Coverage
Where the ground gives way.
Each subject below lists the place students most often lose it. In almost every case the failure is older than the course they are failing.
- SEC
- Pre-algebraFractions and negative numbers. Nearly every later collapse starts in one of these two.
- SEC
- Algebra IThe moment a letter stops being a mystery number and starts being a quantity that varies.
- SEC
- GeometryProof. Students who can compute fluently often cannot yet argue, and this is where that shows.
- SEC
- Algebra IIFunctions as objects rather than instructions. The abstraction that decides who continues.
- AP
- PrecalculusTrigonometry as ratio and as wave at the same time. Usually taught twice, understood once.
- AP
- Calculus ABLimits are the hard part, not derivatives. Most courses hurry past them.
- AP
- Calculus BCSeries. Convergence is the first genuinely subtle idea most students meet.
- AP
- StatisticsInference. The arithmetic is easy; knowing what has been claimed is not.
- TEST
- ACT mathematicsSixty questions, sixty minutes. Pace is the skill; content is the prerequisite.
- TEST
- SAT mathematicsFewer questions, deeper traps, a calculator that will not save anyone.
- UNI
- Calculus I–IIIFor undergraduates who arrived underprepared and have worked out that they did.
- UNI
- Linear algebra & differential equationsWhere a weak grasp of functions finally becomes unignorable.
A note on placement
The subject a student is failing is rarely the subject to teach.
A student losing marks in calculus is usually losing them to algebra learned badly four years earlier — sign errors, fraction errors, a shaky grip on what a function is. Teaching more calculus to that student is teaching on sand. The assessment exists to find the sand.
Not sure which of these it is?
That is what the consultation is for. It is unpaid precisely because working out where to start is our job, not yours.