Designing an Online Course

Opportunities to Rethink Our Face-to-Face Courses

Andrew Adrian Pua

2025-09-29

What could online courses ever teach us F2Fers?

The pandemic

  • MOTS and BAU but in online form

  • Each one of us has designed an online course.

    • What did you learn from the experience?
    • What did you complain about?
    • Did you radically change things for your own courses?

  • Each one of us has actually attended an online course at some point.

Realities we face

  • Student preparation is never ideal
  • Never mind student retention of past materials
  • Need quick and direct solutions to onboard students
  • Cannot teach in the usual way for face-to-face classes

Motivations for rethinking

  • Environment upon which DLSU operates

    • Trimestral system
    • Rate of class suspensions getting higher
    • Playing the game of rankings
    • Maintaining the brand to justify the fees

Motivations for rethinking

  • Student welfare

    • High student workload (18*3 contact hours)
    • Complaints about fast pace leading to being overwhelmed
    • Students don’t necessarily know what their future looks like

Motivations for rethinking

  • Faculty welfare

    • Difficult to play multiple roles anymore
    • Accountability to colleagues when teaching prerequisites
    • Strong need for solutions outside the university infrastructure, especially in the age of reduced funding

What solutions have been incubating in my mind?

Distilled in one slide

  • Be brutal about shortening the course content.
  • Want to add a pet topic? Remove a different topic.
  • Don’t use up the total contact hours. Aim for using only half of it for lectures.
  • Present the difficult applications right away.
  • Exploit technology which can be reused.

Origins of the previous slide

  • Recent funding from Korean Ministry of Education for two courses:

    • Differential calculus for economic analysis
    • Precalculus in the age of AI

  • Audience: First year economics majors

  • Participation: Completely voluntary

  • Demands: Lectures and problem sets

Design choices

  • Differential calculus for economic analysis (ECOCAL1 pre-ID125)

    • 1st of 3 math courses taken by first-year economics majors
    • \(12*1.5\) offline contact hours, \(12*1.5\) online contact hours

Design choices

  • How to address student, faculty, industry suggestions

    • Content must be very short to be flexible: \(6*1.5\) online
    • Enough theory from a standard calculus course
    • Early exposure to material in intermediate microeconomics
    • Early exposure to symbolic computation in Python

Design choices

  • Precalculus in the age of AI

    • Not a course at DLSU
    • Response to observed and persistent decline in skills

  • Why this course?

    • Adding more content to ECOCAL1 was not feasible
    • More emphasis on problem solving with different contexts
    • Accept that there is AI use

Can you give examples?

Solving nonlinear equations

  • If \(x\) is on the horizontal axis and \(y\) is on the vertical axis, when does \(y= x^6 +3x^2 -2x-1\) cross the horizontal axis?

  • Let’s ask MathGPT this question.

    • It will answer using the rational roots theorem.
    • It will suggest a numerical method and produce two solutions.
    • The numerical method uses SciPy and contains many lines.

Solving nonlinear equations

  • What do you think students are supposed to learn from this?

    • What MathGPT does first
    • What MathGPT does not do on the first prompt
    • Is prompt engineering really the only solution? Is prompt engineering worth the time?
    • How do we measure time use?

Solving nonlinear equations

  • Is the question useful for first-year economics majors?

    • It shows that equations don’t have literally exact answers.
    • It shows the need for seeing abstractions.
    • It shows that students have to draw from something in order to make progress.
    • It is ‘unrealistic’ and has no conceivable application – but what about those FOCs lying around?

Solving nonlinear equations

  • There was an opportunity to graph the function, but it did not.
  • MathGPT does not give an answer drawing from the course.
  • It gives a Python script which needs to be understood.
  • Verification skills are needed. How can students take responsibility?
  • What if we change the function to \(y=x^2+x+1\)?

Solving nonlinear equations

  • Knit precalculus, calculus, applications, and the use of AI

    • Precalculus skill: graphing functions, solving equations
    • Calculus skill: Newton’s method, function curvature
    • Applications: Not all equations have an answer.
    • Economics: Can change to first-order conditions.
    • Programming: Symbolic computation using SymPy

Questions for discussion

  • What evidence suggests that reducing lecture hours will improve learning outcomes rather than weaken knowledge retention?
  • How can we simplify and reduce course content in online learning without compromising academic rigor?
  • How can students be guided to use AI tools like MathGPT critically, rather than passively relying on them?

Concluding remarks

  • Don’t miss out on alternative course delivery modes as opportunities to rethink face-to-face courses.

  • Don’t teach courses the way it was taught to you.

  • Teach so that students could be left alone to discover things.

  • Think of bringing forward advanced topics.

    • It is an opportunity to test even your own understanding!
    • Don’t shy away from them!