The final examination consisted of 31
questions covering basic statistics, making calculations in bases other
than ten, determining slope and intercept from raw data for both linear
and quadratic systems, writing the equation of the arc of a ball in the
air, and making siteswap calculations.

Most of the material would be familiar to mathematics instructors, the
siteswap mathematics is a fairly young and immature field of applied
mathematics that permitted me to introduce a mathematical system
different from anything the students had encountered before. The one
day exercise also assisted in making the point that there is more to
mathematics than algebra, geometry, trigonometry, and calculus. In
fact, this traditional sequence was designed by mathematicians with the
goal of moving students along to calculus.

Student performance on the final examination was fairly strong with, on
average, 83% of the students answering all questions correctly. The
percentage of students getting a specific question correct is given in
the following table, along with a descriptor of the question.

1 | Find minimum value in a data set | 97% |

2 | Find maximum value in a data set | 100% |

3 | Calculate the range for a data set | 83% |

4 | Determine the mode for a data set | 100% |

5 | Determine the median for a data set | 67% |

6 | Determine the mean for a data set | 83% |

7 | Critical thinking: inference from a mean | 87% |

8 | Hexadecimal RGB color code matching | 97% |

9 | Hexadecimal RGB color code matching | 97% |

10 | Hexadecimal RGB color code matching | 100% |

11 | Hexadecimal RGB color code matching | 97% |

12 | Hexadecimal RGB color code matching | 97% |

13 | Calculate a result in base five | 87% |

14 | Calculate a result in base sixteen | 100% |

15 | Calculate a result in base sixteen | 93% |

16 | Plot points on a graph | 100% |

17 | Find the slope from points on a graph | 80% |

18 | Find the y-intercept from points on a graph | 93% |

19 | Write the slope-intercept equation | 67% |

20 | Predict a result from a slope-intercept equation | 67% |

21 | Predict a result from the inverse of the slope-intercept eqn | 57% |

22 | Square a set of data values | 100% |

23 | Find the slope from points on a graph of x² versus y | 83% |

24 | Find the y-intercept from points on a graph of x² versus y | 90% |

25 | Determine a and c in y = ax² + c | 80% |

26 | Predict a result from a quadratic equation | 3% |

27 | Read a given value | 83% |

28 | Determine the average distance to the roots given formula | 93% |

29 | Write out the quadratic equation of a ball arc | 7% |

30 | Determine the number of balls in a siteswap sequence | 93% |

31 | Determine the number of balls in a siteswap sequence | 87% |

For problem number twenty-six, with only a single student getting the problem correct, the difficulty was not that students used the wrong equation. 80% of the students had determined that the coefficient a for y = ax² + b was 4 and that the constant b was 0. When asked to determine the y-value for an x-value of 20, couched in the language of the language (time and distance), students primarily forgot to square the 20 seconds.

Reasons for the collapse on number 29 are less clear, but many students simply did not understand how to use the y-intercept and roots to set up the quadratic equation. The task was actually one of substitution into a given equation and simplification, but this eluded all but two of the students.

Overall students appear to have become comfortable with plotting data and then deriving slopes and intercepts from the graph. Many are able to go on and use that equation to make predictions for other values of x (67%) and to infer an x-value from a y-value (57%).