Variance In Mathematics Achievement Research Articles

The relationship between mathematics self-efficacy and mathematics achievement: multilevel analysis with NAEP 2019

BackgroundThis empirical study aims to investigate the association between mathematics self-efficacy and mathematics achievement gaps among students in Grades 4, 8, and 12, utilizing data from the 2019 National Assessment of Educational Progress (NAEP). The study also considers student-level (e.g., mathematics self-efficacy, gender, race/ethnicity) and school-level (e.g., school location, proportion of underrepresented students) demographics to provide a comprehensive analysis of the factors contributing to mathematics achievement gaps.MethodsA two-level cross-sectional multilevel modeling approach was employed to analyze the variance in mathematics achievement, partitioning it into within- and between-school components. This approach allowed for an examination of association between mathematics self-efficacy and achievement gaps while considering various student and school characteristics. The rationale behind this methodology lies in its ability to capture the hierarchical nature of educational data and provide a nuanced understanding of the factors associated with mathematics achievement.ResultsThe analysis of the NAEP data revealed substantial variability in mathematics achievement across schools in the United States at all grade levels. Furthermore, mathematics self-efficacy emerged as a robust predictor of students' mathematics achievement, exhibiting significant effect sizes for Grades 4, 8, and 12. Remarkably, when students' mathematics self-efficacy was held constant, the mathematics achievement gaps among different student subgroups by gender, race/ethnicity, ELL, IEP, NSLP status narrowed, highlighting the importance of self-efficacy in addressing these disparities. The study also identified the presence of significant school contextual effects, further emphasizing the role of the educational environment in shaping mathematics achievement.ConclusionsThis study underscores the critical role of mathematics self-efficacy in influencing mathematics achievement gaps among students. By acknowledging the association between self-efficacy beliefs and mathematics achievement, policymakers and educators can develop targeted interventions to enhance students' confidence and motivation in mathematics, ultimately promoting equitable educational outcomes. The findings also emphasize the significance of school-level factors, calling for comprehensive approaches that consider both individual and contextual factors in narrowing achievement gaps. The implications of adopting a self-efficacy perspective to address mathematics achievement gaps extend to educational policy, curriculum development, and instructional practices, ultimately fostering more inclusive and effective mathematics education for all students.

The role of students' mathematics perception and self‐efficacy toward their mathematics achievement

AbstractDeterioration of students' mathematics achievement has been a common problem while their mathematics perception and self‐efficacy have been reported to determine their achievement. However, little is known about the potential relationships among them. Therefore, this study attempted to investigate the extent of influence of students' mathematics perception and self‐efficacy toward mathematics achievement. Randomly selected 643 students for questionnaire, six mathematics teachers for interview and two FGDs were conducted with students. The findings revealed that students' mathematics perception and self‐efficacy were positively and strongly related to their mathematics achievement (r = 0.767, p < .001 and r = 0.797, p < .001) respectively. Regression result reported 75.4% of the variation in students' mathematics achievement was accounted for by students' mathematics perception and self‐efficacy (R2 = 75.4). The two predictors explained a statistically significant amount of variance in mathematics achievement, [F (2637) = 975.99, p = .001]. Mathematics perception [β = .44, t (17.56), p = .001] and self‐efficacy [β = .52, t (637) = 20.84, p = .001] were reported as significant predictors of students' mathematics achievement. There was a statistically significant gender difference in students' mathematics perception [t (641) = 2.77, p < .001], self‐efficacy [t (638) = 5.43, p < .001], and mathematics achievement [t (638) = 5.43, p < .001].

Mathematics achievement in the last year of primary school. Longitudinal relationship with general cognitive skills and prior mathematics knowledge

The aim of this study was to analyze the joint, relative, and unique predictive value of students’ prior knowledge of mathematics (knowledge of fractions and ability to divide natural numbers) and general cognitive ability (fluid intelligence and working memory) upon general mathematics achievement in the last year of primary school. Seventy-five students participated (M age = 11.2 years old, SD = 0.40). Hierarchical regression analysis showed that the ability to divide and fractions knowledge accounted for 41% of the variance in mathematics achievement, both acting as significant predictors. By incorporating working memory and fluid intelligence into the model, fraction knowledge showed to be no longer a significant predictor. These general cognitive skills explained an additional 8% of the variance in mathematics knowledge, both being significant predictors and contributing to mathematics achievement in a unique way. The implications of these results for mathematics teaching are discussed.

The Relationship Between Sources of Mathematics Self-Efficacy and Mathematics Test and Course Achievement in High School Seniors

In school settings, sources of self-efficacy have the potential to directly and indirectly influence performance. The problem of this study is the direct relationship between sources of self-efficacy and achievement. In connection with this problem, the impact of sources of mathematics self-efficacy on high school senior students’ mathematics test and course achievement was investigated. The study consisted of 257 12th-grade high school students. The findings of the study showed that mathematics course and test performance increased, whereas the scores for mastery experience, social persuasions, vicarious experience, and physiological state increased, too. According to the results of the regression analysis on mathematics course achievement, the mastery experience significantly predicted mathematics course performance. It also explained 56% of the total variance in mathematics achievement. On the contrary, mastery experience, social persuasions, and physiological state significantly predicted mathematics test achievement, as well as explained 27% of the total variance in mathematics test achievement. In conclusion, sources of mathematics self-efficacy have effects on both mathematics test and course achievement.

An examination of the relationship between secondary school students’ abstract thinking skills, self-efficacy perceptions and attitudes towards mathematics

This study aims to examine whether there is a relationship between abstract thinking skills, self-efficacy perceptions and attitude towards mathematics and how these variables predict mathematics achievement. The study was conducted with 198 eighth-grade students who were selected by random sampling and the relational screening model was used. For data collection, the tools of “Abstract Thinking Test in Mathematics”, “Self-Efficacy Perception Scale towards Mathematics”, “Mathematics Attitude Scale” and Mathematics course notes of students were resorted to. According to the findings, it was concluded that there were significant relationships between students’ abstract thinking skills, self-efficacy perceptions and attitudes towards mathematics, and these variables explained 37% of the variance in mathematics achievement. There was no significant difference in mathematics achievement between the groups according to the type of school, while it was found that the scores of the students' abstract thinking skills, attitude towards mathematics and self-efficacy perceptions differed in favor of the students studying in non-boarding secondary school. In addition, no significant difference was observed between the groups in terms of students' mathematics achievement according to their boarding status. It was found that there were significant differences in terms of the other three variables. Suggestions were made to increase mathematics achievement, especially in boarding secondary schools, and it was also offered to increase the feasibility of the environment of the boarding secondary schools.

Examining educational inequalities: insights in the context of improved mathematics performance on national and international assessments at primary level in Ireland

BackgroundEvaluations of effectiveness of educational reforms are often based on the level of improvement in student performance from one cycle of a particular assessment to the next. However, improvements in overall performance do not necessarily translate to improved equality. Indeed, improvements that favour certain subgroups of students can exacerbate educational performance gaps and thus, inequality. This research examines changes in equality of mathematics achievement and subgroup performance differences in Irish primary school students over time. Ireland constitutes an interesting case study due to the introduction of a new National Literacy and Numeracy Strategy in 2011, the initial implementation of which has been linked to significant improvements in student mathematics performance. This paper aims to investigate whether these improvements have been accompanied by improvements in equality.MethodsUsing data from the Irish National Assessments of Mathematics and English Reading (NAMER) and the Trends in International Mathematics and Science Study (TIMSS) from the period before and after the introduction of the Strategy, the study examines (i) deviations in student scores, (ii) variability in achievement at student and school levels and (iii) performance gaps based on demographic and socioeconomic factors over time. Bivariate analyses and multilevel regression models were used to identify student- and school-level variables related to mathematics performance.ResultsThe results showed a decrease in variability in students’ mathematics performance after the introduction of the Strategy; this decrease was statistically significant only for TIMSS. Additionally, there was a considerable decrease in variance in mathematics performance attributed to between-school differences over time. These findings constitute evidence of increased equality as performance differences between students and schools tended to shrink. Regarding performance gaps and variance in mathematics performance explained by background characteristics, this study provided mixed results. In NAMER, subsequent to the introduction of the Strategy, the performance gaps and variance in mathematics achievement explained by selected demographic and socioeconomic characteristics decreased considerably. However, this was not the case for TIMSS.ConclusionsThe evidence provided by this study suggests that Ireland has made reasonable progress in addressing inequality. However, there is room for improvement, as a significant proportion of the variance in student mathematics performance is still explained by demographic and socioeconomic characteristics.

The Contribution of General Cognitive Abilities and Specific Numerical Abilities to Mathematics Achievement in Students Who are Deaf or Hard-of-Hearing

General cognitive and specific numerical abilities that underlay mathematical performance have been heavily investigated among hearing students; however, the inquiry has rarely been applied to students who are deaf or hard-of-hearing (d/Dhh). We examined whether general cognitive abilities (i.e. nonverbal IQ, processing speed, and spatial ability) and specific numerical abilities (i.e. symbolic and non-symbolic numerical magnitude processing) are related to mathematics achievement in 198 d/Dhh students in Grades 3 to 9. The results of our regression models indicated that, the three general cognitive abilities independently explained the variance in mathematics achievement when entered in one step; and spatial ability and processing speed had an independent contribution to mathematics achievement in the presence of the specific numerical abilities. The specific numerical abilities independently explained the variance in mathematics achievement when entered in one step; however, none of them had an independent contribution to mathematics achievement in the presence of the general cognitive abilities. These findings suggested that mathematics achievement in d/Dhh students depended more on general cognitive abilities, such as spatial ability and processing speed, than on specific numerical abilities.

The Relationship between Sixth Grade Students’ Mathematics Learning Approaches and Perceived Teacher Constructive Affective Support and Mathematics Achievements

Bu çalışmanın temel amacı, altıncı sınıf öğrencilerinin matematik öğrenme yaklaşımları, algılanan öğretmen yapıcı duygusal destek ve matematik başarıları arasındaki ilişkiyi belirlemektir. Araştırmaya 416 altıncı sınıf öğrencisi katılmıştır. Araştırmaya katılan öğrencilerin %54.3’ü (n=226) kız, %45.7’si (n=190) erkektir. Çalışmada veri toplama aracı olarak, Algılanan Öğretmen Yapıcı Duygusal Destek ile Matematik Öğrenme Yaklaşımları ölçekleri kullanılmıştır. Öğrencilerin matematik başarılarını belirlemek için dönem sonu matematik not ortalamaları kullanılmıştır. Verilerin analizinde, Pearson momentler çarpımı korelâsyon katsayısı ve çoklu doğrusal regresyon kullanılmıştır. Elde edilen bulgulara göre, öğrencilerin matematik başarıları ile derinlemesine öğrenme yaklaşımı, yüzeysel öğrenme yaklaşımı, stratejik öğrenme yaklaşımı ve algılanan öğretmen yapıcı duygusal destek arasında anlamlı ilişkiler tespit edilmiştir. Çoklu regresyon analiz sonuçlarına göre, matematik öğrenme yaklaşımları ile algılanan öğretmen yapıcı duygusal destek matematik başarısındaki varyansın %26’sını açıklamıştır. Aynı zamanda algılanan öğretmen duygusal destek ile öğrenme yaklaşımları matematik başarısının anlamlı yordayıcıları olmuştur. Elde edilen bulgular ışığında birtakım önerilerde bulunulmuştur.

A study regarding relations b/w parental involvement and students achievement in mathematics, science in batticaloa, Sri Lanka

This study investigated how were correlates with the parental involvement and the achievement of students in the urban and semi-urban type 2 schools in mathematics and science. The descriptive survey research design was employed to carry out this study. One hundred and ninety two (192) students from 16 type 2 schools in Batticaloa educational zone, Sri Lanka were stratified randomly selected for this study. The type 2 school was selected for maintaining the homogenous values. From the results of this study, parental involvement accounts for 26.1% of the total variance in mathematics achievement of secondary schools (R2= 0.261; p< 0.05) and 19.4% of the total variance in science achievement of secondary schools (R2 =0.194; p < 0.05). These percentages are significant at 0.05 level of confidence. It shows that parental involvement is an important predictor of mathematics and science achievement. There exists a significant difference in the parental involvement of urban and semi-urban type 2 school students (t = -8.12; p<0.05). Urban school students enjoy more parental involvement than their counterparts in the semi-urban school students. It shows that there is a correlation between parental involvement and male, female students in type 2 schools (t = -7.34; p <0.05), and also there is a significant difference in the academic achievement of male and female students in mathematics and science (t = -0.432 and, - 0.512 respectively; p < 0.05). It also shows the finding reports that, there is a significant difference in the academic achievement of mathematics and science with urban, semi-urban schools students (t = -9.142 and, -8.314 respectively; p <0.05). Teachers and Counselors need to enlighten parents on the need to personality get involved in the academic activities of their children.

The impact of perceived teachers’ autonomy support on students’ mathematics achievement: evidences based on latent growth curve modelling

According to the self-determination theory, autonomy-supportive teaching is considered an effective approach to motivate students to learn. The present study investigates the effect of students’ perceived autonomy support on math achievement over time, i.e. from grades 4 to 6, using a longitudinal survey administered in Chinese elementary schools. A total of 1624 participants were assessed over four waves. Autonomy need satisfaction and classroom engagement were included as predictors of achievement growth. Latent growth curve modelling (LGCM) indicated that perceived autonomy support accounted for more variance in mathematics achievement among 4th- and 5th-grade students than it did for 6th-grade students. Furthermore, student autonomy need satisfaction positively predicted the growth rate of their achievement, while behavioural engagement significantly and positively predicted both the growth rate and the average initial level of mathematics achievement.

Relationship of Physical Education Curriculum Implementation and Mathematics Achievement in Chinese Youth

ABSTRACTPurpose: Previous studies indicated a positive association between physical education (PE) and mathematics achievement (MA). This study explored how PE curriculum implementation relates to MA using data from the China National Assessment of Education Quality (CNAEQ) in 2015, including Mathematics (CNAEQ-MA 2015) as well as Physical Education & Health (CNAEQ-PEH 2015). Method: This study included 22,619 students (48.7% girls) age 13.96 ± 0.64 yr. from the national sample of Grade 8 students from CNAEQ. During 2015, MA and cardiorespiratory fitness (CF) were assessed. PE curriculum implementation, personal hygiene, eating habits, PE interest, mathematics interest, and self-confidence were collected via a self-report student survey. Personal hygiene and eating habits were combined to create the latent variable, healthy lifestyle (HL). Structural equation modeling was applied to examine the associations. Socioeconomic status, school location, Body Mass Index (BMI), and sex were all controlled. Results: PE curriculum implementation had an indirect, positive association with MA through CF, HL-mathematics interest, and HL-mathematics self-confidence. Together, the model explained 27.8% of the variance in MA. Conclusion: PE curriculum implementation may benefit mathematics education, and this link is mainly through HL, CF, mathematics interest, and self-confidence.

How Classroom Assessment Affects Science and Mathematics Achievement : Findings from TIMSS 2015

In this study, it is aimed to examine the effect of classroom assessment on science and mathematics achievements. For this purpose, hierarchical linear modeling is performed using variables of like learning science/math, engage teaching in science/math, confidence in science/math, and home resources for learning variables at student level, and experience, education level, homework, and assessment at teacher-level. The sample of the study consists of 4th grade students who participate in TIMSS 2015 in Turkey. According to the findings; 36% of variance in science achievement, and 40% of variance in mathematics achievement are due to variability between classes. In random coefficient model, all student variables are statistically significant predictors of science and mathematics achievement. Among these variables, the greatest effect size is the self-confidence variability. Only the teacher variables are added according to the Means as outcome model; the teacher's experience and the emphasis to national achievement tests of monitoring students’ progress have a statistically significant effect on science and mathematics achievement. Finally, according to the intercept and slopes as outcomes model, the most important variable is the emphasis to national achievement tests of monitoring students’ progress is followed in both science and mathematics.

Predictive Relation between Early Numerical Competencies and Mathematics Achievement in First Grade Portuguese Children.

Early numerical competencies (ENC) (counting, number relations, and basic arithmetic operations) have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children (n = 123). The children’s ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC) were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties.

How affective-motivational variables and approaches to learning predict mathematics achievement in upper elementary levels

The relationship between students' motivation and attitudes towards mathematics, the approaches to learning they use, and their achievement in mathematics has been widely documented in middle school and further academic levels. However, the empirical research in earlier educational stages remains scarce. This study analyzed the predictive value of affective-motivational variables and deep and surface approaches to learning on mathematics achievement in a sample of 524 upper elementary students. Multiple linear regression analysis was used to examine the predictors of mathematics achievement. Mathematics enjoyment positively predicted mathematics achievement and age and the use of the surface approach to learning negatively predicted mathematics achievement. The variables in the model explained 21.3% of the variance in mathematics achievement. Mean differences in the affective-motivational variables and approaches to learning occurred between students with very high and very low achievement in mathematics, yielding further evidence of important differences between the achievement extremes.

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This study explores the sources of variability in Mathematics achievement of Ugandan students at the student, classroom and school level. The Mathematics score and questionnaire responses of 4,819 first-year secondary school students (Grade Seven, about 14-15 years old) from 78 classrooms of 49 schools were analysed. A three-level linear model was used. The results indicate that out of the total variance in Mathematics achievement 68.8%, 14.2% and 17.0% are situated at student, classroom and school level, respectively. Of all the considered explanatory variables at the three levels, i.e. socio-economic status, gender, prior Mathematics achievement, parental support, peer influence, class mean of prior Mathematics achievement and of students’ perception of good classroom assessment, school mean of class climate (class mean of attitude toward mathematics) and of parental support were significant predictors of Mathematics achievement. The relevant factors could explain 7.6%, 73.1% and 84.3%, respectively, of student-, classroom- and school-level differences. Implications of our study are considered. Keywords : mathematics achievement, multilevel analysis, secondary school, Uganda

Prekindergarten children’s executive functioning skills and achievement gains: The utility of direct assessments and teacher ratings.

An accumulating body of evidence suggests that young children who exhibit greater executive functioning (EF) skills in early childhood also achieve more academically. The goal of the present study was to examine the unique contributions of direct assessments and teacher ratings of children’s EF skills at the beginning of prekindergarten (pre-k) to gains in academic achievement over the pre-k year. Data for the current study come from a subsample of children recruited for a large-scale pre-k curriculum intervention. This subsample (n = 719) was restricted to all children who were native English speakers and had at least 1 pretest and posttest score on the assessments. Several important findings emerged. Teacher reports of EF and direct assessments were correlated, particularly when EF direct assessments were modeled as a single component score. When entered into the models simultaneously, both teacher ratings and direct assessments significantly predicted academic gains in literacy and mathematics; however, the direct assessments were only marginal in predicting gains in language. EF skills accounted for the largest proportion of variance in mathematics achievement gains. The value of using both types of measures in future research is discussed.

Assessment of Metacognition in Mathematics: Which One of Two Methods is a Better Predictor of Mathematics Achievement?

Article History: Received 03.12.2013 Received in revised form 14.03.2014 Accepted 22.03.2014 Available online 21.04.2014 In recent years metacognition was discussed as a significant concept in mathematics education. However, means of measuring metacognition efficiently is still a problem. This problem has been at the center of a scientific debate about which instruments are more suitable. In this study two off-line methods, student and teacher evaluations were used. The aim of this research is to investigate which one of the evaluation form (teacher form versus student form) is the predictor of mathematic achievement. For this aim two studies were carried out. In the first study mathematics achievements of students were measured by mathematic scores in their reports. In the second study it was measured by more standard test called Placement test (Seviye Belirleme Sinavi -SBS). In the first study 408 primary school students from a state school participated. Only sixth grade students who attended SBS exam of the first study were taken the second study. According to results of this study that aimed to investigate which one of the evaluation forms (teacher form versus student form) is the predictor of mathematics achievement, instead of the results of students evaluation form, the results of teacher evaluation form are the main predictor of the mathematics scores of students. Teacher evaluation form alone explains about 51 % of the variance in mathematics achievement. © 2014 IOJES. All rights reserved

Mathematics achievement in high- and low-achieving secondary schools

This paper identifies the amount of variance in mathematics achievement in high- and low-achieving schools that can be explained by school-level factors, while controlling for student-level factors. The data were obtained from 2679 Iranian eighth graders who participated in the 2007 Trends in International Mathematics and Science Study. Of the total sample, 1422 and 1257 students were from high- and low-achieving schools, respectively. Two-level hierarchical linear modelling was applied. The results indicated that of the total variance in mathematics achievement, 27.95 and 6.70% were due to between-school differences in the high- and low-achieving schools, respectively. Controlling for the school-level factors, the better-performing students were those with a higher level of confidence in learning mathematics in both samples. After controlling for the student-level factors, inadequacies in school resources and school type yielded the strongest link to achievement in the high- and low-achieving schools, respectively.

Factors determining educational quality: Student mathematics achievement in Nepal

This study employed the multiple regression analysis to examine the effects of family characteristics, student characteristics, parental involvement, and school characteristics with regard to learning achievements in mathematics of students of eighth grade in Nepal. Mathematics test was administrated with 762 students (400 girls) of 21 secondary schools in nine districts of three ecological zones-mountain, hill and lowland (tarai). Findings indicated that family characteristics explained the largest amount of variance in mathematics achievement, followed by student characteristics, school characteristics and parental involvement. Variables – parental education, number of books at home, absenteeism, parental support for homework, school type and location, teacher training, the number of school days in the academic year and school physical facilities were significantly related to students’ mathematics achievement. The implications of this study for improving educational quality are discussed.

Mathematics Achievement as a Function of Within- and Between-School Differences

Achievement in mathematics of eighth-grade students is modeled as a function of within-school, between-school and cross-country differences. The data were obtained from 217,728 students, within 7,216 secondary schools, in 48 countries, who participated in the 2007 Trends in International Mathematics and Science Study. Multilevel analysis showed that out of the total variance in mathematics achievement, 40.39%, 20.61%, and 38.99% were accounted for within-school, between-school-within-country, and cross-country differences, respectively. Mathematics self-concept followed by socioeconomic status was the strongest predictor of achievement at the student level. At the school level, school location yielded the strongest link to achievement, while at the country level socioeconomic status was the main predictor of national mathematics average.