The first analysis intended to evaluate the difficulty of the items and the adequacy of their adjustment to the model, thus evaluating the impact of each item individually (Bond & Fox, 2001). These analyses were conducted with adjustment indices, which are a method for comparing what was predicted by the model with what was empirically observed (Smith, 2004). In this case, residuals refer to these differences, and there were two indexes employed: infit (an index to check for discrepancies in items whose difficulties are close to the subject’s ability) and outfit (an index to check for discrepancies in extreme items). An analysis of item-theta correlations was conducted to evaluate each item’s capacity to recover the theta of the respondent.

Considering the requirement of unidimensionality for this type of analysis, the indices evaluated in each of the areas of the scale were determined separately. The results of the first three factors are presented in Table 2. The difficulty index for the Intellectual Ability scale ranged from -0.54 to 0.37. The mean of the items was anchored at zero to determine the metric as well as the possibility of an association between the parameters of the items and the individuals. The infit statistics ranged between -0.57 and 1.27. The outfits ranged from 0.54 to 1.35. All indices were satisfactory. Generally, all items showed a high correlation with theta (greater than 0.82), and the precision was estimated at 0.85, proving to be adequate.

Table 2.

Factor	Precision	Item	Difficulty	Infit	Outfit	Item-theta Correlation
General intelectual ability	0.85	CI2	0.37	1.04	1.04	0.85
		CI7	0.31	1.27	1.35	0.82
		CI8	0.23	1.27	1.27	0.82
		CI4	0.22	1.14	1.27	0.83
		CI6	-0.05	1.05	1.10	0.83
		CI5	-0.26	0.93	0.82	0.84
		CI3	-0.29	0.67	0.63	0.87
		CI1	-0.54	0.57	0.54	0.87
Academic Ability	0.75	HA4	0.78	1.38	1.40	0.72
		HA8	0.34	1.10	0.98	0.72
		HA3	0.10	1.16	1.10	0.68
		HA9	0.05	0.94	1.35	0.69
		HA7	0.03	1.04	0.97	0.70
		HA5	0.00	0.84	0.91	0.72
		HA6	-0.10	1.00	0.86	0.69
		HA2	-0.58	0.72	0.69	0.68
		HA1	-0.62	0.91	0.79	0.66
Creativity	0.74	CR8	0.49	1.29	1.22	0.72
		CR7	0.47	1.37	1.49	0.69
		CR5	0.28	0.95	1.10	0.73
		CR6	0.10	0.96	0.91	0.74
		CR3	-0.26	0.96	0.94	0.69
		CR1	-0.26	0.85	1.03	0.71
		CR2	-0.30	0.81	0.75	0.73
		CR4	-0.51	0.77	0.80	0.71

On the second factor, Academic Ability, the item difficulty varied between 0.61 and 0.78, while the infits varied between 0.72 and 1.3. The outfits ranged from 0.69 to 1.40. The indices were all appropriate. All items exhibited high correlations with theta (greater than 0.66), and the precision was estimated at 0.75, considered adequate.

The difficulty indexes for the items comprising the Creativity factor ranged from -0.51 to 0.49, while the outfit index ranged from 0.77 to 1.37. The outfit index ranged between 0.75 and 1.49. In general, all items demonstrated high correlations with theta (greater than 0.69) and a precision of 0.74, which proved to be adequate.

Next, two other factors of the TIAH/S were examined: leadership and artistic talent, the results of which are presented in Table 2. The items that comprise the Leadership factor had difficulty between -0.56 and 0.40, infit between 0.81 and 1.29, and outfit between 0.83 and 1.41. The precision for this factor was 0.93, and the item-theta correlations were higher than 0.75.

Finally, the difficulty indexes for Artistic Talent ranged from -0.67 to 1.50, infits ranged from 0.82 to 1.15, and outfits ranged from 0.76 to 1.28, which is adequate. The precision was 0.81, and the item-theta correlation coefficients were greater than 0.66 (Table 3).

Fator	Accuracy	Item	Difficulty	Infit	Outfit	Item-theta correlation
Leadership	0.75	LI7	0.40	1.29	1.41	0.75
		LI6	0.38	0.81	0.83	0.83
		LI4	0.38	0.86	0.88	0.82
		LI2	0.09	1.12	1.13	0.78
		LI1	-0.14	0.93	0.95	0.80
		LI5	-0.25	0.88	0.85	0.79
		LI3	-0.29	1.07	0.98	0.77
		LI8	-0.56	1.03	1.01	0.76
Artistic Talent	0.81	TA8	1.50	1.14	0.98	0.77
		TA6	0.89	1.29	1.28	0.73
		TA4	-0.02	0.82	0.90	0.73
		TA5	-0.10	1.15	1.13	0.69
		TA9	-0.32	0.86	0.76	0.72
		TA2	-0.35	0.92	0.89	0.71
		TA3	-0.38	0.90	0.81	0.71
		TA1	-0.55	1.04	1.13	0.68
		TA7	-0,67	1.14	1.02	0.66

According to the results, the closest residues (infit) are all in good condition; they have found responses at levels higher than expected, notably in two items, one belonging to the Creativity factor (outfit = 1.49) and one belonging to the Leadership factor (outfit = 1.41). Given that part of the sample represented gifted individuals, with average performances usually higher than expected, this result can be interpreted in a more meaningful manner.

Following, the person-item maps were prepared. As a result of their application, the results are interpreted based upon the different levels of the scale, i.e., the thetas (Figure 1).

Figure 1. Note: CI: General Intellectual Ability, CR: Creativity, HI: Academic Ability

Regarding intellectual capacity, items 2 and 7 have the greatest potential to identify individuals with higher levels of ability (“Needs little information to solve difficult problems”; “Showing a variety of interests”). As a result, teachers indicate higher alternatives only for students who have a higher general intellectual level than the average student.

As regards specific academic ability, items 3, 9, 8, and 4 have the greatest potential for the achievement of such ends, especially the fourth (“Presents superior performance in mathematics”). In terms of creativity, items 7 and 8 require a higher level of ability to be endorsed (“Usually ask many questions in the classroom”; “Prefers non-routine tasks”). For the teacher to endorse such items, the ability level of the assessed student, in this case, giftedness indicators, will probably stand out as being higher than the average of all other students.

For the Leadership factor, items 6 (“Demonstrates an ability to lead others”) and 7 (“Has a high level of empathy”) are more discriminating; for the Artistic Talent factor, items 6 (“Exhibits ease in non-verbal expressions, such as gestures and gestures”) and 8 (“Follows the lead of a musical instrument”), which have a higher level of difficulty, are more suitable. Such results can be seen in Figure 2.

Figure 2. Note: TA: Artistic Talent, LI: Leadership.

Other items in the five analyzed factors have a difficulty level below or equal to the average, so students with average abilities receive points in those areas represented by the items and are not required to be highlighted. As a result, such items may not be very effective in identifying individuals with high levels of ability in the areas assessed. This is because the results indicate that even individuals with ability levels below or equal to average are positively assessed by teachers in the other items.

Having analyzed the items, we could determine the items that most discern such individuals, i.e., items whose difficulty level is above one standard deviation from the mean. This case involves items 2 and 7 of the intellectual capacity factor, item 4 for the academic ability factor, items 7 and 8 for the creativity factor, items 4, 6, and 7 for the leadership factor, and items 6 and 8 for the artistic ability factor. On the other hand, it allowed the identification of items that are not effective - that is, the difficulty of being endorsed by the teachers is so low that any student, regardless of their level in the investigated ability, is positively evaluated. This is the case with items 1 and 2 of the Specific Academic Ability area (“Excellent in one or more school subjects” and “Shows good performance on tests and school assignments” respectively), where students with ability levels of more than one standard deviation below the mean score highly. In other words, a teacher may evaluate any student as a student who shows good academic performance without such performance being sufficient to suggest giftedness.

Lastly, we compared the performance of the items according to gender. Among the 42 items on the scale (0.05%), only two items showed DIF. In the creativity dimension, the item “Usually asks a lot of questions in the classroom” showed a DIF in favor of females, showing a lower difficulty value of (+ 0.04) than for male participants (+ 0.077), with a contrast value of -0.72 and a Maentel-Haenszel probability of 0.0001. Additionally, item 8 of the artistic talent dimension (“Dominates some musical instrument”) demonstrated differential functioning, with more difficulty for females (+ 1.81) when compared to males (+ 1.31), with a DIF contrast value of -0.50 and Maentel-Haenszel probability of 0.0014.

The Item Response Theory has several distinct advantages over the investigation of the psychometric properties of teacher rating scales, but this type of analysis is rarely employed in gifted education (Ridgley et al., 2019). It was possible to evaluate the parameters of the five dimensions with the help of this analysis model to contemplate the heterogeneity of the group. A more comprehensive understanding of the phenomenon includes many characteristics in addition to intelligence (Kaufman & Sternberg, 2018), which has long been mistakenly regarded as the sole synonym for giftedness (Dai, 2018).

Our analysis allowed us to identify the behaviors that most differentiate gifted students from those who do not have these signs in each of the five dimensions. It was noted, for instance, that the individual with the highest level of intellectual capacity (whose performance is equal to or greater than one standard deviation when compared to peers of the same age) is usually regarded by teachers as the one who has little information required to solve problems and has a wide range of interests. Using the same method, an analysis was carried out in each of the dimensions to identify the behaviors that best distinguish individuals with high ability in each of the domains in which the teacher evaluates the student.

In addition to understanding the adjustment indices of the items, the analysis performed allowed us to determine the level of difficulty of each item, thus identifying those that are most likely to indicate behaviors that are common among gifted individuals. Based on this, we can later compose a reduced version of the instrument, consisting only of items that demonstrated the greatest potential for differentiating between the two groups (identified as gifted and regular students, unidentified). It would include the more commonly observed characteristics in gifted individuals as items.

It listed the following characteristics in this group of students that were identified by teachers as being important: easily solving complex problems, having a wide range of interests, high performance in mathematics, curiosity, preference for non-routine activities, leadership, empathy, and comfort with artistic expression. Such characteristics are also mentioned in the literature as typical of gifted students (Alves, 2020; Turkman, 2020) and in the main theories of giftedness, for example, the Three Rings Model (Renzulli & Reis, 2021), the Triarchic Theory of Intelligence (Sternberg, 2000), and the Differentiated Model of Giftedness and Talent (Gagné, 2010).

However, it is important to highlight that part of these characteristics, such as questioning and difficulties with routine, are commonly seen as undesirable by teachers, involving indiscipline, high critical level, or disruption of the class after quickly finishing activities (Mendonça et al., 2020). Thus, teachers must be made aware of the peculiarities and potential of these students so that they are not harmed in the academic path.

The analysis of the items pointed to a tool whose items present adequate fit indices. The items proved adequate to estimate the variety of abilities present in the study sample, considering inferior to superior performances in each of the evaluated areas. None of the items showed maladjustment, so there was no need to exclude any of them.

As a major contribution to the area, the instrument proposal presented here provides the opportunity to identify giftedness indicators by using a scale, which can be used as a first filter in the screening process of students with higher potential. Given that Brazilian teachers indicate students for evaluation (Alencar et al., 2018) and that subjective beliefs or misguided expectations may affect the process (Matheis et al., 2017), the use of standardized observation tools can reduce the possible influence of these factors. Two major concerns have been identified by Cao et al. (2017): a lack of training of teachers for the proper identification of the various manifestations of the phenomenon; and the assessment of giftedness based on personal understandings that may not reflect scientific definitions. These issues can be addressed with the use of a standardized instrument to observe these behaviors.

In the context of education, one of the key features of the instrument is that the scale is answered by the teacher, who has usually been trained in the area of education and development, which enables all students in the classroom to be evaluated and compared in a variety of situations with their peers of the same age (Rothenbusch et al., 2018). The scale, quick, and easy-to-response tool provides a means to identify the levels of performance that can be high and with a significant reduction in costs compared to the traditional broad evaluation process. This information may complement information obtained through other sources, both at the time of screening and during the subsequent follow-up of students already identified, regarding their progress (Mohamed et al., 2017).

The obtained results support the validity of the instrument, which is more pronounced compared to those previously investigated (Nakano, Campos et al., 2018; Nakano & Oliveira, 2019; Nakano et al., 2016; Nakano, Gozzoli et al., 2018; Nakano et al., 2020). Additionally, the instrument is suited to the purpose for which it was built and can assess signs of AH/S in each of the five dimensions that constitute TIAH/S.

Studies that characterize the psychometric characteristics of the teacher assessment scales are essential because, according to Benson and Kranzler (2018), there are comparatively few studies that investigate their psychometric properties using nonstandardized instruments. It is common for these scales not to show any evidence of validity or accuracy (Pfeiffer, 2015).

In general, the data suggested that the items of the TIAH/S are, for the most part, neutral in relation to differences based on a participant’s gender. In light of the low reporting of female cases, this information is critical to illustrate that the use of the instrument can assist teachers to ensure a more equitable assessment process (Zaia et al., 2019). That is a contrast to the situation that has been reported in the literature (Kruczeveski & Silva, 2018).

It is hoped that the TIAH/S will benefit professionals in relation to the gaps which exist within the subject in Brazil (Alencar et al., 2018; Wechsler et al., 2018), specifically regarding the availability of instruments to identify this phenomenon (McCluskey, 2018).

Talents’ losses due to difficulties in identifying students with giftedness result in a society that is missing out on the contributions that these individuals could make. In addition, this limits the opportunities for these students, diminishing their potential for personal and professional development. Nevertheless, the benefits of a screening phase will only be realized if the evaluation system employed is of high quality and efficiency, suitable for the targeted group, and capable of identifying the specific indicators. Otherwise, the reduction in the cost and time allocated for the evaluation will lead to false negatives, resulting in the loss of students who may otherwise have been identified by other procedures.

As a result of the procedures used in this study, certain limitations were identified. A major factor relates to teachers’ evaluations possibly having been influenced by their conception of giftedness. The qualification of teachers for this identification has been the subject of many debates. It must be noted, however, that the evaluation of the criterion group, which made up more than two thirds of the sample, was conducted by teachers in specialized educational services for identified students so that they are familiar with the topic in great depth. In contrast, the remaining unidentified students (control group) were evaluated by professors who may have little or no knowledge of the subject matter, even though they were asked to assess students based on a series of specific behaviors.

Considering that teachers who have received specific training in gifted education are more likely to identify the signs that indicate the phenomenon than non-trained classroom teachers, the difference in training between the two groups that evaluated the students cannot be ignored. There is a possibility that this difference may have affected the results, so future studies should include the assessment of the teacher of the students already identified in the regular classroom and not only of the teacher of the specialized educational service program.

We recommend that future studies examine the differential functioning of the items concerning other variables, such as age group and region of origin. In addition to the six dimensions discussed in this study, other TIAH/S studies are already planned to expand the screening tool to include additional dimensions. They include socioemotional, psychological, and motivational components. With the expansion of the areas, teachers will be able to evaluate students’ indications for a more detailed psychological evaluation in a broader way and to consider other types of giftedness.