. The Modules include detailed lesson plans, sprints, problem sets, exit tickets, homework, and mid- and end-of- module assessments. The sprints are designed to build computational fluency. The exit tickets are used as a quick assessment of the daily objective.
We are continuing to apply our mapping process to adapt the Engage NY Math Modules to meet the diverse needs of our students. As we meet, we identify opportunities to differentiate and enrich instruction while gathering and creating additional resources to supplement the modules. Some of the resources include:
- Adapted student pages (for example: provided more work space, added lines for explanations)
- Skill building games (for reinforcement and extension of concepts and computational fluency)
- Vocabulary cards with pictorial representations (for bulletin boards and students journals)
- Challenge and extension projects
- Tiered lesson plans (see below)
- Guided math activities (see below)
As educators we understand children have different degrees of readiness for mathematical learning. We meet this range of needs through well-established models of instruction, including tiered lesson planning and guided math.
Tiered instruction is a layered lesson. A teacher selects an objective, teaches a mini-lesson to the whole class, and immediately assesses for understanding. Based on that feedback, students are grouped and assigned parallel tasks, all of which pertain to the day's lesson, but are tiered to meet the students' needs. Because the groups are based on real-time assessment, they are flexible. This allows students to work at their own pace with material that is accessible to them, thereby maximizing learning outcomes. The classroom teacher is able to either meet with small groups or move throughout the room guiding, assessing, and supporting students. All tiers should build understanding, challenge students, be engaging, and respect all learning styles.
Teachers in our district have had ongoing opportunities to learn about and implement Tiered Instruction in their classrooms. They have reviewed samples of tiered lessons, designed instructional plans with their colleagues, and participated in demo lessons as part of their professional development.
"Tiering is a readiness-based instructional approach in which all students work with the same essential knowledge, understanding, and skill, but at different levels of difficulty based on their current proficiency with the ideas and skills. Tiering enables a student to work both with critical content at an appropriate challenging level." (Tomlinson, Carol A and McTighe, Jay, Integrating Differentiated Instruction and Understanding By Design, Virginia: Association for Supervision & Curriculum Development; 1st edition, 2006).
Another opportunity to differentiate instruction even further is through Guided Math. These lessons are used to further support students who struggle with basic number sense and computation and to provide enrichment for others. These lessons do not necessarily pertain to the current unit of math study, but instead meet students' needs in developing their understanding of numbers and operations. During guided math the teacher works with small groups of students.
The goal of instruction is to maximize student potential. Only students who will benefit from a particular lesson take part in the group. This also means that not all students in a class will receive guided math support, because their needs can be met within the structure of the math workshop. The guided math lesson is focused on one skill related to number sense and operations. By maintaining a narrow focus for the lesson, the teacher maximizes success. The teaching point is determined by continuous student assessments and observations. The groups are fluid and temporary, depending upon the needs of the class and the students. The instructional time varies per lesson and per group depending on the topic. The lessons are scaffolded to support the gradual release of responsibility. A teacher's goal for his or her students is independence - the ability to solve a problem or apply a strategy consistently when doing independent work. In a guided math lesson, a concept or strategy is introduced with the support of manipulatives, visual representations, and verbal/written prompting. These supports are gradually removed as a child gains confidence and they are able to demonstrate the skill independently.