I am trying to use a mixed-effects model to examine the effects of three teaching approaches on the learning of English past tense measured through language tests at five testing points. The dependent variable of my model is the learners' test score. The fixed-effect variables are group (three treatment group and a control group) and testing time (five testing points including a pre-test and four post-tests). In addition, I also set subjects as the random-effect variable. Pre-test scores are controlled for as a covariate in the model because they are not comparable among the four groups.
My model is:
The full mark of the five tests is the same, which is 24. My questions are: Should I use the raw scores or z-scores for the covariate (pre-test) in this model? If yes, should I convert raw scores to z-scores for the dependent variable as well?