Differentiating instruction in primary and middle schools: Does variation in students’ learning attributes matter?

Abstract

This study sought to determine the significant relationship between student attributes (background knowledge, readiness, interests, and learning profiles) and the teachers’ use of DI elements (content, process, product, and learning environment differentiation) in primary and middle schools of Enjibara and Chagni town administrations of Awi zone, Ethiopia. A total of 364 randomly selected teachers were part of this study. The measurement scale has 27 items, and the Cronbach’s alpha (α) estimates for internal consistency reliability were ranging from .80 to .93. Convergent and discriminant validities of the constructs were established. Standardized factor loadings from CFA were ranging from .65 to .81. The study affirmed that variation in students’ attributes has a strong direct influence on content and learning environment differentiations. Differentiating content has a stronger direct influence on process differentiation. Likewise, process and learning environment differentiations have stronger direct influence on product differentiation. Moreover, mediation analyses showed that variation in students’ attributes has indirect effect on product differentiation via process and learning environment differentiations. Also, process differentiation has fully mediated the influence of content differentiation and partially mediated the influence of learning environment differentiation on product differentiation. In conclusion, this study provides strong evidence on the direct and indirect influence of variation in students’ attributes on differentiated instruction by applying more advanced approach of structural equation modeling. In order to address the student attributes, varying the contents and learning environments need to give priority than varying the process and the product.

Keywords:

• differentiated instruction
• student attributes
• content differentiation
• process differentiation
• product differentiation
• learning environment differentiation

PUBLIC INTEREST STATEMENT

The present classroom is a versatile “zoo” of students’ abilities, interests, readiness, and learning profiles. The overarching goal of schooling is to recognize and promote the abilities of each learner. As a result, a one-size-fits-all approach to education is unlikely to succeed. Instead, teaching should be crafted systematically to achieve the educational outcomes required of these diverse students that face teachers in their classrooms.

Accordingly, in order to address the diverse attributes of students (background knowledge, interest, readiness, and learning profile), theorists, researchers and policy makers are favoring the instruction to be differentiated in terms of content, process (method), learning environment and product (assessment). Addressing the diverse interests of students, therefore, is rested on the shoulder of teachers who have the responsibility to diversify these components of differentiated instruction.

1. Introduction

Globally, there is a belief in inclusive education that all learners, including those with special needs, learn in regular schools rather than in segregated schools. This inclusion of children with special needs in regular schools prompts the classroom to more diverse learners (Mngo & Mngo, 2018). A neglect of these fundamental diversities as well as the use of a singular teaching approach portends the classroom inclusiveness and may put learners with special needs at the risk of dropping out, lagging, losing motivation, getting bored, failing to learn, and not maximizing their potential (Siam & Al-Natour, 2016). The presence of diverse learners with varying interests, abilities, intelligence and learning styles has portrayed the need for teachers to rethink on the practice of relevant and research-based instructional strategies that will enable them to meet these diversities (Heacox, 2012; Suprayogi et al., 2017; Tadesse, 2020, 2021). This places an increased responsibility on the teacher who has to diversify instructional content, methods, materials, assessment strategies and learning environment through the use of differentiated instruction (henceforth DI).

1.1. Conceptualizations of differentiated instruction

As the traditional one-size-fits-all teaching approach neglects the diverse needs of students (Sun & Xiao, 2021; Tadesse, 2021), historical perspective has shaped DI into a philosophy and praxis (Suprayogi et al., 2017). DI is inquiry-based, learner-oriented and activity-intensive approach that enables teachers to plan strategically to meet the learning needs of individual students (Gentry et al., 2013; Tadesse, 2020, 2021). Also, DI is deliberated as a pedagogical model that addresses student diversity in the classroom (Bongco & David, 2020) and helps teachers adjust their teaching methods accordingly (Griful- Freixenet et al., 2020).

In order to address learners’ diversity, DI can serve as creating a balance between academic content and students’ attributes (background knowledge, interest, readiness and learning profile) by modifying four specific elements of DI: content—the information and skills that students need to learn; process—the method students learn the content being taught; product—the way students demonstrate what they have learned; and learning environment or affect—the school setting where learning takes place and facilitates an effective working relationship between teacher and students (Tomlinson & Eidson, 2003) or the feelings and attitudes that influence students’ learning (Tomlinson & Imbeau, 2010). This modification is guided by the teacher’s understanding of learner diversities (Roy et al., 2013). Accordingly, instigating DI allows teachers to plan strategically while operating within a common curriculum framework and adaptations to facilitate student learning in the same classroom (Chamberlin & Powers, 2010; Smale- Jacobse et al., 2019). DI also suggests that teachers can craft lessons in ways that tap into multiple student interests to endorse learner needs (Gentry et al., 2013; Lauria, 2010).

However, across the globe, the demand for coping with student diversity seems challenging (Roy et al., 2013). The arduous nature of DI can deter the teacher from executing the method in spite of the fact that it has widely been recognized to meet the learners’ diverse learning needs (Martin, 2013). This tends to create multiple problems for students and the education system (Lunsford, 2017). Likewise, the problem of effecting DI in African countries, including Ethiopia, is still below expectation (Deunk et al., 2015; Nicolae, 2014; Tadesse, 2020, 2021). Many teachers take children as if they are a homogenous group and teach them the same curriculum content, use the same method of teaching, and expect them to express what they have learned in the same way (Tadesse, 2018a, 2021).

These teachers, without taking cognizance of their students’ varying background knowledge, interests, readiness and learning profiles, apply a one-size-fits-all approach, which leaves too many students behind instead of moving them forward (Sun & Xiao, 2021; Tadesse, 2021). This could be due to lack of competence and experience on the part of the teachers (Nicolae, 2014; Roberts & Inman, 2013; Tadesse, 2021; Whitley et al., 2019); teachers’ perception problems towards DI (Tadesse, 2018a); the time consuming nature of DI to plan lessons, instruction and assessment (Nicolae, 2014; Whitley et al., 2019); large class size (Smit & Humpert, 2012; Tadesse, 2021; Whitley et al., 2019), lack of professional support (Lunsford, 2017; Tadesse, 2021), and lack of safe and stimulating learning environment for students’ learning (Santangelo & Tomlinson, 2012). Nevertheless, from the theoretical point of view, learners learn best when they are exposed to learning contents in ways that speak to their individual levels of expertise/zone of proximal development, specific intelligences and learning needs (Gardner, 1983; Vygotsky, 1978).

1.2. Theoretical and conceptual framework

DI is the one of the constructivist philosophical approach many schools worldwide use to ensure an inclusive classroom environment (Jarvis et al., 2017), and the framework by Tomlinson (2014) is widely known. Heacox (2012) also defined DI as “a constructivist approach to alternative instruction that changes the pace, level, or kind of instruction provided in response to individual learner’s needs, styles, or interests” (p. 5). Thus, the study is anchored on Vygotsky’s social constructivist theory and Gardner’s theory of multiple intelligences. As learning is simulative and collaborative, Vygotsky (1978) stressed that social interaction and culture interplay and exert a significant role in learning. Vygotsky believes that there is a gap between what a child can learn independently and what the child can learn with the assistance of adults or skilled peers which he referred it as “zone of proximal development (ZPD)”. As the ZPD is achieved through dialogue, it is the responsibility of the teacher to scaffold by changing the level of support and guidance to move the child from where he is to a level he can attain. This theory, therefore, has implications for DI. Social interaction which is the drive of this theory has implications for student–teacher as well as student–student interactions that favor collaborative learning which is pertinent in DI. On the other hand, Gardner’s 1983 theory of multiple intelligence holds that intelligence encompasses the ability to create and solve problems, craft products, and provide services that are valued within the context of diversity (Gardner, 1983). Consistent with this, DI seeks to equip the students with skills for problem-solving and creating products that are desirable in the context of the content being learned.

Accordingly, to accommodate the different ways that students learn, the idea of Tomlinson’s DI has a substantial study support in the theory of education (Fox & Hoffman, 2011; Heacox, 2012). As a student-centered instruction, the goal of DI was for teachers to extend the potential of all learners by identifying students’ needs through insightfully designing classroom educational experiences (Hall, 2002; Santangelo & Tomlinson, 2012). To that end, Tomlinson’s Comprehensive Model of DI (CMDI) was selected as the theoretical construct for this research because it was an all-inclusive model established and frequently cited within professional journals (Santangelo & Tomlinson, 2012). As a conceptual frame also, this paper is based on the contemporary Tomlinson’s (2014) conceptual framework of DI. The framework highlights ways teachers can differentiate content, process, product and learning environment to address students’ interest, readiness, and learning profile (Tomlinson, 2014).

1.3. The current study

The current study sought to investigate the relationship between the teachers’ practice of DI elements and the different student attributes. Earlier studies showed that teachers need to provide appropriate challenges for learners who have learning difficulties and those who are gifted (Ismajli & Imami-Morina, 2018). Also, teachers who differentiate allow pupils to work cooperatively with peers, individualize teaching, use assessment to inform instruction, and give the students multiple options to express what they have learnt (Tomlinson, 2014). Hence, it has been suggested that teachers need more information about the development of rubrics, conduct student-directed assessments, use projects to solve problems in the classroom, manage large class while executing DI and differentiate instructions without watering down the curriculum (Aldossari, 2018; Lunsford, 2017).

Previous research in the field of DI has mainly focused on the classroom level (e.g., Santangelo & Tomlinson, 2012; Smit & Humpert, 2012) and has put forward four components of DI (content, process, product, and learning environment) to describe how teachers match their classroom instruction to students’ individual differences—background knowledge, readiness, interest and learning profile (Roy et al., 2013; Santangelo & Tomlinson, 2012; Tobin & Tippett, 2013; Tomlinson & Imbeau, 2010). The main question here is whether all students feel safe, accepted, and valued while teachers differentiate instruction in terms of content, process, product and learning environment (Tomlinson & Imbeau, 2010). Teachers can cultivate such feelings by ensuring that students interact and discuss in constructive ways, without making a person or certain part of the group feel smaller (Tomlinson, 2001).

Despite this knowledge, researchers on the practice of DI have reported that teachers frequently displayed an unwillingness to employ differentiation in their classroom practices (Goddard et al., 2010; Van Geel et al., 2019). Findings revealed that although there are decades of articles examining DI, the changes in teaching practices remain unclear (Bondi et al., 2019). There are no comprehensive evaluations of DI models (Hall et al., 2003) and there are few large-scale experimental studies focused exclusively on its effects (Reis et al., 2011). A recent study found that teachers across different countries, e.g., Canada (Tobin & Tippett, 2013), Switzerland (Smit & Humpert, 2012), Romania (Nicolae, 2014) and Hong Kong (Wan, 2017), infrequently adapt their instruction to student characteristics. Struggling students may work on too difficult tasks or, conversely, high ability students may practice skills they have already mastered (Tomlinson et al., 2003). As a result, many teachers continue adopting their current teaching style although they realize the related disadvantages (Van Geel et al., 2019). The study of Whipple (2012) also revealed a disconnection between teachers’ understanding of DI and their actual practice, showing a lower rate of DI enactment compared to understanding of DI.

Similarly, in Ethiopia, by recognizing the critical role of DI in addressing the learners’ readiness, interest and learning profile, the Ethiopian Education Development Roadmap (Ministry of Education (MoE), 2018) and the Ministry of Education (MoE; 2020) in its ESDP VI has stipulated its concern of delivering quality education that meets the diverse learning needs of all children, youth and adults through applying differentiated/flexible curriculum and DI. However, teacher-centered classroom approach is still a dominating practice (Joshi & Verspoor, 2013; Tadesse, 2020, 2021; Tesfaye, 2014). Despite the fact that student diversity is increasing in the classrooms from time to time, the practice of DI is very low (Tadesse, 2020, 2021) and many teachers still apply a traditional lecture approach (Joshi & Verspoor, 2013; Ministry of Education (MoE), 2018, 2020; Tadesse, 2021), whereby every child is subject to learn the same material in the same way and the performance of each measured by the same standards (Tadesse, 2020). Hence, addressing the learning needs and interests of diversified students in such a homogenous instructional process through varying the DI elements is a timely concern (Tadesse, 2021). Moreover, there is no study conducted in Ethiopia that shows the extent to which student attributes (background knowledge, interest, readiness and learning profile) are correlated with the major DI elements (content, process, product and learning environment differentiations).

Therefore, the purpose of this study was to examine the significant relationship between student characteristics and the teachers’ use of DI elements in primary and middle schools. Besides, the study aimed at examining the mediating effect of content differentiation, process differentiation, product differentiation and learning environment differentiation in addressing student learning characteristics in the case of primary and middle schools of Enjibara and Chagni town administrations of Awi zone, Ethiopia. Accordingly, the following hypotheses were raised.

1. Variation in students’ attributes (background knowledge, interest, readiness and learning profile) has direct influence on differentiating instruction (content, process, product and learning environment differentiations).

2. Differentiation in content, process and learning environment mediate the relationship between variation in student attributes and product differentiation.

3. Differentiating content, process and learning environment has direct influence on product differentiation.

4. Differentiating instructional process mediates the relationships between content differentiation, learning environment differentiation, and product differentiation.

2. Method

2.1. Participants and procedure

A sample of 364 primary school teachers randomly selected from the two town administrations (Injibara and Chagni) of Awi zone were part of this study. From the sample teachers, 187(51.4%) were males and 177(48.6%) were females, showing almost negligible gender difference among the participants. Sample teachers involved in the current study voluntarily, and the informed consent was received before administering a questionnaire to each participant. They were informed that their data would be kept anonymous and serve only for academic purpose. Regarding the sample teachers’ educational qualification, 241 (66.2%) were Diploma graduates, 112 (30.8%) were first-degree graduates, and 11 (3%) were certificate (TTI) graduates. Furthermore, 151 (41.5%) teachers had between 1 and 10 years of work experience, 149 (41%) teachers had between 11 and 20 years of work experience, and 64 (17.6%) teachers had work experience above 20 years. Distribution of sample teachers by gender, qualification and experience revealed the heterogeneity of the participants’ demographic characteristics.

2.2. Measures

2.2.1. Content differentiation

Content differentiation is one component of DI. To measure the practice of content differentiation, five items were adapted from differentiated instruction survey instrument originally developed by Adlam’s (2007) and Whipple’s (2012) and lately revised and tested by Tadesse (2018b). The practice of content differentiation was measured using four items with Cronbach’s alpha (α) coefficient of .84, suggesting acceptable internal consistency reliability. Sample items include“ … during lesson delivery: I differentiate major concepts of the contents based on students understanding and needs; I articulate to the students what I want them to know, understand and do.” Content differentiation practice scale had 4-point Likert type frequency scores ranging from 1 (Never) to 4 (Always).

2.2.2. Process differentiation

Process differentiation is another component of DI. To measure the practice of process differentiation, 11 items were adapted from DI survey instrument originally developed by Adlam’s (2007) and Whipple’s (2012) and currently revised and tested by Tadesse (2018b). The practice of process differentiation was measured using for four items with Cronbach’s alpha (α) coefficient of .93, suggesting acceptable internal consistency reliability. Sample items include “ … during the lesson delivery: I design activities that require students to do based on their prior knowledge; I provide different level activities for different students to perform.” Process differentiation scale had 4-point Likert type frequency scores ranging from 1 (Never) to 4 (Always).

2.2.3. Learning environment differentiation

Furthermore, learning environment differentiation is also another element of DI. To measure the practice of learning environment differentiation five items were adapted from DI survey instrument originally developed by Adlam’s (2007) and Whipple’s (2012) and revised and tested by Tadesse (2018b). However, during EFA, two items from learning environment differentiation scale (LEn35 and LEn36) were suppressed because of low factor loading estimates below threshold value of 0.40. As a result, the practice of learning environment differentiation was measured using for three items with Cronbach’s alpha (α) coefficient of .80, suggesting acceptable internal consistency reliability (see, Table 1 and 2). Sample items include “I create conducive classroom environment to support a variety of activities; I create conducive psychological environment for diversified learners.” Learning environment differentiation scale had 4-point Likert type frequency scores ranging from 1 (Never) to 4 (Always).

Table 1. Model fit indices of first-order confirmatory factor analysis (CFA)

Criteria	Threshold value	Result	Goodness-of-fit conclusion
Relative chi-square (χ^2/df)	≤5	1.607	Fit
CFI	≥.90	0.958	Fit
TLI	≥.90	0.953	Fit
RMSEA	≤.08	0.041	Fit
SRMR	≤.08	0.039	Fit

Note: χ² = 504.475, df = 314, p-value < .001.

Table 2. Results from confirmatory factor analysis

Latent constructs	No. of items	α	Range of R^2	Range of β	Range of S.E.	Range of C.R.	p-Value
Student attributes	4	.85	.52–.64	.72–.80	.06–.07	13.52–14.47	.000
Content differentiation	5	.84	.43–.60	.65–.77	.07–.08	12.01–13.68	.000
Process differentiation	11	.93	.49–.63	.70–.80	.06-.07	12.80–14.55	.000
Environment differentiation	3	.80	.49–.66	.70–.81	.07–.07	11.98–12.67	.000
Product differentiation	4	.82	.50–.58	.69–.76	.07–.07	11.86–13.19	.000

2.2.4. Product differentiation

Product differentiation is again another element of DI. To measure the practice of product differentiation, six items were adapted from DI survey instrument originally developed by Adlam’s (2007) and Whipple’s (2012) and tested by Tadesse (2018b). During exploratory factor analysis (henceforth, EFA), however, two items from product differentiation scale (Prod33 and Prod34) were dropped because of low factor loading less than the threshold value of 0.40. Results from EFA are presented in the following section with details. As a result, the practice of product differentiation was measured using four items with Cronbach’s alpha (α) coefficient of .82, suggesting acceptable internal consistency reliability. Sample items include “I support students to present their learning products individually and in groups; I give product assignments that differ based on readiness and interest of students.” Product differentiation scale had 4-point Likert type frequency scores ranging from 1 (Never) to 4 (Always).

2.2.5. Student attributes

Students’ attributes such as background knowledge, interest, readiness and learning profile are commonly known variables associated with differentiated instruction elements, viz. product, process, content, and learning environment differentiation. To measure the variation in students’ attributes, four items were adapted from the original measurement scale developed by Whipple’s (2012) and lately revised and validated by Tadesse (2018b). The variation in students’ attributes was measured using four items with Cronbach’s alpha (α) coefficient of .85, suggesting acceptable internal consistency reliability (see Table 2). The sample items include “Variance in individual students” prior knowledge impacts what and how I teach; my understanding of variance in individual students’ interest impacts what and how I teach.’ The instrument had 5-points Likert scale scores ranging from 1 (Strongly Disagree) to 5 (Strongly Agree).

2.3. Factor analyses for instrument validation

2.3.1. Exploratory factor analysis (EFA)

Prior to performing EFA, the suitability of data for factor analysis was assessed. Thus, we assessed the adequacy of the recruited sample and the existence of significant relationships using Kaiser–Meyer–Olkin’s (KMO) test and Bartlett’s test of Sphericity SPSS outputs (Hair et al., 2019), respectively. The KMO test value greater than .5 shows adequacy of the study sample size, and a significant Bartlett’s test (p < .05) indicates that correlation matrix has significant correlations among some variables (Hair et al., 2019), supporting the suitability of data for factor analysis. The Kaiser–Meyer–Olkin value was .913, exceeding the recommended value of .5 and Bartlett’s Test of Sphericity reached statistical significance (Approx. Chi-Square = 2638.937, df = 253, p < .001), supporting the factorability of the correlation matrix. Based on this evidence, the 27 items of the differentiated instruction scale were subjected to exploratory factor analysis using SPSS version 23.

Exploratory factor analysis (EFA) by using a promax oblique rotation was employed to uncover underlying dimensions of differentiated instruction, how the factors intercorrelate, and how the variables load on the factors. As a result, the inspection of the factor correlation matrix revealed a significant positive correlation that ranged from r = .39 to r = .63. EFA of 27 DI measurement items set with promax rotation extracted four factors, which explained 41.03% of the total variance. An inspection of the scree plot also revealed a clear break after the fourth factor. The dimensions of DI were labeled as follows: process differentiation (Factor 1, 11 items, 28.19% of variance explained with 7.08 eigenvalue), content differentiation (Factor 2, 5 items, 5.92% of variance explained with 1.98 eigenvalue), product differentiation (Factor 3, 4 items, 3.91 % of variance explained with 1.45 eigenvalue), and learning environment differentiation (Factor 4, 3 items, 3.02% of variance explained with 1.20 eigenvalue).

The rotated solution revealed the presence of simple structure, with both factors showing a number of strong loadings and all variables loading substantially on only one factor. From 27 items subjected to EFA, 23 items were retained by suppressing items with loading values less than .40. As a result, two items from product differentiation (Prod33 and Prod34) and two items from learning environment differentiation (LEn35 and LEn36) were suppressed because they had factor loading estimates less than threshold value of 0.40. Factor loadings for process differentiation variables ranged from .49 to .75, for content differentiation variables ranged from .46 to .72, for product differentiation variables ranged from .51 to .74, and for environment differentiation variables ranged from .43 to .89. Furthermore, EFA for students’ background attributes revealed that this construct had a single-factor solution with four variables measured variations in students’ background knowledge, students’ interest, students’ readiness, and students’ learning profiles. EFA of four students’ attributes measurement items set with promax rotation extracted one factor, which explained 58.02% of the total variance and with eigenvalue of 2.74. An inspection of the scree plot also revealed a clear break after the first factor. Factor matrix revealed higher factor loadings of indicators that ranged from .72 to .80.

2.3.2. Confirmatory factor analysis (CFA)

The more important aspect of confirmatory factor analysis (CFA) is determination of the extent to which a hypothesized measurement model fits the observed sample data. The results of AMOS for measurement model indices and threshold cut of values for each index are summarized in Table 1. The goodness-of-fit of measurement model and the validity of constructs or latent variables were established through CFA conducted in AMOS version 23. The goodness-of-fit of both measurement model and structural equation model was determined using commonly used and scientifically suggested model fit assessment indices, particularly relative chi-square test (χ²/df), Tucker–Lewis Index (TLI), Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR; Collier, 2020; Hu & Bentler, 1999). Table 1 depicts the threshold values and the calculated values for model fit indices. CFA results revealed a good fit of measurement model, which yielded chi-square value (χ²) = 504.475, df = 314, p < .001, relative chi-square (χ²/df) = 1.607, RMSEA = .041, TLI = 0.953, CFI = 0.958, and SRMR = 0.039.

In addition, RMSEA value of .041 with the 90% confidence interval ranging from .034 to .047 and the p-value for the test of closeness of fit equal to .99 showed a good fitting measurement model. As a result, it can be concluded that the degree of approximation in the population is very small and the measurement model fits the data well. As another evidence of model fit, given the lower ECVI value (1.742) for the measurement model, compared with both the independence (13.617) and saturated models (2.083), we conclude that it represents the best fit to the data. Besides, standardized residual covariances were assessed against a criterion value of 2.58 to test whether the final model was well specified or not, suggesting the local fit of the model. Accordingly, the standardized residual covariances ranged between −2.54 and 2.41 (<2.58), denoting well specified reflective CFA model (Collier, 2020). Table 1 presents AMOS outputs for measurement model fit indices with threshold cut of values.

As results from CFA showed, the unstandardized estimates of all freely estimated parameters are statistically significant at p < .001 (range of Bs = .80–.98) and the standardized factor loadings (β) were ranging from .65 to .81. To assess the validity and reliability of the measurement model using CFA, Collier (2020) suggests reporting the standardized regression coefficient (β) as it allows a comparison of the weights of indicators by converting factor loadings to a range of 0 to 1 scale, and proportion of explained variance (R²). Squared multiple correlations (R²) describes the proportion of explained variance with each indicator that help the researcher understand how much of the variance in the indicator is explained by the unobserved construct (Collier, 2020). Accordingly, the factor loading estimates revealed that the indicators had moderate-to-high correlations with their purported factors (range of R²s = .43–.66), which indicated medium-to-large effect size as suggested by Cohen (1988). In other words, the range of effect size estimates showed that from 43% to 66% of the variance of the five constructs (latent variables) were attributable to their respective indicators (observed variables).

As AMOS result revealed, the measurement model (CFA) had 378 distinct sample moments and 64 distinct parameters to be estimated, which resulted in 314 degrees of freedom (378–64). Since the degree of freedom is greater than zero, the model is an overidentified model. The summary of parameters also showed 96 total parameters in the model, which consisted of 32 fixed parameters and 64 unlabeled or free parameters. The model has a total of 59 variables, which comprised 27 observed variables and 32 unobserved variables (see Figure 1). Figure 1 portrays CFA results with standardized factor loadings.

Figure 1. First-order CFA model with standardized estimates.

Notes: VarAttributes = variation in students’ background attributes; VarBK = variation in background knowledge; VarSI = variation in student interest; VarSR = variation in student readiness; VarLP = variation in student learning profile; C = content differentiation; P = process differentiation; Prod = product differentiation; LEn = learning environment differentiation.

2.3.3. Construct validity and reliability assessment

To determine composite reliability, convergent validity and discriminant validity of five constructs (latent variables), CFA was conducted using AMOS version 23. CFA is a key analytical approach to test construct reliability and validity that provides compelling evidence of the composite reliability, convergent validity and discriminant validity of theoretical constructs used in educational research (Brown, 2015).

2.3.3.1. Composite reliability

Beyond the internal consistency reliability measured by Cronbach’s alpha analysis, composite reliability is another popular technique to assess construct reliability, which is also known as Raykov’s Rho (r) or factor rho coefficient (Collier, 2020; Kline, 2016). Similar to Cronbach’s alpha level for internal consistency reliability, the composite reliability has the same range and cutoff criteria for acceptable level of reliability, i.e., >.70 (Collier, 2020). Based on this criterion value, the composite reliability values ranged between .80 for learning environment differentiation and .93 for the construct of process differentiation (see Table 3).

Table 3. Inter-correlations, composite reliability, and validity testing CFA outputs

Latent variables	CR	AVE	MSV	MaxR(H)	1	2	3	4	5
1. Environment differentiation	.80	.57	.15	.81	.76
2. Product differentiation	.82	.54	.18	.83	.37*	.73
3. Process differentiation	.93	.53	.30	.93	.35*	.42*	.73
4. Students’ attributes	.85	.58	.06	.85	.24*	.22*	.20*	.76
5. Content differentiation	.84	.51	.30	.84	.38*	.35*	.55*	.22*	.71

Notes: CR = composite reliability, AVE = average variance extracted, MSV = Maximum Shared Variance, MaxR(H) = Maximum Construct Reliability, *p ≤ .001.

2.3.3.2. Convergent validity

In Collier’s (2020) view, convergent validity helps determine the construct validity by specifying the degree to which all indicators of a given construct are measuring the same construct they are intended to measure. As a criterion to establish convergent validity, the average variance extracted (AVE) should be above .50 (Collier, 2020; Hair et al., 2019). Based on this criterion, as depicted in Table 3, the values of AVE for all constructs ranged from .51 for the indicators of content differentiation to .58 for the indicators of for the indicators of variation in students’ attributes, suggesting acceptable convergent validity across constructs.

2.3.3.3. Discriminant validity

Discriminant validity determines whether or not a construct is distinct and different from other constructs in the study, and it can be established by using the shared variance method (Collier, 2020). According to Fornell and Larcker (1981), as a decisions rule, the discriminant validity can be established for two scales if the AVEs for both are higher than the squared factor correlation between the scales. In other words, in shared variance method the discriminant validity of each construct can be determined by computing the shared variances between constructs and comparing them to the AVE values for each construct (Collier, 2020). Likewise, the discriminant validity can be established if inter-correlations among a set of constructs are not too high (commonly, <.85; Brown, 2015; Collier, 2020; Kline, 2016). In the current study, all coefficients for inter-correlations between constructs were below 0.85, which ranged from .22 to .55. This evidence showed that all constructs in the current study have measured distinct (see, Table 3). In the same vein, the shared variance between variations in students’ attributes and content differentiation (.22)² = .048 was far lower than the AVE for students’ attributes (.58) or AVE for content differentiation (.51), which suggests an acceptable discriminant validity. Moreover, the shared variance between content differentiation and process differentiation (.55)² = .303 was less than the value of AVE for content differentiation (.51) or AVE for process differentiation (.53), which indicates an acceptable discriminant validity.

3. Results

3.1. SEM Analyses’ results

3.1.1. Assessment of structural model fit

The results of the SEM AMOS analyses are summarized in Table 4. The model fit for the initial structural model (Model 1) of the hypothesized SEM represented somewhat less well-fitting, as indicated by SRMR (.13) value greater than the threshold value of .08, as SRMR value less than .08 indicates a good fit of the model (Collier, 2020). In addition, AMOS output modification indices (M.I. = 70.12, with parameter change = 0.57), suggested modification of structural model by adding a regression path from content differentiation to process differentiation. Likewise, the AMOS output modification indices (M.I. = 23.53, with parameter change = 0.31), also suggested modification of structural model by adding a regression path from learning environment differentiation to process differentiation. As a result, through model modifications, goodness-of-fit for Model 2 produced a very good fit to the data and exhibited substantial improvement over Model 1 as depicted in Table 4. The improvement of Model 2 was evidenced by the changes in chi-square (χ²), df, and other goodness-of-fit indices. By assessing these criteria, the modified structural model (Model 2) signified a well-fitting model that yielded: χ² = 504.475, df = 314, χ²/df = 1.61, TLI = .95, CFI = .96, RMSEA = .04, and SRMR = .04, further suggesting that Model 2 represented an adequate fit to the data and supporting acceptance of the re-specified Model 2

Table 4. Comparison of model-fit-indices of initial and re-specified structural models

Model	χ^2	df	χ^2/df	TLI	CFI	RMSEA	SRMR
Model 1	630.943	317	1.99	.92	.93	.05	.13
Model 2	504.475	314	1.61	.95	.96	.04	.04
Change (Δ)	126.468	3	0.38	.03	.03	.01	.09

To assess the extent to which each newly specified structural model (Model 2) exhibits an improvement in fit over its predecessor, we examined the difference in chi-square (∆χ²) between the two models in order to determine if the difference in fit between the two models is statistically significant. This differential is itself chi-square distributed, with degrees of freedom equal to the difference in degrees of freedom (∆df) and can, thus, be tested statistically; a large ∆χ² value indicates a substantial improvement in model fit. Changes in chi-square value over its predecessors (Model 1) were statistically significant at the significance level of .01 (i.e., for Model 2 over Model 1, ∆χ² = 126.468, df = 3, p < .001). Likewise, the improvements in the values of relative chi-square (χ²/df), TLI, CFI, RMSEA, and SRMR value by .38, .03, .03, .01, and .09, respectively, showed a re-specified structural model (Model 2) as a better-fitting model over the initial model (Model 1). As other inspections of model fit, RMSEA for Model 2 shows .04, with the 90% confidence interval ranging from .034 to .047 and the p-value for the test of closeness of fit equal to .99. Thus, it can be concluded that the degree of approximation in the population is very small and Model 2 fits the data well. As another evidence of model fit, given the lower ECVI value (1.74) for the Model 2, compared with both the independence (13.62) and saturated models (2.08), we conclude that it represents the best fit to the data. Moreover, the smallest ECVI value (1.74) of Model 2 as compared to its predecessor’s (Model 1ʹs) ECVI value (2.07) showed greater potential for replication of the re-specified structural model (Model 2). Beyond this comparison, the confidence interval for ECVI of Model 2 ranged from 1.58 to 1.92. Taken together, these results suggest that Model 2 is well fitting the data and represents a reasonably close approximation to the population. The final solution representing the data is presented schematically in Figure 1.

3.1.2. SEM Analyses of direct effects

In this study, the researchers hypothesized direct influence of variation in students’ attributes (students’ background knowledge, interest, readiness and learning profile) on four dimensions of DI, viz. content differentiation, process differentiation, learning environment differentiation, and product differentiation. Results from SEM analyses revealed that a variation in students’ attributes has a positive direct influence on differentiating contents (β = .25, p < .001) and learning environment (β = .27, p < .001). In contrast, SEM analyses results delved statistically non-significant direct influence of variation in students’ attributes on differentiating process (β = .06, p = .282) and product (β = .09, p = .165).

As SEM analysis result revealed, differentiating learning contents has a strongly positive direct influence on process differentiation (β = .48, p < .001); however, it has no statistically significant direct influence on product differentiation (β = .10, p = .191). On the other hand, SEM analyses results delved that differentiating learning environment has significantly positive direct influence on instructional process differentiation (β = .16, p = .013) and on product differentiation (β = .22, p = .003). Furthermore, results revealed that differentiating instructional process has a significantly positive direct influence on instructional product differentiation (β = .27, p = .001).

As squared multiple correlations (R²) disclosed, variation in students’ attributes, content differentiation, and learning environment differentiation together explained 33% of variance on instructional process differentiation. Likewise, variation in students’ attributes, content differentiation, learning environment differentiation, and process differentiation together explained 25% of variance on product differentiation. Table 5 presents the SEM analysis results.

Table 5. Structural model analysis results for direct effects

Hypothesized relationships	β	p-value	95% CI		Hypothesis supported
			Lower	Upper
Students’ attributes →environment differentiation	.27	.000	.14	.40	Supported
Students attributes→ content differentiation	.25	.000	.13	.37	Supported
Students attributes →process differentiation	.06	.282	−.05	.16	Not supported
Students attributes →product differentiation	.09	.165	−.04	.21	Not supported
Content differentiation →process differentiation	.48	.000	.36	.58	Supported
Content differentiation →product differentiation	.10	.191	−.06	.26	Not supported
Environment differentiation →process differentiation	.16	.013	.04	.27	Supported
Environment differentiation →product differentiation	.22	.003	.08	.34	Supported
Process differentiation →product differentiation	.27	.001	.12	.41	Supported

Like that of CFA, AMOS result revealed that the structural model (SEM) has 378 distinct sample moments and 64 distinct parameters to be estimated, which resulted in 314 degrees of freedom (378–64), which indicated an over-identified structural model. The summary of parameters also showed 98 total parameters in the model, which consisted of 34 fixed parameters and 64 unlabeled or free parameters. Moreover, the structural model has a total of 61 variables, which comprised 27 observed variables and 34 unobserved variables as well as 32 exogenous variables and 29 endogenous variables (see Figure 2) se

Figure 2. Modified structural equation model with standardized estimates.

Notes: Content= Content Differentiation, VarAttributes= Variation in students’ background attributes, Process= Process differentiation, Learning Environment = Learning environment differentiation, Product = Product differentiation.

3.2. Mediation analysis with bootstrapping

Mediation analysis was carried out to determine the mediating role of differentiating learning environment, content and process on the relationships between variations in students’ attributes and product differentiation. As a result, differentiating learning environment has fully mediated the effect of variation in students’ attributes on product differentiation (β = .06, p = .001). Similarly, differentiating instructional process has fully mediated the effect of variation in students’ attributes on product differentiation (β = .06, p = .001). However, differentiating contents have no statistically significant mediating role on the relationships between variation in students’ attributes and instructional product differentiation (β = .03, p = .06; see Table 6).

Table 6. S This table shuld go under 3.2 i.e, below mediation analysis with bootstrapping immidately above the Discussion part

Hypothesized indirect relationships	β	p-Value	Bootstrapping		Hypothesis supported
			Bias-corrected percentile 95% CI
			Lower	Upper
Students attributes environment →differentiation product →differentiation	.06	.001	.02	.12	Supported
Students attributes content →differentiation product →differentiation	.03	.06	−.001	.07	Not supported
Students attributes process →differentiation product →differentiation	.06	.001	.02	.12	Supported
Content differentiation process →differentiation product →differentiation	.13	.000	.06	.22	Supported
Environment differentiation →process differentiation →product differentiation	.04	.006	.01	.09	Supported

Furthermore, mediation analysis was also conducted with bootstrapping to determine the mediating role of process differentiation on the relationships between content differentiation and product differentiation as well as between learning environment differentiation and product differentiation. In this regard, mediation analysis result showed that differentiating instructional process fully mediated the effect of content differentiation on product differentiation (β = .13, p < .001) and partially mediated the effect of environment differentiation on product differentiation (β = .04, p = .006).

4. Discussion

In the current study, it was hypothesized that the variation in students’ background attributes (students’ background knowledge, interest, readiness and learning profile) would have direct influence on four dimensions of differentiated instruction, viz. content differentiation, process differentiation, learning environment differentiation, and product differentiation. As standardized regression weights (βs) revealed variation in students’ attributes has a relatively stronger direct influence on learning environment differentiation (.27) and content differentiation (.25), as compared to its effect on process differentiation (.06) and product differentiation (.09). Based on standardized regression weights (βs), differentiating learning contents has a relatively stronger direct influence on instructional process differentiation (.48), as compared to the influences of learning environment differentiation (.16) and variation in students’ attributes (.06).

Furthermore, as standardized regression weights (βs) indicated, process differentiation has a relatively stronger direct influence on product differentiation (.27) followed by learning environment differentiation (.22), as compared to influences of content differentiation (.10) and students’ attributes (.09). As results from mediation analyses showed, variation in students’ attributes has completely indirect effect on product differentiation through differentiating learning environment and instructional process. In other words, learning environment differentiation and process differentiation have fully mediated the influence of variation in students’ attributes on product differentiation. Moreover, instructional process differentiation has fully mediated the influence of content differentiation and partially mediated the influence of learning environment differentiation on product differentiation. In other words, content differentiation has completely indirect influence on product differentiation through differentiating instructional process. Likewise, differentiating learning environment exhibits both direct influence and indirect influence via process differentiation on instructional product differentiation.

This study affirmed that variation in students’ attributes has stronger direct influence on content differentiation and learning environment differentiation as compared to its moderate effect on process differentiation and product differentiation. Similarly, differentiating learning contents has a relatively stronger direct influence on process differentiation. Process differentiation and learning environment differentiation in turn have respectively stronger direct influence on product differentiation and learning environment differentiation. This showed that, though the degree of influence varies, the four DI elements have influences on student attributes. Consistent with this finding, the previous study findings of different scholars (e.g., Chamberlin & Powers, 2010; Hall, 2002; Santangelo & Tomlinson, 2012; Sousa & Tomlinson, 2011; Tobin & Tippett, 2013; Tomlinson & Imbeau, 2010; Tomlinson et al., 2015) also affirmed that there is a direct influence between student attributes and major DI elements (content, process, product and learning environment differentiations).

In terms of the direct or indirect influence of the DI elements on student attributes, as this finding showed, the influence of student attributes on content differentiation was direct. Similarly, differentiating learning contents has a strongly positive direct influence on process differentiation, but the influence of content differentiation on product differentiation was indirect (i.e, via differentiating instructional process). Unlike studies that showed the influence of content differentiation on product differentiation is meager, various research findings substantiated consistent results with this study. For instance, various scholars’ findings (e.g., Chamberlin & Powers, 2010; Heacox, 2002; Rodriguez, 2012; Tomlinson & McTighe, 2006; Tomlinson, 2001) delved that there is a positive and direct link between student attributes, content differentiation and process differentiation. Moreover, as this study revealed, even though the variation in students’ attributes has non-significant direct influence on process and product differentiations, conversely, differentiating the process has fully mediated the effect of variation in students’ attributes on product differentiation. This finding is somehow consistent with the study findings of (Anderson, 2007; Bender, 2012; Benjamin, 2006; Cox, 2008; Thakur, 2014; Wan, 2017).

On the other hand, the result of this study disclosed that differentiating the learning environment exhibits both direct influence and indirect influence (via process differentiation) on instructional product differentiation. Learning environment differentiation has also fully mediated the effect of variation in students’ attributes on product differentiation. Congruent with this finding, other study findings (e.g., Chamberlin & Powers, 2010; Collie et al., 2012; Kanevsky, 2011; Nicolae, 2014; Tomlinson, 2014; Santangelo & Tomlinson, 2012; C.,& Tomlinson & Eidson, 2003) also inveterate the direct and mediating effect of learning environment differentiation on addressing the different student attributes (student background knowledge, interest, readiness and learning profile).

Nonetheless, in this study, as results from mediation analyses showed, variation in students’ attributes has completely indirect effect on product differentiation which is not consistent with the findings of fome studies (Adami, 2004; Anderson, 2007; Heacox, 2002; Tomlinson, 2014; Tomlinson & Strickland, 2005). However, learning environment differentiation and process differentiation have fully mediated the influence of variation in students’ attributes on product differentiation.

5. Conclusions

By applying more advanced approach of structural equation modeling, this study provided strong evidence on the direct and indirect influence of variation in students’ attributes (background knowledge, interest, readiness and learning profile) on differentiating instruction (content, process, product and learning environment differentiations). The findings designate that variation in students’ attributes has a relatively stronger direct influence on learning environment differentiation and content differentiation as compared to its effect on process differentiation and product differentiation. The verdicts also indicate that differentiating learning contents has a relatively stronger direct influence on instructional process differentiation as compared to the influences of learning environment differentiation and variation in students’ attributes. Also, process differentiation has a relatively stronger direct influence on product differentiation followed by learning environment differentiation compared to influences of content differentiation and students’ attributes.

On the other hand, process differentiation and learning environment differentiation have fully mediated the influence of variation in students’ attributes on product differentiation. Moreover, instructional process differentiation has fully mediated the influence of content differentiation and partially mediated the influence of learning environment differentiation on product differentiation. In other words, content differentiation has completely indirect influence on product differentiation via differentiating instructional process. Likewise, differentiating learning environment displays both direct influence and indirect influence via process differentiation on instructional product differentiation. This delved that in order to assist students to tenaciously demonstrate what they have learned (product differentiation) based on their attributes, first, varying the method of teaching (process differentiation) and the physical and psychological environment (learning environment differentiation) is decisive.

This study further affirmed that variation in students’ attributes have stronger direct influence on content differentiation and learning environment differentiation as compared to its moderate effect on process differentiation and product differentiation. Similarly, differentiating learning contents has a relatively stronger direct influence on process differentiation. Process differentiation in turn has stronger direct influence on product differentiation and learning environment differentiation. This showed that, in order to address the interests, readiness and learning profiles of students, varying the contents and learning environments need to give priority than varying the process and the product.

6. Limitations and implications

6.1. Limitations

As squared multiple correlations (R²) showed, variation in students’ attributes, content differentiation, and learning environment differentiation together explained 33% of variance on instructional process differentiation. Likewise, variation in students’ attributes, content differentiation, learning environment differentiation and process differentiation together explained 25% of variance on product differentiation. Besides, the scope of our study is only delimited to two town administration primary and middle schools that might restrict the generalizability of the findings to other woredas and school contexts. Therefore, a more wide-ranging study should be conducted by other researchers by involving other additional variables and covering diverse private primary and middle school contexts at regional or national levels.

6.2. Implications

In a multi-cultural, multilingual and multi-ethnic country like Ethiopia, the presence of diverse learners with varying interests, abilities, intelligence and learning profiles (Tadesse, 2018a, Tadesse, 2021) has portrayed the need for teachers to rethink on the practice of relevant and research-based instructional strategies that will enable them to meet these diversities (Heacox, 2012; Suprayogi et al., 2017; Tadesse, 2020, 2021). This study places an increased responsibility on the teacher who has to diversify instructional content, methods, materials, and assessment strategies through the use of differentiated instruction (DI).

In public primary and middle school classrooms, student academic abilities can span across different grade levels (Hertberg-Davis & Brighton, 2006), with different background knowledge, interest, readiness, and learning profile (Tadesse, 2020, 2021). However, many teachers use a one-size-fits-all instructional approach primarily using whole-class instruction (Bondie et al., 2020; Tadesse, 2015, Tadesse, 2021). Yet, the use of one-size-fits-all instruction no longer meets the needs of the majority of learners (McBride, 2004; Tomlinson, 2001) and the use of single-paced lessons delivered through a single instructional approach disregards the different learning interests and learning profiles of students in all classrooms (Subban, 2006; Tadesse, 2021). Therefore, in recent schools, addressing the diversified background knowledge, interest, readiness and learning profile of students is becoming the timely concern for schools in many countries (Guay et al., 2017; Tadesse, 2021). This has made it necessary for teachers to apply differentiated teaching and learning through employing content, process, product and learning environment differentiation strategies (Bender, 2012; Siam & Al-Natour, 2016). Consequently, altering schooling and attitudes of teachers into a deep cultural change to address individual learners’ needs through quality teaching and the need to provide learning environments that respond to individual differences is being a timely concern (Guay et al., 2017; Roy et al., 2013; Tadesse, 2021).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Tadesse Melesse

Tadesse Melesse received his MA and PhD in Curriculum & Instruction from Addis Ababa and Bahir Dar Universities, respectively. He worked as an instructor and leader at different positions in different universities and colleges. He is now an Associate Professor in Curriculum and Instruction. He published many articles related differentiated instruction, teacher education, education quality, curriculum, multiculturalism and teacher professional development and he also wants to proceed doing research on these major areas.

Sintayehu Belay received both his MA and PhD in Curriculum & Instruction from Bahir Dar University. He published several articles related to teacher education and learning. He has been involved in teaching different teacher education courses. His major areas of research include teacher professionalism, professional capital development and life-long learning. He is now an Assistant Professor at Enjibara University.