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Mathematics course materials

The careful design of curriculum and pedagogy has the power to change students’ lives. The Dana Center’s current higher education curricular resources serve three aligned mathematics pathways: quantitative reasoning, introductory statistics, and the path to calculus.

These courses may be adopted together, individually, or may be used as exemplars by curriculum committees as they engage in the design or selection of course materials. The in-class activities, along with the accompanying homework, are openly available for use by any instructor. 

All of our course materials are available to faculty and curricular leaders at K-12 and postsecondary institutions for free download.

Request access to the materials

In addition, a college-level learning frameworks course, Frameworks for Mathematics and Collegiate Learning (FMCL), is available for download from the Dana Center Mathematics Pathways website. Similar to a student success course but incorporating elements of learning science, this course supports students in developing mindsets and strategies to increase persistence and success.

Explore below for more information about the research-based design of the courses.

DCMP Course Design

  • Overview

    Individual Dana Center Mathematics Pathways (DCMP) courses form pathways for students to and through college-level mathematics. The concept of the pathway is critical, as these courses are designed to articulate in a way that provides students with the experience of learning mathematics and/or statistics through coherent, consistent practices and structures.

  • DCMP Curriculum Design Standards & Learning Goals

    All DCMP mathematics courses are designed around eight standards and five learning goals that are aligned with recommendations from national professional mathematics and statistics communities. Learn about the standards and goals here. Additionally, learn more about how the five learning goals are applied in each course by visiting the specific course pages.

  • Common Design Features

    The in-class component of each mathematics course is designed as a series of 25-minute learning episodes. Episodes can be pieced together to conform to any class length. These short bursts of active learning, combined with whole-class discussion and summary, are linked to increased memory retention.

    Each three-step lesson cycle includes a preview assignment, an in-class activity, and a practice assignment.

    • Students complete the preview assignment on Lumen's Ohm platform before attending class. This helps to refresh the background skills necessary to successfully engage in the class activity. 
    • Students actively engage in doing mathematics during class. Students work in collaboration with peers. In-class activities are application-based and use authentic contexts whenever possible. They are available in a pdf document that institutions or students can print or use digitally.
    • Students complete the auto-graded Lumen Ohm practice assignment after class, practicing skills within a new context or extending their learning within the same context.
  • Embedded Student Success Features

    DCMP mathematics courses contain both overt and covert features designed to create stronger learners.

    Overt features include:

    • A short series of student success lessons within each course helps students develop behaviors of self-regulation, help-seeking, community building, and useful study habits.
    • Preview assignments that teach students the value of advance preparation. Each preview contains a section in which students monitor their own learning and engage in metacognitive analysis of their level of preparation.
    • A variety of scaffolding options to promote constructive perseverance.
    • Resource pages in the student notebook that provide support with explanations of foundational skills. These resources help students develop their skills and understanding by providing definitions, worked examples, and explicit connections to prior learning. These serve as an additional resource for at-home and in-class work.


    Covert features include:

    • A variety of scaffolding options to promote constructive perseverance.
    • Resource pages in the student notebook that provide support with explanations of foundational skills. These resources help students develop their skills and understanding by providing definitions, worked examples, and explicit connections to prior learning. These serve as an additional resource for at-home and in-class work.
  • Pedagogical Approach

    DCMP courses are designed to actively engage students in doing mathematics during class by posing non-routine, non-familiar math problems. These offer multiple entry points to promote concept development and constructive perseverance.

    Preview assignments reduce the need to spend class time refreshing background skills and introducing new definitions and concepts. During class meetings, instructors guide a brief opening discussion. They then circulate the room, acting as facilitators while students collaborate with their peers in completing carefully scaffolded, student-centered learning activities.

    At the end of each activity, instructors play a vital role by ensuring students have extracted the intended mathematical content from the applied context and made connections to prior and future learning.

  • Support for Instructors

    Extensive lesson planning suggestions accompany each class activity. Suggestions are written to provide comprehensive guidance to first-time instructors of the course. Instructors are invited to modify these plans as necessary to meet the needs of their students.

    Instructor supports include:

    • Framing for lessons—ideas for multiple entry points to facilitate collaborative learning.
    • Suggestions to create opportunities for discussion of different mathematical approaches and strategies.
    • Facilitating and guiding questions to support students’ constructive perseverance.
    • Grouping strategies to promote effective collaboration.
    • Literacy supports to highlight potential vocabulary challenges.
    • Wrap-up guided discussion suggestions to dispel misconceptions and provide opportunities for students to check the reasonableness of ideas and results.
    • Technology suggestions when appropriate, including spreadsheets, calculators, statistical software, interactive components and more.
  • Corequisite Support Courses

    Most DCMP courses have companion co-requisite support materials, based on the following design considerations:

    • Corequisite support courses should run throughout the term and should provide adequate contact hours to support the success of underprepared students. We recommend three contact hours per week for our support courses.
    • Corequisite support courses should be highly-structured rather than a tutorial period or homework lab. We provide worksheets for use in the support course that are backmapped from the parent course activities.
    • Students work collaboratively on the support course worksheets; this work prepares them to be able to complete the upcoming preview assignments on their own.
    • Instructor suggestions are provided for each worksheet.
    • A variety of calendaring options are suggested for both cohort and co-mingled implementation models.
    • Additional structures and support course options exist for underprepared students at different levels.

    Since these materials are aligned with DCMP activities, they are only suitable for use with the partner DCMP course. In general, they are unlikely to work well as support for traditional texts.

    Our professional learning team offers services in designing corequisite course structures and content. Visit the professional learning page to learn more.

  • Supporting Departmental Course Redesign

    A textbook is a resource, not a curriculum. When redesigning courses, departmental design teams have many factors to consider related to structure, content, and pedagogy. We encourage teams to use any of the resources provided here and on the individual course pages when engaging in their redesign and development work. These resources provide information on design standards and learning goals, embedded student success strategies, and others. Our professional learning team offers services to support departments engaged in course redesign. Visit the professional learning page to learn more.

Student Voice

Holly completed the Foundations of Mathematical Reasoning and statistics courses.

Watch the Video

Online Homework Platform

The Dana Center has partnered with Lumen Learning to provide faculty and students with an optional online homework platform for these courses. To learn more about using the Dana Center’s courses on Lumen Learning's Online Homework Manager (OHM), fill out this form.

Learning from the Practitioners

In this three-part series titled Learning from Practitioners, two field practitioners walk us through how adopting the DCMP courses has impacted them and their institution. The series consists of an overview, classroom norms, and classroom engagement.

Watch and learn if the DCMP courses can work for you and your institution.