Discover Linear Algebra works best in some degree of “flipped” classroom, where a majority of class time is devoted to working through discovery guides in groups. Discovery sessions can be followed up with textbook readings and consolidation lectures, whether delivered through pre-recorded video or by scheduling every third or fourth class meeting as “traditional” lecture to review.

• Students should work on each Discovery Guide before reading the corresponding chapter in the book — the book is structured to allow students the opportunity to discover many of the basic patterns for themselves!
• As much as possible, access to the textbook/internet/chatbots should be restricted while working through each Discovery Guide, to remove the temptation to shortcut the discovery process. Instead, display the Discovery Guide from the online version of the textbook on the classroom screen and/or have the students print it out before class.
• Note that it is not necessary (nor is it really intended) for every student to complete every problem of every Discovery Guide. The point is the journey, not the destination. As long as the students are engaged, focussed, and making reasonable progress during a discovery session, the "gaps" can be filled in with textbook reading and/or consolidation/video lectures.

1. Begin with a short introduction to get the students' minds back into linear algebra mode: a short recap of the previous period; examples; some bit of theory that deserves highlighting; motivation for the day's new topic; some important fact(s) they'll need to recall to make good progress on the day's new activities; etc. (Don't try to cram all of this into every start-of-class intro! Pick and choose what is appropriate for that day, taking care not to take too much time centred on the instructor and away from what's really important: student engagement in their own learning.)
2. Let them loose on the new Discovery Guide in groups. Encourage them to be loud and ask lots of questions (of the instructor/TAs, of their peers).
3. Throughout this time, walk around the room answering questions, giving encouragement, prodding students who are not engaging, etc.
4. Let groups work ahead at their own pace, but to ensure that the whole class eventually progresses together, give periodic time limits. E.g. “In X minutes we'll come back together and discuss Activities Y and Z.”
5. Periodically during the session, interrupt the group work to have a brief whole-class discussion of both the “answers” and the “point” (learning objective) of a handful of activities that most students should have completed by that point. Then let them loose again to make more progress from that point.
6. In the final few minutes of the period, wrap up with some “big picture” learning objectives for the topic, and/or a preview of how the day's topics lead into the next.

Some sample scheduling scenarios

These assume a flipped classroom model with follow-up textbook reading and/or video consolidation lectures.

One-semester version

31 × 60 min 24 × 90 min

Two-semester version

First semester Follow the one-semester version schedule for the first semester (adjusting chapter numbers as necessary).
Second semester 31 × 60 min

Addition of end-of-chapter exercises (with answers/solutions) to Discover Linear Algebra is on-going. In the interim, 3,000 Solved Problems in Linear Algebra (Lipschutz) is an inexpensive supplementary textbook for students to use as a source of solved practise problems. Here are chapter-by-chapter lists of practise problems that can be recommended to students from this supplementary text.

One-semester version

Two-semester version

First semester Use the One-semester version practise problem lists above for those chapters that overlap, taking care to adjust the chapter numbers.
Second semester

Chapter-by-chapter WeBWorK problem sets for Discover Linear Algebra. The problem sets are not balanced — some chapters have a lot of problems, some only a few. The average is 8 problems per set, which may seem low, but is based on the philosophy that large numbers of repetitive, algorithmic, calculation-based "drill" problems are best left as practise problems (see above).

In each case, unzip into your WeBWorK course's templates directory, import the .def files using WeBWorK's Hmwk Sets Editor, and then adjust the opening/closing dates for each set.

One-semester version

Note If you are using this collection for the first semester of a course using the two-semester version of the book, you will need to adjust some chapter numbers.

Two-semester version

Note This collection is only for those chapters that are not shared with the one-semester version (so only for the second semester), and assumes that the second semester will begin with a selected review of the first semester.

DISCLAIMER These are not professionally produced/edited. Use at your own risk.

Note YouTube started forcing ads even in educational videos a few years ago. Despite the presence of ads, these videos are not monetized, and I don't make any money from them.

One-semester version Additional videos for two-semester version