Experiences of Students on The Problem of Understanding Derivatives

Authors: – Vishal Gupta (F1 Batch : 21230023804)

                   Vaibhav Kumar (F1 Batch : 21230023885)

                   Manish Gautam (F1 Batch : 21230023922)

Introduction: – Understanding derivatives is a critical aspect of financial literacy and investment strategy. Derivatives are financial contracts that derive their value from the performance of an underlying asset, such as a stock, bond, commodity, currency, or index. However, the problem of understanding derivatives goes beyond the simple concept of underlying asset.

Objectives: – To understand the underlying phenomena of this problem.

Literature review: – Research suggests that common challenges include the abstract nature of the concept, the need for a solid foundation in algebra and functions, and the lack of real-world context in traditional teaching methods. Studies have indicated that students often struggle with visualizing the geometric interpretation of derivatives and fail to connect it to real-world applications. Moreover, the transition from basic calculus to derivatives introduces new mathematical notations and concepts, contributing to the complexity of the learning process.

Testing of Hypothesis-

H0: μ=3

H1: μ≠3

Data Collection-

  1. I have a basic understanding of what derivatives are used for.
  2. I understand the connection between derivatives and slope of a graph.
  3. I understand the difference between instantaneous and average rate of change.
  4. The use of mathematical notation in derivatives confuses me.
  5. I can apply the chain rule and product rule to differentiate more complex functions.

These 5 questions were asked in Google form to students and for every question standard deviation, standard error, mean and t-stat was calculated.

Data analysis-

  • I have a basic understanding of what derivatives are used for.

            MEAN= 2.99   SD= 1.096   SE= 0.109   T-STAT= -0.091

  • I understand the connection between derivatives and slope of a graph.

      MEAN= 3.1     SD= 1.105   SE= 0.110   T-STAT= 0.905

  • I understand the difference between instantaneous and average rate of change.

      MEAN= 3.14    SD= 1.064    SE= 0.106    T-STAT= 1.316

  • The use of mathematical notation in derivatives confuses me.

MEAN= 3.24   SD= 1.280    SE= 0.128   T-STAT= 1.875

 

  • I can apply the chain rule and product rule to differentiate more complex functions.

MEAN= 3.2   SD= 1.064    SE= 0.106   T-STAT= 1.880

 

Conclusion:

  • I have a basic understanding of what derivatives are used for.
  • T-stat is -0.091 which is between 1.96 and – 1.96 we accept the null hypothesis, and it is negative more than 1.96. It means people are neutral towards the statement.

 

  • I understand the connection between derivatives and slope of a graph.
  • T-stat is 0.905 which is between 1.96 and – 1.96 we accept the null hypothesis, and it is positively less than 1.96. It means people are neutral towards the statement.

 

  • I understand the difference between instantaneous and average rate of change.
  • T-stat is 316 which is between 1.96 and – 1.96 we accept the null hypothesis, and it is positively less than 1.96. It means people are neutral towards the statement.

 

  • The use of mathematical notation in derivatives confuses me.
  • T-stat is 1.875 which is between 1.96 and – 1.96 we accept the null hypothesis, and it is positively less than 1.96. It means people are neutral towards the statement.

 

  • I can apply the chain rule and product rule to differentiate more complex functions.
  • T-stat is 1.88 which is between 1.96 and – 1.96 we accept the null hypothesis, and it is positively less than 1.96. It means people are neutral towards the statement.

References

https://www.investopedia.com/terms/d/derivative.asp

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