I regularly encounter students without prerequisite skills even though they passed the prerequisite course. It shouldn't be any surprise, since a "pass "is only 50%. What does a 50% mean? Are they competent at 50% of the material? Are they 50% competent at all of the material? Some mix of the two? It's silly that our prerequisite system is based on entire courses.
Do students really need an entire course as a prerequisite? Should we perhaps be concentrating on what is fundamental in each course (especially outcomes that students struggle with) and making those the prerequisites?
Consider the Alberta Math 9 Program of Studies. There are 21 outcomes. I have highlighted the outcomes that I view as foundational, both as prerequisites to Math 10C, and to high school math as a whole.
| Math 9 Topics | Number of Outcomes |
|---|---|
| Powers with integral bases | 2 |
| Rational Numbers | 1 |
| Order of Operations | 1 |
| Square Roots | 2 |
| Linear Equations | 4 |
| Polynomials | 3 |
| Circle Geometry | 1 |
| 3D Surface Area | 1 |
| Similarity of Polygons | 1 |
| 2D Scale Diagrams | 1 |
| Line and Rotation Symmetry | 1 |
| Data Analysis (Samples etc.) | 2 |
| Probability | 1 |
So now instead of evaluating 21 outcomes as a prerequisite, just evaluate the above highlighted 11. This will give a much better prediction of student success in Math 10C. But it gets easier than that, because carefully chosen assessments of Polynomials will also assess Powers with Integral Bases. Similarly, assessments of Linear Equations will also assess Order of Operations.
Similarly, consider Math 10C. There are 18 outcomes. I have highlighted the outcomes that I view as foundational, both as prerequisites to Math 20-1/20-2, and to Math 30-1/30-2/31.
| Math 10C Topics | Number of Outcomes |
|---|---|
| SI & Imperial Units | 3 |
| Trigonometry | 1 |
| Factors (Numbers) | 1 |
| Irrational Numbers | 1 |
| Powers with Integral and Rational Exponents | 1 |
| Polynomial Multiplication | 1 |
| Polynomial Factoring | 1 |
| Relations (General) | 3 |
| Linear Functions | 5 |
| Systems of Linear Equations | 1 |
Evaluating the highlighted 8 outcomes, rather than all 18, will give a much better prediction of student success in Math 20-1/20-2.
Of course, it goes without saying that these prerequisite assessments should include conceptual understanding as well procedural understanding. (Don't get me started on "good guys and bad guys" for solving equations 😃.)
My 2 cents on our prerequisite system.