Before WIENER, COSTA, and WILLETT, Circuit Judges. WIENER, Circuit Judge: Plaintiffs-Appellants T.O. and his parents, Terrence Outley and Darrezett Craig (collectively, “Plaintiffs-Appellants”) appeal the dismissal of their claims arising under the Fourth and Fourteenth Amendments, Title II of the Americans with Disabilities Act (“ADA”) and § 504 of the Rehabilitation Act of 1974 (“§ 504″), in connection with a primary school disciplinary incident experienced by T.O. We agree that the injuries T.O. allegedly sustained in an altercation with a teacher resulted from a disciplinary incident. We are therefore bound by our precedent to affirm the dismissal of Plaintiffs-Appellants’ constitutional claims. For different reasons, we affirm the district court’s dismissal of their statutory claims. BACKGROUND This case arises from injuries that the minor child T.O. alleged to have sustained during an altercation with a teacher at Hunters Glen Elementary School, when he was a first-grade student there. T.O. has Attention Deficit Hyperactivity Disorder and Oppositional Defiant Disorder. Based on these conditions, Defendant-Appellee Fort Bend Independent School District (“FBISD”) provided T.O. with a behavioral aide and a Behavioral Intervention Plan, which called for oral redirection and placement in a quiet area whenever T.O. misbehaved, and praise when he engaged in appropriate behavior. After T.O. exhibited disruptive classroom behavior on a day in 2017, his aide took him into the hallway and instructed him to remain there until he calmed down. Defendant-Appellee Angela Abbott, a fourth-grade teacher, happened to be walking down the hall at the same time and offered her assistance. Although T.O.’s aide explained that the situation was under control, Abbott positioned herself between T.O. and the classroom door while he yelled that he wanted to return to class. In an attempt to re-enter the classroom, T.O. tried to push Abbott away from the classroom door and hit her right leg. Abbott responded by seizing T.O.’s neck, throwing him to the floor, and holding him in a choke hold for several minutes. During that incident, Abbott yelled that T.O. “had hit the wrong one” and needed “to keep his hands to himself.” She released T.O. after his aide asked Abbott “to release him . . . because he needed air and she was holding him the wrong way.” FBISD investigated the incident on three separate occasions, but Abbott was never fired or otherwise disciplined. Plaintiffs-Appellants sued Abbott under 42 U.S.C. § 1983 for violations of T.O.’s Fifth and Fourteenth Amendment liberty interest in his bodily integrity, and his Fourth Amendment right to be free from unreasonable seizure. They also sued FBISD for disability discrimination in violation of the ADA and § 504. In lieu of filing an answer, Abbott and FBISD moved to dismiss all claims. A magistrate judge issued a memorandum and recommendation, concluding that (1) Abbott was entitled to qualified immunity because her use of force was not a constitutional violation under Fee v. Herndon,[1] and (2) T.O had failed to state a claim for disability discrimination against FBISD. The district court adopted the recommendation in full, dismissing all claims and denying Plaintiffs-Appellants leave to file a proposed second amended complaint. Plaintiffs-Appellants timely appealed, challenging the dismissal of their § 1983 claims and their discrimination claims. They also appealed the denial of their motion to file a second amended complaint. STANDARDS OF REVIEW A motion to dismiss granted on the basis of qualified immunity is reviewed de novo, accepting all well-pleaded facts as true and drawing all inferences in favor of the plaintiff.[2] “To survive a motion to dismiss, a complaint must contain sufficient factual matter, accepted as true, to ‘state a claim to relief that is plausible on its face.’”[3] Conclusional allegations, naked assertions, and “formulaic recitations of the elements of a cause of action will not do.”[4] The denial of a motion for leave to amend a complaint is reviewed for abuse of discretion.[5] A trial court abuses its discretion when its ruling is “based on an erroneous view of the law or a clearly erroneous assessment of the evidence.”[6] ANALYSIS Section 1983 Claims “To state a claim under 42 U.S.C. § 1983, a plaintiff must first show a violation of the Constitution or of federal law, and then show that the violation was committed by someone acting under color of state law.”[7] However, “[t]he doctrine of qualified immunity protects government officials from civil damages liability when their actions could reasonably have been believed to be legal.”[8] Once the defense of qualified immunity has been asserted, the plaintiff has the burden of demonstrating that “(1) the official violated a statutory or constitutional right, and (2) the right was ‘clearly established’ at the time.”[9] Plaintiffs-Appellants claim that Abbott violated T.O.’s right to be free from (1) state-sanctioned harm to his bodily integrity under the Due Process Clause of the Fourteenth Amendment and (2) unreasonable seizure under the Fourth Amendment, when Abbott held him down and choked him. Based on our precedent, we disagree. The Fourth Amendment is applicable in a school context.[10] In this circuit, however, claims involving corporal punishment are generally analyzed under the Fourteenth Amendment.[11] It is well-established in this circuit that “corporal punishment in public schools implicates a constitutionally protected liberty interest” under the Fourteenth Amendment.[12] But, “as long as the state provides an adequate remedy, a public school student cannot state a claim for denial of substantive due process through excessive corporal punishment.”[13] This rule was developed in Ingraham v. Wright[14] and applied in Fee v. Herndon.[15] It recognizes that, while “corporal punishment in public schools ‘is a deprivation of substantive due process when it is arbitrary, capricious, or wholly unrelated to the legitimate state goal of maintaining an atmosphere conducive to learning,’” when the state provides alternative post-punishment remedies, the state has “provided all the process constitutionally due” and thus cannot “act ‘arbitrarily,’ a necessary predicate for substantive due process relief.”[16] Based on the foregoing, we have consistently dismissed substantive due process claims when the offending conduct occurred in a disciplinary, pedagogical setting. For example, we dismissed substantive due process claims (1) when a student was instructed to perform excessive physical exercise as a punishment for talking to a friend;[17] (2) when a police officer slammed a student to the ground and dragged him along the floor after the student disrupted class;[18] (3) when a teacher threatened a student, threw him against a wall, and choked him after the student questioned the teacher’s directive;[19] (4) when an aide grabbed, shoved, and kicked a disabled student for sliding a compact disc across a table;[20] and (5) when a principal hit a student with a wooden paddle for skipping class.[21] In contrast, we have allowed substantive due process claims against public school officials to proceed when the act complained of was “arbitrary, capricious, or wholly unrelated to the legitimate state goal of maintaining an atmosphere conducive to learning.”[22] For example, we held that a substantive due process claim could proceed when a teacher allegedly molested a student,[23] and when a teacher tied a student to a chair for two days as part of an experimental technique.[24] We allowed those claims to proceed because, unlike disciplinary measures, these alleged acts were “unrelated to any legitimate state goal.”[25] Fidelity to our precedent requires us to affirm the dismissal of the instant claim of substantive due process. The aide removed T.O. from his classroom for disrupting class, and Abbott used force only after T.O. pushed and hit her. Even if Abbott’s intervention were ill-advised and her reaction inappropriate, we cannot say that it did not occur in a disciplinary context. The facts alleged simply do not suggest that T.O. was the subject of a “random, malicious, and unprovoked attack,”[26] which would justify deviation from Fee. To borrow from the unpublished opinion in Marquez, in which this court dismissed § 1983 claims brought by an autistic seven-year old whose aide yelled at, grabbed, shoved, and kicked that student for sliding a compact disk across a desk, “the setting is pedagogical, and [T.O.'s] action was unwarranted.”[27] Furthermore, we have consistently held that Texas law provides adequate, alternative remedies in the form of both criminal and civil liability for school employees whose use of excessive disciplinary force results in injury to students in T.O.’s situation.[28] Plaintiffs-Appellants’ Fourth Amendment claim fares no better. This court has not conclusively determined whether the momentary use of force by a teacher against a student constitutes a Fourth Amendment seizure. We have rejected Fourth Amendment claims brought by a student who was choked by a teacher on the basis that allowing such claims to proceed would “eviscerate this circuit’s rule against prohibiting substantive due process claims” stemming from the same injuries.[29] But we have also noted that the claims of excessive force and unlawful arrest against other school officials “are properly analyzed under the Fourth Amendment.”[30] In light of this inconsistency in our caselaw, we cannot say that it was clearly established, at the time of the incident, that Abbott’s actions were illegal under the Fourth Amendment. Plaintiffs-Appellants unpersuasively attempt to avoid this outcome by suggesting that Fee has been abrogated by Knick v. Township of Scott[31] and Kingsley v. Hendrickson.[32] Not so. Knick concerns Fifth Amendment Takings claims, and Kingsley concerns excessive force claims brought by pretrial detainees—circumstances markedly distinguishable from substantive due process claims brought in an educational context.[33] In any event, Knick was decided after the offending incident in this case, and Kingsley has never been interpreted by this court as altering the law in the manner Plaintiffs-Appellants suggest. Even if these cases do call Fee‘s validity into question,[34] they would not have been sufficient to put Abbott on notice of the illegality of her conduct at the time of the incident. To defeat a claim of qualified immunity, the illegality of the conduct must be “clearly established” at the time it took place.[35] It is certainly true that “[b]y now, every school teacher . . . must know that inflicting pain on a student . . . violates that student’s constitutional right to bodily integrity.”[36] But, for more than thirty years, the law of this circuit has clearly protected disciplinary corporal punishment from constitutional scrutiny. Neither Knick nor Kingsley permits us to deviate from out established precedent in this regard. Statutory Claims Plaintiffs-Appellants also contend that the district court erred in dismissing their claims of disability discrimination under the ADA and § 504. Both the ADA and § 504 generally prohibit discrimination against persons with disabilities.[37] Claims brought under § 504 or the ADA, or both, are subject to the same analysis. “The only material difference between the two provisions lies in their respective causation requirements.”[38] “Cases concerning either section apply to both.”[39] To prevent dismissal, a plaintiff must allege sufficient facts to show: “(1) that he is a qualified individual . . .; (2) that he is being excluded from participation in, or being denied benefits of, services, programs, or activities for which the public entity is responsible, or is otherwise being discriminated against by the public entity; and (3) that such exclusion, denial of benefits, or discrimination is by reason of his disability.”[40] A plaintiff need not identify an official policy to sustain such a claim, and a public entity may be held vicariously liable for the acts of its employees under either statute.[41] Evidence of intentional discrimination is necessary to support a claim for monetary damages, but a plaintiff seeking only equitable relief may succeed on a disparate impact theory.[42] Plaintiffs-Appellants’ theory of liability for these claims is hardly evident from the face of their complaint. On appeal, however, they stress that their discrimination claims are based on (1) Abbott’s physical acts against T.O. on January 31, 2017; (2) FBISD’s failure to ensure that Abbott knew how to approach the situation; (3) FBISD’s failure to investigate the incident; and (4) FBISD’s failure to discipline Abbott.[43] The trouble is that none of the factual allegations contained in the complaint permit the inference that T.O. was ever discriminated against because of his disability. With respect to vicarious liability for Abbott’s involvement in the physical altercation, the only allegations linking Abbott’s conduct to T.O.’s disability are conclusional ones that cannot withstand Rule 12(b)(6) scrutiny.[44] The complaint is devoid of any allegations concerning FBISD’s failure to properly train Abbott,[45] and the complaint acknowledges that FBISD conducted at least three investigations into the incident. Plaintiffs-Appellants’ assertion that these investigations were “designed to exonerate” Abbott and FBISD from liability are legal conclusions, not factual allegations that support their claim. Lastly, with respect to FBISD’s alleged failure to discipline Abbott following the incident, there are no allegations that permit the inference that this decision was made because of T.O.’s disability status. In sum, the amended complaint contains no factual allegations that permit the inference that either Abbott’s actions or FBISD’s failure to train, investigate, or discipline Abbott, were “by reason of his disability”—an essential element of a discrimination claim. Leave to Amend Plaintiffs-Appellants lastly contend that the district court erred by denying them leave to amend their complaint. Federal Rule of Civil Procedure 15 provides that, even though leave of court is required when a party seeks to amend a pleading after the time for amending as a matter of course has passed, “[t]he court should freely give leave when justice so requires.”[46] When, however, a party seeks to amend pleadings in a fashion that would alter a deadline imposed by a scheduling order, Rule 15 is superseded by Rule 16, which requires good cause and the judge’s consent for modification.[47] Whether good cause exists depends on “(1) the explanation for the failure to timely move for leave to amend; (2) the importance of the amendment; (3) potential prejudice in allowing the amendment; and (4) the availability of a continuance to cure such prejudice.”[48] “If a party shows good cause for missing the deadline, then the ‘more liberal standard of Rule 15(a) will apply to the district court’s denial of leave to amend.’”[49] Plaintiffs-Appellants sought leave to file a second amended complaint more than seven months after the scheduling order’s deadline for amending pleadings had passed. The proffered second amended complaint contained additional allegations about (1) statements Abbott made during the incident; (2) details of FBISD’s investigation of the incident; and (3) FBISD’s history of “underserving its students in need of special education services.” Additionally, the proposed amendment asserts for the first time that FBISD violated the ADA and § 504 by failing to hold a “section 504 referral” meeting with T.O.’s parents in a timely manner. We cannot hold that the district court abused its discretion by denying leave to amend. The proposed complaint expands on statements made by Abbott and T.O.’s aide at the time of the incident—information Plaintiffs-Appellants had at their disposal when they filed the original and first amended complaints. Further, the alleged failure to hold a § 504 referral meeting occurred in 2016, well before the incident underlying the original complaint. Similarly, two of the media articles cited in support of FBISD’s history of mistreating students with disabilities were published before the deadline for amendments passed. Simply put, it is difficult to conceive of a reason why Plaintiffs-Appellants would not have been able to amend their complaint to include these various allegations in a timely manner. Because good cause did not exist, the district court did not abuse its discretion in denying leave to file the proposed amended complaint. CONCLUSION For the foregoing reasons, all rulings of the district court are AFFIRMED. WIENER, Circuit Judge, with whom JUDGE COSTA, Circuit Judge, joins, specially concurring: Twenty years ago, I called for en banc reconsideration of Ingraham v. Wright, 525 F.2d 909 (5th Cir. 1976) (en banc), aff’d, 430 U.S. 651, and Fee v. Herndon, 900 F.2d 804 (5th Cir. 1990), in which we held that injuries resulting from corporal punishment do not violate the Fourteenth Amendment as long as the forum state provides adequate alternative remedies.[50] I write separately today to re-urge the same, hoping that the intervening decades of experience will have persuaded my colleagues that the rule is not only unjust, but is completely out of step with every other circuit court and clear directives from the Supreme Court. At the time I concurred in Moore, our circuit was already isolated in its position, with the Third, Fourth, Sixth, Seventh, Eighth, Ninth, Tenth, and Eleventh Circuits all holding that corporal-punishment-related injuries implicate constitutional rights regardless of the availability of state remedies.[51] Since then, the Second Circuit has joined the fray, siding with the majority.[52] These cases, like our own, rely on the Supreme Court’s acknowledgement in Ingraham that “corporal punishment in public schools implicates a constitutionally protected liberty interest.”[53] In Ingraham, the Supreme Court held that procedural due process rights were not violated by corporal punishment if alternative remedies existed, but declined to consider whether such punishment implicated substantive due process rights.[54] Unlike this court, all other circuit courts have declined to apply Ingraham‘s procedural due process reasoning to substantive due process claims, instead concluding that under particular circumstances, excessive corporal punishment can violate substantive due process rights (or Fourth Amendment rights), regardless of the availability of alternative remedies. The Supreme Court has yet to be called on to resolve this dramatically lopsided circuit split, but it is only a matter of time. More importantly, subsequent writings by the Supreme Court highlight a major problem in the reasoning we applied in Ingraham and Fee. Specifically, the Supreme Court has made it clear that the availability of state remedies does not replace a cause of action under § 1983. In Parratt v. Taylor,[55] and Hudson v. Palmer,[56] the Supreme Court held that an individual deprived of a constitutionally protected property interest by the random and unathorized act of a state actor could not bring procedural due process claims under § 1983 unless the forum state failed to provide adequate post deprivation remedies. Notably, the Supreme Court in Parratt approvingly cited its own ruling in Ingraham, affirming that Ingraham‘s reliance on the availability of post-deprivation remedies was properly cabined to procedural due process claims.[57] The theory underlying Parratt/Hudson and their progeny is that a procedural due process violation challenges not the deprivation itself, but merely the procedure (or lack thereof) according to which the deprivation occurs. But a substantive due process violation is fundamentally different, insomuch as a § 1983 substantive due process action challenges not the procedure attendant to the deprivation, but the deprivation itself. The Supreme Court stressed this distinction in Zinermon v. Burch,[58] in which it explained that, with respect to substantive due process claims, “the constitutional violation actionable under § 1983 is complete when the wrongful action is taken. A plaintiff . . . may invoke § 1983 regardless of any state-tort remedy that might be available to compensate him for the deprivation of these rights.”[59] In other words, while a procedural due process violation may be eliminated by an adequate, state-provided, post-deprivation process, a substantive due process violation occurs at the moment of the deprivation itself, making the availability of alternative remedies wholly irrelevant. Fee, decided just three months later, makes no mention of Zinermon‘s explicit pronouncement, instead citing this circuit’s decision in Ingraham, among others, for the proposition that the existence of state remedies forecloses any substantive due process violations in an educational context.[60] Nevertheless, this circuit has repeatedly recognized that Parratt/Hudson‘s focus on alternative remedies is inapplicable to substantive due process claims in other contexts.[61] In other opinions, we have recognized that Fee‘s reasoning is in conflict with Zinermon.[62] For the foregoing reasons, I remain firm in my conviction that Fee and Ingraham were wrongly decided—a conviction that has only grown stronger with the clarity of hindsight and thirty years of watching this rule being applied to the detriment of public school students in Texas, Mississippi, and Louisiana.[63] This rule flies in the face of the many decisions by our colleagues in other circuits and those sitting on the highest court of this land. Let us fix the error before the Supreme Court decides to fix it for us.