Reference no: EM132390368
Question Task:
Prepare a research paper on topic "Performance Outcomes After Repair of Complete Achilles Tendon Raptures in National Basketball Association Players" and organize it into the structure listed.
In the paper, please simplify the mathematical language and clarify the mathematical theories of the research so it's not like the paper is intended for those who know math only. Fully explain each step of the analysis and illustrate some of the tables using charts and graphs.
Outline of Mathematical Modeling
Aim: to develop a mathematical model of the data so we can use this model to make predictions.
1) Introduction
Tell in general what the paper will be about. Define the problem and your variables.
2) Observations (Data Collection and Preparation for Analysis)
a. Gather data using a clear mathematical strategy. You may have to do calculations to get your data. Your systematic choice of values to calculate will demonstrate your strategy.
b. Organize your data – usually in a table or some sort of list.
c. Process and display the data, preferably using more than one form of mathematical representation (graph, diagram, equation). Label this diagram or graph in detail, and define the variables and parameters in your equation.
3) Analysis
a. Identify trends in the data (increasing or decreasing, how does it increase or decrease, end behavior, intercepts, asymptotes, maximum or minimum values, etc.)
b. Discuss possible function model types (quadratic, exponential, logarithmic, trigonometric, rational, piecewise, etc.) that might fit the data.
c. Choose a function model type and state why this fits best.
d. Tell the reader your steps/thinking. Describe with appropriate terminology and notation.
e. Show the reader your steps/thinking. Use graphs, tables, diagrams and other visuals.
4) Interpretation (Equation of the Function Model)
a. Create a model analytically using your knowledge of parameters in the function type, using transformations, or using technology. Give the domain and range of this function.
b. Write the equation of the function model using correct math terminology/notation.
5) Goodness of Fit (Testing the Function Model)
a. Show your function model on a graph with the data. Compare the model to the data, and comment on how well the model fits the data. Comment in context wherever possible.
b. Compare the model to another model found with regression or another technological tool.
6) Applications, Modifications and Limitations
a. Modify your function model if necessary and describe what you are changing and why.
b. If you do not modify your function model, state why it does not need to be changed.
c. Apply the model to a different, yet related situation. Comment in context on how well the function models this situation. Explain modifications that would need to be made.
d. Scope is written with limitations in mind.
7) Evidence (Justification/Proof)
a. Provide evidence throughout the paper, not just in one place. All examples should be placed with your text as you describe things to make it easier for the reader to understand.
b. You can justify things in many ways – using examples or non-examples, by showing diagrams, by doing new calculations, or demonstrating patterns in tables of values.
8) Reflection and Conclusion
Write about what you learned, other possible related problems that could be explored, or reflect on the correctness of your findings or the accuracy and precision used, or the impact of technology in your task. Suggest realistic improvements. Then “wrap it up.”
9) Mathematical Terminology and Notation and Mathematical Communication
a. Check for appropriate math terminology (words) and math notation (symbols).
b. Check for logical organization (introduction, conclusion). Check for coherence (logical development, easy to follow). Diagrams should be part of the paper, not at the end.