One project might be to examine criticisms and defenses of Kohn's work. What do other professionals think of it? Has it held up well over time?
Another project might be to examine how academic success is achieved and promoted in other countries in which such success is demonstrable. For example, how do countries whose students perform well in math encourage or reward such performance?
Medicine is a field in which good grades are strongly stressed. The U. S. has some of the finest hospitals and medical researchers in the world -- perhaps the very best. You might want to explore how seriously Kohn's theories are taken by people who teach medicine, since medicine is a field in which the U. S. does quite well when compared with other countries.
One implied effect that you might investigate are the roles of shame and guilt in pay-for-performance incentives. Conversely, you might investigate the roles of superiority and even bullying related to pay-for-performance incentives. These feelings related to punishment by reward may be explored from the schoolroom to the workplace.
You might want to try and linnk Kohn's ideas into the concepts of intrinsic and extrinsic motivation. Clearly, out of the two, intrinsic motivation is something to be encouraged if at all possible, where students engage in work because they are interested in it intrinsically and in learning itself. Extrinsic motivation is where students only do the work for what they get for doing it. This clearly links in very closely to Kohn's ideas on rewards and how this produces a lesser kind of learning that is not intrinsic.
In terms of project ideas, Kohn's work gives much in way of thought. One particular project can be done in terms of taking his basic ideas and seeing how much modern education goes against it. Examine a classroom, any classroom, and see how much the concept of "rewards" are being used. Kohn's basic argument is that the notion of rewards in the classroom setting essentially amounts to, "Do this and you will get ________." Kohn feels that this amounts to legitimized bribery, whereby students do things for the wrong reasons. Students read books for pizza parties, complete homework for a candy bar, and write an essay in order to play games. All of these represent inverted values. For Kohn, this is something that marks our modern education system. An interesting project would be to see how the modern classroom embodies what Kohn is striving against. Essentially, your project becomes the analysis of if Kohn is right.
Another project idea would be to extend what Kohn is saying about rewards to the concept of standardized testing. For Kohn, the idea of rewards is an extension of the concept of standardized testing, the biggest reward out there. Schools are praised (rewarded) for doing well on their standardized tests. Schools are punished (not rewarded) if they do not do well. Kohn's argument here is that rewards in the domain of standardized tests are used to initiate compliance and adherence to the Status Quo, as opposed to critically thinking about it. The reason why rewards are dangerous for Kohn is that they normalize the idea of high stakes standardized testing. It is here where a project could be done to explore how schools are in fact "rewarded" for doing well and how the opposite is true. In this project, you would be focusing on how Kohn's ideas have real world implications and relevancy.