During my five years of teaching experience as a teaching assistant including teaching, grading and math tutoring at Washington State University (WSU) and American University of Sharjah (AUS), I have noticed that many students are not motivated because they are scared of subjects that deal with mathematics, and because there is a common belief that math is a complicated and boring subject. When they go to any math class in general and freshmen and sophomore levels in particular, they already have a prejudice against the subject matter. One of my major obstacles as a teacher is to create a friendly environment. With patience and encouragement, I then proceed to build their self-confidence in learning mathematics. A successful math teacher must make the students feel that mathematics is learnable, applicable and enjoyable. The following is a list of two examples that I do in my Calculus II class to help my students overcome their fears from topics such as tests of convergence and divergence for series, and absolutely and conditionally convergent series:

Tests of Convergence and Divergence for Series: Students do not usually like this important section of Calculus II curriculum because when they go to the exam, they get confused with two or more tests due to the similarity between some tests. As a result, they do not do well in exams and eventually in the course itself. Therefore, I decided to help them all by creating a table that contains all tests together, and I also added a “notes” section so they understand my notes and comments about each test. This table is available on my course webpage. Here is a sample of my table:

Absolutely and Conditionally Convergent Series: Students usually consider deciding whether series is absolutely convergent or conditionally convergent is one of the most difficult things in Calculus II. However, I created for them a table, and I called it “Binary Method for Alternating Series Test”. The name of this method stems from the fact that binary numbers are 0 0, 0 1, 1 0, and 11, and they represent divergence-divergence, divergence-convergence, convergence-divergence, and convergence-convergence, respectively. This table is available on my course webpage. The following is the Binary Method for Alternating Series Test table:

In conclusion, I also believe that students must engage with this learning environment during class discussions by asking challenging questions that make us both (teacher and student) think about these questions. For example, when I create a handout for my Calculus II students, I usually like to include one challenging question and ask my students to think about it. Then, we can start the class discussions about that challenging question. A perfect example of one of my challenging questions in Calculus II is the following:

To see more examples like this and other handy methods, please see my course webpage. Best of luck and feel free to reach out if you have questions!

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