Math 221 - Introduction to Linear Algebra

Summer 2006 - Matthias K. Gobbert

Learning Goals and Detailed Learning Plan

This page can be reached via my homepage at http://www.math.umbc.edu/~gobbert.

Learning Goals

After this course, you should:

understand and remember the key ideas, concepts, definitions, and theorems of the subject (--> the quizzes test this foundational knowledge),
be able to apply mathematical theorems and computational algorithms correctly to answer questions, and interpret their results correctly, including potentially non-unique solutions or breakdowns (--> the homework and tests address these skills),
be able to choose the the most useful theorem or most efficient computational algorithm in a particular circumstance (--> these more subtle skills are best discussed in a learning group),
appreciate the power of mathematical abstraction and understand how mathematical theory is developed (--> these integration goals will be supported by the lectures),
be comfortable discussing mathematical ideas and algorithms with the instructor as well as other students (--> the formation of learning groups will contribute to this goal),
improve self-confidence in learning mathematics (--> self-confidence comes from implementing the learning plan below).

Role of the Instructor

With the learning goals of the students as focal point of the course, it becomes clear that you as student are responsible for active participation in your learning. I urge you to follow the learning plan outlined below.

So, what is the role of the instructor in this learner-centered environment? The role of the instructor is to help you achieve these learning goals. Concretely, the instructor will:

highlight the important ideas and concepts and put them into the context of the material of this course and mathematics and applications outside of this course,
explain how to interpret mathematical definitions and theorems and introduce computational algorithms with examples,
show how rigorous mathematical theory is developed using the topic of this course as example,
make all supporting learning aids available in a timely fashion,
be available for help and advice,
give you honest feedback on your performance and be available for suggestions how to improve,
maintain an appropriate learning environment in class.

In summary, the instructor will provide all help possible towards your learning, but, as student, you must take responsibility and initiative for your own learning in the end, because no instructor can learn for you.

Detailed Learning Plan

This learning plan is a detailed implementation of a strategy to reach the learning goals above, using the concrete teaching and learning aids available for this course. Remember that the goal is for you to actually learn the material and retain it in the long run.

We use the textbook as learning tool as well as to organize the activities throughout the semester. Moreover, we will use the course management software Blackboard to post additional information in the Course Documents area, organized by the numerical order of the textbook sections (not necessarily chronologically as covered in the course). Most information for the section will be contained there, including study guides, worked examples with voice-over, and the on-line quizzes. The only other area of Blackboard that we will use is the Discussion Board that is available to ask questions on the material at any time.

The learning plan divides activities in three parts -- before, during, and after class --, which apply to every covered section of the textbook:

Before class:
- Check the study guide posted for the section in Blackboard, which provides specific information on which pages to focus on in your reading and points to other resources available for the section, e.g., worked examples.
- Study the section in the textbook following the study guide and supported by the worked examples with voice-over.
- Take the on-line quiz posted in Blackboard and receive immediate feedback on your performance. These quizzes focus only on reading comprehension and basic vocabulary and are simply intended to prepare you for class discussion.
Before you arrive in class, you should have an overview of the material in the section, have read and/or seen several examples for its use, and be ready to attempt the homework problems under the guidance of the instructor.
During class:
- Briefly discuss with all members of your learning group to assess everybody's understanding of the material and collect questions the group would like clarified in the following lecture.
- Follow the lecture which highlights the material and puts it into context.
- Participate actively in work with all members of your learning group to start solving representative homework problems at the end of class.
I will circulate from group to group during the group work periods and be available for questions and guidance. By the end of class, you should have fully understood the material, have obtained answers to your questions either from group members or the instructor, and have an idea of how to solve most of the homework problem.
After class:
- Finish the solution of the homework problems started in class as well as solve all remaining ones. It may be helpful to re-view some of the worked examples posted in Blackboard.
- If questions arise, review the textbook, notes from class, and examples in textbook or posted on-line; monitor the Discussion Board in Blackboard for questions and answers and use it to ask your own questions if necessary.
With the shift of work towards preparing more intensively for class as opposed to seeing material for the first time in class, the activities after class should consist mainly of putting all pieces together.

In addition to the instructor, the members of your learning group, other students, as well as the entire class (via the Dicussion Board in Blackboard) are available for communications at all times.

This learning plan relies on your active participation in all learning activities; precisely for this reason, you will learn the material better, retain more in the long run, and increase your self-confidence as a learner!