Quote from Gunnii

Positive reinforcement has been proven over and over as a more effective way, endorsing good behavior does work better then punishing bad behavior, that much was established by B.F. Skinner and the like in the 1930's and -40s. They showed that punishment showed positive effects in the short term, but looking at longer periods of time it did not prove effective.
Most psychologists agree that corporal punishment it not effective, Elizabeth Gershoff and Graham Bermann analyzed decades of research into the matter and published a paper about their research in 2008. In the paper they encouraged caretakers not to use corporal punishment. The paper was endorsed by a number of institutions, including the American Academy of Pediatrics, American Medical Association and Psychologists for Social Responsibility.
Yet classes in those time periods ran efficiently, without half the class texting their friends and talking while in-session. A large part of all the negative effects of Corporal Punishment can be attributed to the incompetency and aggression of teachers. I refer you to the link below so you can have a look.

I'd think that the American Psychoanalytic Association is a fairly scientific institution, and the references they list seem legit. I have also yet to see a single psychological institution that endorse corporal punishment.
Here you go.

I would argue that has more to do with the actual way the educational system is set up as a whole, rather then the lack of punishment. For example, the problem with class sizes isn't that teachers don't have an effective way to discipline the class as a whole, the problem is that the class is to big. I believe the current educational system needs a complete overhaul.
I can agree with that. Non-violent methods of punishment would work well and do much better if class sizes were smaller. As of right now, class sizes are not small though, hence why I think Corporal Punishment works better in this case.

Yet classes in those time periods ran efficiently, without half the class texting their friends and talking while in-session. A large part of all the negative effects of Corporal Punishment can be attributed to the incompetency and aggression of teachers. I refer you to the link below so you can have a look.

I can agree with that. Non-violent methods of punishment would work well and do much better if class sizes were smaller. As of right now, class sizes are not small though, hence why I think Corporal Punishment works better in this case.

Quote from Gunnii

The study you referred to only underlined the lack of research that has been made into this matter and didn't really make any real points for, or against it, again, I would say that children should get to enjoy the benefit of the doubt.

All the data that went into that (Click to Show)

1. For an horrific list of offenses for which school children in South Africa have been physically punished, see T.L. Holdstock, "Violence in Schools: Discipline," in Brian McKendrick and Wilma Hoffmann (eds.), People and Violence in South Africa (Cape Town: Oxford University Press, 1990), pp. 348, 349. There is extensive record of the kinds of offenses for which children in American schools have been subject to physical punishment. See, for example, Adah Maurer, "It Does Happen Here," in Irwin Hyman and James Wise (eds.), Corporal Punishment in American Education (Philadelphia: Temple University Press, 1979).
2. The most well-known case that was brought before the United States courts is that of Ingraham v. Wright. Briefly, the facts of the case are that on 6 October 1970 a group of pupils at Drew Junior High School in Florida were slow in leaving the stage of the school auditorium when a teacher asked them to do so. The principal, Willie Wright, Jr., took the pupils to his office to be paddled. One pupil, 14-year-old James Ingraham, refused to accept the punishment. An assistant principal and an assistant to the principal held Ingraham prone across a table while Wright hit the child over twenty times with a paddle. The beating caused a hematoma, from which fluid later oozed. A doctor had to prescribe painkillers, laxatives, sleeping pills and ice packs. The child had to rest at home for over ten days and could not sit comfortably for three weeks. There are numerous other instances of corporal punishment in American schools that are less well known but no less serious.
3. I mean here physical injury. To include psychological injury would be to rule out many objections to corporal punishment -- those that suggest that all physical punishment results in psychological injury. I want to reject this view, but by argument rather than stipulation. I am happy to stipulate the absence of physical injury because the claim that all corporal punishment results in such injury is more demonstrably false.
4. There is a further argument -- that corporal punishment violates constitutional provisions against cruel punishment. I shall not attend to this argument here, but I do so in "The Child, the Rod and the Law" in Acta Juridica, 1996, pp. 197-214; repr. in Raylene Keightley (ed.), Children's Rights (Kenwyn: Juta and Co., 1996).
5. Adah Maurer, "The Case Against Corporal Punishment in Schools," in John Cryan (ed.), Corporal Punishment in the Schools: Its Use is Abuse (Toledo: University of Toledo, 1981), p. 22.
6. Murray A. Straus, Beating the Devil Out of Them: Corporal Punishment in American Families (New York: Lexington Books, 1994), p. 81. He does concede, however, that not all studies have supported the idea that abusive parents use corporal punishment more than nonabusive parents (p. 84).
7. For references to both kinds of study, see Straus, Beating the Devil Out of Them, pp. 83-84.
8. Richard J. Gelles and Ake W. Edfeldt, "Violence Towards Children in the United States and Sweden," Child Abuse and Neglect 10 (1986): 501-10.
9. E.g., Holdstock, "Violence in Schools: Discipline," pp. 356, 357; Richard Dubanoski, Michel Inaba, and Kent Gerkewicz, "Corporal Punishment in Schools: Myths, Problems and Alternatives," Child Abuse and Neglect 7 (1983): 271-78, p. 274; Straus, Beating the Devil Out of Them, chap. 5.
10. Straus, Beating the Devil Out of Them.
11. E.g., John Rosemond, "Should the Use of Corporal Punishment By Parents Be Considered Child Abuse? -- No," in Mary Ann Mason and Eileen Gambrill (eds.), Debating Children's Lives: Current Controversies on Children and Adolescents (Thousand Oaks, Cal.: Sage Publications, 1994), p. 215.
12. Straus, Beating the Devil Out of Them, p. 167.
13. Ibid., p. 70. The (adjusted) increase for one episode of corporal punishment is only two points on the index. For two episodes of corporal punishment, there is a decrease of nearly one point on the index. The index then rises five points for nineteen instances of corporal punishment.
14. Ibid., p. 73. I have described the data that were adjusted to control for other variables.
15. See, for example, Adah Maurer, "Corporal Punishment," American Psychologist (August 1974), p. 621; Holdstock, "Violence in Schools: Discipline," pp. 358-59; Straus, Beating the Devil Out of Them, chap. 8.
16. Straus, Beating the Devil Out of Them, pp. 126-29.
17. E.g., Irwin Hyman, Anthony Bongiovanni, Robert Friedman, and Eileen McDowell, "Paddling, Punishing and Force: Where Do We Go From Here?" Children Today 6 (Sept.-Oct. 1997): 17-23, p. 20; Adah Maurer, "The Case Against Corporal Punishment in Schools," p. 19.
18. Maurer, "The Case Against Corporal Punishment in Schools," p. 20.
19. Dubanoski et al., "Corporal Punishment in Schools," p. 274.
20. Robert Larzelere, "Should the Use of Corporal Punishment By Parents Be Considered Child Abuse? -- No," in Mason and Gambrill (eds.), Debating Children's Lives, pp. 204-9.
21. E.g., Holdstock, "Violence in Schools: Discipline," pp. 353-54, 360-61; Hyman et al., "Paddling, Punishing and Force," p. 20.
22. E.g., Holdstock, "Violence in Schools: Discipline," p. 353; Dubanoski et al., "Corporal Punishment in Schools," p. 273.
23. One study cited by opponents of corporal punishment is that of Richard Walters and Lillian Demkow, "Timing of Punishment as a Determinant of Response Inhibition," Child Development 34 (1963): 207-14. The study is not specifically about corporal punishment. The punishment used was a loud unpleasant sound from a buzzer.
24. Hyman et al., "Paddling, Punishing and Force," p. 19.
25. Robert E. Larzelere, William N. Schneider, David B. Larson, and Patricia L. Pike, "The Effects of Discipline Responses in Delaying Toddler Misbehavior Recurrences," Child and Family Behavior Therapy 18 (1996): 35-57.
26. Robert E. Larzelere, "A Review of the Outcomes of Parental Use of Nonabusive or Customary Physical Punishment," Pediatrics 98, Supplement (1996): 824-28.
27. Graeme Newman, Just and Painful: A Case for Corporal Punishment of Criminals (New York: Macmillan, 1983), p. 43.
28. However, as in other forms of punishment, there may be a moral stigma for the family.
29. E.g., Steven Shaw and Jeffrey Braden, "Race and Gender Bias in the Administration of Corporal Punishment," School Psychology Review 19 (1990): 378-83.
30. George Bernard Shaw, cited with approval by Gertrude J. Rubin Williams, "Corporal Punishment: Socially Sanctioned Assault and Battery," in Cryan (ed.), Corporal Punishment in the Schools, p. 37.