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JA1. Overcoming Struggle

Statement

Take one homework problem you have worked on this week that you struggled to understand and solve and explain how the struggle itself was valuable.

  • Describe the struggle
  • How you overcame the struggle
  • Discuss whether struggling built aspects of character in you (e.g. endurance, self-confidence, competence to solve new problems) and how these virtues might benefit you in later ventures.

Solution

The discussion question was very difficult for me; the problem asked about the Y = A sin (x) + B cos (X) function; explain it, explain its characteristics, describe what happens if A or B or both change, and lastly document your findings.

The entire problem was difficult to me, but especially describing the changes in the function graph according to the values of A and B; part of the problem was mentally actually since high school I was scared of trigonometric functions, and I was always scared from them.

I used Desmos online tool to graph the function, I was able to zoom out to see a bigger picture from the one that I was having on my head. I also have put the different values for A and B and sketched them all on one graph with different colors to see the changes. Analyzing different graphs and comparing how they behave allowed me to understand the function better, and I was able to describe the changes in the graph according to the values of A and B.

The struggling is always a good thing in the learning process as it helps the learner to go deep into the details of the problem, and help retain the information for a longer time. Learners usually shine more in areas where they struggled and get more self-confidence around the topic, and become more competent in general, and sometimes they become a help for their colleagues.

Other problem I struggled with was finding if a function is even or odd; the concept was confusing, but easy to understand with the graph; but graphs are not always available, so being able to proof that a function is even or odd is a good skill I learned from the struggle. The struggle helped me to understand the concept better, and I was able to identify the entry point to solve such problems. I will always start by finding f(-x) and then compare it with f(x) . If f(-x) = f(x) then the function is even, if f(-x) = -f(x) then the function is odd, and if none of the above is true, then the function is neither even nor odd.

As a conclusion, struggling is essential to the learning process, as non-struggling indicates that the learner is not learning anything new, and the learning process is not effective. Struggling raises the self-confidence of the learner, and makes him/her more competent in the topic, and sometimes the learner becomes a help for his/her colleagues.