The evidence that retrieval practice is an excellent way to learn is vast (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/11/07/Retrieval-Practice). But retrieval is simply the act of brining something to mind, so do we need to use quizzes? Well, the answer is no, we do not need to, but I think, for Maths at least, they are the most effective form of retrieval.
I am currently doing this with my S3 and S4 classes every week. They know that they will be having a quiz each week, and at the start of the year I explained my reasons for doing this. Firstly, there is writing the quiz. It is split into three sections: This Unit; Last Unit; Further Back.
This is already quite a different approach to how I started the year. I have formalised the choosing of questions a little so that troublesome topics keep coming up each week, as well as breaking it up into the three sections. The reflection sheet is also a new addition, and we shall see how well that works. I will have to make time in class for students to review them as well so they are not just another piece of paper!
Hendrick, C and MacPherson, R (2017), What Does This Look Like In The Classroom?, John Catt Educational Limited, pp34-35