Overcoming Challenges in Teaching ComputationSayonita Ghosh Hajra, Mathematics and Statistics, California State University-Sacramento
One of the biggest challenges in teaching multi-variable calculus is the visualization of 3D spaces. In single-variable calculus, students are adept at working with graphs of functions of one-variable. However, the same group of students would find graphing of functions of two variables challenging. For example, students can easily plot graph of the function y=x in 2D, however, they struggle visualizing the graph of y=x in 3D. In these situations, we can use technology, MATLAB or other computational tools, to help students smoothly transition from 2D to 3D.
One of the challenges is how to keep a balance between content and technology and how to structure the course to embed both in a coherent way. Recently, I had an opportunity to chat with a student who had taken multi-variable calculus with me in the last semester. I told her that I will be using MATLAB in the Fall semester in multi-variable calculus class. The first response was "oh-no!". I asked her about her experience with MATLAB and she described that she did not have a pleasant experience in calculus 1 and 2, however, she said that she had a wonderful experience in her physics class that used MATLAB. In her physics class, MATLAB was used as a support to improve student's learning. Students did their assignments using MATLAB; instructor provided multiple attempts for students to correct their solutions. This process helped students to learn from their mistakes. This conversation was useful for me to learn that students find computational tools helpful when the course materials were directly tied in and used as a tool to support students in their learning rather than treating computational tools as an additional or extra component of the course.
Another challenge is how to assess students when students have different levels of computational skills. Some students have used mathematical software in other courses, some are completely new to them. Hence, it becomes challenging to assess students based on how much they knew prior to class verses students' present learning. Those students who are already scared of the new mathematics they are going to learn, this new technology is like something added extra to their learning. This could be perceived as a barrier towards their ability to learn computing and mathematics together. Personally, the biggest challenge is to break the mind-set "I am not good in math and computing" and find ways for student buy-in.To overcome the first challenge, I would design multi-step assignments with guided instructions starting from simple to complex assignments. I would also provide a rubric highlighting the expectations of the assignments and describe the learning objectives of the assignments. For the second challenge regarding student buy-in, I have invited professionals from the industry, who interacted with students and spoke about the importance of computational skills and how these skills could be beneficial later in their career.