The article accounts for achievement differences of eighth graders in three African countries, Egypt, Morocco, and South Africa. Using data from the Trends in International Mathematics and Science Study (TIMSS, 2015), I found that African students struggle to attain the lowest international benchmark across the three countries. Consequently, efforts were made to explain this phenomenon primarily through the motivational factors of self-concept, interest, and usefulness of mathematics. Findings from single-level and multi-level analyses extended common findings especially the synergy between self-concept and achievement and the eroding gender gap. Interesting findings emanated from the multi-level analyses, especially the inverse relationship between achievement and interest of mathematics at the student and school levels respectively. Amidst the poor achievement of students on the continent, the article extends previous findings on the need for African countries to be more attentive to educating its young ones if it is to develop their untapped potential.
Research Article
A motivational account of achievement differences in mathematics using TIMSS data: an African focus.
https://doi.org/10.21203/rs.3.rs-4835055/v2
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Interest
Mathematics Achievement
Motivation
Self-concept
Usefulness
The success of students as operationalized by performance either on teacher-made tests or achievement in high stakes assessments has elicited a rave of conversations over the latent and manifest factors that account for the differences between them (Awofala et al., 2024). Nowhere are these accounts of achievement differences as important as Africa where students have consistently demonstrated lower than expected results in comparative studies. For example, in a ranking of 41 participating countries in TIMSS 2003, Wilkins (2004) found student and country-level achievement gaps of 145 and 144 points between overall scores and those of African eighth graders obtained from South Africa. Occupying the last position, it fell a whopping 241 points below students in Korea (1st). In an earlier cycle, achievement gaps were also striking with South Africa giving up the last position for Morocco, pitching them in the 37th and 38th place respectively (Shen, 2002). A similar pattern is observed in the most recent TIMSS data, with Egypt (53rd), South Africa (57th), and Morrocco (58th) trailing Singapore (1st) by 203, 227, and 228 points.
Lodged within this is an understanding that being agentic individuals as well as members of classrooms, schools, and citizens of distinct countries, student achievement in mathematics is contingent upon influences located within as well as without. Owing to this, researchers have put this understanding to use, informing a multitude of variables that have been enlisted to explain the criterion and normative categorizations of students by achievement results. To this end, salient themes have emanated and put into factors that are either domiciled within the student (e.g., Kirkham & Chapman, 2022), teacher (e.g., Bofah & Hannula, 2015), school (e.g., Shin et al., 2009), or nature of instructional resource/intervention (Olaguro et al., 2019). Especially with reports on international assessments, these accounts have found convincing reasons to believe in the potential of students’ achievement to be influenced both by the structures and cultures of the immediate and wider community (e.g., Stankov, 2010), acting, indicating, and interacting reflexively with one another.
Such factors within the students have been stated to include gender (Kirkham & Chapman, 2022; Mejía-Rodríguez et al., 2021), age (Wilkins, 2004), socioeconomic status (Ersan & Rodriguez, 2020), study expectations (Winberg & Palm, 2021), achievement history (Ma, 1996) and a commitment to further studies which was particularly found to have the most influence on achievement in Ghana, Botswana, South Africa, Egypt, and Morocco (Bofah & Hannula, 2015). Researchers have also relied on findings from school characteristics to explain the rationale for differences in student achievement. In one of those studies, Lee and Chen (2019) found bullying and sense of belonging as holding varying relationships with achievement in Egypt, Morocco, and South Africa. Other factors outside of the students’ control include the school’s socio-economic status, readiness, and quality of instruction (Ersan & Rodriguez, 2020), school location (Webster & Fisher, 2000), curricula coherence (Linn et al., 2000), teachers’ responsiveness (Bofah & Hannula, 2015) and expressing belief in student’s ability (Winberg & Palm, 2021). This line of research has also reinforced the place of the home environment in the achievement profiles of students, touching on learning resources (Winberg & Palm, 2021), parents’ education and involvement (Bofah & Hannula, 2015), attitudes and expectations (Mejía-Rodríguez et al., 2021).
While not discounting the value in identifying and quantifying the basis for achievement differences, many of these variables are either not within the students’ spheres of influence, or the reach of the individuals (e.g., teacher) and institutions (e.g., school) with direct touch on both short- and long-term students’ success. Against the backdrop that the affect drives the intellect (Schoenfeld, 1983), certain noncognitive variables have become prominent in this regard. Consequently, some researchers have sought to explain achievement differences via state-like affective constructs (Middleton et al., 2017) whose malleability offers more pedagogical implications for individuals as well as groups that work closely and make decisions that directly impact students’ outcomes. Prominent among these variables have been attitudes (Kadijevich, 2008; Webster & Fisher, 2000), anxiety (Sengul, 2015; Winberg & Palm, 2021), interest (Lee & Chen, 2019), self-concept (Wilkins, 2004), and usefulness of mathematics (Winberg & Palm, 2021).
Although the studies have sought various means of explaining achievement disparities, they have mostly been restricted to western countries or taken a holistic look at the data. The few ones that have focused solely on Africa have not gone beyond establishing correlational relationships between the motivational variables and achievement, leaving out other key findings such as the slopes that convey directions like correlations does, as well as provide their relative contributions within control conditions. For example, in Shen (2002), the negative association between the duo of interest and self-concept and achievement were based on country-level aggregated analyses of the almost 40 participating countries. Similarly, Bofah and Hannula’s (2015) focus was on the psychometric features of the motivational variables within the African population viz-z-viz the direction and strengths of relationships among, and with achievement. With many of these studies returning significant relationships, it becomes a matter of interest to want to know the precise magnitude of the self-concept, usefulness, and interest parameters relative to achievement at different units of analyses.
Motivation and Students’ Achievement
The prominence of research on students’ mathematical achievement within the motivational lens owes to the latter’s conception as a measure of the degree an individual intends to engage in quantitative situations (Jones, 2018). Following the multitude of factors underlying achievement both within and outside of an individual (Siegler et al., 2012), accounting for students’ achievement within the motivational framework maps into a parallel understanding of motivation as driven by forces within and without (Ryan & Deci, 2020), influencing cognitive outcomes through the intentionality that underpins students’ choice, latency, and persistence in mathematics (Graham, 2020). To this end, a near-consensus exists in the literature that motivation plays crucial roles in students’ achievement (Middleton & Spanias, 1999). This has informed a plethora of studies that have found justifications for explaining achievement differences based on variations in students’ levels of motivation (Wilkins, 2004; Winberg & Palm, 2021).
In implementing this, researchers have masked motivation within finer-grained constructs that capture the foundational principle determining an intent to engage with mathematics, returning findings that have placed such motivational proxies like engagement (Awofala et al., 2024), enjoyment (Živković et al., 2023), self-efficacy (Schöber et al., 2018), and the self-determination taxonomies of amotivation, extrinsic, and intrinsic (Taylor et al., 2014) at influential roles for cognitive outcomes. For example, Ozen’s (2017) meta-analysis study of 205 published works on the motivation-achievement relation over a 6-year period found low to medium effect of motivation on students’ achievement across individual and collectivist societies. Suggestive of the affinity between them, motivation played a greater role in students’ achievement in mathematics than in reading, science, and the aggregate academic measure. In another study, Schöber et al. (2018) affirmed the findings of Ozen in all but the strength of association relative to English/language, informing their conclusion that a stronger motivation-achievement relationship in mathematics owes to perceived difficulty of the subject. More recently, Živković et al. (2023) parsed motivation into enjoyment and self-efficacy returning significant positive associations with achievement.
The overwhelming evidence for the role of motivation in accounting for achievement differences in mathematics owes to the proclivity of motivated students to engage in effortful situations requiring significant intellectual capital (Froiland & Worrell, 2016) and perform personalized, self-assessments in relation to set goals (Middleton & Spanias, 1999) that underscore making informed attributions on achievement outcomes (Graham, 2020).
Achievement within the Motivation Triad
Although motivational variables are not solely responsible for students’ achievement, they are arguably the most influential. Informed by the need to make lasting improvements in students’ achievement, these variables, more than any, have been reckoned to lend themselves to influential tendencies. In pursuit of this, Ersan and Rodriguez included malleable factors (e.g., interest) into their model even as they found that “SES at both student and school levels is a dominant factor related to mathematics achievement and a much stronger predictor at the school level” (2020, p. 1). Relatedly, Winberg and Palm’s (2021) study of 300 variables that were hypothesized to account for achievement differences magnified the fundamental roles of students’ self-concept, interest, and usefulness. Perhaps a consequence of their multicollinear nature, they found that these variables better function as a collective rather than isolated predictors of achievement. In particular, the affinity between interest and usefulness owes to the commonality that exists between them as value-laden constructs, differing but marginally (Eccles & Wigfield, 2020).
The theoretical basis for self-concept in the explication of achievement differences owes to its potential to foster “engagement, goal-setting, task choice, persistence and effort, intrinsic motivation, strategy use, performance and achievement, and even career selection” (Bong & Skaalvik, 2002, p. 7), a reality that has found strong footing in empirical studies both in isolation and within a set of competing influences across the motivational, social, and economic spectra. In his study of attitudes as a composite of self-concept, interest, and usefulness of mathematics, Kadijevich (2008) found that self-concept holds a positive relationship with achievement in all the countries at a range of magnitude between 25% in Belgium to 61% in Korea. Results from the African representation was captured at 33% and 44% for Morocco and Tunisia respectively.
While this pattern is retained in most studies (e.g., Lee & Chen, 2019; Wilkins, 2004), within-country analyses offer valuable insights into the nature of this relationship. A case in point is Wilkins (2004) and Lee and Chen (2019) whose analyses confirmed between-country variations in self-concept but found parallels in the strengths of their associations by achievement scores. Like them, Bofah and Hannula (2015), restricting their analyses to African countries also communicated similar findings. An affirmation of the big-fish-little-pond effect (Marsh et al., 1987), both studies found the strength of association between self-concept and achievement as a function of relative position. Surprisingly, this not only occurred at the global level where vivid achievement differences existed, but within low achieving countries. As recorded, global high achievers like Asian countries (e.g., Korea; r = .46) and least achievers (e.g., South Africa; r = .00) had strong and weak associations between self-concept and achievement respectively. Within Africa, the top achieving nation, Tunisia and the least, South Africa also had the strongest and weakest self-concept-achievement relationship.
Although interest does not contribute as much as self-concept in explaining achievement differences among learners at different units of analyses, it nevertheless has proven to have a formidable influence especially given how inextricable it is with self-concept. Advancing this point, Bong and Skaalvik wrote that “there exist different views among researchers regarding whether academic self-concept also includes emotional reactions to the tasks such as interest, enjoyment, and satisfaction. Some regard these as part of self-concept, whereas others consider them a distinct construct” (2002, p. 7). In what could be a demonstration of the former, a host of researchers have found affinity between findings involving both variables.
For example, amidst country-level variations between self-concept, interest, usefulness, teacher responsiveness, and parental involvement, Bofah and Hannula (2015) found the strongest correlation between the first pair across five African nations although achievement correlated with interest less than it did with self-concept and usefulness. Like self-concept, interest of mathematics (1.5) was the only predictor of achievement above the mean (1.1), with students’ interest of biology, physics, and chemistry predicting their achievement by 1.0, 0.9, and 0.9 points respectively (Winberg & Palm, 2021). Offering more specificity in the relationship, Ersan and Rodriguez (2020) found that students’ interest of mathematics positively influenced their achievement by at least 13 points. With engagement playing a mediating role, such predictive tendency of the positive kind was also recorded by Froiland and Worrell (2016) in their study of African American and Latino high school students.
But students that like mathematics have also been found to perform below their counterparts that do not. As reported by Kadijevich (2008), such relationship was found in 30 out of 33 countries enrolled in TIMSS (2003), with many of those having positive associations occupying magnitudes close to zero (e.g., Macedonia, 0.05; Chile, 0.10). The dislike of mathematics by African students may also be a pointer to their low achievement. As Bofah and Hannula (2015) indicated, not only did all five African countries performed below the international benchmarks, but they were also unanimous in their dislike of mathematics and their view of it as having little use.
Usefulness pertains to the relevance of mathematics. Although this understanding is obvious given the prioritization of mathematics within school subjects and across professional training programs, it should not be surprising that such perception may not be so obvious to young learners who are for the most part unsure of how well mathematics “fits into an individual’s present or future plans” (Eccles & Wigfield, 2020, p. 5). Unsurprisingly, the utility value of mathematics was mostly predicted by the extent learning is related to students’ lives (Winberg & Palm, 2021). Kadijevich (2008) followed this in relation to achievement, returning with positive associations in 12% of participating countries, implying that achievement differences alternate between a lack or negative influence in majority of countries. Although usefulness appears to hold zero relationship with achievement in many global studies, such trend is largely reversed within the African continent especially in non-Arab countries where achievement correlated more strongly with students’ perception of mathematics as a useful endeavor than self-concept (Bofah & Hannula, 2015). The basis for students’ perception of self-concept, interest, and usefulness sits at the intersection of the demonstrated potential of intrinsic and extrinsic motivation to influence cognitive outcomes (Ryan & Deci, 2020), offering justifications for making causal inferences across academic and non-academic fields of study.
The Current Study
The purpose of this study is to investigate the achievement of African eighth grade students as a unit relative to the influences of motivational and control factors. These motivational influences include their interest, self-concept, and the extent they find mathematics useful. Given the evidence from literature that motivational factors drive achievement, the study hypothesizes that all three variables would be positively associated with achievement. A similar expectation will be made for the relationship between SES and achievement. I also hypothesize that gender differences will exist by region in favor of the males in North Africa and females in South Africa. In brief, the study hopes to find answers to these research questions:
- What accounts for the variance that exists in achievement?
- What is the relationship between achievement and interest, self-concept, and usefulness of mathematics at the (i) student (ii) school levels?
- Does (i) gender (ii) School SES and (iii) country effect exist across the motivational variables and achievement?
Data
The data from this study were drawn from the Trends in International Mathematics and Science Study (TIMSS, 2019). Although several countries participated in the study across fourth and eighth grades, this research is focused on eighth grade students in the three participating countries in Africa: Egypt, Morrocco, and South Africa. A total of 36, 441 students nested in 945 schools participated in the study. Among them were 52.6% females and 47.4% males. South Africa had the most representation with 20, 786 students nested within 520 schools followed by Morocco with 8, 456 students in 251; and Egypt who had 7, 199 students in 174 schools. Although several data were obtained from the participants, this study is restricted to three motivational variables (self-concept, interest, usefulness), gender, socioeconomic status, and achievement.
Measures
Level-1
Self-concept: the average of nine items made up this construct (e.g., I usually do well in mathematics).
Usefulness: the average of nine items made up the usefulness construct (e.g., I think learning mathematics will help me in my daily life).
Interest: the average of nine items made up the interest construct (e.g., I enjoy learning mathematics). Responses from all three motivational items were measured via a 4-point Likert scale on this range: 4 (agree a lot), 3 (agree a little), 2 (disagree a little), to 1(disagree a lot). Negative items were also re-coded so that higher position on the scale reflected positive level of agreement.
Gender: dummy variables 0 and 1 represent male and female respectively.
Achievement: achievement was based on the average of five separate computations per plausible value as recommended by Fishbein et al. (2021). The items whose aggregate scores comprised the achievement measure cover four content areas (number, algebra, geometry, and data/probability) and three cognitive domains (knowing, applying, and reasoning).
Level-2
Mean Interest: created by averaging the interest within each school.
Mean Self-concept: created by averaging the self-concept within each school.
Mean Usefulness: created by averaging the usefulness within each school.
School SES: this measure was based upon the three-point school composition by socio-economic background scale ranging from more affluent (1) to more disadvantaged (3). The scale was reverse coded so that higher values reflected more economic advantage.
Prop_Female: dummy of 1 represented proportion of females in the school or country.
Country: three dummy variables (D_Egypt, D_SA, and D_MAR) represented the individual countries.
Mean Achievement: obtained by averaging students’ achievement across separate estimations of the plausible values in each school.
Analytic Plan
The qualitative differences in the formulated research questions necessitate different analytic pathways. Three models were created to cater for each research question. The first analytic plan is the Unconditional Model (Model 1) to explain variability in the outcome variable (achievement). For this reason, no predictor was included. In addition, three parameters were of relevance in the result of this model: γ00 which is overall true mean mathematics achievement and the two variance components (σ2: individual deviation from school mean/unique effect of student i in school j; τ00: unique effect of school j). The proportion, τ00/ τ00+ σ2 gave an estimate of the intraclass correlation (correlation of student scores in the same school/percentage of variance in mathematics achievement that lies between schools).
Level-1 Model
ACHIEVEMij = β0j + rij
Level-2 Model
β0j = γ00 + u0j
Mixed Model
ACHIEVEMij = γ00 + u0j+ rij
With the Compositional/contextual effects model (Model 2), the three predictor variables and their means were composed at the first and second levels. Through this model, the predictors-outcome relationships were determined. The relevant parameters are: β1j, change in student achievement by a unit change in interest; β2j: change in student achievement by a unit change in self-concept; and β3j: change in student achievement by a unit change in usefulness. The model also quantifies the true student and school-level relationships between the predictor and outcome variables. The six parameters in this regard include γ10 and γ01, between achievement and interest; γ20 and γ02, between achievement and self-concept; and γ30 and γ03, between achievement and usefulness—at the student and school levels respectively. The difference in each pair was used to determine the compositional or contextual effect estimates. Specifically, interest (γ01 - γ10), self-concept (γ02 – γ20), and usefulness (γ03 – γ30). Finally, the level-1 and level-2 variance parameters were used to quantify the amount of variation due to the predictors at each level.
Level-1 Model
ACHIEVEMij = β0j + β1j*(INTERESTij) + β2j*(SELF_CONij) + β3j*(USEFULNEij) + rij
Level-2 Model
β0j = γ00 + γ01*(INTERESTj) + γ02*(SELF_CONj) + γ03*(USEFULNEj) + u0j
β1j = γ10
β2j = γ20
β3j = γ30
Model 3 is the Means and slopes as outcome model aimed at ascertaining the effects of gender, school SES, and country on the motivational and achievement variables. The parameters relevant to answer the questions are γ02, country effect; γ04, gender effect; and γ05, school SES effect—on achievement. Unique effects of these control variables on the predictors were also included. They are γ11 (Egypt), γ12 (South Africa), and γ13 (Morocco)—country effect; γ14, gender effect; and γ15, school SES effect on interest. For self-concept, they include γ21 (Egypt), γ22 (South Africa), and γ23 (Morocco)—country effect; γ24, gender effect; and γ25, school SES effect. Finally, γ31 (Egypt), γ32 (South Africa), and γ33 (Morocco)—represent country, gender (γ34), and school SES (γ35) effect on usefulness respectively. The variance components also came handy in determining the amount of achievement variations due to the predictors at the student (R2L-1) and school (R2L-2) levels.
Level-1 Model
ACHij = β0j + β1j*(INTERESTij) + β2j*(SELF_CONij) + β3j*(USEFULNEij) + rij
Level-2 Model
β0j = γ00 + γ01*(CONCEPTj) + γ02*(D_COUNTRYj) + γ03*(INTERESTj) + γ04*(PROP_FEMj)
+ γ05*(SES_SCHOj) + γ06*(USEFULNEj) + u0j
β1j = γ10 + γ11*(CONCEPTj) + γ12*(D_COUNTRYj) + γ13*(INTERESTj) + γ14*(PROP_FEMj)
+ γ15*(SES_SCHOj) + γ16*(USEFULNEj) + u1j
β2j = γ20 + γ21*(CONCEPTj) + γ22*(D_COUNTRYj) + γ23*(INTERESTj) + γ24*(PROP_FEMj)
+ γ25*(SES_SCHOj) + γ26*(USEFULNEj) + u2j
β3j = γ30 + γ31*(CONCEPTj) + γ32*(D_COUNTRYj) + γ33*(INTERESTj) + γ34*(PROP_FEMj)
+ γ35*(SES_SCHOj) + γ36*(USEFULNEj) + u3j
Single-level Analyses
The single level analyses feature both descriptive and inferential statistics with graphical accompaniments. Given that this study was inspired by the achievement differences that exist among students of different countries, the first table presents the percentage of students in Morocco, South Africa, and Egypt that met the four benchmarking cutoffs. As is shown in Table 2, across all countries, less than 1% of students reached the advanced level. Except for Egypt, more than half of them failed to meet the lowest cutoff point. Aggregating the results over the three countries indicate that the continent of Africa struggles to attain even the least benchmark.
Table 2: Within-country achievement by international benchmarks
|
|
Benchmarks (%) |
|||
|
Country |
Low (SE) |
Inter (SE) |
High (SE) |
Adv (SE) |
|
Morocco |
41.22 (1.22) |
11.62 (.87) |
1.94 (.37) |
.12 (.07) |
|
S Africa |
40.77 (1.26) |
13.15 (.69) |
3.18 (.30) |
.56 (.09) |
|
Egypt |
55.43 (2.28 |
26.84 (1.69) |
7.31 (1.08) |
0.88 (25) |
|
Total |
45.81 (.96) |
17.20 (.75) |
4.14 (.39) |
.52 (.09) |
Low: 400; intermediate: 475; high: 550; advanced: 625
To understand these differences qualitatively, I partitioned the schools within each country by school socio-economic status. Owing to the opportunities afforded by wealthier schools, it is not surprising that there is a prevalence of underachievement on the continent. As indicated in Table 3, at least 70% of schools in each of the countries offer services to poor pupils. The effect of this is reflected in the downward trend in achievement from mostly affluent, neither affluent nor disadvantaged, to mostly disadvantaged. Focusing on the continental average, we can see that attending a school in an affluent neighborhood might increase a students’ score by more than 40 points.
Table 3: Country-level achievement relative to School composition by SES
|
|
Mostly Affluent |
Neither |
Mostly Disadvantaged |
|||
|
Country |
% |
Ach |
% |
Ach |
% |
Ach |
|
Morocco |
7.08 (2.13) |
457.89 (18.19) |
13.35 (2.82) |
392.76 (6.43) |
79.57 (3.42) |
380.35 (2.92) |
|
S Africa |
10.09 (1.60) |
462.77 (16.03) |
12.94 (2.08) |
412.65 (10.19) |
76.97 (2.44) |
379.34 (3.39) |
|
Egypt |
11.44 (2.80) |
430.50 (13.59) |
19.07 (3.50) |
418.42 (14.16) |
69.49 (4.29) |
403.06 (6.37) |
|
Total |
9.53 (1.29) |
450.39 (9.26) |
15.12 (1.65) |
407.94 (6.20) |
75.34 (2.00) |
387.58 (2.59) |
To further understand the nature of these differences within each country, I computed the achievement by gender. One of the motivations for this is the cultural cum religious heterogeneity that exist between the conservative North African countries of Egypt and Morocco, and South Africa. As contained in Fishbein et al. (2021), significance exists to the degree the t-statistic (p value) is either greater than 1.96 or less than -1.96 for the reference and comparison groups respectively. Apart from Egypt where significance was not reached, males outperform females in Morocco. The reverse occurred among South Africans where females significantly outperformed their male counterparts (see Table 4 and Figure 2).
Table 4: Achievement differences by gender
|
|
Ach |
Gender |
p |
|
|
Country |
(SE) |
F |
M |
|
|
Morrocco |
388.19 (2.28) |
385.72 (2.51) |
390.67 (2.57) |
2.21* |
|
S Africa |
389.48 (2.27) |
392.77 (2.42) |
386.23 (2.54) |
-3.15* |
|
Egypt |
412.88 (5.21) |
419.90 (5.29) |
404.52 (7.91) |
-1.89 |
|
Average |
396.85 (2.04) |
399.47 (2.11) |
393.80 (2.90) |
|
*Significance at .05
While Table 2 and Figure 1 show glaring achievement differences among the three countries, it is not clear whether they are significant. To answer that, a between-country t-test was conducted. Results from Table 5 confirmed that the Egyptians perform significantly better than their Moroccan and South African counterparts. Students of Morocco and South Africa appear to have no significant difference in achievement scores (p=.05).
Table 5: t-statistic of between-country mean differences in mathematics achievement
|
Country |
1 |
2 |
3 |
|
|
(1) Morocco |
.00 |
|
|
|
|
(2) S Africa |
.40 |
.00 |
|
|
|
(3) Egypt |
4.34* |
4.12* |
.00 |
|
*Significance at .05
Having found that the three countries are not entirely homogenous in terms of achievement, I now turn to investigate how they fare in the three motivational constructs. As Table 6 depicts, students tend to have less confidence in their mathematical ability than they do like or find mathematics useful in all the countries. As measured on the scales, none of them failed to meet the median threshold of 2.0 in any of the three variables, with the bulk of the perception of usefulness triumphing others in each country and across the continental average. Additionally, unlike with usefulness and interest, self-concept scores follow a rank order that is invariant to achievement.
Table 6: Case summaries of interest, self-concept, and usefulness of mathematics by country
|
|
|
Interest |
Concept |
|
Usefulness |
|||||||||
|
|
|
E |
M |
Z |
T |
E |
M |
Z |
T |
|
E |
M |
Z |
T |
|
Mean |
|
3.10 |
3.05 |
3.05 |
3.07 |
2.82 |
2.67 |
2.45 |
2.65 |
|
3.35 |
3.37 |
3.46 |
3.39 |
|
SD |
|
.86 |
.79 |
.78 |
.81 |
.76 |
.70 |
.67 |
.71 |
|
.85 |
.76 |
.72 |
.78 |
|
Min |
|
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
|
1.00 |
1.00 |
1.00 |
1.00 |
|
Max |
|
4.00 |
4.00 |
4.00 |
4.00 |
4.00 |
4.00 |
4.00 |
4.00 |
|
4.00 |
4.00 |
4.00 |
4.00 |
E: Egypt; M: Morocco; Z: South Africa; T: Total
Table 7 reports on the correlations between achievement and each of the motivational variables within the three countries which are all positive and significantly different from zero (.14 ≤ r ≤ .33; p<.01), with self-concept exerting the greatest amount.
Table 7: Within-country predictor-achievement correlations
|
Variable |
Self-concept |
Interest |
Usefulness |
|
Morocco |
.33** |
.25** |
.20** |
|
South Africa |
.28** |
.14** |
.21** |
|
Egypt |
.35** |
.24** |
.25** |
**Significance at .01 level (2-tailed)
Multi-level analyses
To better understand the results of the preceding section, I conducted hierarchical analyses. In accordance with the research questions, three models (Model 1 [M1], Model 2 [M2], and Model 3 [M3]) were created to capture achievement variability across student and school levels. These are the Unconditional Model (M1), Compositional/contextual effects model (M2), and the Means and slopes as outcome model (M3) respectively. M3 was especially useful for capturing both achievement and motivational variables at the country levels. The values of the fixed effect components and standard errors of each model are as shown in columns 2 (for M1), 3 (for M2), and 4 (for M3) under the Fixed effects (standard errors) header in Table 9 below. The parameters of focus at the student level for M2 and M3 are contained under the Intercept-slopes (βi) header of Table 9 with the variance components of all three models stationed under the Variance components heading.
Table 9: Fixed and random effects from multilevel models
|
Fixed effects |
M1 coeff (SE) |
M2 coeff (SE) |
M3 coeff (SE) |
|
|||||
|
Initial status (β0) |
Fixed effects (standard errors)
|
|
|||||||
|
Intercept (γ00) |
403.60(1.88) |
403.67(1.57) |
397.97(1.64) |
|
|
||||
|
Interest (γ01) |
|
-144.09(8.03) |
-127.59(8.40) |
|
|
||||
|
Self-concept (γ02) |
|
111.76(7.34) |
113.219(8.70) |
|
|
||||
|
Usefulness (γ03) |
|
92.80(8.01) |
80.82(8.57) |
|
|
||||
|
Prop_Female (γ04) |
|
|
|
10.53+ |
|
||||
|
Sch_SES (γ05) |
|
|
|
27.78 |
|
||||
|
D_Egypt (γ06) |
|
|
|
-8.55+ |
|
||||
|
D_SA (γ07) |
|
|
|
41.42 |
|
||||
|
D_Mar (γ08) |
|
|
|
-25.25 |
|
||||
|
Intercept-slopes (βi)
|
|
|
|
|
|
||||
|
Interest (γ10) |
|
6.76(.52) |
|
|
|
||||
|
|
|
|
D_Egy(γ11) |
-.007+ |
|
||||
|
|
|
|
D_SA(γ12) |
-3.82+ |
|
||||
|
|
|
|
D_MAR(γ13) |
2.80+ |
|
||||
|
|
|
|
Prop_F(γ14) |
-1.45 |
|
||||
|
|
|
|
Sch_SES(γ15) |
-1.06+ |
|
||||
|
Self-concept (γ20) |
|
25.11(.57) |
|
|
|
||||
|
|
|
|
D_Egy(γ21) |
.78+ |
|
||||
|
|
|
|
D_SAγ(22) |
6.04+ |
|
||||
|
|
|
|
D_MARγ(23) |
-5.11+ |
|
||||
|
|
|
|
Prop_F(γ24) |
3.86+ |
|
||||
|
|
|
|
Sch_SES(γ25) |
3.34+ |
|
||||
|
Usefulness (γ30) |
|
2.96(.50) |
|
|
|
||||
|
|
|
|
D_Egy(γ31) |
.94+ |
|
||||
|
|
|
|
D_SAγ(32) |
-.43 |
|
||||
|
|
|
|
D_MAR(γ33) |
-.21+ |
|
||||
|
|
|
|
Prop_F(γ34) |
-.06+ |
|
||||
|
|
|
|
Sch_SES(γ35) |
-1.27+ |
|
||||
|
Variance components |
|
||||||||
|
ICC |
0.4698 |
|
|
|
|
||||
|
R2L-1 |
|
0.1334 |
|
0.1559+ |
|
||||
|
R2L-2 |
|
0.3101 |
|
0.4554+ |
|
||||
+No significance at .001
RQ 1: what accounts for the variance that exists in achievement?
Results of the unconditional model with achievement as the outcome variable shows an overall mean mathematics achievement of 403.60 (see column 2 in Table 9 above). This score is however distributed almost evenly among the students and schools indicating that African schools are significantly heterogenous. With an intraclass correlation (ICC) of 0.47, it implies that about 47% of the variance in students’ achievement owes to differences between the schools they attend, leaving approximately 53% of the variation to differences among the students.
RQ 2: what is the relationship between achievement and interest, self-concept, and usefulness of mathematics at the (i) student (ii) school levels?
The compositional effects model returned consistent results at the individual and group levels except for interest whose relationship with achievement was positive at the student level (β10 = 6.76, p<.001). but negative at the school level (β01 = -144.09, p<.001). A more consistent picture is evinced at the student level for all three motivational variables whose relationships with achievement were positive and statistically significant (self-concept: β20 = 25.11, p<.001; usefulness: β30 = 2.96, p<.001). As indicated, interest in mathematics leads to about 7-point increase and 144-point decrease in student and school achievement respectively. At both levels, a positive association exists between achievement and the perception of mathematics as a useful subject at a magnitude of approximately 3 and 93 points for the student and school. The pattern of relationship between self-concept and achievement is more robust. At both student (β20 = 25.11, p<.001) and school (β02 = 111.76, p<.001) levels, confidence in mathematics leads to achievement: a unit increase in confidence causes students’ achievement to go up by at least 25 points. The size was in excess of 111 points in schools. Compositional effects of interest (γ01 - γ10), self-concept (γ02 - γ20), and usefulness (γ03 - γ30) return approximately -150, 87, and 90 points respectively suggesting the unique roles accrued to students by their membership in schools. While it is positive for self-concept and usefulness, schools tend to have a net negative influence on students’ achievement relative to their love of mathematics. Finally, although the inclusion of the three motivational and control variables explained 13.3% of L-1 achievement-variation, their means as predictors of school achievement explained an additional 57% relative to L-1 variance.
RQ 3: Does s (i) gender (ii) school SES and (iii) country effect exist across the motivational variables and achievement?
Based on the final model, it can be inferred that gender effect does not significantly exist except for interest (β14 = -1.45, p<.001), implying that being a female decreases the chances of being interested in mathematics by about 1.5 points. In contrast, school affluence positively relates with mathematics achievement by at least 27 points (β05 = 27.78, p<.001). The results, although mixed for the motivational variables, are not statistically different from zero. Furthermore, membership in countries also reflects mixed but interesting results across the outcome and independent variables. Unlike in Egypt, students in South Africa and Morocco are significantly impacted by their overall country achievement scores in the positive sense for the former (β07 = 41.42, p<.001) and negatively for Morocco (β08 = -25.25, p<.001). The only other country effect was recorded in usefulness within South Africa (β32 = -.43, p<.001). In conclusion, the inclusion of the predictor variables in this model contributed 15.6% and 45.6% to the student and school-level variations in mathematics achievement respectively[1].
[1] All parameter and variance estimates are as contained in Table 9.
Achievement differences exist irrespective of the unit of analysis, informing a need to further account for such occurrence (see Devine et al., 2012; Sarouphim & Chartouny, 2017; Shin et al., 2009),. Especially given how much these differences owe to factors that relate to opportunity to learn, tending to achievement disparities also follows the trail of equity (e.g., Forgasz & Rivera, 2012). But since most of those factors are not easily influenced by interventions, especially within the students and those who work closely with them, there has been a greater focus on understanding how malleable factors interplay with achievement (e.g., Jones et al., 2012). Following results of international comparative achievement, this paper focused on the achievement disparities of African countries that have for decades performed lower than their counterparts in other places of the world. I relied on data from the Trends in International Mathematics and Science Study (2019) to primarily examine the interplay between achievement of mathematics and motivational perceptions of interest, self-concept, and usefulness.
Preliminary analyses confirmed the achievement gaps between African countries relative to international benchmarks as determined by the percentage of students with knowledge and applications of mathematical ideas to diverse situations (Pirls et al., 2020), with the continental achievement averaging less than 50% for the lowest cutoff. Across each of the participating countries, only Egypt recorded more than the continental average in that regard. To better situate this in perspective, 87%, 56%, 25%, and 5% of students met the low, intermediate, high, and advanced benchmarks globally (Pirls et al., 2020), an indication of African students relatively mediocre performance. One explanation for this was provided by parsing their achievement through school composition by socioeconomic background that showed that at about three-quarters of African eighth graders attend mostly disadvantaged schools.
Furthermore, average achievement scores of schools at the middle and top positions both surpass the continental average and least benchmark cutoff. As intended, this study joins others (e.g., Reilly et al., 2019) that have investigated the influence of gender on achievement and motivation. Although the lack of significant gender difference in Egypt extends their finding of a closing, almost nonexistent gender gap, it nevertheless manifests in Morocco and South Africa. Similarly, recall that Wilkins (2004), as did Bofah and Hannula (2015) to some degree reported direct achievement-self-concept relations based on country achievement ranks which also existed in this study with the most achieving country, Egypt. Although self-concept holds almost parallel relationship with achievement across the countries, the association is strongest in the most achieving country (Egypt) and weakest in the least (South Africa) aligning with previous findings such as Wilkins (2014) and (Kadijevich, 2008). Unlike what Bofah and Hannula (2015) reported, a direct trend exists between self-concept and mathematics achievement among countries.
Like the single-level statistics, several interesting results emanated from the multi-level analyses to either confirm or disconfirm previous findings, with the predictive capacity of self-concept being the most manifestation of the former (Kadijevich, 2008; Wilkins, 2004), and the latter manifesting in its country-level relationship with achievement (Wilkins, 2004). Furthermore, the insignificant country effects on the motivational variables (except usefulness in SA) joins the long trail of others such as Wilkins’ (2014) self-concept in South Africa. Also in alignment with previous studies is the positive effect of school socio-economic status on school average mathematics achievement (Ersan & Rodriguez, 2020). In conclusion, the frame of reference effect (Marsh et al., 1987) appears not to be influential going by the overall student and school-level data of self-concept slopes contrary to Bofah and Hannula (2015). While the same can be gleaned for usefulness, the positive and negative slopes for interest at the student and school levels suggest the existence of the effect.
Ethical Approval: not applicable
Funding: not applicable
Availability of Data and Materials: The data for this study can be accessed online for free at https://timssandpirls.bc.edu/timss-landing.html
Conflict of Interest Statement: The author has no relevant financial or non-financial interests to disclose.
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The authors declare no competing interests.