What's the optimal way to space out rewards in order to maximise motivation?
To add gaming element to education, you have two options:


Look at currently successful examples of products that gamify learning
Check most successful mobile games (short engagement times)


Here are a couple examples of language learning products that gamify learning (Duolingo and ChineseSkill) They use:


Very short lessons which produce instant sense of gratification (3-5 minutes each)
Diverse word sets, so each lesson feels fresh
Score and timing concepts (for example Chinese Skill app lets you peek at a word meaning, but subtracts points from the final score for doing so)
Competition against "general public" - apps tell you how you are doing compared to other people
Use of pretty graphics and friendly imagery


For example chinese skill app starts with just a couple lessons per module, each focusing on a few words. Later on the app expands and starts to add more lessons. 

Duolingo has similar approach, although they have a lot more reward systems - you can win points by doing good during lessons. 

To specifically address your timing question, I can bring up personal experience - I tried both products, and hit a slump when the number of lessons per module exceeded 5. There was less motivation to progress. I quit duolingo completely once I hit a module with 13 courses. To avoid this, I've seen some apps break large word sets into stuff like "Clothing 1", "Clothing 2", etc. 

ChineseSkill app


Duolingo App: