Mathematical Foundations for Teaching Secondary School Math

Why do students have such a difficult time with basic math concepts such as working with fractions and negative numbers? It could be because arithmetic is significantly more complex than we initially suspect. For instance, the symbol ½ has at least four different interpretations, and students need to be able to quickly figure out which interpretation will be of most use for solving a particular problem. This course was created for middle and high school mathematics teachers to give them a chance to explore the inner workings of fundamental mathematical concepts involved in arithmetic as well as the basis for working with a variety of number systems. The course deconstructs basic math concepts that many people often take for granted, but yet which can continue to give students difficulties throughout their school years. The course emphasizes mathematical reasoning rather than memorizing facts and formulas. In addition to the mathematical content, we also discuss how different methods of teaching affect students differently and we explore a variety of activities and games that teachers can bring to their own classrooms to enhance their students' understanding and enjoyment of mathematics.