Concept before question
No question is attempted until the idea behind it can be stated in the student's own words.
Teaching method
Mathematics becomes easier when the student understands the logic behind it
Memorized procedures collapse the moment a question is phrased unfamiliarly. Understanding does not. Every lesson is built to move a student from the first state to the second.
That is slower in week one and considerably faster by week six.
Four principles, applied every lesson
One method, then a second
Two routes to the same answer, compared for speed and risk. Choice is what creates confidence.
Silence is part of teaching
The student solves alone in every lesson. Watching that happen is how gaps are found.
Homework follows the lesson
Assigned from what actually happened, and reviewed at the start of the next session.
The error log
Mistakes are data, not verdicts
Every wrong answer is classified. After three weeks a pattern is usually obvious, and the plan changes to attack that pattern rather than covering topics evenly.
Students see their own log. It is the fastest way to prove that a weakness is fixable.
| Error type | Domain | Logged |
|---|---|---|
| Sign error when rearranging | Algebra | ×7 |
| Misread the axis scale | Data Analysis | ×5 |
| Chose the slower method | Advanced Math | ×4 |
| Did not draw the figure | Geometry | ×3 |
| Answered the wrong quantity | All domains | ×3 |
Sample data shown for design purposes. Real logs are per student and private.