I believe mathematics is learned through a hierarchy of reasoning levels. Students begin their mathematical journey as toddlers using counting strategies. When they enter elementary school they move into additive reasoning, where they develop number relationships and strategies to efficiently add and subtract. This leads to multiplicative reasoning, where more sophisticated brain processes are applied in order to multiply and divide whole numbers, fractions, and decimals.
Middle school mathematics relies on these reasoning methods to progress into proportional, algebraic, and spatial reasoning. It is during these crucial years that students apply reasoning strategies to delve into rational number operations, probability, and percents. They generate equivalent expressions, solve one and two-step linear equations and inequalities, as well as develop spatial reasoning through geometric concepts and statistical relationships through investigations of bivariate data.
I want my students to be flexible in their ability to look at the numbers in a problem and consider more than one way to solve it.
It is my goal to give students many experiences with different strategies and problem types so that they will be able to consider the numbers in a problem before they decide on an efficient strategy to solve it.
