In  and , the authors look at problem solving in terms of defining learning issues. In this course, when we apply problem solving techniques to the touchstone problems, the learning issues will be the various topics in numerical analysis. This top-down approach to learning provides students with a context for why the various numerical analysis techniques are important. Traditional numerical analysis courses use a bottom-up approach which first details the various numerical analysis techniques, and then uses them in example problems. To encourage learning and efficient material coverage, I suggest an iterative approach which iterates between top-down and bottom-up lecture techniques.
From a learning standpoint, the top-down approach is more effective because the touchstone problems motivate the need for numerical analysis techniques. However, the top-down approach can be very time consuming depending on how the learning issues are determined. If the instructor directly presents the learning issues then more material can be covered in the same amount of time. If the instructor coaches the students in determining the learning issues, then more interaction occurs between the students and the material. The coaching approach requires in-depth knowledge from the instructor and more time.
In order to cover a lot of material efficiently, the bottom-up approach works better, because for example many numerical analysis techniques conceptually use the same type of error analysis. To take advantage of the efficiency from the bottom-up approach and the learning benefits of the top-down approach, I suggest iterating between the big picture(top-down) and understanding the little details(bottom-up). An iterative approach requires instructors to iterate between creating context, learning issues, and intuition, and exploring the theoretical and mechanical details of the learning issues themselves. Iterating between a top-down and bottom-up the two can be considered the middle ground (or a compromise) between the traditional lecture format which disseminates a large amount of information, and the problem solving interactive format which takes longer but helps the students build the context and discover learning issues on their own.
In this course, I will coach the students in their discovery of numerical analysis learning issues. To ensure interaction, the students will be required to answer questions on an interactive participation form (see example in section 7.3) during lecture which are then turned in. The typical format will be to introduce a problem, have the students answer some questions about the problem on their own for approximately 2 minutes. Then have the students spend 5 minutes talking to their neighbors. Finally, spend 5 minutes on presentation and feedback of their responses. The forms will have spaces for how they answer the questions themselves, what things change upon peer interaction, and what things change upon full class presentation and feedback.
The bottom-up approach will be used in the required lab sections. By using a top-down approach in lecture with interactive forms, the student will develop the ability to formulate and solve engineering problems and communications skills. In lab the student will practice applying numerical methods using Matlab.