*448On September 25, 2015, a judge of the Probate and Family Court (probate court) dismissed a petition filed by the mother pursuant to G. L. c. 190B, § 5-212, for removal of the paternal grandfather as *105guardian of the mother's son, Kelvin.2 The judge also issued a decree on the guardian's general petition *449regarding visitation, establishing the parameters for weekly parenting time between the mother and Kelvin. On appeal, the mother contends that the judge (1) erred by placing the burden of proof on the mother to prove her fitness; (2) failed to make specific and detailed findings of fact that established the mother's unfitness by clear and convincing evidence; and (3) erred by refusing to allow the mother to present relevant evidence concerning her ability to parent another child in her custody. Because we conclude that the judge applied the incorrect burden of proof with regard to the mother's petition to remove the guardian, we vacate the judgment of dismissal and remand the matter to the probate court for further proceedings consistent with this opinion.
1. Background. We summarize the relevant facts and procedural history from the judge's findings, supplemented by additional undisputed facts from the record. The mother gave birth to Kelvin in January of 2011. She and Kelvin's father never married, and they are no longer in a relationship.3
In February of 2012, the mother and the maternal grandmother had a physical altercation in the presence of Kelvin, prompting an investigation by the Department of Children and Families (department). The department created a service plan for the mother, which included parenting classes and drug testing. On March 16, 2012, the paternal grandfather filed a petition in the probate court to become Kelvin's guardian. A probate judge immediately entered an order appointing the paternal grandfather as Kelvin's temporary guardian, finding that the mother was homeless, mentally unstable, and violent. This appointment was extended at regular intervals until the trial.
On July 10, 2013, the judge issued a decree and order appointing the paternal grandfather as Kelvin's permanent guardian. The judge found that the mother was unfit to parent Kelvin because her contact with him over the prior sixteen months had been limited, she had failed to educate herself on Kelvin's medical condition (asthma ), and she continued to have anger management issues. In the decree, the judge granted the mother six hours of unsupervised parenting time per week.
Between July and November of 2013, the mother had approximately twenty unsupervised visits with Kelvin. She and the guardian shared a notebook in which they communicated with each other *450about Kelvin's meals and snacks, his health, his developmental progress, and his activities during the time that he spent with each caregiver. In September of 2013, during this same period, the mother gave birth to a daughter from a subsequent relationship. The relationship between the mother and her daughter's father was marked by domestic violence, the couple is no longer together, and each has obtained an abuse prevention order against the other pursuant to G. L. c. 209A.
Due to concerns about the people with whom Kelvin was spending time while in the mother's care, the guardian filed a *106general petition on December 11, 2013, seeking to terminate the mother's parenting time or, in the alternative, to restrict her parenting time to supervised visits. Following a hearing, the judge entered a temporary order reducing the mother's parenting time to one two-hour supervised visit per week. A few months later, the judge modified the terms of her order to increase the mother's parenting time to three hours per week, with the first hour being unsupervised and the second two hours being supervised. On September 18, 2014, the mother filed a petition for removal of the guardian pursuant to G. L. c. 190B, § 5-212.4
A three-day trial was held on the two petitions in January and April of 2015.5 Both the mother and the guardian were represented by counsel. At the outset, the judge stated the following regarding the burdens of proof: "[J]ust so we know, so the petition regarding visitation, it will be [the guardian's] burden of proof on that and, [mother's counsel], your burden of proof on the petition for removal of the guardian." Neither party objected or requested further instructions. The judge heard testimony from the mother, the mother's therapist, Kelvin's father, the guardian, the visitation supervisor, a department social worker, and the office manager from Kelvin's day care provider. Over the mother's objection, the judge declined to allow the mother to introduce any evidence relating to her ability to parent her daughter on the ground that such evidence was irrelevant to the mother's ability to parent Kelvin.
On September 25, 2015, the judge dismissed the mother's petition for removal of the guardian. The judge found that although *451the mother had made some strides since the guardian had been appointed on July 10, 2013, the mother continued to suffer from depression and anxiety, and she had not yet resolved her anger management issues. The judge found that the mother had failed to develop an understanding of Kelvin's medical condition, that she did not always adhere to the guardian's list of suggested foods (which was designed to avert Kelvin's purported allergies),6 and that she had given Kelvin sugary snacks. In addition, the judge found that although the mother was scheduled to attend weekly therapy sessions, she had canceled her appointment at least once a month. The judge found that because the relationship between the mother and the guardian was contentious and mistrustful, it interfered with the mother's ability to act in Kelvin's best interest.7 Notwithstanding the judge's finding that the mother and Kelvin have a loving relationship, the judge found that the mother was not currently fit to parent Kelvin, and that it was not in Kelvin's best interest to leave *107the guardian's care and return to the mother's custody.
In a separate decree on the guardian's general petition regarding visitation, issued on the same day as the judgment of dismissal, the judge stated that the mother was entitled to three hours of parenting time with Kelvin per week, the first ninety minutes of which would be unsupervised in a public place, and the last ninety minutes of which would be supervised at a specified bookstore. The judge further stated that only the mother and Kelvin could be present during parenting time and that the mother was not permitted to give Kelvin any food unless it had been provided by the guardian. The present appeal ensued.8
*4522. Discussion. The mother first argues that the judge, when considering her petition for removal of the guardian, erroneously placed the burden of proof on the mother to establish her own fitness. She contends that, notwithstanding the Legislature's enactment of G. L. c. 190B, § 5-212, nearly a decade ago, the issues of which party bears the burden of proof on a petition to remove a guardian, and what standard of proof is necessary to satisfy this burden, remain unsettled. See L.B. v. Chief Justice of the Probate & Family Court Dep't, 474 Mass. 231, 243, 49 N.E.3d 230 (2016). That being the case, the mother urges this court to articulate clear guidance on these matters and, then, to conclude that the judge incorrectly allocated the burden of proof on the mother's petition.
Preliminarily, the guardian argues that because the mother did not challenge the judge's allocation of the burden of proof at trial, the issue has not been preserved for appellate review. Although not our usual practice, an appellate court may consider an issue that was not properly preserved where, among other reasons, such issue is unresolved in the Commonwealth, is a matter of public importance, is likely to arise again, and has been fully briefed by the parties. See Clark v. Rowe, 428 Mass. 339, 341, 701 N.E.2d 624 (1998) ; Petition of the Dep't of Social Servs. to Dispense with Consent to Adoption, 392 Mass. 696, 697, 467 N.E.2d 861 (1984). See also McSweeney v. City of Cambridge, 422 Mass. 648, 653, 665 N.E.2d 11 (1996) ;
*108McLeod's Case, 389 Mass. 431, 434, 450 N.E.2d 612 (1983) (appellate court may consider question of law not argued or decided below where injustice might otherwise result); Quazi v. Barnstable County, 70 Mass. App. Ct. 780, 783 n.2, 877 N.E.2d 273 (2007). This principle is particularly apt here, where the *453mother likely would file a new petition to remove the guardian upon any change of circumstance, and the probate court would then need our guidance on the issues of the burden and standard of proof. Given that the issues have been fully briefed by the parties, and that uncertainty will continue to exist if these matters are left unresolved, we proceed to decide them. See Wellesley College v. Attorney Gen., 313 Mass. 722, 731, 49 N.E.2d 220 (1943).
It is well established that "parents have a fundamental liberty interest in the care, custody, and management of their children." Matter of Hilary, 450 Mass. 491, 496, 880 N.E.2d 343 (2008). See Santosky v. Kramer, 455 U.S. 745, 753, 102 S.Ct. 1388, 71 L.Ed.2d 599 (1982). That said, the probate court may appoint a guardian for a minor if, among other reasons, "the court finds the parents, jointly, or the surviving parent, to be unavailable or unfit to have custody." G. L. c. 190B, § 5-204 (a ). See Guardianship of Estelle, 70 Mass. App. Ct. 575, 578, 875 N.E.2d 515 (2007) (custody of child belongs to parent unless parent is unfit). More specifically, if a judge "finds that a qualified person seeks appointment, venue is proper, the required notices have been given, the conditions of [§] 5-204 (a ) have been met, and the welfare and best interest of the minor will be served by the requested appointment, [the judge] shall make the appointment." G. L. c. 190B, § 5-206 (c ). Although the appointment of a guardian displaces the parent's rights and responsibilities for the duration of the guardianship (except as provided in the decree or otherwise by law), it does not terminate them. See L.B., 474 Mass. at 237-238, 49 N.E.3d 230. See also Guardianship of V.V., 470 Mass. 590, 592, 24 N.E.3d 1022 (2015) ; Bezio v. Patenaude, 381 Mass. 563, 575, 410 N.E.2d 1207 (1980) (appointment of guardian does not diminish weight given to bond between parent and child). As a result, a parent retains the right to later petition for modification or termination of a guardianship involving their child. L.B., supra at 238, 49 N.E.3d 230.
Here, the mother petitioned, although unsuccessfully, under G. L. c. 190B, § 5-212 (a ), to remove the guardian and regain custody of the child. See Care & Protection of Jamison, 467 Mass. 269, 283, 4 N.E.3d 889 (2014) (because guardianships are solely creatures of statute, see G. L. c. 190B, § 1-302, "they may be limited in scope or revoked entirely"). General Laws c. 190B, § 5-212 (a ), states, in relevant part, that "[a]ny person interested in the welfare of a ward ... may petition for removal of a guardian on the ground *454that removal would be in the best interest of the ward."9 Because a petition to remove a guardian involves an issue of custody, a judge is required to make a determination as to the petitioning parent's fitness in *109considering the child's best interest. See R.D. v. A.H., 454 Mass. 706, 715, 912 N.E.2d 958 (2009). "The tests of parental unfitness and the child's best interest 'are not separate and distinct but cognate and connected.' " Guardianship of Cheyenne, 77 Mass. App. Ct. 826, 829, 934 N.E.2d 827 (2010), quoting Guardianship of Estelle, 70 Mass. App. Ct. at 580, 875 N.E.2d 515.
Unlike G. L. c. 190B, § 5-204 (a ), which governs the initial appointment of a guardian for a minor, G. L. c. 190B, § 5-212 (a ), does not expressly mention parental fitness. Nonetheless, it is clear from our case law that "consideration of parental fitness, when parental fitness is at issue, will be highly relevant to a determination of a child's best interest." L.B., 474 Mass. at 238 n.13, 49 N.E.3d 230. See Petition of the Dep't of Pub. Welfare to Dispense with Consent to Adoption, 383 Mass. 573, 589, 421 N.E.2d 28 (1981) (unfitness is standard by which courts "measure the circumstances within the family as they affect the child's welfare"). The "critical inquiry" in such cases is finding parental unfitness by clear and convincing evidence. Adoption of Nancy, 443 Mass. 512, 515, 822 N.E.2d 1179 (2005). We conclude this same standard of proof applies to a petition to remove a guardian under G. L. c. 190B, § 5-212.
Because G. L. c. 190B, § 5-212, is also silent as to who bears the burden to prove parental unfitness, we find it useful to look to the care and protection process under G. L. c. 119 for guidance. A review and redetermination proceeding under G. L. c. 119, § 26 (c ), is a readjudication of a custody order wherein the judge must decide whether to maintain the separation of parent from child.10 See Care & Protection of Erin, 443 Mass. 567, 571, 823 N.E.2d 356 (2005) ;
*455Care & Protection of Thomasina, 75 Mass. App. Ct. 563, 570, 915 N.E.2d 569 (2009). Such a proceeding is, "primarily, the means by which a parent or other interested party ... may bring to a judge's attention a change in the situation of a child, or of a child's parent, which might warrant reconsideration or modification of the original order adjudicating the child in need of care and protection." Care & Protection of Isaac, 419 Mass. 602, 611-612, 646 N.E.2d 1034 (1995). Similarly, a proceeding to remove a guardian pursuant to G. L. c. 190B, § 5-212, is a reevaluation of the original guardianship decree whereby a judge must again decide whether to maintain the separation of parent from child. Although these two types of proceedings are not identical, see L.B., 474 Mass. at 238 & n.13, 49 N.E.3d 230, the parent's same liberty interests are at stake and, thus, our determination as to who shoulders the burden of proof in a proceeding on a petition to remove a guardian is guided by the well-established principles governing a care and protection proceeding under G. L. c. 119, § 26 (c ).
For example, in Care & Protection of Erin, 443 Mass. at 568, 823 N.E.2d 356, the Supreme Judicial Court held that where a party files a petition for review and redetermination of an adjudication that a child is in need of care and protection, "the moving party bears an initial burden to produce some credible evidence that circumstances have changed since the initial determination, such that the child *110may no longer be in need of care and protection." Because a judge does not start with a blank slate, "[t]he proper focus of inquiry ... is on those facts that have undergone some metamorphosis since the previous order or are newly developed and, in consequence, alter the relationship between the biological parent and the child." Id. at 570, 823 N.E.2d 356, quoting Custody of a Minor (No. 2), 22 Mass. App. Ct. 91, 94, 491 N.E.2d 283 (1986).
The Supreme Judicial Court further held in Care & Protection of Erin, supra at 568, 823 N.E.2d 356, that once the moving party satisfied her initial burden of production, the department bore the ultimate burden of proving, by clear and convincing evidence, the child was still in need of care and protection. See Adoption of Lorna, 46 Mass. App. Ct. 134, 139, 704 N.E.2d 200 (1999) ("The burden is on the department in proceedings to dispense with parental consent to adoption to prove current parental unfitness by clear and convincing evidence. That burden never shifts to the parents" [citations *456omitted] ). "This necessarily involves showing that the parent is still unfit and [that] the child's best interests are served by remaining removed from parental custody." Care & Protection of Erin, supra at 572, 823 N.E.2d 356. Because a review and redetermination proceeding "implicates the same liberty interests that exist at an initial determination that a child is in need of care and protection," the Supreme Judicial Court saw no reason to shift the ultimate burden of proof away from the department and onto the mother who had filed the petition. Id. at 571, 823 N.E.2d 356. That same burden of proof applies equally to this case.
In the present case, the mother previously had been found unfit to care for Kelvin. Accordingly, at trial on her petition to remove the guardian, the mother had the initial burden, similar to the mother in Care & Protection of Erin, 443 Mass. at 568, 823 N.E.2d 356, of producing some credible evidence of changed circumstances since the initial guardianship determination, such that Kelvin may no longer be in need of a guardian. Once the mother satisfied this burden of production, the guardian then bore the ultimate burden of proving, by clear and convincing evidence, that the mother remained unfit and that continuation of the guardianship served Kelvin's best interest. See L.B., 474 Mass. at 237, 49 N.E.3d 230.
In her instructions to the parties at the outset of trial, however, the judge erroneously placed the burden of proof solely on the mother with respect to her petition to remove the guardian. Because the issues of the party bearing the burden of proof on such a petition and the standard of proof necessary to satisfy this burden have been unsettled since the enactment in 2009 of the Massachusetts Uniform Probate Code, the judge did not have the benefit of appellate court precedent in ruling on the mother's petition. Therefore, a remand for further proceedings, with the guidance we have provided herein, is necessary.
On remand, after hearing such additional evidence as the judge deems appropriate, and applying the standards we have articulated, the judge shall determine, with detail and specificity, first, whether the mother has presented some credible evidence showing some change in circumstances from the initial appointment of the guardian, and second, whether the guardian has established, by clear and convincing evidence, that the mother remains currently unfit and that Kelvin's best interest would be served by continuation of the guardianship. See Adoption of Stuart, 39 Mass. App. Ct. 380, 383, 656 N.E.2d 916 (1995) ("ultimate determination of current parental unfitness does not clearly and *111convincingly follow *457from the cursory findings made, even when seen as not clearly erroneous and taken together as a whole"). See also Custody of Eleanor, 414 Mass. 795, 799-801, 610 N.E.2d 938 (1993). In making this determination, the judge must ensure that the evidence on which she relies is not stale. See Adoption of George, 27 Mass. App. Ct. 265, 268, 537 N.E.2d 1251 (1989) (stale information cannot be basis for finding of current parental unfitness, but prior history can have prognostic value); Petitions of the Dep't of Social Servs. to Dispense with Consent to Adoption, 18 Mass. App. Ct. 120, 126, 463 N.E.2d 1187 (1984) ("isolated problems in the past or stale information cannot be a basis for a determination of current parental unfitness").
For the sake of providing additional guidance to the judge on remand, we address one final matter. The mother contends that the judge erred in refusing to allow the introduction of any evidence regarding her ability to parent her daughter on the ground that such evidence was irrelevant to the mother's ability to parent Kelvin. It is well established that a parent may be fit to raise one child and unfit to raise another. See R.D., 454 Mass. at 715, 912 N.E.2d 958 ; Guardianship of Estelle, 70 Mass. App. Ct. at 581, 875 N.E.2d 515. A judge may conclude that "[one] child is in need of particular parental skills and stability that the mother [is] unable to provide." Petition of Catholic Charitable Bureau of the Archdiocese of Boston, Inc., to Dispense with Consent to Adoption, 395 Mass. 180, 185 n.6, 479 N.E.2d 148 (1985). However, while certainly not dispositive, evidence of a parent's demonstrated willingness and ability to care for another child in her custody is relevant to her general fitness as a parent and is a consideration in proceedings to remove a guardian. See Adoption of Rhona, 57 Mass. App. Ct. 479, 487, 784 N.E.2d 22 (2003). See also Guardianship of Cheyenne, 77 Mass. App. Ct. at 830, 934 N.E.2d 827.
3. Conclusion. We vacate the judgment of dismissal on the mother's petition for removal of the guardian, and we remand the matter for further proceedings consistent with this opinion.
So ordered.