Most students are taught mathematics as a list of rules to be obeyed. Some of those rules are theorems, and a student who knows which is which is a different kind of student.
Mathematics is the only school subject where a child can be told the truth and still not believe it, because nobody showed them why it has to be true. That gap is where confidence is lost, and it is almost never a gap in ability.
So the work here is not covering topics faster. It is closing the distance between what a student can do and what a student can justify. A child who can justify a method can rebuild it when they forget it, which is what an examination actually tests once the questions stop being routine.
One question, answered three times. This is not a syllabus. It is what the same idea looks like at three different ages, and it is the clearest way to show how your child would be taught rather than tell you.
We write out a times table and walk it downwards, one step at a time, and the child reads the pattern out loud.
Then we do the same with a negative on the left and let them predict the next line before I write it.
Every step so far has gone up by three. The child says plus three before I do. Nobody has been told a rule and nobody has been asked to remember one.
By this age a pattern is not enough, and it should not be. So we assume only one thing, that multiplying out brackets works the way it always has, and see what it forces.
The left hand side is zero. So has to be the number that turns into zero, and there is only one of those.
This is the first time many students see that a rule they were told in Grade 4 was not a decision somebody made. It was the only option available.
At this level the question changes shape. We are no longer asking what the answer is, we are asking what we assumed in order to get it. The argument above used exactly three properties: that multiplying by zero gives zero, that the distributive law holds, and that additive inverses are unique.
Any system with those three properties is called a ring, and the result holds in all of them, including ones that look nothing like the integers.
What a student takes out of this is not the identity. It is that some of what they were told were rules are consequences, and that they are allowed to ask which is which. That habit is the difference between a student who is good at mathematics and a student who will still be good at it at university.
There is no fixed syllabus on this page because there is no fixed syllabus in the practice. Two students in the same grade, in the same week, are usually working on different things. The plan is written after I have watched your child work, it is shared with you before the first class, and it is revised every term.
School work at any level from Grade K to 12 is covered whether or not an examination is involved.
Ninety minutes: forty five with your child, working real problems, and thirty with you. Within forty eight hours you receive a written assessment of your child’s reasoning: what they understand, what they only appear to understand, and what I would do about it. Yours to keep, whatever you decide.