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Online resources for active learning in college mathematics

Curricula, textbooks, and activities (by course)

Active Calculus textbook series (3-semester sequence, free PDF)

Calculus in context textbook series (2-semester sequence, free PDF)

Calculus (1-semester text from the "Discovering the Art of Mathematics" project, a really interesting approach, PDF)

Active learning materials for calculus (misc. activities and "tactivities" from the Boulder/Omaha Active Learning Alliance)

Combinatorics through guided discovery textbook (complete textbook, free PDF)

Intro to proof via IBL (complete text for an intro to proof course, e.g., M307)

Number theory through inquiry (complete textbook, PDF)

Number theory (complete textbook from the "Discovering the Art of Mathematics" project, PDF)

Inquiry oriented linear algebra (complete curriculum for a first course in linear algebra)

An inquiry-based approach to abstract algebra (complete textbook, PDF)

Teaching abstract algebra for understanding (a complete active learning course in Abstract Algebra)

Differential equations - Chris Rasmussen:

Chris Rasmussen and colleagues have developed and studied active-learning approaches to differential equations for the past 15 years. I don't know that there is a curriculum online, but there are a lot of papers that describe the approach and some activity sequences:

Contemporary mathematics/Math for liberal arts: Discovering the art of mathematics series (11 books with interesting mathematical topics, e.g., art, dance, knots, infinity. Plus, an extensive website with other resources)

Closer and closer (first course in real analysis. The link takes you to the instructor's guide. The textbook isn't available for free) 

Questioning and classroom voting

Resources for classroom voting (e.g., clickers) in mathematics. 

Free classroom voting systems

  • Plickers (students hold up cards, teacher scans the room with a cell phone to collect votes. Up too 100 votes at a time)
    To use LaTeX with Plickers, use these steps from Gerald:
  • Poll everywhere (students respond via cell phone or internet device—app, web, or text. Free plan is limited to 40 responses per poll)
  • (free,  web-based. Students respond via Internet device)
  • Socrative (web- or app-based. Up to 50 responses per poll for the free version)
  • "Analog" clickers: colored paper

Flipped classroom

Places to find videos:

  • Video lecture archive: hundreds of courses, arranged by topic
  • MIT OpenCourseWare: Free, complete courses in every class you can imagine. Mostly, these are videotaped lecture sessions of course meetings at MIT. The lectures are complete, course-length lectures.
  • "Just Math Tutorials" - short videos (3-10 min) on a wide variety of topics from algebra to differential equations
  • Khan academy: Like PatrickJMT, short videos on a wide variety of topics, from kindergarten through introductory diff eqs. 
  • Videos arranged by course. Combination of short, topic-length videos (like Khan Academy and Patrick JMT) and course-length lectures. 


Journal of inquiry-based learning in mathematics (refereed course notes for IBL in a myriad of courses included calculus, analysis, topology, linear algebra, abstract algebra...)

PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies (peer-reviewed practitioner-focused journal, whose mission is to serve as a forum for "exchanging ideas about teaching collegiate mathematics." Many of the articles document teaching sequences.)