Linking Self-Regulation Scaffolding to Early Math Achievement: Evidence from Chilean Preschools

Abstract

Self-regulation is widely theorized as a foundation for early mathematics achievement, yet little is known about how specific forms of teacher scaffolding advance this process in preschool classroom contexts. Drawing on sociocultural and self-regulation theories, this study conceptualizes scaffolding as a mechanism through which teachers support children’s attention, working memory, and behavioral regulation during mathematics instruction. We extend theory by distinguishing three domains of scaffolding—Instructional Strategies, Management Organization, and Warmth Responsivity—and examining how each uniquely relates to children’s math outcomes. Participants were 416 preschoolers (M age = 59.7 months) and 18 head teachers in Santiago, Chile. Teachers’ scaffolding behaviors were video recorded and coded at the beginning and end of the school year, and children’s math achievement was assessed with the Woodcock-Muñoz III. Multilevel models controlling for prior achievement, age, income, and gender revealed that Management Organization was positively associated with math achievement, while Warmth Responsivity was negatively associated, and Instructional Strategies showed no significant effect. These findings refine theoretical models by showing that organizational scaffolding plays a particularly important role in supporting math learning, whereas warmth responsivity may function as compensatory scaffolding in response to children’s difficulties. The study advances understanding of how the quality and type of scaffolding shape the developmental pathway from self-regulation to mathematics achievement.

1. Introduction

The preschool classroom is one of the most influential early contexts for children’s development, providing the foundation for later success. To benefit from its learning opportunities, children must be able to sustain attention, follow rules, and complete tasks independently—abilities that rely on self-regulation, a set of neurocognitive skills including working memory, inhibitory control, and attentional flexibility that enable purposeful management of thoughts, emotions, and actions (McClelland & Cameron, 2011; McClelland et al., 2019; Morrison et al., 2010). Because of this central role, self-regulation is considered foundational, predicting not only early academic achievement but also broader outcomes such as social competence and long-term well-being (Duncan et al., 2007; Garner & Waajid, 2012).

A growing body of evidence highlights self-regulation as a powerful predictor of children’s early mathematics achievement (Cameron et al., 2019; Clements et al., 2016; Bardack & Obradović, 2019). Mathematics places unusually high demands on self-regulatory capacities: children must sustain attention during multi-step problem solving, hold and manipulate quantities in working memory, inhibit impulsive or ineffective strategies, and persist through abstract or cognitively demanding tasks (McKinnon & Blair, 2019; Purpura et al., 2017; ten Braak et al., 2022). In this sense, self-regulation is not merely supportive but essential, shaping the degree to which young children can benefit from mathematics instruction. Beyond predicting math outcomes, self-regulation also conditions the effectiveness of instruction itself, with structured classrooms and sustained engagement amplifying children’s learning (DeFlorio et al., 2019; Schmitt et al., 2020). Consistent with this, organizational practices such as establishing routines and managing group activities have been positively linked to early math skills (Cameron & Morrison, 2011); Martin et al., 2024). Taken together, these findings underscore that mathematics places especially strong demands on self-regulation and point to teachers’ scaffolding behaviors as a central mechanism for supporting children’s success in this domain.

The rationale for examining how domain-general skills support the acquisition of more specific academic abilities is grounded in several complementary theoretical perspectives. From a sociocultural standpoint, Vygotsky (1978) emphasized that higher-order cognitive functions, such as self-regulation, emerge through social interaction and subsequently enable children to benefit from formal instruction in academic domains. Cognitive models of executive function (Miyake et al., 2000; Zelazo, 2015) further conceptualize self-regulation processes—including working memory, inhibitory control, and cognitive flexibility—as domain-general mechanisms that scaffold learning in specific areas, such as early mathematics. Similarly, school readiness frameworks (Blair & Raver, 2015) highlight self-regulation as a core mechanism underlying children’s capacity to engage with and benefit from instruction, while developmental cascade models (Masten & Cicchetti, 2010) illustrate how strengths in general cognitive regulation can generate positive spillover effects across academic domains. Together, these theories provide a strong conceptual foundation for hypothesizing that children’s early self-regulation skills play a pivotal role in supporting the development of mathematics and other content-specific competencies.

Consequently, early childhood is a critical period for the development of self-regulation through social interaction and teacher support (Montoya et al., 2023; Vygotsky, 1997). The very abilities that enable children to persist with complex tasks—such as those required in mathematics—are nurtured in everyday classroom interactions. Teachers play a central role in this process: through scaffolding behaviors, they provide cues, routines, and support that help children manage attention, regulate behavior, and control emotions. Over time, such scaffolding enables children to internalize self-regulatory strategies and apply them independently (Cameron & Morrison, 2011; Montoya et al., 2023). Consistent with Vygotsky’s sociocultural theory, scaffolding is not simply support but a form of mediated learning, where teachers act as cultural tools who guide children through their Zone of Proximal Development (Vygotsky, 1978, 1997). Through modeling, prompting, and structuring routines, teachers externalize regulatory strategies that children gradually appropriate as their own. In this sense, scaffolding behaviors represent a process of guided participation in which responsibility is progressively shifted from teacher to child (Arievitch & Haenen, 2005). Our coding of instructional, organizational, and emotional scaffolds reflects this mediational perspective: teachers regulate attention, reduce cognitive load, and provide socioemotional cues that enable children to internalize strategies necessary for mathematics learning.

Teachers’ self-regulation scaffolding behaviors can be understood as intentional cues—such as verbal prompts, modeling, or structured routines—that guide children’s attention, working memory, and inhibitory control while reducing cognitive load (Arievitch & Haenen, 2005; Munakata et al., 2012; Vandenbroucke et al., 2018). These behaviors are typically classified into three domains: instructional (e.g., explaining concepts, modeling strategies, structuring sequential activities), organizational (e.g., consistent routines, clear rules, and classroom management), and emotional (e.g., encouragement, praise, and positive feedback). Prior work shows that instructional scaffolding supports engagement and mediates the effects of curriculum on math achievement (Cadima et al., 2016; Hofer et al., 2013); organizational scaffolding has been linked to gains in counting and problem-solving (Cameron & Morrison, 2011; Martin et al., 2024); and emotional scaffolding, though less consistent, may foster persistence in challenging tasks (Christopher & Farran, 2020; Vandenbroucke et al., 2018).

In recognition of teachers’ central role in shaping children’s regulatory development, recent research has turned to observational methods to identify the specific practices that foster self-regulation in the classroom. A systematic review and meta-analysis by Vandenbroucke et al. (2018) concluded that three dimensions of teacher behavior—emotional support (warm, responsive, and sensitive interactions), instructional guidance (modeling, questioning, and scaffolding), and classroom organization (structures, routines, and preparedness)—are reliably associated with preschoolers’ self-regulatory ability. Consistent with those results, Phillips et al. (2022) reported that preschoolers’ self-regulation developed most strongly in classrooms where teachers combined emotionally supportive interactions, instructional scaffolding that promoted autonomy, and consistent organizational practices. By contrast, Martin et al. (2024), working with kindergarten classrooms, found that classroom management was the only dimension consistently linked to self-regulatory gains. In their study, emotionally supportive practices showed limited or even negative associations with outcomes, and explicit promotion of regulation strategies yielded little evidence outside of structured curricula. Taken together, these findings suggest that the impact of teacher behaviors on children’s self-regulation may depend not only on the type of practice but also on the developmental stage and instructional context in which they are enacted.

Further evidence reinforces the idea that the effects of scaffolding depend on context. Montoya et al. (2023) showed that Chilean preschool teachers’ scaffolding behaviors, while stable across the school year, varied considerably across learning opportunities: in greeting routines, teachers tended to use social prompts to encourage communication and participation, whereas in mathematics instruction they relied more on procedural supports such as repeating directions to sustain attention and persistence. Instructional scaffolding appeared more frequently than warmth or management behaviors, yet potentially valuable practices—such as step-by-step guidance or explicit encouragement of perseverance—were rarely observed. These findings highlight the importance of examining scaffolding not only by developmental stage but also within specific instructional domains.

To date, however, little is known about whether, and in what ways, scaffolding behaviors enacted specifically during mathematics instruction contribute to children’s learning in preschool. The present study addresses this gap by investigating preschool teachers’ self-regulation scaffolding behaviors—defined here as targeted instructional, organizational, and emotional strategies that help children manage cognitive load, sustain engagement, and regulate behavior—within the context of mathematics lessons. Using a fine-grained observational coding system, the study seeks to clarify the mechanisms through which teacher scaffolding fosters self-regulation and, in turn, supports children’s early mathematics achievement.

1.1. Math in the Chilean Context

Observations of preschool classrooms in Chile provide a valuable lens through which to examine the organization of mathematics instruction and its implications for children’s learning and development. In these contexts, whole-group instruction is the predominant approach, particularly in early mathematics lessons. This instructional format places considerable demands on children’s ability to sustain attention, follow collective routines, and regulate their behavior in order to fully benefit from shared learning opportunities (Prykanowski et al., 2018; Rimm-Kaufman et al., 2005; Vitiello & Williford, 2020). Children with stronger behavioral regulation skills are better positioned to engage productively in these environments, whereas those with weaker skills tend to derive fewer benefits. Such findings underscore the importance of considering how teachers’ scaffolding practices can support the development of self-regulation within mathematics instruction.

Despite the growing body of research on early mathematics in Chile (Susperreguy et al., 2020), instructional time devoted to mathematics remains limited. On average, kindergarten classrooms allocate approximately 15 min per day to mathematics, with even less time observed in schools serving children from low socioeconomic backgrounds (Ponce & Strasser, 2019). Furthermore, mathematics lessons are most often delivered in whole-group formats, while opportunities for individualized or small-group instruction are scarce (Bautista et al., 2018; Ponce & Strasser, 2019). The combination of limited instructional time and reliance on whole-group teaching highlights Chile as a critical context for investigating how teachers’ scaffolding practices may help children regulate their behavior and, consequently, maximize the benefits of mathematics learning opportunities.

The broader organization of preschool mornings in Chile also provides important contextual insights. A typical urban classroom day consists of instructional segments interspersed with non-instructional activities, and the quality of language input varies significantly across these activities. For instance, structured learning experiences and book discussions elicit richer language than greetings or free play (Strasser et al., 2018). Within mathematics instruction specifically, classroom tasks tend to emphasize basic counting and number operations, with fewer opportunities for extended conceptual discussions (Bautista et al., 2018). Notably, teachers also demonstrate identifiable self-regulation scaffolding behaviors both during mathematics lessons and in seemingly peripheral activities such as greetings, which may represent a crucial mechanism through which teachers support children’s engagement and capacity to benefit from mathematics instruction (Montoya et al., 2023).

1.2. The Current Study

This study employs a fine-grained coding system designed to capture teachers’ targeted self-regulation scaffolding behaviors, which are theoretically linked to children’s regulatory development (Cameron & Morrison, 2011; Montoya et al., 2023; Vandenbroucke et al., 2018). We focus on Chilean teachers and preschool children within the specific instructional context of mathematics lessons. Prior research suggests that instructional scaffolding can enhance persistence and conceptual understanding (Cadima et al., 2016; Hofer et al., 2013), organizational scaffolding provides the structure necessary for sustaining attention and maximizing instructional time (Cameron & Morrison, 2011; Martin et al., 2024), and emotional scaffolding may help children persist through challenges (Christopher & Farran, 2020).

Building on prior research, we expected teachers’ self-regulation scaffolding behaviors to be positively associated with preschoolers’ mathematics achievement. Although previous studies have produced mixed findings across contexts—with organizational supports often emerging as the strongest predictors, instructional scaffolding showing limited effects outside of structured curricula, and emotional scaffolding sometimes displaying inconsistent or even negative associations—we grounded our hypotheses in the theoretical view that all three domains play a supportive role in children’s learning.

Specifically, we predicted that:

• Instructional self-regulation scaffolding behaviors would be positively associated with children’s mathematics scores.
• Organizational self-regulation scaffolding behaviors would be positively associated with children’s mathematics scores.
• Emotional self-regulation scaffolding behaviors would be positively associated with children’s mathematics scores.

2. Method

2.1. Participants

Participants were part of a broader study examining family and instructional factors influencing early math skills in Chile (Susperreguy et al., 2020). 419 children (Age_T2 M = 59.72 months, SD = 4.21 months, Range = 46–70 months; 52.3% girls) with diverse socioeconomic backgrounds were recruited from seven schools in the urban area of Santiago, Chile. The research involved initially 18 preschool classrooms, where we observed the lead teacher in each, with an average age of 36.62 years (SD = 8.04). All teachers were female, Spanish-speaking monolinguals, university graduates, and had experience ranging from 1 to 20 years (M = 6.59; SD = 6.35).

2.2. Ethical Considerations

The project and data collection procedures have been approved by the [name deleted to maintain the integrity of the review process] Ethics Review Committee. Comprehensive information, both written and oral, was provided to the staff, parents, and caregivers. Those who voluntarily wished to participate in the project gave their written consent. The consent form stated that all participants had the right to withdraw from the research project at any time. For parents and caregivers, this consent also included their children. During the data collection process, the researcher recurrently asked the children before recording activities and was attentive to the children’s signs of discomfort. Additionally, the camera focused solely on the head teacher, who was wearing a portable microphone. These considerations were especially important in attention to the power asymmetry that exists between adults and children. To safeguard anonymity and confidentiality, pseudonyms and anonymized sketches were used during data collection and analysis, as well as in the results presentation. The research team managed all data, storing it in a secure format and location to ensure anonymity and confidentiality.

2.3. Procedure

Preschool Teachers’ Video Recordings

Data collection took place at two different times: at the start (T1) and the conclusion (T2) of the 2016 school year. The math video recordings were made on two separate days, with the camera focused solely on the lead teacher, who was equipped with a portable microphone. The camera remained focused on the head preschool teacher during the recording time.

The data consisted of a total of 36 videos, with an average length of 97 min (SD = 51.5 min). Within each video, only the segments that captured math learning experiences were analyzed. On average, math instruction segments lasted 31 min (SD = 6.15) at the beginning of the school year (T1) and 29 min (SD = 6.14) at the end (T2).

2.4. Instruments

2.4.1. Coding System

This study used a coding system consisting of 13 codes. Each one of them represents a scaffolding behavior aimed at supporting children’s self-regulation during preschool classroom instruction. The codes are organized into three scales: four from the Instructional Strategy scale, six from the Management/Organization scale, and three from the Warmth/Responsivity scale (

Table 1. Self-regulation scaffolding behaviors by scale and their examples.

Instructional Strategy (IS)	Examples
Models an example (provides external cues to explain to children what they should do)	“With my finger up and down… I can draw number 1,” while drawing the number 1.
Promotes establishing connections (supports children in linking different concepts)	“Heavy and light are two qualities of the objects. Heavy as me because I’m bigger and tall than you. Anyone can answer you are light or heavy than me?”
Engages in in-depth analysis of the material (engages children in analyzing a section of the material)	“Now we are going to observe the number line that we have here. We are going to look at the spaces of distance between numbers… Look at the difference between 14 and 18… let’s count them”.
Management Organization (MO)	Examples
Reminds children about behavior expectations (reinforces rules of good conduct when children demonstrate expected behavior or when they misbehave)	“We need silence to listen us. Please let’s hear what xx have to say…she was saying that sorting is…”
Gives step-by-step instructions (provides step-by-step instructions for an activity or behavior)	“Now we are going to read the challenge and then we are going to write the first part of it”
References schedule for the day (explain the daily schedule)	“After eat lunch we are going to learn counting strategies using blocks. Please don’t forget that for this time we are going to read a book before it”
Repeats instructions (repeats an instruction verbally more than two times in a interval of 30s each)	“We need to separate those (group of balls) in three equal parts” then the teacher goes to another group and repeats “remember that this group have to be divided in three parts, and they have to be equal”
Provides students support (supports children as they transition between activities or settings)	“Teacher help children to pick up the materials from math corner at the classroom”
Secures attention (employs verbal and/or physical support to capture children’s attention)	Teacher uses a puppet called “Perico” to secures attention and being able to read a math problem on the blackboard.
Warmth Responsivity (WR)	Examples
Offers recommendations for improvement (advises children on their work during activities)	When the child answers 29 instead of 19, the teacher writes on the blackboard “29 is this number you wrote… you see it have a 2…you see, but 19 has a 1. That way you can write the 19 and name it correctly”
Provides positive reinforcement (offers praise or tangible reinforcement when children successfully complete an activity or display positive behavior or attitude)	Gives a star for good answer when children put the correct number in a sequence.
Encourages perseverance (Gives verbal encouragement to help children persevere with challenging activities)	Children are comparing two bags of different wight. Teacher says: “Let’s go again and see what happen when you compare this bag with this other. Can you tell me what bag is heavier? See, I knew it that you were capable to solve that”.

Source: (Montoya et al., 2023).

):

(i)

Instructional Strategy (IS): It indicates whether preschool teachers employ self-regulation scaffolding behaviors to guide children in participating and engaging with the learning processes in the classroom.

(ii)

Management Organization (MO): It reflects behaviors that foster self-regulation as teachers manage and structure their classroom environment. The codes illustrate how preschool teachers handle classroom organization to enhance the learning process, thereby promoting self-regulation skills.

(iii)

Warmth Responsivity (WR): It reflects the scaffolding behaviors that preschool teachers use to motivate children to achieve and complete tasks.

These codes were developed in a previous study that began with 34 potential preschool teachers’ scaffolding behaviors designed to foster children’s self-regulation (Montoya et al., 2023). The initial system was grounded in a review of classroom intervention literature and drew on two established instruments: Optimizing Learning Opportunities for Students (OLOS; Connor et al., 2020) and the Quality of Classroom Learning Environment (Q-CLE; Connor et al., 2014; McLean et al., 2016).

To refine the initial coding system, a frequency-of-occurrence criterion was applied: codes were retained if they appeared in at least 10% of coded intervals, whereas behaviors observed very rarely (fewer than five coded segments) were excluded, as their low frequency limited both reliability and interpretability. This process yielded the 13 codes that balanced comprehensiveness with parsimony while maintaining ecological validity.

The reliability of the final coding system was acceptable, with an average intra-class correlation coefficient (ICC) of 0.81 across all coding rounds (range = 0.62–0.89). Additional reliability checks conducted during coding yielded an average ICC of 0.80 (range = 0.78–0.84), which falls within the “acceptable to good” range according to Cicchetti’s (1994) guidelines (Montoya et al., 2023). Table 1 summarizes the code system.

For analysis purposes, each math instruction video was divided into 30 s intervals. Two coders independently observed each interval and assigned 1 point for the presence of each of the 13 codes and 0 for their absence (Degol & Bachman, 2015), even if a behavior occurred multiple times within the same interval. A total of 122 intervals were analyzed (SD = 12.29 for T1; SD = 10.39 for T2), and most of them (90.64%; M = 55.97; SD = 8.31) corresponded to learning activities.

To compare the frequency of the teaching behaviors represented by each code, an index was calculated that reflected the percentage of intervals in which the same code appeared relative to the total number of intervals. This index enabled comparisons across segments and time periods of varying lengths. Since Montoya et al. (2023) found no differences in the frequency of codes between T1 and T2, the analysis for this study was conducted using the average total number of behaviors observed in each 30 s interval throughout the year. Moreover, for the analyses, when both T1 and T2 observations were available, we used the average across the two time points for each teacher. Two teachers had only one recording (either at T1 or T2), and in these cases, the single observation was retained as their score. In addition, one teacher left due to maternity leave and was replaced; because the students continued to receive instruction, both recordings (before and after the replacement) were combined and treated as a single case. This decision reflects the inherent variability of classroom recordings—differences in daily routines, student dynamics, and contextual factors can influence the frequency of observed behaviors in any single session. By averaging across waves, we obtain a more stable estimate of each teacher’s instructional profile over the school year, while minimizing the impact of single-day measurement error. Importantly, math achievement was measured about two months after the second observation, so both T1 and T2 precede the outcome. As a check, we tested whether short-term fluctuations (Δ = T2–T1) predicted achievement beyond T1. None of the Δ terms were significant (Instructional Strategies: b = 0.42, SE = 0.46, p = 0.39; Management Organization: b = −0.68, SE = 0.38, p = 0.10; Warmth Responsivity: b = −0.02, SE = 0.33, p = 0.96). This indicates that averaging across T1 and T2 provides a stable estimate of teachers’ scaffolding behaviors and does not introduce endogeneity.

For the teaching behavior scales, the average frequency of Instructional Strategies (IS) was 0.22 (SD = 0.09), Management Organization (MO) was 0.16 (SD = 0.04), and Warmth Responsivity (WR) was 0.18 (SD = 0.06). This means that IS-related behaviors were present in 22% of coded intervals, MO-related behaviors in 16%, and WR-related behaviors in 18% of intervals, when pooling across all teachers.

Figure 1 complements these overall averages by displaying the distribution of behaviors across teachers. Most teachers showed a balanced composition of IS, MO, and WR, with “No scaffolding observed” (NSO) typically occupying a smaller portion of intervals. However, there was substantial variability: IS reached up to 65% of intervals in some classrooms, while WR could be as low as 12%. The “No scaffolding observed” category ranged from 2% to about 29%. Together, the averages and Figure 1 provide complementary perspectives, illustrating both the overall prevalence of scaffolding behaviors and the degree of variability between teachers.

2.4.2. Children’s Math Achievement

The subtest Applied Problems of the Woodcock-Muñoz Battery III (Muñoz-Sandoval et al., 2005) was used to evaluate math achievement. Woodcock-Muñoz is the Spanish version of Woodcock-Johnson III- Test of Achievement. The subtest Applied Problems assesses a child’s ability to solve practical math problems (e.g., ‘If you have 3 apples and someone gives you 2 more, how many apples do you have now?’). Children receive one point per correct answer. The test is terminated when the child has incorrectly answered six consecutive items. Published reliability for 4- to 5-year-olds in a Spanish-speaking population ranges from 0.93 to 0.95 (Muñoz-Sandoval et al., 2005). Reliability was calculated in the sample of children by dividing the sample into two, resulting in a Cronbach’s α of 0.65. On average, children scored 11.37 (SD = 3.49) at T1 and 15.07 (SD = 3.80) on math achievement at T2.

2.4.3. Control Variables

We included child- and family-level covariates given established associations between self-regulation, socioeconomic context, and early mathematics achievement (McClelland & Cameron, 2012; Skibbe et al., 2019; Watts et al., 2018). Gender (binary) and age at T2 (months) were entered at Level 1. Family income was reported on a six-point scale (M = 4.11, SD = 1.29) and dichotomized into low–middle (≤US$1900/month; categories 1–4) versus high (>US$1900; categories 5–6). Descriptively, the sample was balanced by gender (47.7% boys, 52.3% girls) and had a mean age of 59.72 months (SD = 4.21). For the income dichotomy, 54.9% of families were classified as low–middle and 35.6% as high, with 9.5% missing.

2.4.4. Analytic Plan

Given the hierarchical nature of the data, where children were nested in classrooms, the multilevel technique was used (Raudenbush & Bryk, 2002). The null model indicated an intraclass correlation coefficient (ICC) of 0.20, meaning that approximately 20% of the variance in the math achievement at T2 was attributable to differences between teachers, thus justifying the use of multilevel modeling.

All models were estimated in R using the lme4 package (Bates et al., 2015), with missing data addressed through multiple imputation (m = 40) implemented in the mice package (van Buuren & Groothuis-Oudshoorn, 2011). This approach allowed us to retain the full analytic sample while accounting for uncertainty in the imputed values.

At the Level 1 (student level), the variables included the child’s prior mathematics achievement, age, family income (recoded as a binary variable, with low- to middle-income families as the reference group, determined by the median of the total sample), and gender (recoded as a binary variable). At the Level 2 (classroom/teacher level), the variables consisted of the self-regulated scaffolding behaviors related to Instructional Strategies, Management Organization, and Warmth Responsivity. The dependent variable was children’s mathematics achievement at the end of the school year (wave 2). The analyses proceeded in steps. First, a null model was estimated, including only the dependent variable and variables of interest. Model 1 incorporated the Level 1 variables (student-level variables), while Model 2 added the Level 2 variables (teacher-level variables).

The equation for the model is presented below:

The HLM level 1 equation is:

Applied Problems_T2ij = β_0j + β_1j(Applied Problems_T1ij) + β_2j(Age_ij) + β_3j(Family Income_ij) + β_4j(Gender_ij) + e_ij

The HLM level 2 equation is:

Applied Problems_T2ij = β_0j + β_1j(Applied Problems_T1ij) + β_2j(Age_ij) + β_3j(Family Income_ij) + β_4j(Gender_ij)+e_ij;

β_0j = γ₀₀ + γ₀₁ (Instructional Strategy) + γ₀₂ (Management Organization) + γ₀₃ (Warmth Responsivity) + u_0j

where Applied Problems (T2) is the math achievement at the end of the school year for each child i in classroom j. β_0j is the intercept, representing the average math achievement across the sample when all predictors are 0. At Level 1, the coefficients β_1j–β_4j capture the effects of children’s prior math achievement (Applied Problems T1), age, family income (coded as a binary variable, 0 = lower income, 1 = higher income), and gender (0 = boys, 1 = girls). e_ij is the error term for the child-level equation. At Level 2, γ₀₀ is the overall intercept of the dependent variable, while γ₀₁–γ₀₃ capture the effects of the self-regulated scaffolding behaviors: Instructional Strategies, Management Organization, and Warmth Responsivity. u_0j is the error term for the teacher-level intercept, representing variance in math achievement between teachers. All continuous predictors (child age, prior math achievement, and the self-regulated scaffolding behaviors) were grand-mean-centered before estimation.

2.4.5. Missing Data

Formal tests of missingness yielded mixed results: the Hawkins test rejected MCAR under multivariate normality (p < 0.001), while a non-parametric alternative did not (p = 0.61). Logistic regressions predicting missingness from observed variables indicated no systematic associations for most measures. Based on these diagnostics, we assumed a MAR mechanism and addressed missingness using multilevel multiple imputation. Sensitivity analyses comparing models with and without imputation yielded substantively similar conclusions (see Supplementary Materials).

Missing data were imputed for a limited number of cases: 9.5% for family income (40 students), 3.3% for math achievement at T2 (14 students), 3.3% for child age (14 students), and 1.4% for prior math achievement (6 students), while no imputation was required for gender or the self-regulated scaffolding behaviors. We handled missing data using multiple imputation with the mice package in R. The imputation model included all variables from the analytic model and respected the multilevel structure by treating the teacher identifier as a cluster variable. We generated 40 imputed datasets and estimated the hierarchical linear model (HLM) separately on each, then pooled the results using Rubin’s rules (Rubin, 1987) to obtain final parameter estimates and standard errors. This procedure allowed us to retain the full analytic sample and reduce bias due to missingness in student-level variables, while preserving the nested structure of the data.

2.5. Results

2.5.1. Descriptive Statistics

Bivariate correlations are reported in

Table 2. Pearson Correlations for students and teacher levels.

Level 1 (Student) Correlations
Variable	Math achievement (T2)	Math achievement (T1)	Age	Family income (1 = high)	Gender (1 = boy)
Math achievement (T2)	—
Math achievement (T1)	0.59 ***	—
Age	0.25 ***	0.27 ***	—
Family income (1 = high)	0.29 ***	0.34 ***	0.11 *	—
Gender (1 = boy)	−0.02	−0.05	0.01	−0.12 *	—
Level 2 (Teacher) Correlations
Variable	Instructional Strategies	Management Organization	Warmth Responsivity
Instructional Strategies	—
Management Organization	0.37 ***	—
Warmth Responsivity	0.28 ***	0.54 ***	—

* p < 0.05; ** p < 0.01; *** p < 0.001. Pairwise deletion (N student level = 367 to 419; N teacher level = 399).

. At the student level, math achievement at T2 correlated strongly with T1 scores (r = 0.59, p < 0.001) and was positively associated with age (r = 0.25, p < 0.001) and family income (r = 0.29, p < 0.001). A small negative association was observed between gender (coded 1 = boy) and family income (r = −0.12, p < 0.05). At the teacher level, significant positive correlations were found between the three instructional scales, particularly between Management Organization and Warmth Responsivity (r = 0.54, p < 0.001).

2.5.2. Hierarchical Linear Model Analysis

The estimation parameters for the models of the dependent variables on children’s math achievement at the end of the school year are found in

Table 3. Model for math achievement at the end of the year (pooled sample).

Effect	Null Model	Model 1	Model 2
Predictor	Coef. (SE)	Coef. (SE)	Coef. (SE)	95% CI	Std β
Fixed effects
Level 1 (students)
Intercept	15.06 *** (0.44)	14.80 *** (0.40)	14.79 *** (0.36)	[14.07, 15.50]	—
Math Achievement (T1)	—	0.58 *** (0.05)	0.58 *** (0.05)	[0.49, 0.67]	0.53
Children age	—	0.07 * (0.04)	0.08 * (0.04)	[0.01, 0.15]	0.08
Family income (binary)	—	0.42 (0.38)	0.52 (0.38)	[−0.24, 1.27]	0.07
Gender (binary)	—	0.16 (0.29)	0.17 (0.29)	[−0.41, 0.74]	0.02
Level 2 (teachers)
Instructional Strategies	—	—	−0.09 (0.60)	[−1.28, 1.09]	−0.01
Management Organization	—	—	1.62 * (0.77)	[0.12, 3.13]	0.20
Warmth Responsivity	—	—	−1.51 * (0.59)	[−2.66, −0.35]	−0.22
Random effects (variance components)
Teacher-level variance	2.87	1.40–1.75	0.89–1.36
Residual variance	11.79	7.65–8.11	7.66–8.13
Total variance	14.66	9.11–9.70	8.66–9.37
ICC (Teacher %)	20%	15–18%	10–15%

* p < 0.05; ** p < 0.01; *** p < 0.001.

. In the null model, the intraclass correlation coefficient (ICC) was 20%, indicating that one-fifth of the variance in children’s math achievement at the end of the school year was attributable to differences between teachers (Raudenbush & Bryk, 2002).

2.5.3. Association Between Preschool Teachers’ Behaviors and Children’s Math Achievement

In Model 1, which incorporated child-level characteristics, math achievement at T1 was positively associated with math achievement at the end of the year (b = 0.58, SE = 0.05, 95% CI [0.49, 0.67], p < 0.001, Std β = 0.53), indicating that a one-unit increase in prior math achievement corresponded to more than half a standard deviation increase in T2 math scores. Children’s age was also positively associated with math achievement at T2 (b = 0.08, SE = 0.04, 95% CI [0.01, 0.15], p = 0.031, Std β = 0.08), reflecting a modest effect in SD units. No associations were found for family income (b = 0.52, 95% CI [−0.24, 1.27], Std β = 0.07) or gender (b = 0.17, 95% CI [−0.41, 0.74], Std β = 0.02).

In Model 2, teacher-level factors were added. Instructional Strategies showed no association with math achievement (b = −0.09, SE = 0.60, 95% CI [−1.28, 1.09], p = 0.876, Std β = −0.01). Management Organization was positively associated (b = 1.62, SE = 0.77, 95% CI [0.12, 3.13], p = 0.035, Std β = 0.20), indicating that classrooms with stronger organizational practices scored approximately one-fifth of a standard deviation higher in math. Higher scores on the Warmth Responsivity scale were statistically associated with lower math scores (b = −1.51, SE = 0.59, 95% CI [−2.66, −0.35], p = 0.011, Std β = −0.22), indicating that greater use of warm–responsive behaviors was linked to approximately one-fifth of a standard deviation lower math achievement. This finding does not imply that teachers’ warmth is inherently detrimental. Descriptive data (Figure 1) shows that these behaviors represented only about 18% of observed intervals and varied considerably across classrooms. This suggests that the negative association should be interpreted cautiously, as higher Warmth Responsivity may either reflect teachers’ compensatory responses to children experiencing greater difficulties or may simply co-occur with lower math achievement, rather than indicating an adverse effect of warmth itself. At the student level, math achievement was positively associated with prior performance (Std β = 0.53) and age (Std β = 0.08), but not with family income or gender.

In terms of points in the math achievement scale, teacher-level variance decreased from 2.87 in the null model to a range of 1.40–1.75 in Model 1 and further to 0.89–1.36 in Model 2, reflecting estimates across models fitted to different imputed datasets. The ICC decreased from 20% in the null model to 15–18% in Model 1 and 10–15% in Model 2, indicating that differences between teachers explained a moderate proportion of the variance once individual- and teacher-level factors were included.

In summary, math achievement was positively associated with Management Organization and negatively associated with Warmth Responsivity, highlighting distinct aspects of teachers’ scaffolding behaviors that relate to children’s math outcomes.

3. Discussion

This study examined whether preschool teachers’ self-regulation scaffolding behaviors, observed specifically during mathematics instruction, were associated with Chilean children’s mathematics achievement at the end of the school year. The results indicated a significant association between teachers’ self-regulation scaffolding behaviors and children’s performance in mathematics. Consistent with our theoretical framework, we hypothesized that each of the three scaffolding dimensions—Instructional Strategies, Management Organization, and Warmth Responsivity—would be positively related to children’s mathematics scores.

3.1. Instructional Strategy Behaviors and Children’s Math Achievement

The results indicated no association between instructional self-regulation scaffolding behaviors and children’s mathematics achievement; therefore, our hypothesis was not supported. Similar findings have been reported in prior research. For instance, Schmitt et al. (2020) found that teachers’ instructional support was unrelated to preschoolers’ mathematics achievement, likely due to the generally low levels of mathematics instruction provided. Consistent with these results, Chilean preschool teachers often fail to deliver high-quality mathematics instruction. Studies conducted in Chile have shown that mathematics tasks are frequently limited to number recognition and counting, offering little cognitive challenge (Bautista et al., 2018). Future research should aim to describe in greater detail the instructional strategies teachers use to teach mathematics and examine more closely how these strategies relate to children’s self-regulation skills and mathematics achievement. It is also possible that the lack of significant findings in this study reflects limitations in the sensitivity of the scale employed or the variability in how preschool teachers displayed self-regulation scaffolding behaviors related to instructional strategies.

Evidence from Northern Hemisphere countries, including the United States (Schmitt et al., 2020), Portugal (Cadima et al., 2016), the Netherlands (Vandenbroucke et al., 2018), Germany (Hofer et al., 2013), and Nordic contexts such as Norway and Finland (ten Braak et al., 2022), presents a mixed picture. In several of these settings, instructional scaffolding has shown limited or no direct association with math achievement unless it is embedded within structured, cognitively challenging curricula (Cadima et al., 2016; Hofer et al., 2013). By contrast, interventions that deliberately integrate explicit, high-quality scaffolding with rich math content have been linked to gains in problem-solving and persistence (Clements et al., 2016). Compared with these contexts, the Chilean preschool setting provides fewer opportunities for cognitively demanding math instruction, which may help explain why instructional strategies showed no measurable effect in our study. Future research should describe instructional practices in greater detail across diverse international settings and examine how scaffolding interacts with both self-regulation supports and the quality of math content to influence children’s achievement.

3.2. Management Organization Behaviors and Children’s Math Achievement

Our study found a positive relationship between behaviors related to the Management Organization scale (e.g., providing reminders about behavioral expectations, offering step-by-step instructions, referring to the daily schedule, repeating instructions, offering support to students, or securing children’s attention) and math achievement. Therefore, we confirmed our hypothesis. These findings align with previous studies, which have shown that children with stronger self-regulation skills benefit most from well-organized classrooms (Schmitt et al., 2020). Similarly, Christopher and Farran (2020) reported that specific teacher practices, such as giving step-by-step instructions, were positively associated with kindergartners’ math achievement, highlighting the importance of organizational supports for sustained task engagement.

Internationally, however, the evidence is mixed. For instance, Carr et al. (2019) found that the overall quality of classroom organization in U.S. pre-kindergarten was not consistently related to math outcomes, suggesting that the strength of this association may not only depend on the instructional context but also on children’s age. In European studies, classroom structure and clear routines are often emphasized as central to fostering children’s executive function and learning, though direct effects on mathematics vary across settings (Cadima et al., 2016; Vandenbroucke et al., 2018).

In turn, Chilean preschool teachers exhibited self-regulation scaffolding behaviors related to the Management Organization scale, which was associated with positive outcomes in math tasks. If the environment is well organized and the routines are clear, they facilitate task engagement related to math and self-regulation skills (Cameron & Morrison, 2011). Together, these findings suggest that management and organization are most beneficial when they not only provide order but also create opportunities for children to sustain attention and engage with cognitively demanding tasks. Yet, further research is necessary to gain a deeper understanding of this association.

Our findings are also consistent with emerging research showing that teachers’ scaffolding of executive functions contributes both to children’s regulatory and learning achievements. In this sense, Bardack and Obradović (2019) found that teachers’ scaffolding of planning and cognitive flexibility produced improvements in children’s executive function skills throughout the school year. Given the well-established role of executive functions in supporting early mathematics (Blair & Razza, 2007; Clark et al., 2010), their results suggest that teacher scaffolding behaviors may promote math achievement indirectly by strengthening children’s self-regulation capacities. Our study extends this line of work by focusing on preschool classrooms in Chile, a context where observational research on fine-grained scaffolding practices is still limited. Together, these findings underscore the value of examining how teacher scaffolding of regulatory skills operates across developmental stages and educational contexts.

3.3. Warmth Responsivity Behaviors and Children’s Math Achievement

The negative association observed between warmth responsivity and children’s math achievement contradicts previous evidence (Schmitt et al., 2020) that have shown that teachers with good emotional support benefit their math instruction in children with low self-regulation skills. Giving time to persist on-task is also essential to math achievement in kindergarten (Christopher & Farran, 2020). This pattern is consistent with a compensatory explanation, in which teachers may provide more warmth and encouragement in response to children experiencing greater difficulties, rather than warmth itself undermining learning. Alternatively, teachers may reduce these behaviors once they perceive that children are succeeding. Future research is needed to clarify the direction of this association. Both explanations would need to be further explored in future studies.

One useful lens for interpreting this result is the notion of compensatory scaffolding. This framework suggests that teachers often increase warm, supportive behaviors when children display greater academic or behavioral difficulties, which can generate negative statistical associations even though the intent of the practice is supportive (Hamre & Pianta, 2005; Schmitt et al., 2020). From this perspective, our findings may capture teachers’ adaptive responses to children’s needs rather than a harmful effect of warmth. Situating our results within this framework helps reconcile the apparent contradiction with international studies, where emotional support is generally associated with positive outcomes, particularly when combined with instructional and organizational scaffolds (Phillips et al., 2022; Martin et al., 2024).

Given that previous evidence is mixed about the role of teacher emotional support, these results need to be interpreted in a caution and broader manner. Quality classroom interactions theories claim that when they are emotionally supportive, children’s engagement, persistence, and self-regulation improve which, in turn, provide better scaffolding opportunities for learning (Hamre & Pianta, 2005; Vandenbroucke et al., 2018). These theories have found empirical support in studies showing that classrooms that provide children with emotional support tend to promote better academic outcomes especially for those who exhibit lower developmental levels of regulatory skills (Schmitt et al., 2020).

While other international evidence has found that those previous results are either not as strong as them or even contradict the patterns observed. That is the case of the study conducted by Phillips et al. (2022) that found that self-regulation is better promoted in classrooms where emotional support is combined with instructional scaffolding and organizational consistency. In this way, emotional support alone was not found to be predictive. In similar terms, Martin et al. (2024) observed that classroom management was most consistently associated with self-regulatory gains in kindergarten. These findings might suggest that the role of warmth responsivity needs to be analyzed in conjunction with other children’s and classroom’s variables such as developmental profiles or classroom management practices for example. Our findings contribute new evidence to this debate by highlighting that, at least in Chilean preschools, higher levels of warmth responsibility may be an indirect indication of teachers’ compensatory responses to children struggling in mathematics.

These patterns may have other alternative explanations. First, the three observed teacher behaviors—warmth, classroom organization, and instructional support—often occur together and may share elements of overall interaction quality. When modeled side by side, the estimate for warmth likely reflects only what is distinctly warmth after accounting for overlap with the other domains; this residual component could relate negatively, even if, in general, warmer and well-organized instruction supports learning. Second, in the Chilean context, warm teacher–child exchanges are culturally expected and may be particularly evident when children are struggling during whole-group activities (Leyva et al., 2015). Under these conditions, higher observed warmth might function as a marker of challenging moments rather than as a cause of lower achievement. These possibilities offer a cautious reading of the finding and point to directions for future work.

Finally, a key contribution of this study lies in addressing an important but underexplored gap in the literature. Although prior research has established that teachers play a central role in supporting or undermining children’s self-regulation (Phillips et al., 2022), most of this evidence has come from high-resource contexts with individualized or small-group instruction and global measures of classroom quality. By contrast, our study focuses on low-resource Chilean preschools where mathematics is primarily taught in whole-group settings, placing particularly high demands on children’s ability to regulate attention and behavior. In this context, we applied an ecologically valid, fine-grained observational coding system that captured teachers’ moment-to-moment scaffolding behaviors. This design moves beyond descriptive accounts of classroom quality to provide theoretically grounded evidence of how specific forms of teacher mediation—organizational, instructional, and emotional—relate to mathematics outcomes under conditions of constrained instructional time and limited resources. By situating scaffolding within a sociocultural framework, our findings advance theory by clarifying which forms of teacher support are most consequential in contexts where self-regulation is both highly taxed and most essential for children’s engagement in mathematics learning.

3.4. Limitations and Future Directions

This study has several limitations that should be taken into account when interpreting the findings. First, although we used repeated classroom observations and lagged outcomes, the design remains correlational and cannot establish causality; teachers’ scaffolding behaviors may also reflect responses to children’s math performance. Second, the coding system employed has not yet undergone formal validation in larger and more diverse samples, which may limit the precision of measurement. Third, our sample consisted only of female teachers from urban Santiago, which constrains the generalizability of the results to other Chilean preschool contexts. In addition, the reliability of the Applied Problems test was moderate in this sample (α = 0.65), which may have attenuated observed associations. Finally, teacher characteristics such as age and years of experience were not included in the models and should be examined in future work. Despite these limitations, the study provides novel evidence on the role of fine-grained scaffolding behaviors in mathematics instruction, highlighting the need for replication across diverse populations and instructional settings.

3.5. Policy and Practice Implications

These results have meaningful implications for policy and teacher preparation, particularly regarding how to scaffold early mathematics learning through structured, regulatory-supportive practices. First, because Management Organization (e.g., step-by-step directions, securing attention, clear routines) was positively associated with math achievement, we recommend that initial teacher education and in-service coaching prioritize practice-based preparation on these micro-practices during whole-group math. In the Chilean context, this aligns with national efforts to professionalize early childhood education through the National Guiding Standards for Initial Teacher Preparation (Estándares Orientadores para la Formación Inicial Docente), which emphasize the development of pedagogical skills to scaffold learning in structured environments (CPEIP, 2021). Additionally, our findings highlight theoretical frameworks that connect domain-general skills—such as executive function and behavioral self-regulation—with domain-specific learning in early mathematics. Rather than treating these as separate targets, recent research emphasizes their interdependence: self-regulation capacities support children’s engagement, persistence, and accuracy during cognitively demanding math tasks (Blair & Raver, 2015; Clements et al., 2016; Cameron et al., 2019). Designing math lessons that embed brief regulatory prompts—such as attention cues, behavioral scripts, or planning routines—may optimize children’s ability to benefit from instruction.