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Instructional Support in Mathematics

Graphic for instructional support for mathematics

Teaching the content and skills described by the Colorado Academic Standards in mathematics requires an understanding of instructional practice, curriculum materials, how students learn, and how to support struggling learners. This page lists some useful resources, and for comments and questions about what is (or isn't) available here, please contact Raymond Johnson.

Best, First Instruction in Mathematics

Best, First Instruction gives all students the best opportunity to learn standards-based, grade-level content and skills the first time they receive instruction. Best, First Instruction rests on four pillars:

  • Building Relationships: BFI should deepen student agency through caring, positive, and authentic connections with peers and adults.​
  • Meeting the Needs of All Students: BFI should include accessible, equitable, and flexible instruction to meet the changing needs of diverse student populations.​
  • Creating Relevancy: BFI should engage students in authentic, meaningful, real-world, and engaging work.​
  • Fostering Disciplinary Literacy: BFI should position students to work, think, talk, and plan as experts in the content would.​

Mathematics Teaching Practices

In mathematics, a framework for Best, First Instruction combines the content and skills described by the Colorado Academic Standards for Mathematics, the Colorado Essential Skills, the Standards for Mathematical Practice, and two sets of mathematics teaching practices, described below.

Effective Mathematics Teaching Practices

The eight Effective Mathematics Teaching Practices come from the National Council of Teachers of Mathematics (NCTM), in a publication called Principles to Actions: Ensuring Mathematical Success for All (2014).

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

Equity-Based Mathematics Teaching Practices

The five Equity-Based Mathematics Teaching Practices come from an NCTM publication titled The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices by Aguirre, Mayfield-Ingram, & Martin (2013). These practices complement the eight practices from Principles to Actions, which author Danny Martin has criticized as lacking the focus on equity needed for substantial reform and improvement in the mathematical education of traditionally underserved students. Each of these five practices is expanded on in the book but are named here:

  1. Going deep with mathematics.
  2. Leveraging multiple mathematical competencies.
  3. Affirming mathematics learners’ identities.
  4. Challenging spaces of marginality.
  5. Drawing on multiple resources of knowledge.

Lesson Planning for Learning and Reflection

The resources shared here represent a sample of the nationally-known tools available to support mathematics teachers and the work of Colorado math educators. These materials are designed to go beyond typical lesson plans that describe a set of steps to do with students. Instead, these help build lessons that have a particular focus on aspects of teacher planning, instructional practice, and reflection. They are better thought of as lessons to learn from rather than to teach with, and each lesson should prompt you to think about your own approach to lesson planning and reflection. Lesson planning in this way requires using one of each kind of these four resources:

Examples of each one of these kinds of tools can be used to support planning and delivering a lesson designed to help teachers better understand and improve their own practice. For an example lesson and more information, see the math resources from Phase IV of the District Sample Curriculum Project.

General CDE-SIS Resources for Lesson Planning

As part of Phase IV of the District Sample Curriculum Project, the following resources were used to help educators of all content areas plan lessons and improve instruction.

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Supporting Struggling Learners in Mathematics

Sometimes, despite our best efforts to provide best, first instruction, or simply due to the special needs of learners, students need additional support to learn mathematics. The following resources may be useful:

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District Sample Curriculum Project

Colorado's District Sample Curriculum Project brought together educators from across the state to build curriculum support resources for the successful implementation of the Colorado Academic Standards. The project, under the guidance of the Standards and Instructional Support team, evolved over four phases and involved educators from 121 school districts:

  • Educators in Phase I (Fall 2012) translated the Colorado Academic Standards into curriculum overview samples.
  • Educators in Phase II (Spring 2013) provided feedback on the project, refined the curriculum overview samples, and directed future project work.
  • Educators in Phase III (Fall 2013-Winter 2015) developed instructional units based on the curriculum overview samples.
  • Educators in Phase IV (Summer 2016) came together to discuss instructional shifts within their disciplines and engaged in reflective lesson planning.

The mathematics curriculum overview samples for covered kindergarten through high school, with separate overviews for both traditional (Algebra-Geometry-Algebra 2) and integrated high school math course sequences. The mathematics instructional unit samples included at least one unit for each grade level from kindergarten through high school.

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Research and Practice Guides

CDE Word Problems Research and Practice Guide

Word problems have an undeserved reputation within mathematics. With a better understanding of why people struggle with word problems and ideas for supporting them in instruction, word problems can be a useful tool for learning mathematics.

PLC Bytes

PLC Bytes are 7-10 minute presentations or longer segmented presentations designed to be used in Professional Learning Communities (PLC) or faculty meetings.

Practice Guides from the What Works Clearinghouse

The What Works Clearinghouse (WWC), part of the U.S. Department of Education's Institute of Education Sciences (IES), has published a set of Practice Guides with recommendations for educators to address challenges in their classrooms and schools. The guides are based on reviews of research and are written by panels of nationally recognized experts. The practice guides cover topics ranging from using technology, preventing dropouts, to using achievement data. The six guides (as of Summer 2019) that directly address mathematics are:

Research Briefs and Clips from the National Council of Teachers of Mathematics (NCTM)

The National Council of Teachers of Mathematics provides a set of Research Briefs and Clips to provide a foundation for understanding what research says about mathematics teaching and learning to a broad audience. The 26 guides (as of Summer 2019) include reviews on teaching specific content, effective instruction, assessment, selecting curriculum, working with dual-language learners, involving parents, homework, mathematics coaching, and video games.

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STEM Education

STEM education is:

An interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons as students apply science, technology, engineering and mathematics in context that make connections between school, community, work, and the global enterprise, enabling the development of STEM literacy and with it the ability to compete in the new economy.”
- Tsupros, Kohler, & Hallinen, 2009

View Colorado's STEM Education Roadmap

  • Colorado Department of Education STEM
    This site provides a hub of STEM information and resources to support the academic achievement of all students in Colorado.
  • Colorado Education Initiative STEM
    Education Foundation committed to STEM education.
  • Colorado Experiential STEM Learning Network
    Their mission is to collaborate with schools, policy makers, and businesses in order to create extraordinary STEM experiences for students and teachers. Thus, increasing science literacy and promoting science identity construction. The network is designed to create an online and offline community of practice such that interactions lead to an action, whether it be schools reaching out to businesses for hands-on activities, or community involvement in student projects and intiatives.
  • Destination Imagination
    Encourages teams of learners to have fun, take risks, focus and frame challenges while incorporating STEM (science, technology, engineering, and mathematics), the arts and service learning. Participants learn patience, flexibility, persistence, ethics, respect for others and their ideas, and the collaborative problem-solving process. Teams may showcase their solutions at a tournament.
  • National Math and Science Initiative
    NMSI was formed to address one of this nation’s greatest economic and intellectual threats – the declining number of students who are prepared to take rigorous college courses in math and science and are equipped for careers in those fields. To flourish in the 21st Century, the United States must continue to generate intellectual capital that can drive the economic engine of our future prosperity. This crucial project was initiated as a public-private partnership, led by private donors such as Exxon Mobil Corporation, the Bill and Melinda Gates Foundation and the Michael and Susan Dell Foundation.
  • Next Generation Science Standards
    Through a collaborative, state-led process managed by Achieve, new K–12 science standards have been developed that are rich in content and practice and arranged in a coherent manner across disciplines and grades to provide all students an internationally-benchmarked science education. The NGSS are based on the Framework for K–12 Science Education developed by the National Research Council.
  • Research + Practice Collaboratory
    Research and Practice collaboratory engages researchers and practitioners around the country in an effort to address the long-standing gap between educational research and practice in STEM education.
  • STEM Education Coalition
    Works to support STEM programs for teachers and students at the U.S. Department of Education, the National Science Foundation, and other agencies that offer STEM-related programs.
  • STEMworks Database
    The STEMworks! Change the Equation (CTEq) hosts a database of programs that deepen young people's learning in science, technology, engineering and mathematics (STEM). The database aims to be a critical resource for funders, program developers and STEM advocates alike.
  • The 10 best STEM Resources from NEA
    The National Education Association (NEA) has compiled ten resources for curriculum and professional development.

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For website assistance in mathematics, please contact: 

Raymond Johnson, Ph.D.
Mathematics Content Specialist
P 303.866.6582