The purpose of this nots is to describe how I combine projected MathCad sheets with fill-in lecture notes to deliver university-level math lectures.

The basic idea is simple: MathCad is a "white-board"-type of software in which you can combine text and live mathematics (results, graphs, etc. change in real time when you change parameter values). This makes the math come alive, and students really "see" what is going on.

A good example is the standard deviation σ of a normal distribution which will appear in the sample file given below. You can tell students until you're blue in the face that the density is more concentrated around the mean when the standard deviation σ is smaller. Alternatively, you can show with a videoprojector the density instantly changing for different values of σ and they will understand right away.

Presenting the material is one thing. An equally important issue is the manner in which students interact with and record the presentation. I've tried everything, starting with the obvious blank notebook that the students fill in by hand as they watch the lecture unfold. This is terribly slow and inefficient as students tend to want to write everything that is projected. Drawing graphs by hand is awkward and the results are obviously not very good.

At the other extreme, I've tried giving the exact projected text in paper format ahead of time: you're lucky if students come at all, and if they do come, they spend the whole lecture looking at the notes, not at the projection. They are distracted, and lack the focus that comes fom having to write things down. This is Pedagogy 101: you remember something better if you write it down than if you listen "distractedly" while doodling in the already written lecture notes.

It then seemed obvious that one should try a compromise between the two methods. At the beginning of the term I give each student a "fill-in lecture note" in paper form that has the exact same text/graphs, etc. as the projection, but with strategic bits of text deleted and replaced by enough white space for the student to fill in the blanks by hand. I remove roughly half the original text. If there are graphs, histograms, etc. I leave the empty frame if I want them to plot the graph by hand. Otherwise I leave the whole graph.

The method is flexible and it is easy to fine-tune the quantity of material left out of the fill-in notes. For example I sometimes feel that there is too much text left in the notes, and students become distracted. Next time I give the course I simply leave less text in the fill-in notes and the students pay more attention.

Click to access a Sample MathCad File that illustrate the method with an introductory lesson on the normal distribution (make sure the extension of the file is .xmcd)

The file uses data collected in a previous lecture on the heights and weight of the students by gender (HeightWeightSurvey.xls). (You may have to fiddle to make sure the MathCad sheet reads the Excel file properly).

The FillInNotes.xmcd file (and its pdf version MathCad - FillInNotes.pdf) is the MathCad file obtained by deleting the material students will have to add by hand (again, make sure the extension of the file is .xmcd).