I have been running the Orange Math Group in the Explorer Class since Lisa left on maternity leave. This “third grade” curriculum focuses on the nuts and bolts of arithmetic: fractions, decimals, place value, adding and subtracting, shapes, multiplication math facts and basics of probability. For these students, 8 and 9 year olds, my main focus is to encourage them to “get into their math brain” and to “trust the math.” I find myself emphasizing these same ideals with the middle school students as they tackle the more complex versions of Orange Math: multiplying and dividing fractions, scientific notation, negative numbers and negative exponents, geometric proofs and growth and decay.
One analogy I make to the math brain is that of a toolbox. Each skill mastered becomes another tool the students can employ when working on their math. For the 8 year olds those skills include using a straight edge when drawing lines to connect points and how to measure an angle with a protractor. For the middle school students those skills include using the distance formula to calculate the distance between two points on a coordinate grid. The second of these math ideals is “trusting the math.” At its root this means accepting that mathematical processes, if done the same way each time, will always get the same results. For example, the Pythagorean Theorem finds the hypotenuse of a right triangle every time or that cross multiplication used to find an un-known in a ratio works every time.