Hello,

In my classroom, 24 students took an essay test. Each essay has six questions, and each question has its own level of cognitive complexity from lowest to highest, let's call it C1 to C6. Each question is graded on a scale of 0 - 100. Now, I administered this essay test at two different times, so we can call one the pre-test, the other, the post-test, presuming that, in-between the tests, an academic intervention was employed to test its effectiveness on the students' cognitive capacities. I assume that, in this case, we need to employ the paired t-test; but how can we set up the variables to determine this? After the post-test, there may be evidence that the gain (n-gain analysis) in the learning outcomes falls in favor of the higher C-levels. What this means is, if during the pre-test more students scored high scores for lower C-levels (maybe C1, C2, or C3), then in the post-test, more students scored higher for higher C-levels (say, C4, C5, or C6), then we can conclude that the gains in learning outcomes lean toward the higher C-levels after the treatment was applied. A similar scenario is shown in the resource below, and although in there they're testing cognitive levels from C2 to C6, the principles or core ideas are not too different from this one I have presented. I hope this may serve as a guide. Please, I need to be clear that this is not a quiz, neither am I requesting to have my paper completed for me; I am only testing my methodologies in my research study, and I need tips or ideas so I can set up the appropriate mathematical structures that I can use effectively. Thank you!

References:

Chinaka, T. W. (2021). The Effect of PhET Simulation vs. Phenomenon-based Experiential Learning on Students' Integration of Motion Along Two Independent Axes in Projectile Motion. African Journal of Research in Mathematics, Science and Technology Education, 25(2), 185-196. https://doi.org/10.1080/18117295.2021.1969739

Hake, R., R. (1999). Analyzing change/gain scores. Indiana University: Woodland Hills, CA -USA.

Ndihokubwayo, K., Uwamahoro, J., & Ndayambaje, I. (2020). Effectiveness of PhET Simulations and YouTube Videos to Improve the Learning of Optics in Rwandan Secondary Schools. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 253-265. https://doi.org/10.1080/18117295.2020.1818042

Stahre Wstberg, B., Eriksson, T., Karlsson, G., Sunnerstam, M., Axelsson, M., & Billger, M. (2019). Design considerations for virtual laboratories: A comparative study of two virtual laboratories for learning about gas solubility and colour appearance. Education and Information Technologies, 24(3), 2059-2080. https://doi.org/10.1007/s10639-018-09857-0