## Thursday, September 15, 2011

### DA with first principles and limits

Here is an example of how I have changed the definition of an exam.  Before, when assessing first principles and limits in my calculus class, I would have each student write an exam.  This year, I am giving students the option of writing an exam or completing the following to demonstrate their learning.

Unit 1 Assessment Project
1.      Create a formula for the distance of an object at any time t.  The formula must be at least degree 2 with a minimum of 2 terms.  Using your formula you must:
·         Determine average velocity of the object for the first 10 seconds.
·         Determine, with an explanation, the instantaneous velocity after 10 seconds.
·         Determine, with an explanation, the instantaneous velocity for any time t.
·         Determine if the object is ever traveling 50 m/s.
2.      Create a piecewise function over the domain of the real numbers. The function must contain at least 3 different pieces and may not be continuous and may not have a limit at at least one point.  Using your function you must:
·         Provide a graph of your function.
·         Explain why your function is not continuous at the specific point.
·         Explain why a limit does not exist at the point above. Explain how you could change your function such that there is a limit.  Calculate the left and right side limits at this point.
3.      Demonstrate, through a real life application, how you can calculate the instantaneous rate of change at a specific data point.  You may use data from a chart, create a video, etc., but the data may not follow a specific function.  The point at which you calculate the rate is entirely up to you, but must have an explanation.
4.      Create three functions, one which:
·          approaches infinite,
·         one which approaches 0,
·         and another which approaches a line which is not 0
as you extend these functions to infinite.  Explain how you can determine the limit as x approaches infinite, for each of your functions.
5.      Create a real life example of a convergent series, and calculate the sum of this series.

1. Hi Dave, I am curious what you are learning from the way students respond to the possibility of DA? How often do they not opt for the exam? And what do you learn about their learning?

2. I must say I find it irritating that the author never responds to comments. What's the point of a blog if you don't interact with readers?

3. jehe I asked my students about their ideas around the new assessment, and here were the results.