Depends on the measurement and conceptualization of the variables i.e., instructional methods and academic performance. If the instructional methods is a nominal variable, you may run independent samples t-test, or One way ANOVA depending upon the distributional pattern of the variables' data.
I concur with Ben's comments above regarding challenges faced in this question. Additionally, Hattie's Visible Learning will be a valuable source.
Finally, one point I would add is that correlational research CANNOT be used to justify causation. Given you used potential preceding effect that might have been expressed but I would caution you to avoid words like effect when using correlation because it tends readers towards thinking cause/effect but you are not justified in making such claims with correlational research. You can notice relationships that may be of particular interest but aren't justified in making claims of effect/causation.
I do understand and concur with the comments that have already been given. My worry , though, is that instructional methods are many and varied. Besides , the instructional methods that can be used effectively to contribute to academic performance depend on the subject in question. How are you going to isolate what instructional method leads to performance in which subject area? I hope you have clearly defined what you mean by instructional methods and academic performance!
Coincido con las apreciaciones de los colegas, desde la variedad de metodos que se pueden utilizar hasta los estadisticos sugeridos. Debo enfatizar en el marco teorico como esta definiendo cada una de las variables, creo que mas que un estudio correlacional, puede ser un cuasi experimental ya que queremos ver los efectos de uno sobre otro. Para lo cual a pesar de que trabajara con estudiantes deben de tratar de controlar en la medida de sus posibilidades la presencia de variables extrañas, aunque sabemos que se trabaja hasta un 95% o un valor p menor a 0.05, lo cual podria explicar la presencia de otros factores.
I totally concur with Kevin that correlation research CANNOT be used to justify causation. Additionally instructional methods by themselves stand. I like how Ben argue about other factors like how a method is used by an instructor and other out of school factors. When you use correlation design how will you manipulate these factors? Wanjala also guides that one can use a particular instructional method best based on a specific subject. I would then conclude that by using this design you might not get true result for a study of this nature.