Your research topic is a valid topic. It is very similar to my dissertation where I studied the impact of higher order thinking skills and student engagement. Would the teacher be using both teaching strategies and you be comparing against a control group where no teaching strategy would be used at all or would be comparing the two strategies against each other? I was not sure. Would you mind clarifying that?

Research Scenario in which z-score is valuable:

Consider the research scenario in which the researcher interested to compare the effectiveness of two teaching methods on the students of an institution. For this study the researcher selected two groups of 20 students each and taught the same course using the two teaching methods. After completion of the course conducted a test and recorded corresponding test scores for analysis.

Let the researcher interested to perform a two-sample analysis using the t-test assuming equal population variances. The assumption must be satisfied to make the t-test procedure valid is that the population distributions from which the samples drawn are normal or approximately normal. So to check whether the distributions of the two populations under study, i.e. scores of all the students who undergone those two different teaching methods, we have to use the z-scores.

Using the z-scores obtained to the sample observations, i.e. recorded test scores, we can easily identify whether there is any deviation to the normality assumption or not. There are some other methods such as normality check through various graphs like histogram or box-plot etc. but the use of z-scores or normal probability plot is appropriate to check the normality of the population under study.

Independent and Dependent Variables:

For this study the independent variable (IV) is the method of teaching used for the course. It has two levels as we are comparing two methods for their effectiveness.

The dependent variable (DV) for this study is the score of the student that participated in this research.

Here researcher had collected 20 sample observations on the dependent variable for each of the two levels of the independent variable.

Use of z-score in this Scenario:

First obtain the means (M) and standard deviations (SD) from the two samples.
Obtain z-scores for each observation of the sample using its respective sample mean (M) and standard deviation (SD) by the following formula:
Z = (X - M)/SD

Check the obtained z-scores whether all of those falls in between -3 and 3 or not. If yes, then the population distribution of test scores is approximately normal, otherwise it indicates a deviation from normality.