Led by James B. Thomson Simulacrum
About this course
Module 1 ended on a deliberate cliff: you could write and read any number, and do nothing with one. This is where the arithmetic begins, and it is the longest module in the school — because everything after it, fractions and decimals and measurement and interest, is one of these four operations performed on a differently-shaped quantity.
Three of Thomson's disciplines govern every sitting. One new difficulty at a time, never two: carrying arrives alone, in a column that is otherwise trivial, because if you fail on a step with two novelties in it neither of us can say which one defeated you. Mental before slate: small numbers first so the reason is visible, large numbers second so the method is needed — you must meet the difficulty before you are handed the remedy. And the General Rule is yours: you work enough cases to see the pattern and state the rule in your own words, and only then are you shown Thomson's, as a confirmation rather than a revelation.
The module also introduces the technique that makes word problems tractable. Thomson calls it ANALYSIS, and it does not begin by choosing an operation. It begins by reasoning to the value of one. If 6 yards cost 42, then 1 yard costs one-sixth of 42, which is 7; if 1 yard costs 7, then 9 yards cost 9 times 7, which is 63. You give the whole chain, with the if and the then intact, and the answer carries its denomination — sixty-three is not an answer.
Mental answers may be spoken or typed. Slate work is done in an exercise book, because the arrangement of the figures in columns is part of what is being taught.
Led by James B. Thomson Simulacrum
The question
Addition, subtraction, multiplication and division of whole
Outcome
The student can perform addition, subtraction, multiplication and
Sub-units
Practice scenarios
A pupil computes faster than anyone in your class and gets roughly one answer in five wrong. He cannot tell you why any of his methods work. Asked to prove an answer, he re-does the same operation the same way, gets the same result, and considers it proved. His parents are pleased with him. He is thirteen, and he is about to meet fractions.
Your goals