The natural father (Father) of two minor children, S.D.E., age 11 at time of the district court proceedings, and K.E., a/k/a/ K.A.M., age 9 at that time, appeals the district court’s termination of his parental rights. He argues on appeal that the court’s denial of both his request for a continuance and his request to testify by phone violated his due process rights, citing and relying on In re J.O., 43 Kan. App. 2d 754, 232 P.3d 880 (2010). We conclude that although Father’s claim of error regarding the denial of a continuance has been abandoned, the denial of phone participation denied him procedural due process, thus requiring that we reverse and remand for further proceedings.
Factual and Procedural Background
Following a remand order from this court vacating a prior order terminating Father’s parental rights, the State filed a subsequent *220motion to terminate his rights. The matter was set for hearing, and there is no dispute that Father received adequate notice of the hearing.
Despite notice of the hearing, Father did not appear in person. He had indicated an intent to be present but called his counsel on the day of the hearing to advise that he was unable to afford transportation from Georgia to Kansas. At the beginning of the hearing, Father was called on the telephone by the district court. His counsel requested a continuance because Father had planned and wanted to be present but was unable to arrange transportation due to financial issues. Both the State and the guardian ad litem objected to the continuance, and the court denied the request because “it is in the best interest that these children have this proceeding concluded one way or the other.”
The court then inquired how Father might be allowed to participate, but learned that Father was on a phone in a church and there was no notary public at that location. In an exchange with the court, Father indicated there was a notary just “down the street” at a funeral home, but the court indicated the notary needed to be in the church. Again, the State and the guardian ad litem objected to Father’s telephonic participation because he could not be sworn and would not be subject to effective cross-examination. The court then decided that Father would be permitted to listen to the hearing but he would not be permitted to participate. The court reasoned in part:
“I’ll deny the request that you be allowed to present sworn testimony by telephone since first of all we don’t have a simple process to get you sworn, but furthermore, that the court has decided that you were given the option to appear in person, chose not to do so, and in fact the right of confrontation and participation is severely limited by your not being here in person to view exhibits and be observed as far as demeanor and such.”
At the close of the hearing, and at the repeated requests of the State to find that K.S.A. 60-414(a) applied, the district court applied the statutory presumption of unfitness under K.S.A. 2010 Supp. 38-2271(a)(5), (a)(6), (a)(9), and (a)(13). Father’s counsel indicated that he was unable to rebut the presumption because the court had denied his client the right to participate by phone, but *221he reminded the court that Father had sent “forty some letters” to the children.
Ultimately, the district court held that Father had not rebutted the presumption of unfitness and that the termination of his parental rights was appropriate “under K.S.A. 38-2271 as far as the list that’s provided there,” as well as under the statutory factors in K.S.A. 2010 Supp. 38-2269(a)(3) or (a)(4). The district court further found from the bench that termination of Father’s parental rights was in the children’s best interests. The court then asked Father if he had questions, and Father responded, “I have been trying to get in contact with my kids. Why was I not allowed to get in touch with my kids at all? . . . How can you get to know your kids when they refuse to let you even talk to the kids?” The court then stopped Father and said in part, “You can talk to your attorney further about this matter.”
The journal entry of termination reflects that Father was presumed unfit under K.S.A. 38-2271(a)(5), and (a)(6), as well as K.S.A. 38-2269(b)(4), (b)(8), and (c)(2).
Father timely appeals.
Standards of Review
Appellate courts generally review a district court’s refusal to grant a continuance for an abuse of discretion. In re J.A.H., 285 Kan. 375, 384, 172 P.3d 1 (2007). Under this highly deferential standard of review, we will not overturn a district court’s discretionary decision on appeal if reasonable persons could differ about the propriety of that decision. See Schuck v. Rural Telephone Service Co., 286 Kan. 19, 24, 180 P.3d 571 (2008).
A district court’s discretionary decisions are not unfettered, however, and must necessarily be made within and take into account any applicable legal standards. Thus, this court will also find Are district court abused its discretion on appeal if its decision goes outside the framework of or fails to properly consider statutory hmitations or legal standards. State v. Woodward, 288 Kan. 297, 299, 202 P.3d 15 (2009); see also In re Adoption of B.G.J., 281 Kan. 552, 563, 133 P.3d 1 (2006) (“ ‘Discretion must be exercised, *222not in opposition to, but in accordance with, established principles of law. It is not an arbitrary power.’ [Citation omitted.]”).
We have unlimited review of the questions whether Father’s due process rights were violated and whether the district court misconstrued a court rule or statute. See In re Adoption of B.J.M., 42 Kan. App. 2d 77, 81, 209 P.3d 200 (2009) (unlimited review of legal question of due process); see also Double M Constr. v. Kansas Corporation Comm’n, 288 Kan. 268, 271, 202 P.3d 7 (2009) (unlimited review when statutory construction involved).
Did the District Court Err in Refusing to Grant Father a Continuance?
Father references in the headings of his brief that the district court erred in refusing to grant him a continuance, but the brief fails to discuss or support this argument in any way thereafter. Instead, Father’s appellate brief focuses exclusively on his argument that he was denied due process when the district court refused to allow him to testify over tire phone. Thus, Father’s claim that the district court erred in granting him a continuance must be denied as an abandoned point. An issue not briefed by the appellant is deemed abandoned. Kingsley v. Kansas Dept. of Revenue, 288 Kan. 390, 395, 204 P.3d 562 (2009). A point raised incidentally in a brief and not argued there is likewise deemed abandoned. Cooke v. Gillespie, 285 Kan. 748, 758, 176 P.3d 144 (2008).
We deem this claim of an abuse of discretion to be abandoned on appeal.
Did the District Court Err in Refusing to Allow Father Full Telephonic Participation?
Father next argues that the district court erred in denying his request to testify by phone and that this denial violated his right to procedural due process, relying exclusively on In re J. O., 43 Kan. App. 2d 754.
Indeed, we find this court’s decision in In re J. O. to be instructive here, but not determinative given later legislative developments. The district court in that case denied the father’s request to participate by phone from prison on the basis that Supreme *223Court Rule 145 (2009 Kan. Ct. R. Annot. 236) and K.S.A. 60-243(a) only permitted in-court testimony. 43 Kan. App. 2d at 756-57. On appeal, the issue before the Court of Appeals was whether the district court correctly concluded that Rule 145 and K.S.A. 60-243(a) strictly prohibit a witness from testifying by phone. At that time, K.S.A. 60-243(a) stated: “ ‘In all trials the testimony of witnesses shall be taken orally in open court, unless otherwise provided by this article.’ ” 43 Kan. App. 2d at 760. A panel of this court held that the district court’s strict application of Rule 145 and K.S.A. 60-243(c) to prohibit telephonic participation under these circumstances violated constitutional due process requirements.
“The integrity of the judicial process obviously must include incorporation of some flexibility in the mode of appearance at a trial on the merits for good cause in compelling circumstances, as recognized in FRCP 43(a). Where the only manner of appearance for an incarcerated person to participate in a proceeding to protect a fundamental liberty interest is by telephone, neither the rule nor the statute should prohibit that modicum of due process.” 43 Kan. App. 2d at 761-62.
Although counsel and the parties fail to cite the legislative change here, the 2010 Kansas Legislature altered the statute to conform to Federal Rule of Civil Procedure 43(a). K.S.A. 60-243(a) now reads in material part:
“At trial, the witness’ testimony must be taken in open court, unless otherwise provided by law. For good cause in compelling circumstances and with appropriate safeguards, the court may permit testimony in open court by contemporaneous transmission from a different location.” K.S.A. 2010 Supp. 60-243(a).
Thus, the questions framed by this appeal are compound: Did Father show compelling circumstances for transmission by phone of his testimony? Were appropriate safeguards available under these circumstances? Did the district court abuse its discretion in denying full telephonic participation under these circumstances? Whether or not the amended statute was satisfied, did the denial of such participation violate Father’s procedural due process rights?
With regard to compelling circumstances, we share the district court’s consternation about Father’s last minute decision and declaration that he was unable to be present in person at this hearing. *224Father received timely notice and — despite his financial issues— he and his counsel could have made advance arrangements for an appearance by telephone and notified the court of that request before the hearing began. Due to the belated appearance by phone, it becomes a close question whether these circumstances were compelling. Here, the district court made no finding either way as to compelling circumstances, but it appears that the court was prepared to accept Father’s testimony by phone if it could have been sworn. Thus, compelling circumstances or the lack thereof does not appear to be dispositive here.
But, it appears that the principal issue for the district court was the lack of a notary for administration of an oath. First, this issue may have been a legitimate concern for “appropriate safeguards” as contemplated by the statute. Cf. Fed. R. Civ. Proc. 43a, Advisory Committee Notes, 1996 amendment (“Safeguards must be adopted that ensure accurate identification of the witness . . . .”) We note, however, that such safeguards may have been available in the form of a notary public “down the street” and within a few minutes and with a subsequent phone call. It is unclear to this court why the district court did not further explore what appeared to be a viable alternative under the circumstances. Moreover, any concern about identity of Father was alleviated by a voice identification by the State’s first witness.
Second, it does not appear that the court considered telephonic administration of the oath. Although there is recent emerging and competing authority regarding testifying by phone, at least one jurisdiction has held that an oath maybe administered by the judge to a witness testifying by phone — whether or not the witness is present in the jurisdiction of the court.
“We are not persuaded that a state’s boundaries are the con-ect measure of a judge’s ability to administer a valid telephonic oath. Alaska’s recognition of the validity of telephonic oaths is not premised upon the witness’ physical location, but rather on the witness’ constructive presence in the courtroom and ability to provide testimony. One testifying telephonically is physically absent from the courtroom to the same extent whether across the street or on the far side of the globe. Alaska’s interests thus dictate that its judicial officers be able to telephonically administer a valid oath to a witness located anywhere in the world, provided *225she is constructively present in the courtroom via the telephone.” Gregg v. Gregg, 776 P.2d 1041, 1044 (Alaska 1989).
Although this appears to be the more enlightened view, we are not yet prepared to hold that Kansas law permits administration of oaths by telephone to one in another state. We note, however, there is no bar to this practice in K.S.A. 2010 Supp. 60-243(a), which clearly contemplates that telephone testimony is permissible under compelling circumstances.
Given our analysis of factors to be considered in construing and applying the amended statute, we turn to the requisite procedural due process analysis set forth in Mathews v. Eldridge, 424 U.S. 319, 335, 96 S. Ct. 893, 47 L. Ed. 2d 18 (1976). This analysis requires us to weigh the following factors: (1) the individual interest at stake; (2) the risk of erroneous deprivation of the interest through the procedures used, and the probable value, if any, of additional or substitute procedural safeguards; and (3) the State’s interest in the procedures used, including the fiscal and administrative burdens that the additional or substitute procedures would entail. In re Adoption of B.J.M., 42 Kan. App. 2d at 84.
With regard to the first factor, our appellate courts have consistently determined that parents have a fundamental liberty interest in the care, custody, and control of their children. See, e.g., In re J.D.C., 284 Kan. 155, 166, 159 P.3d 974 (2007). This interest is “perhaps the oldest of the fundamental liberty interests recognized by [the United States Supreme] Court.” Troxel v. Granville, 530 U.S. 57, 65, 120 S. Ct. 2054, 147 L. Ed. 2d 49 (2000).
With regard to the second factor, we consider that the employment of the presumption of unfitness under K.S.A. 2010 Supp. 38-2271 without any opportunity to mount a rebuttal under 38-2271(b) substantially risked an erroneous deprivation of Father’s fundamental interest in the children. Moreover, consideration and reliance by the district court on these and other factors that assessed Father’s neglect of the children, failure to maintain contact or communication with the children, and substantial neglect or willful refusal to work toward reintegration of the children, without a full exploration of Father’s clear protest that he had been pro*226hibited from such contact by State actors, also risked an erroneous deprivation of his fundamental interest in the children. As is reflected by our analysis above, substitute procedural safeguards should have been considered, including: (1) employment of a notary down the block and subsequent phone testimony; (2) consideration of swearing in Father by the Kansas court; (3) permitting Father to submit a sworn affidavit after the hearing; (4) allowing counsel to explore and present details of Father’s protest of prohibited contact of his children before closing the record. Under these circumstances, we must conclude that there was great risk, indeed, that Father was unlawfully deprived of his fundamental liberty interest in his children.
Finally, with regard to the State’s interest in the procedures used, it is clear that our statute and case law demonstrate a preference for live testimony in open court where witnesses’ credibility is on display for full assessment by the factfinder. We are aware, however, of no fiscal or administrative burden that would have been borne by the State in permitting any of the substitute safeguards posed above. Although the State and the district court correctly noted the need for these proceedings to be completed, the alternatives assuring Father’s due process rights would not have extended the proceedings more than a few minutes or a few days at most.
For these reasons, we conclude that Father’s due process rights were violated when he was deprived of tire opportunity to be heard prior to the termination of a fundamental liberty interest.
Since we have found a constitutional violation, the next question is whether Father is entitled to a reversal of the district court’s ruling and remand for a retrial. Here, we are concerned that all of the bases for terminating his parental rights could have been tempered or mitigated by Father’s testimony. The testimony by State actors regarding Father’s efforts toward reintegration after his recent release from prison, coupled with his numerous letters to the children and his complaint that he was denied direct contact with his children, cause us to believe that the error in precluding Father’s testimony was necessarily unquantifiable and indeterminate. See State v. Calderon, 270 Kan. 241, 250, 13 P.3d 871 (2000) (cit*227ing Arizona v. Fulminante, 499 U.S. 279, 111 S. Ct. 1246, 113 L. Ed. 2d 302 [1991]). Thus, the due process error was structural and entitles Father to a reversal and remand for further proceedings.
We recognize that Father may have a substantial hill to climb to rebut presumptions of unfitness, but this should not mitigate the degree of due process to which he is entitled before his parental rights are terminated.
Reversed and remanded.