So as to have the function be increasing, 2016-m^{2} must be positive. Therefore, 2016 must be greater than m^{2}. Since 2016 is a positive number, m has to range from \(-\sqrt{2016}\) to \(\sqrt{2016}\). In other words, m has to be between -44.899 and 44.899. Since m is a whole number, the minimal value of m is -44 and the maximum is 44. To calculate the number of values, we use this formula: \(N=\frac{44-(-44)}{1}+1=89\)

To conclude, there are 89 values of m such that the function is increasing.