I totally agree with you, I also hate 'heads up' notifications. Unfortunately, there is no way to turn them off easily in Marshmallow (but at least there's a way) or even any settings at all in Lollipop (where they were introduced). Since I'm not sure which version of the OS your tablet has, I'll tell you both options.
1) Marshmallow. While you CAN disable these ugly notifications in the settings, they didn't include a 'general' kill switch, so you have to do this on a per-app basis. Yup. It sucks. You have to go into your settings, Notifications, Advanced, and turn off 'Previews in pop-ups' option for every single app you wish to disable this for.
2) Lollipop. No way to disable them in the settings, but at least there is an underlying 'global kill switch' that 3rd party apps (I've used HeadsOff in the past and it does work) can access. These apps, however, won't work in Marshmallow, since that OS version got rid of the global switch.