You might want to use screen picture capture software such as Grab which is generally on all Macs. If you have advice about Windows software for screen picture capture, please let me know.
You might want to use screen video capture software such as Snapz Pro X for Macs or SnagIt for Windows or Macs. I'm not sure how well this would work for you in recording a tutoring session. If you try this, please let me know how it works out for you.
You might want to have spread sheet software such as Excel. This could be useful in Reimann sum calculations or statistics for example.
If you have a mac, you should have a copy of Grapher software already. Pacific Tech's Graphing Calcultor is available for both Windows and Mac. These graphing calculators are generally useful over a number of topics and are typically more useful than the TI's graphing calculators.