The Learning Outcomes of Figurenotes Music Activities for Children With Special Needs Based on the ARMA Models

Abstract

This study explores Learning Performance Analytics in the context of the Figurenotes Music course for young children aged 2 to 6 with special needs in Taiwan. Using the ARMA model, the researchers analyze the dynamic learning outcomes of 46 participants in two-stage courses over 32 weeks. The empirical findings reveal that children aged 2 to 3 show a positive change in learning performance, while children aged 3 to 6 exhibit a negative change, regardless of rhythm pairing intervention. When rhythm pairing is added, the learning process becomes more challenging, resulting in lower average learning outcomes than the Figurenotes Music Program group. The study’s ARMA models demonstrate persistent learning outcomes throughout the process, with a notable time trend observed among children aged 2 to 3. These models effectively interpret dependent variables, achieving a determination coefficient of up to 0.9. In summary, this research sheds light on Learning Performance Analytics and its application to evaluating learning performance in the Figurenotes Music course for children with special needs.

Plain Language Summary

Keywords

children with special needs Figurenotes music program rhythm pairing learning outcomes ARMA model

The importance of music has been closely related to human civilization and life since ancient times. Human speech, language, and communication (SLC) will be connected by the music of participation and presented in various forms in music education and psychological literature (Blackburn, 2017). Music listening is a complex task involving sensory, physiological, behavioral, and cognitive levels. Music is seen as a sound environment, and listening involves exploring this environment and interacting with sound. Instrumental music can be used to change the audience’s internal and external environment (Reybrouck et al., 2020).

In the medically advanced modern era, music therapy uses music for optimal intervention for specific diseases to demonstrate that the active ingredients of effective music intervention provide information. It uses the information as an element (influencer) of music in a particular disease mechanism as a supportive treatment to alleviate the psychological or physical pain of a patient’s disease (Loui, 2020). Some studies have also confirmed that music therapy has a positive and significant impact on social behavior in children with Autism Spectrum Disorder (ASD) while finding that the most significant progress can be made in the area of concentration and takes the initiative (Pater et al., 2021). A study exploring the effects of the music training program on German preschoolers in Motoric inhibition found that music training can increase inhibition in preschoolers (Degé et al., 2022).

Music education in early childhood is given considerable attention, and sharing music activities is an added benefit to children’s prosocial skills and making music for their parents than sharing reading activities—children’s communication. At the same time, children are supported to participate in organized and methodical musical activities outside the home. Also, the quality and appropriateness of these activities have been recognized. Blackburn (2017) confirms that children’s music classes correlate significantly positively with executive functions. Instrumental music training improves executive functions for children aged 6 to 7 year and believes that training effectiveness may be related to the trajectory of executive functions (Frischen et al., 2021)

Das et al. (2020) explore the effects of sound wave/music sample(s) on the human brain while focusing on learning and reading articles. Results support music as an effective tool for various human needs, namely relaxation, temperamental recovery, treatment needs, and helping children with learning, emotional and developmental difficulties. Decision-makers in early childhood music education should include local cultures to improve the guiding principles. In particular, the tripartite relationship between policymakers and policymakers, curriculum designers, and curriculum-implementing teachers should be strengthened to link the ideas and activities needed to facilitate local early childhood music education (Andang’o & Mugo, 2007). Music education can be implemented appropriately for children with special needs, which will significantly improve children’s learning effectiveness with special needs and contribute to their ability to behave in language, movement, and response (Lee & Liu, 2021a).

Early childhood music education for the special needs of early treatment institutions in Taiwan has been gradually developed since 2002, which is a set of preschool music programs for special needs developed by music therapists and early childhood music educators (Ho, 2020; Lee, 2008; Lee & Ho, 2018a, 2018b; Lee & Lin, 2020; Lee & Liu, 2021a, 2021b). The curriculum is based on holistic education’s consideration of local culture and modern computer technology based on Soundbeams (Lee & Ho, 2018a, 2018b). In order to lower the learning threshold for young children with special needs in music, the use of graphics and color pairings to replace a variety of pitches and scales (Poutiainen et al., 2013), the integration of Figurenotes with music therapy materials will be beneficial to music teaching methods (Lee & Lin, 2020) At present, this music therapy program has been widely promoted in the local early intervention center for children in language and communication, attention, physical movements, emotional stability, and interpersonal interaction, and other development for years. It proved to have a significant positive impact (Ho, 2020; Lee & Ho, 2018a, 2018b; Lee & Liu, 2021a, 2021b).

Learning analytics discussed a student’s learning history, understanding the student’s learning status, feedback from students and teachers, and evaluation, interpretation, and prediction through the student’s learning history. More effective individual tutoring for students to improve their learning outcomes (Wang, 2011). The assessment and forecast of the learning effect will be beneficial to educate teachers and experts as a reference for improving teaching methods and resource allocation. They will also be paid attention to by some scholars (Clark et al., 2021). Therefore, through the assessment of learning, the use of motion research to involve students in the joint development of evaluation criteria and the self-assessment process, thereby establishing a learning assessment model, can understand the students in music education experience and feeling assessment translates into how to support learning. In this way, the research can be aimed at assessing the quality of education, the formed feedback, and feedback from teachers on evaluation attitudes (Sicherl Kafol et al., 2017). Second, use technology to improve the quality of teaching, such as innovations in online applications and social networking capabilities to accelerate accessibility and universality, embed these technologies into music education.

Past evaluation models for learning outcomes have been many ways of evaluating extraneous variables, such as learner or instructional factors (Lim & Morris, 2009). Find appropriate influence variables for modeling through statistical methods such as correlation analysis or factor analysis. Still, it is often impossible to fully incorporate effective influence factors, or the included explanatory variables may interfere with each other. So in the absence of overcoming the collection of sufficient explanatory variables, if in a series of learning courses, the lagged periods of the learning performance variables will be used as explanatory variables for learning performance’s autocorrelation, that is, in the course of teaching, the lagged period of learning performance will affect the current period of learning performance. In cases where the learning performance sequence will be autocorrelation, consider using the Autoregressive Moving Average Model (ARMA). ARMA (p, q) model is a model in time series statistical analysis, in which the model is mainly composed of p is the order of the autoregression (AR) part and q is the order of the shift (MA) part, which captures the trajectory of the (weakly) stationary stochastic process so that it can be used as an assessment or prediction of learning outcomes. In the past, ARMA models have been widely used in the economic field (Zia, 2012) or to capture price movements in financial assets (Liu & Lee, 2020; Rounaghi & Nassir Zadeh, 2016). On educational issues, it is used in the higher education model (Xu et al., 2021).

The ARMA model was characterized by the belief that the learning outcome of young children is to continuously transmit systematic and organized signals through the external environment, including the colors and movements that the eyes can see and the sounds and melodies that the ears can hear. Memories of training experiences transmitted to the human brain through sensory stimulation nerves are used as the body’s ability to process or use them later, so learning outcomes can generally accumulate through educational training. This study is based on gathering knowledge and experience through teaching activities. Still, several factors may influence learning outcomes, which are complex and challenging to clarify and usually only partially explain and analyze thoroughly. Capturing the trajectory of these young children’s learning outcomes will face some challenges when robust exogenous variables are not easily controlled during a long series of music education activities.

Based on the average effects on exogenous variables, this study will eventually reflect each phase of learning outcome. It will continue to accumulate into the next period of learning outcomes, so it will be assumed that young children’s learning outcomes will be relevant to past learning outcomes. Therefore, the lagged period of learning outcome can be used as an explanatory variable for the current period of learning outcome, and the learning outcome sequence is subject to the autoregressive process. In this study, the time series model of endogenous variables was used to capture the learning outcomes trajectory of young children with special needs in implementing Figurenotes music teaching.

There are three main issues addressed in this study: First, to explore the integration of Figurenotes into Taiwan’s music therapy activities, whether the implementation of the system of early intervention institutes for children’s experience is indeed significantly improved learning outcomes, and to support the promotion Figurenotes music teaching in Taiwan. Second, whether it is feasible to use the ARMA model in time series analysis to capture the dynamic learning achievement trajectory of Figurenotes music learning for children with special needs. Third, through the difference between age groups and music rhythm intervention, after observing learning outcomes and establishing the learning outcome model by ARMA method, the dynamics and characteristics of learning outcome of young children in implementing teaching activities were further explored according to the model established.

Figurenotes uses graphics and color pairings to replace various high-and-low notes and scales, combined with music therapy materials to facilitate the learning of children with special needs in Taiwan (Lee & Lin, 2020). However, there is no dynamic assessment and specific theory of the learning process of this teaching program in Lee and Lin’s (2020) study. This research will further explore whether this set of teaching plans has been measured by participants’ responses to the curriculum during learning, as well as their learning achievements, and reviewed and corrected them. The study results could be used as a reference for future participants in special early childhood music education, and for music educators to evaluate early childhood with special needs on learning outcomes.

Methodologies

Figurenotes

Figurenotes is a music teaching method that originated in Finland (©Kaarlo Uusitalo, 1996). It can be used in special and general education to learn music teaching methods (Kivijärvi, 2019). It uses graphics and color matching to represent various high and low pitches (Poutiainen et al., 2013). The application of Figurenotes lowers the threshold for learning and teaching music and is especially suitable for educational situations that need to reduce students’ cognitive load (Kivijärvi, 2019). When people with special needs need longer reading time and lack systematic gaze, it is recommended to learn to use graphic symbols to have a higher correlation with learning objects, which is meaningful (Sevcik et al., 2018). Researchers (Lee & Lin, 2020) have confirmed that the Figurenotes teaching method combined with MET applied to special needs of early childhood music education in Taiwan will help children learn.

This study used the Figurenotes music teaching method to integrate the original music therapy strategy (Lee, 2012; Lee & Lin, 2020). This education program is a music education curriculum designed for children with special needs in Taiwan. It attracts children with special needs by using hand-made musical instruments, teaching aids, and multi-sensory musical instruments to achieve learning effects with significant influence. Figurenotes music teaching method marks the scales and pitches with colors and shapes so that learners can replace standard music symbols with familiar colors and shapes to learn and become familiar with music more easily. In addition, the seven colors of red (Do), brown (Re), gray (Mi), blue (Fa), black (Sol), yellow (La), and green (Si) are used to represent the scale (singing Name). Different shapes, such as cross (×) means two octaves lower, square (□) represents one octave lower, circle (○) represents the central octave, and triangle (△) represents one octave higher are used to describe pitches (refer to Figure 1) so that children can easily play musical instruments.

Figure 1.

Seven colors and four graphics in Figurenote.

This innovative music teaching model could improve children’s responses and attention and enhance all aspects of their performance ability. Finally, the curriculum framework is flexible, and the content includes Hello Song, Attendance Song, Musical Storytelling, Musical Movement, Relaxation Time, and Goodbye Song.

ARMA Model

In this study, in evaluating the implementation of Figurenotes music education for early childhood with special needs, the learning outcome of these young children in the time trajectory is captured, mainly using the ARMA (p, q) model. The form of the model is as follows:

C_{t} = a_{0} + \sum_{i = 1}^{p} α_{i} \cdot C_{t - i} + \sum_{j = 1}^{q} β_{j} \cdot ε_{t - j} + ε_{t}

(1)

In Equation 1, the dependent variable $C_{t}$ is the learning outcome of the music teaching activities carried out by the child during the t-period, at which point the sequence ${C_{t}}$ must meet the condition that the stationary series must pass a unit root test, that is, the inference determines that the sequence ${C_{t}}$ does not exist a unit root. Whether the sequence has a static nature, the Augmented Dickey-Fuller (ADF) rule will be used for a unit root test (Said & Dickey, 1984). Whether the sequence is autocorrelation or not can be determined by Q(n) statistics (Ljung & Box, 1978). Second, the $a_{0}$ is a constant; $C_{t - i}$ is the learning outcome on the lagged i period; $α_{i}$ is the estimated parameter for learning outcome on the lagged i period. $ε_{t}$ is a error term in the t period is subject to the random process of white noise; $ε_{t - j}$ is the error term of the lagged j period; $β_{j}$ is the estimated parameter of the lagged j period error term. The best number of lag periods for the model is p and q, determined by Akaike’s Information Criterion guidelines (Akaike, 1974) to find out the p* and q*, which can minimize the AIC values estimated by the ARMA (p, q) model.

Finally, in evaluating model predictive capabilities, this study will be measured using two indexes, Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE). At this point, the $MSE = \frac{1}{T} \times \sum_{t = 1}^{T} {(F_{t} - A_{t})}^{2}$ and $MAPE = \frac{1}{T} \times \sum_{t = 1}^{T} \frac{| F_{t} - A_{t} |}{A_{t}}$ . $F_{t}$ represents the forecast value in the t period; $A_{t}$ is the actual value, and $T$ is the predicted number of samples. When the smaller the values of the two indicators represent, the smaller the model’s bias in making predictions, the better the model’s predictive power.

Data and Results

Data

The identification of children with special needs is based on the Taiwan Special Education Law promulgated by the government of Taiwan. According to regulations, the government issues a physical and mental disabilities handbook after identifying and confirming by qualified professional therapists. In this handbook, there are eight categories of physical and mental disorders: The first category is the structure of the nervous system and the functions of the spirit and mind, which are divided into intellectual disabilities, persistent vegetative state, dementia, autism, chronic psychosis, and refractory (refractory) epilepsy. The second category is eyes, ears, related structures, sensory functions, and pain, including people with visual impairment, hearing impairment, and balance dysfunction. The third category is those who deal with the construction of sound and speech and their functions, including those with sound function or language dysfunction. In the fourth category of circulatory, hematopoietic, immune, and respiratory system structure and function, important organs lose function, including the heart, hematopoietic function, and respiratory organs. The fifth category is digestion, metabolism, and endocrine system-related structures and functions, important organs lose function and are divided into swallowing function, stomach, intestine, and liver. The sixth category is the structure and function of the urinary and reproductive system and the loss of function of important organs, including the kidneys and bladder. The seventh category is the movement-related structures and functions of nerves, muscles, and bones, and is classified as limb disorders. The eighth category is the skin and related structures and their functions, and is the person with facial damage. In addition, categories 1 to 8 are corresponded according to the status of persons with disabilities; there are people with multiple disabilities, people with physical and mental dysfunction caused by rare diseases, and other disorders (chromosomal abnormalities, congenital metabolic abnormalities, and congenital defects).

The more common disabilities in children aged 0 to 6 are intelligence, vision, hearing, language, limbs, cerebral palsy, physical weakness, emotional behavior, learning, multiple disorders, autism, developmental delay, and other disabilities. Therefore, young children are usually based on special needs such as communication, language, motor, and sensory-based, and will have one or more developmental needs in speech, physical ability, interaction with people, and self-exposure. Taiwan currently stipulates that children under the age of 3 who have several diagnosed diseases are temporarily not given a physical and mental disabilities handbook. For example, a diagnosis of intellectual disability is temporarily withheld from being issued a disability manual, and the results of the assessment of intelligence remain reserved. In light of this factor, group tests were administered to participants who possessed a documented status of physical and mental disabilities, as stipulated in the official handbook. According to the medical doctor’s diagnosis and the child’s individual needs, coordinate the medical and other units to handle the early intervention evaluation center, referral system, early treatment center, and other early treatment work to carry out a complete treatment plan, including education services, so that children can develop their full potential and reduce the degree of obstacles. Therefore, these children with special needs were initially planned to be placed in special education institutes to implement music educational therapy programs.

Since this research mainly used the time series model to capture a single group’s dynamic learning outcome trajectory, the study focused on each group’s longitudinal changes and relationships on the time axis rather than the cross-sectional comparison of differences between groups. Therefore, random grouping is carried out by drawing lots, ignoring the influence of differences between groups caused by the categories of physical and mental disabilities. In addition, the participants must be able to act physically and mentally. The study was conducted at a non-profit early intervention center in central Taiwan (the Taiwan Fund for Children and Families—Taichung City Child), with a total of 46 children with special needs aged 3 to 6 year participating after prior parental consent.

All participants were taught music in two stages, the first with the Figurenotes music programs (given code: Y1) and the second with the Figurenotes music programs with Rhythmic Pairing (given code: Y2). Among them, Figurenotes music programs offer specially designed music courses for multisensor instruments for children with special needs, in the light of past methods (Lee, 2012; Lee & Lin, 2020). During each phase, a total of 32 weeks, twice a week, 40 min each. Participants will be divided into Young children aged 2 to 3 (given code: Y, 16 people) and children aged 3 to 6 (given code: C, 30 people). When rhythmic pairing is added by music teaching, it can be distinguished from the teaching method and age group into Young children and Figurenotes Music Program (given code: FM_Y), Young children and Figurenotes Music Program with Rhythm Pairing (given code: RPFM_Y), children and Figurenotes Music Program (given code: FM_C) and children and Figurenotes Music Program with RhythmIc Pairing (given code: RPFM_C). During the course implementation, weekly learning outcomes, that is, learning outcomes that focus on vertical aspects of the music course implementation process, are recorded, while learning outcome is a 5-point Likert scale. This score was evaluated during the teaching process. After pre-recording the video using the video method, at least two professionally trained observers traced it through the videotape, cross-compared and ruled out disagreements, and then calculated the final score.

Results

In Table 1, it can be found that groups with older and non-implemented rhythms paired have higher average learning outcomes, in order of FM_C (Mean = 4.0219), RPFM_C (Mean = 3.7594), FM_Y (Mean = 2.0906), and RPFM_Y (Mean = 1.7219). In Skewness, the Coefficient of skewness of 3 to 6-year-olds was negative to the left-skewed distribution, and the Coefficient of skewness of 2 to 3 year old was positive to the right-skewed distribution. The skewness of different age groups for the distribution of learning outcomes would be different. In Kurtosis, only FM_Y groups of Kurtosis = 2.3983 < 3, where show that is platykurtic distribution. Otherwise, group of kurtosis > 3, where show that is leptokurtic distribution. Finally, at a significant level of 1%, all (four) groups of Q(10)-statistics showed that autocorrelation characteristics in the significantly accepted sequence, so the sequence can consider using the ARMA model for capturing dynamic random processes.

Table 1.

Basic Statistics and Unit Root Tests.

Group estimation	FM_Y	RPFM_Y	FM_C	RPFM_C
Mean	2.0906	1.7219	4.0219	3.7594
Median	1.8	1.7	4	4
Maximum	3.9	3	5	4.8
Minimum	1	1	2.5	2
Std. Dev.	0.8727	0.4368	0.6364	0.7277
Skewness	0.8878	0.6617	−0.5571	−0.9008
Kurtosis	2.3983	3.9632	3.1559	3.2034
Jarque-Bera (p-value)	4.6862 (0.0960)	3.5719 (0.1676)	1.6879 (0.4300)	4.3824 (0.1118)
A. D. F. t-statistic (p-value)	−3.6100* (0.0123)	−5.0233** (0.0003)	−4.3474** (0.0018)	−4.6939** (0.0007)
Q(10)-statistic	74.686**	67.979**	52.444**	88.698**

p < .01. *p < .05.

Table 2 showed that Akaike info criterion’s values were calculated with lagged-term p and q in ARMA (p, q) model. In each group, the Akaike info criterion’s values estimated in the ARMA (p*, q*) model will be smaller than the others if the best lag periods are p* and q*, that is, AIC (p, q*) ≤ AIC (p, q), where p ≥ 0 and q ≥ 0. In Table 2, can found that the best models established by the FM_Y group is ARMA (1, 1) model (AIC (1, 1) = −0.245465), RPFM_Y group is AR (1) model (AIC (1, 0) = −0.717470), FM_C group is AR (1) model (AIC (1, 0) = −0.268730), and RPFM_C group is AR (1) model (AIC (1, 0) = 0.083421).

Table 2.

Akaike Info Criterion’s Values Calculated with Lagged-Term p and q in ARMA (p, q) Model.

ARMA (p, q) model		Group
p	q	FM_Y	RPFM_Y	FM_C	RPFM_C
0	0	2.596192	1.212080	1.964735	2.232970
0	1	3.394446	2.908108	4.528138	4.404199
0	2	2.350343	2.100125	3.523236	3.377598
0	3	0.872652	1.397582	2.744285	2.732139
1	0	−0.164558	−0.717470	−0.268730	0.083421
1	1	−0.245465	−0.671387	−0.254168	0.143791
1	2	−0.190671	−0.648246	−0.206983	0.206201
1	3	−0.157061	−0.685441	−0.184487	0.200550
2	0	−0.212342	−0.681283	−0.265881	0.143732
2	1	−0.192550	−0.713330	−0.289509	0.146605
2	2	−0.130068	−0.677804	−0.229592	0.100247
2	3	−0.185549	−0.615490	−0.167883	0.138548
3	0	−0.150691	−0.685216	−0.223900	0.205818
3	1	−0.130146	−0.674405	−0.142040	0.119139
3	2	−0.062884	−0.615385	−0.170187	0.163191
3	3	−0.083475	−0.581577	−0.107641	0.120151
Best model		ARMA (1,1)	AR (1)	AR (1)	AR (1)

In Table 3, the four groups selected the best interpretation model of learning outcome, respectively. Learn more about whether there is a time trend in learning performance in each group where special young children are learning, that is, learning outcome in each learning group increases as the duration of the course increases. Table 3 is the result of using the maximum Likelihood (OPG—BHHH) method to estimate the parameters of the best model for each learning group, from the four models of the determination coefficient (R-squared) to >.9, indicating that the model has a relatively high explanatory ability. A p-value is more significant than .05 for the Q(10) and Q²(10)-statistics in the four models that neither the residuals in the model nor the squared residuals have autocorrelation characteristics.

Table 3.

The Estimated Results of the ARMA Model.

Model parameter	FM_Y	RPFM_Y	FM_C	RPFM_C
C (constant)	0.0269** (0.001)	0.0172** (0.000)	0.0261** (0.000)	0.0389** (0.000)
T (time trend)	0.1153** (0.000)	0.0764** (0.002)	0.0865 (0.6410)	0.1015 (0.574)
AR (1) (lagged term)	0.9137** (0.000)	0.9826** (0.000)	0.9976** (0.000)	0.9940** (0.000)
MA (1) (lagged term)	0.3608* (0.011)	-	-	-
R-squared	.9636	.9071	.9335	.9242
Adjusted R-squared	.9597	.9007	.9290	.9189
Schwarz criterion	−0.2670	−0.7968	−0.3168	0.0543
Log likelihood	11.2028	17.9475	10.2677	4.3301
Durbin-Watson stat	2.2134	1.6956	1.8906	2.2593
Q(10)—Stat (p-value)	9.9298 (0.111)	3.5902 (0.936)	1.9653 (0.992)	16.2890 (0.061)
Q ²(10)—Stat (p-value)	3.0019 (0.981)	4.7100 (0.910)	1.0705 (1.000)	7.8147 (0.647)

p < .01. *p < .05.

Second, there are the estimated parameters, at a significant level of 1%, it can be found that the estimated parameters of the time trend (t) show that substantial positive results in the parameter of FM_Y group are 0.1153 (p-value: .000 < .01) and the RPFM_Y group is 0.0764 (p-values of 0.002 < 0.01). The results showed that among children with special needs between the ages of 2 and 3 year of age, there was a significant positive relationship between learning outcome and learning time during the learning process, whether they were enrolled in rhythmic pair to the Figurenotes music teaching activities. However, this is not the case in children with special needs between 3 and 6. This result may be related to the immaturity of younger children in physical development. In the estimation coefficient of the lagged period of AR (1), it can be found that the estimated coefficients of all four groups are significantly positive (p-values in the four groups < 0.01). These results show that the higher the learning outcome in the previous issue, the higher the learning outcome in the current period, implying that the learning outcome may have persistence. The estimated coefficients from AR (1) are FM_C groups (0.9976), RPFM_C groups (0.9940), RPFM_Y groups (0.9826), and FM_Y groups (0.9137) in order from large to small, at which point, if there is a higher estimation coefficient for AR (1), the current period’s learning outcome is highly sensitive to the learning outcome changes of the previous period.

Finally, the estimated parameter of MA(1) in the FM_Y group is 0.3608 (p-values = .011 < .05), where is presented significantly positive, showing that the error terms of the lagged period will have a significant positive effect on the current period’s learning outcome and will have partial explanatory power.

In Figure 2, there are four learning outcome trajectory lines and line charts of estimated errors and the predictive capability of the evaluation model. The red line represents the actual value of the average learning outcome for each group. Each group uses the ARMA model of Table 3 to distinguish between the estimated predicted values (actual value) within the sample.

Figure 2.

The results predicted by the models on the in-sample.

It was found that in children with special needs between 2 and 3 year of age, whether using RM or RPFM teaching methods, its learning outcome trajectory line was presented in the pre-teaching implementation (the first 16 periods) learning outcome line rise slowly; In the second half of the teaching implementation (the last 16 periods), the learning outcome trajectory line rises faster. Therefore, the implicit use of this teaching method for early childhood with special needs in the Figurenotes music teaching-learning efficiency is presented later will be higher than the previous situation (accelerated change: slow progress at first, then gradually increased). The results showed that learning performance is getting better and better. Secondly, in children with special needs aged 3 to 6 year, whether using RM or RPFM teaching methods, its learning outcome trajectory line is presented in the pre-teaching implementation (the first 16 periods) of the learning performance line rise faster; The learning outcome line in the second half (the last 16 periods) rises more slowly. Therefore, learning efficiency will show the early period higher than the later period (negative acceleration change: the progress is fast at first, and then the progress gradually slows down). The results showed that learning performance changed from better to worse.

In addition, learning outcome in the four groups is generally a monotonous increase, with only the 17th issue (FM_C) after the period; RPFM_Y) or Issue 18 (FM_Y; RPFM_C) there is a special case of a decrease in learning outcome. This result may be due to the impact of a 2-week break in practice during the middle of the study period. In estimation errors, it was found that the RPFM_Y group’s MSE (0.0172) and MAPE (0.0255) were minimal in the four groups (children with special needs between 2 and 3 year of age using rhythmic pairing to join the Figurenotes music teaching Group). This model has a relatively good predictive ability within the in-sample compared to the other three models.

Discussion

The present study employed a sample of 46 young children exhibiting special needs, ranging in age from 2 to 6 year, within the geographic context of Taiwan. Two-stage courses, including “Figurenotes Music Program” and “Figurenotes Music Program and Rhythm Pairing,” each stage was 32 weeks/twice a week/40 min of music lessons. It was found that after implementing Figurenotes into the original music teaching plan, whether or not the intervention of rhythm matching was added, the final learning outcome of children with special needs showed a significant improvement. This result was consistent with Lee and Lin (2020) using Figurenotes as a core device to intervene with children with special needs in Taiwan, and the results are consistent, showing that there is a significant learning effect. The empirical results of this research on special preschool music education in Taiwan support the view put forward by Kivijärvi (2019) that Figurenotes can be regarded as both a teaching method and a method to promote educational equity.

In the past, discussions on learning outcome evaluation models focused on exogenous factors (Lim & Morris, 2009), including learner or teaching environment factors. Or only model the evaluation indicators of participants at the beginning, mid-term, and end of the term (Lee & Liu, 2021a, 2021b). Although these pieces of literature have successfully found some vital influencing factors that explain learning outcomes, these evaluation model established in the literature does not focus on the cross-sectional explanatory relationship (multiple regression model) or analyzes the learner’s conditions at the beginning of the period, or the factors changed in the mid-term (decision tree). However, these models cannot capture the dynamic changes of the learning effect of the teaching interventions implemented by the learners in the learning process. That is to say, it is impossible to understand that in the process of implementing teaching, the process of learning and growth of students cannot be observed, and usually, only the final evaluation information of teaching results can be obtained. This study proposed using the ARMA model to assess or predict learning outcomes. By establishing this model, it is possible to observe children with special needs’ dynamic learning outcome trajectory in implementing two music teaching programs.

The learning outcome trajectory presented during this teaching period shows a steady upward trend in the four groups discussed in this study. The result is consistent with Lee and Lin (2020). It is believed that most participants would actively participate in activities so that skills can be gradually accumulated growth. In addition, the dynamic evaluation model obtains additional highlights: (1) Among children with special needs aged 2 to 3 (lower age), using Figurenotes music teaching activities (and adding rhythm matching), the learning outcome in the learning process would follow a significant increase in learning time. That is also affected by time. However, this phenomenon did not occur at higher age (3–6 year old). (2) The learning outcome was continuous, and the results were the same regardless of grouping: that is, the learning outcome e of children in the previous period would affect the learning outcome of the current period, and the better the outcome during the last period, the better in the current period. (3) Whether using the RM or RPFM teaching method, children with special needs aged 2–3 year showed an accelerated climb, while the learning outcome trajectory of children with special needs aged 3 to 6 showed a decelerating climb condition. This result indicates that older children can absorb these teaching methods faster and improve the learning effect in the early stages of learning. On the contrary, young children have lower learning effects early and will have higher learning and growth results later after adapting to these teaching methods. (4) Using the ARMA model to establish a dynamic learning outcome evaluation model is feasible. The robust results were obtained from the four group experiences in this study.

Conclusions

Based on the experience of children with special needs in Taiwan through the Figurenotes music teaching activities, this study found that this teaching plan can be recognized by the participants and can significantly improve learning skills and support the continuous promotion of Figurenotes music teaching in Taiwan. In addition, this research used the ARMA model in the field of time series analysis to capture the dynamic learning outcome trajectory of these children with special needs in Taiwan during the implementation of the Figurenotes music teaching plan. This research attempted to extend the ARMA model from the past higher education evaluation model (Xu et al., 2021) to special preschool music education and construct a theoretical model for evaluating the learning outcomes of the Figurenotes music teaching plan.

This study confirms that the ARMA model is used to capture participants’ learning outcomes in the learning process of Figurenotes music programs, which can be used to predict learning outcomes in the learning process in the future. From the ARMA model established, it was found that participants’ learning outcomes were significantly positively affected by the previous period of learning outcome, showing that the learning outcome of early childhood with special needs was persistent in the learning process. After this study attempted to add Figurenotes music teaching programs with rhythmic pairings, participants’ learning outcomes decreased, and young children with special needs of different ages would have different directions in implementing Figurenotes music programs. A learning outcome, where there is a time trend in children with special needs between the ages of 2 and 3, shows that learning outcomes have persistence on learning time. The results of this study can be used as the theoretical development direction and reference basis for researchers and workers in special education to evaluate learning outcomes or performance in the future.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Research Involving Human Participants and/or Animals Ethical Approval

This article does not contain any studies with human participants performed by any of the authors.

ORCID iD

Ying-Sing Liu

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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