I read a paper entitled Assessing conceptual learning from quantitative problem solving of a plane mirror problem, in which the author complete the quantitative analysis of the correlations between quantitative problem solving and conceptual learning with data from 118 secondary three students and 38 junior college year one student.

According to the research content, the experiment data showed a significant difference in the conceptual learning results for students with different quantitative analysis capabilities. He also pointed out that "We need to see physics problem sessions as not merely 'working out the solutions'. A variety of appropriate hands-on and minds-on activities has to be integrated to facilitate both conceptual understanding and problem-solving."

This conclusion is really interesting and reliable to some extent, because the benefit of quantitative methods is relying on the statistical analysis results with massive data the author collected, and it makes generalization possible especially when the author chooses appropriate subjects. While the limitation of statistical methods is that it ignores the individual difference in science learning, both conceptual and quantitative skills learning process, and it just concluded that the two processes are related because the effects are statistically significant. In addition, in this research method, the researcher just acts as an "observer" or an "outsider" to collect data, while in the research of educational psychology focusing on individual learning ability and teaching-studying process, the author should get involved in the real teaching process so that it can provide more in-depth analysis on any phenomena that happened in this process.

Reference:

Yap, K.C., & Wong, C.L. (2007). Assessing conceptual learning from quantitative problem solving of a plane mirror problem. Physics Education, 42, 50 - 55.

https://iopscience.iop.org/article/10.1088/0031-9120/42/1/005