Mathematics in District 109

District 109’s curriculum balances the need for a deep conceptual understanding with procedural fluency. An opening exploration, investigation, or dig-in offers students an opportunity to question, explain, and persevere as they seek to solve problems that encourage abstract thought. The mini-lesson gives students the opportunity to develop procedural fluency using clear, precise mathematical language. Students then engage in independent practice of the skill or concept, an extension, and/or prerequisite learning. Teachers facilitate class discussion, lead number talks, organize flexible groups, provide hands-on tasks, and monitor growth.

The instructional model in K-8 mathematics classrooms is as follows:

• Exploration, Launch, Investigation, Dig-In: A discovery exploration or task that encourages conceptual thinking about the mathematical skill or concept.
• Mini-Lesson: The teacher provides instruction, modeling, and demonstration on the specific mathematical skill or concept.
• Guided Math/Math Stations: Teacher meets with groups of students for small group instruction. Other students are working on engaging activities that are mathematically purposeful, still targeting the skill or concept, but designed at their independent level.
• Daily Closing: Assessment, reflection or closure to solidify student learning and/or provide the teacher with an opportunity to gather information to plan the next steps.

Effective Mathematics Teaching Practices (NCTM, 2014)

• Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
• Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
• Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
• Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. 9
• Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
• Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
• Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
• Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

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