Tag Archives: arithmetic

What is proportional reasoning? Does cross multiplication help learn it?

Proportional reasoning is a capstone of children’s elementary school arithmetic and a cornerstone of all that is to follow (Lesh & Post, 1988). But for some reason, the teaching of elementary school mathematics topics either become an end in itself or has become more a preparation for learning algebra. Proportional reasoning is not being given… Read More »

Fun with ‘definitions’ in algebra

WARNING:  use the following definitions with great caution. A number phrase is a mathematical phrase which does not express a complete thought. An arithmetic expression is any grammatically sensible expression made up of numbers and (possibly) arithmetic operations (like addition, division, taking the absolute value, etc). Notice that it only has to be grammatically sensible; an undefined expression like 5/0 is… Read More »

Mistakes and Misconceptions in Mathematics

Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly. Students can figure out their mistakes by themselves because mistakes are usually due to… Read More »