The mathematics 251 course of Claremont Graduate University covered the main elements of probability theory at an intermediate level. The topics covered included combinatorial analysis, conditional probabilities, discrete and continuous random variables, probability distributions, central limit theorem, and numerous applications.
The topic that provided me with the most challenge was conditional probabilities. I remember spending numerous hours trying to complete and to understand the homework assignments of this topic. Although conditional probabilities was the most difficult topic, it was the one that contributed to my mathematical content knowledge growth the most. After attempting to complete the first homework assignment on the topic, I realized my lack of knowledge or experience of the topic. I struggled with the concept and always sought out for help from my peers, tutor, on line sources, and from the course professor.
In conclusion, completing the math 251 course; not only increased my mathematical content knowledge, but also positively affected by pedagogical knowledge. Teaching the probabilities unit of the high school algebra course was always the most challenging topic to teach, and one in which my students consistently scored the worse on state tests. I realized that it was because I did not fully understand the concept of conditional probabilities. However, all change due to my successful completion of the course and I feel ready and capable of efficiently teaching this concept the next time it comes around.