:: Scheduling and Using Discover Linear Algebra

The Augustana Campus of the University of Alberta has a somewhat unusual calendar: each of Fall and Winter are split into a 3-week "block" term consisting of 13 instructional days with 3 hours of instruction per day, followed by a more "traditional" 11-week term. I have taught Linear Algebra I using Discover Linear Algebra in both types of term, but have only taught Linear Algebra II using Discover Linear Algebra in 11-week terms. Below I give my typical schedules for both courses.

Note that these schedules are built on the assumption of a flipped classroom, where the majority of class time is devoted to the Discovery Guide activities and students watch lecture videos afterwards. In years before I had prepared lecture videos for this purpose, instead I scheduled every third or fourth class to be a "consolidation lecture" where I would go back over the concepts, examples, and theory from the previous two or three chapters. There are many different ways you could make this sort of thing work, depending on the duration of each class meeting and how many total hours of contact time you have over your term. Experiment and see what works for you and your students!

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 class period devoted to discovery activities, the "gaps" can be filled in with textbook reading and/or consolidation/video lectures.

A Typical Discovery Day

• I usually begin with a short introduction to get their minds back into linear algebra mode: a short recap of last time, 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. (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.)
• Then I let them loose on the new Discovery Guide in groups, encouraging them to be loud and ask lots of questions (of me, of their peers). Throughout this time I walk around the room answering questions, giving encouragement, prodding students who are not engaging, etc. I let groups work ahead at their own pace, but to ensure that the whole class eventually progresses together I give periodic time limits: "In five minutes we'll come back together and discuss Activities X and Y."
• Periodically during the class meeting I will interrupt the group work to have a brief whole-class discussion of both the "answers" and the "point" (or learning objective) of a handful of activities that most students should have completed by that point. Then I let them loose again to make more progress from that point.
• In the final 3 to 5 minutes of the period I wrap up with some "big picture" learning objectives for the topic.

Sample Term Schedules

One-semester version

11-week format

60-minute meetings, three times per week. Total of 31 class meetings.

Day 01	Discovery guide 1.1		Day 17	Continue Discovery guide 12.1
Day 02	Begin Discovery guide 2.1		Day 18	Discovery guide 13.1
Day 03	Continue Discovery guide 2.1 Make a start on Discovery guide 3.1, assign rest of Discovery Guide 3.1 to be worked on their own.		Day 19	Discovery guide 14.1
Day 04	Begin Discovery guide 4.1		Day 20	Discovery guide 15.1
Day 05	Continue Discovery guide 4.1		Day 21	Quiz 3 (Chapters 10–13)
Day 06	Discovery guide 5.1		Day 22	Begin Discovery guide 16.1
Day 07	Begin Discovery guide 6.1		Day 23	Continue Discovery guide 16.1
Day 08	Continue Discovery guide 6.1		Day 24	Discovery guide 17.1
Day 09	Quiz 1 (Chapters 1–5)		Day 25	Discovery guide 18.1
Day 10	Discovery guide 7.1		Day 26	Discovery guide 19.1
Day 11	Discovery guide 8.1		Day 27	Quiz 4 (Chapters 14–17)
Day 12	Discovery guide 9.1		Day 28	Discovery guide 20.1
Day 13	Discovery guide 10.1		Day 29	Begin Discovery guide 21.1
Day 14	Discovery guide 11.1		Day 30	Continue Discovery guide 21.1
Day 15	Quiz 2 (Chapters 6–9)		Day 31	Discovery guide 22.1
Day 16	Begin Discovery guide 12.1

3-week compressed format

90-minute meetings, twice per day. Total of 26 class meetings.

Day 01	Morning	Discovery guide 1.1 Begin Discovery guide 2.1		Day 08	Morning	Discovery guide 15.1 Begin Discovery guide 16.1
	Afternoon	Continue Discovery guide 2.1 Begin Discovery guide 3.1, assign rest of Discovery Guide 3.1 to be worked on their own.			Afternoon	Continue Discovery guide 16.1
Day 02	Morning	Discovery guide 4.1		Day 09	Morning	Review for Quiz 3 Begin Discovery guide 17.1
	Afternoon	Discovery guide 5.1			Afternoon	Quiz 3 (Chapters 10–13) Continue Discovery guide 17.1
Day 03	Morning	Begin Discovery guide 6.1		Day 10	Morning	Discovery guide 18.1
	Afternoon	Continue Discovery guide 6.1 Discovery guide 7.1			Afternoon	Discovery guide 19.1
Day 04	Morning	Review for Quiz 1 Begin Discovery guide 8.1		Day 11	Morning	Review for Quiz 4 Begin Discovery guide 20.1
	Afternoon	Quiz 1 (Chapters 1–5) Continue Discovery guide 8.1			Afternoon	Quiz 4 (Chapters 14–17) Continue Discovery guide 20.1
Day 05	Morning	Discovery guide 9.1		Day 12	Morning	Discovery guide 21.1
	Afternoon	Discovery guide 10.1			Afternoon	Discovery guide 22.1
Day 06	Morning	Discovery guide 11.1 Begin Discovery guide 12.1		Day 13	Morning	Review for Final Assessment
	Afternoon	Quiz 2 (Chapters 6–9) Continue Discovery guide 12.1			Afternoon	Final Assessment (comprehensive)
Day 07	Morning	Discovery guide 13.1
	Afternoon	Discovery guide 14.1