Google Science Journal app prompted a lot of people to ask me, in email and on Facebook, if the app would work on Chromebooks. The answer is that it will work on some Chromebooks. To run the Google Science Journal app on a Chromebook you have to have a Chromebook that supports the use of Android apps.
Android Central maintains a list of the Chromebooks that currently support the installation of Android apps. The most recent update to that list was on December 15th. The list is divided into Chromebooks that support Android apps in the "stable" channel (the most recent version of Chrome OS) and the Chromebooks that support Android apps in the beta channel.
It is important to note that just because your Chromebook is listed as being capable of running Android apps, that doesn't mean that you'll necessarily be able to install them on a school-issued Chromebook. Your IT administrator may have placed additional restrictions on your device to prevent you from installing Android apps. I know this because I recently worked with a school that had done just that.