Here is a new project hosted on Github that uses Android C++ NDK to record the audio mic and save the data to a .wav file on the Android device.
You can start the recording, then leave the app (let it in background) and it will keep on recording the input in background.
You can also record a phone conversation by activating the loud speaker when someone calls you (the loud speaker is then recorded by the audio mic input).
This application will soon be available on Google Play Store but for now is in development phase. You can clone it or fork it on GitHub and compile it to use it on your Android phone or tablet.
Click here to go to OboeAudioRecorder project on GitHub.
Click here to go to OboeAudioRecorder main .CPP file that contains the most relevant code for recording the mic input and writing to the .wav file on the Android device.