Understanding mathematics achievement: an analysis of the effects of student and family factors

Educators are increasingly recognising the importance of improving students’ mathematics achievement. Much of the current research focuses on the impact of instructional variables on mathematics achievement. The goal of this study was to examine the influence of less researched variables – family and student factors. Participants were 747 economically disadvantaged elementary students grades K-8 in Ohio. Predictor variables included: (a) 13 factors from a parent survey on both child and family circumstances and (b) reading achievement, measured by a norm-referenced achievement test. Outcome variables included three mathematics scales from the same achievement test. Regression analyses examined the impact of the predictors on the outcomes. Reading achievement significantly predicted mathematics achievement for all three outcomes. Parent pessimism and parent-perceived school/cognitive competence of children also emerged as significant predictors for two of the three mathematics outcomes. Implications for research, policy and practice will be shared.     

THE PREDICTION OF GRADES IN OCCUPATIONAL AND ACADEMIC CURRICULA IN 2-YEAR COLLEGES

Test scores and high school grades were correlated with end-of-second-year college grades for 2,707 students in 12 curricular groups at 27 2-year colleges. Optimally weighted combinations of the aptitude/achievement predictors were found to predict grades for occupational curricula with about the same accuracy as they predict grades in academic criteria. For women, however, the aptitude test scores correlated much less with grades in occupational curricula than with grades in academic curricula.     

Achievement testing with the Wechsler Quicktest: an examination of its psychometric properties and applied utility with a Greek–Cypriot sample

The study aimed to field‐test a Greek version of the Wechsler Quicktest and to examine its psychometric properties. The Quicktest was individually administered to 208 students, aged 5–14 years, along with a reading test. Based on the Rasch analysis, data for the Quicktest subtests showed acceptable fit to the model. Also, correlations were found between the Quicktest subtests. Moreover, the Quicktest was significantly correlated to school grades, teachers’ predictions, scores on the Learning Disability Evaluation Scale (LDES) and Trigka’s Reading Test. A Spearman analysis indicated significant correlations between scores on the Quicktest subtests and the grade level of students. Also, a regression analysis indicated that scores on the Quicktest can predict the scores on the other measures. Results supported the Quicktest’s criterion‐related validity and construct validity and, also, its utility as part of a systematic diagnostic procedure for learning disabilities.     

A longitudinal study of the predictive validity of the system of multicultural pluralstic assessment (SOMPA)

The System of Multicultural Pluralistic Assessment (SOMPA) was initially administered to 700 Anglo, 700 Black, and 700 Hispanic children in California elementary schools in order to develop a nonbiased testing program. Ten years later, 1184 of the original 2100 youths were again tested with the SOMPA in high school. At that time, academic achievement and parental interview data also were collected. The results indicate that: (a) Mean achievement test scores and GPAs for the high school students showed that Anglos obtained higher scores than Hispanics, who received higher scores than Blacks. (b) Among the various medical measures, the Bender Gestalt, Fine Motor Sequencing and Finger-Tongue Dexterity tests of the SOMPA were the only ones able to consistently differentiate between youth who did poorly and those who did well academically ten years after their initial testing. (c) Scores on the 1972 IQ test (WISC-R) showed moderate correlations with achievement test scores ten years later. (d) 1972 IQ scores showed low but reliable correlations with GPAs ten years later. (e) In only a very few instances were IQ correlations with achievement test scores higher for minorities than for Anglos. (f) IQ correlated less well with GPA than with achievement test scores for all three ethnic groups. (g) An adjusted IQ, called Estimated Learning Potential (ELP), was more predictive of school achievement than was verbal IQ, particularly for Blacks in the lowest sociocultural quartile. (h) In the second lowest sociocultural quartile, the VIQ correlations with academic measures were reliably higher than the VIQ-ELP correlations, but only for the Anglo and total groups. (i) In the upper two sociocultural quartiles, for all ethnic groups combined, VIQ correlated slightly, but significantly, higher than ELP with school achievement. (j) Also in the upper two quartiles, VIQ correlated higher with academic measures than did VIQ-ELP for both Blacks and Hispanics in almost half of the comparisons. In conclusion, it appears that some subtests of the SOMPA may have some validity for predicting school achievement for students from different ethnic groups.     

Relationships between age and raw score increases on the Kaufman-assessment battery for children

Raw scores on the 16 K-ABC subtests and the total raw scores on the sequential and simultaneous processing scales and the achievement scale were correlated with age in months for two separate samples, each subdivided by race and sex: the K-ABC standardization sample (N = 2000) and an additional group of blacks and whites tested during the development of the K-ABC sociocultural norms (N = 615). Within each sample, the highest and lowest correlations from all race/sex groups were contrasted across all K-ABC subtests and scales. All correlations between age and raw scores were statistically significant (p ⩽ .05). No significant differences occurred in the magnitude of these relationships as a function of race/sex grouping, supporting the construct validity of the K-ABC as a developmental measure of children's aptitude and achievement for blacks, whites, Hispanics, males, and females.     

Graded Achievement,Tested Achievement,and Validity

Twenty-eight studies of grades, over a century, were reviewed using the argument-based approach to validity suggested by Kane as a theoretical framework. The review draws conclusions about the meaning of graded achievement, its relation to tested achievement, and changes in the construct of graded achievement over time. Graded achievement reflects students' broad accomplishment of classroom and school learning goals, including goals about how to learn. Both high school and elementary grades contain information about school achievement that includes being socialized into the way learning happens in classrooms. Graded achievement reflects specific course learning goals and therefore varies according to subject; academic course grades align more closely with tested achievement than noncore course grades. Graded achievement also reflects individual teachers' grading practices and emphases about what is important to learn. Report card grades can be reliable and valid measures of graded achievement, but may not be depending on individual teachers' grading practices.     

Kindergarten knowledge of print conventions and later school achievement: A five-year follow-up

The Concepts About Print (CAP) test administered during kindergarten and first grade was shown to be highly correlated with various tests of school achievement obtained during the second through the fourth grades and to effectively predict those children who would later be retained in school. Based on the results of this longitudinal study, the CAP may be useful in the kindergarten and first grade as an early identifier of children who are relatively high educational risks.     

Grades and Test Scores: Accounting for Observed Differences

Why do grades and test scores often differ? A framework of possible differences is proposed in this article. An approximation of the framework was tested with data on 8,454 high school seniors from the National Education Longitudinal Study. Individual and group differences in grade versus test performance were substantially reduced by focusing the two measures on similar academic subjects, correcting for grading variations and unreliability, and adding teacher ratings and other information about students. Concurrent prediction of high school average was thus increased from 0.62 to 0.90; differential prediction in eight subgroups was reduced to 0.02 letter‐grades. Grading variation was a major source of discrepancy between grades and test scores. Other major sources were teacher ratings and Scholastic Engagement, a promising organizing principle for understanding student achievement. Engagement was defined by three types of observable behavior: employing school skills, demonstrating initiative, and avoiding competing activities. While groups varied in average achievement, group performance was generally similar on grades and tests. Major factors in achievement were similarly constituted and similarly related from group to group. Differences between grades and tests give these measures complementary strengths in high‐stakes assessment. If artifactual differences between the two measures are not corrected, common statistical estimates of validity and fairness are unduly conservative.     

Comparison of Item Response Theory and Thurstone Methods of Vertical Scaling

Vertical achievement scales, which range from the lower elementary grades to high school, are used pervasively in educational assessment. Using simulated data modeled after real tests, the present article examines two procedures available for vertical scaling: a Thurstone method and three-parameter item response theory. Neither procedure produced artifactual scale shrinkage; both procedures produced modest scale expansion for one simulated condition.     

A Longitudinal Study of Sex-Related Item Bias in Mathematics Subtests of the California Achievement Test

The purpose of this study was to investigate the mathematics components of an achievement battery for differential item performance between boys and girls. By employing a longitudinal study, changes in differential item performance from Grades 4 to 6 were explored, thereby avoiding confounding of age and cohort differences. Two statistical procedures were employed to investigate differential performance at both the test and item level (Spearman's rho and Camilli's chi-square). Items in two mathematics subtests, Mathematics Computation (MC) and Mathematics Concepts and Applications (MCA), did not appear to be a source of sex-related bias. Girls scored higher than boys on MC subtest across grades. Boys scored higher than girls across grades on MCA subtest. However, there were no skill classifications, ability levels, or item locations that favored one sex group consistently across grades.     

School Mobility and Achievement for Children Placed and Not Placed in Out-of-home Care

ABSTRACT

The aim was to investigate the effects of school mobility on achievement in compulsory school in Sweden for children in out-of-home care (OHC) and not in OHC (NOHC). Register data on background variables from four birth cohorts in the cohort-sequential longitudinal project ETF was relied upon, along with student performance on a test of cognitive ability, and school grades according to the leaving certificate. Yearly data concerning school mobility also was available. Results showed that relocation was associated with lower grades for both the OHC and the NOHC groups. The mean effect of one school relocation was 5 percentiles lower grades, but the effect of relocation was twice as large at the end of compulsory school. Given a higher frequency of relocation for children in OHC, they were more negatively affected. School mobility thus is one of several factors which contribute to the poor school achievement of children in OHC.     

Comparing Class- and Task-Level Measures of Achievement Goals

Models of achievement goals suggest that different tasks and contexts influence the goals students adopt at a given time. However, many studies of achievement goals rely on measures assessed at the class level, analyze results with a variable-centered approach, and employ self-report questionnaires, which may reduce understanding of the contextual factors that arise as students interact with tasks. We compared a behavioral, task-level measure of middle school students' achievement goals to a self-reported, class-level measure and analyzed both measures' relations to task performance and quarterly grades using both variable-centered and person-centered approaches. Task-level goals predicted task performance but not quarterly grades, while class-level goals predicted grades but not task performance. The two measures of achievement goals were not related. This work demonstrates the importance of measuring goals at multiple levels and suggests opportunities for changing students' behaviors and achievement through motivation at the task level.     

THE VALIDITY OF ACADEMIC PREDICTORS FOR BLACK AND WHITE STUDENTS AT A PREDOMINANTLY WHITE UNIVERSITY1

High school grades and both the verbal and mathematical scales of the Scholastic Aptitude Test (SAT-V and SAT-M, respectively) were examined as predictors of college grade point average in groups divided by race and sex. Results indicated that high school grades were not correlated as highly with college grades for black males as for the other three groups, although there were no significant differences in the correlation of either SAT-V or SAT-M with college grades. Moreover, the multiple regression equation for the black male group differed from the equations for the other groups in that SAT-V is the predictor of primary importance rather than high school grades. Weights derived on a random sample of the student body caused substantial shrinkage of the multiple R only in the black male sample. Both black males and black females were significantly overpredicted by such weights. The importance of separate prediction equations for race-sex groupings was emphasized.     

Students’ individual and collective efficacy: joining together two sets of beliefs for understanding academic achievement

In this paper, we assume that students’ achievement is influenced not only by a set of individual appraisals such as beliefs about their personal efficacy but also by a set of more systemic factors related to beliefs about their class efficacy as a group. Literature and research review supports that students’ beliefs about their efficacy, both as individuals and as groups, are important predictors of their achievements at school. However, little research has been presented to date that jointly explores the impact of these two sets of beliefs on academic achievement. Therefore, the aim of this paper is to present an integrated view of individual and collective efficacy beliefs, exploring the relationship between them and their causal relationship with students’ achievement. Two cross-sectional studies were developed in the Portuguese secondary school context with 385 and 1,794 students, using Academic Self-Efficacy Scale and Students Collective Efficacy Scale to assess individual and collective efficacy beliefs. The main results showed that individual efficacy beliefs were stronger predictors of students’ grades than collective efficacy beliefs, especially when the specific domain of achievement they refer to was considered (for instance, levels of mathematics self-efficacy had a stronger impact on mathematics grades than on Portuguese grades). Moreover, moderating effects of gender and type of school (public vs. non-public) were found, suggesting that collective efficacy beliefs play a more significant role among boys and among students from public schools.     

Making the written word “speak”: Reflections on the teaching of correspondence courses

Abstract

Learning outcomes for an interactive television‐based distance learning course in introductory high school Japanese were evaluated in three successive years by comparing student achievement in the distance learning course to that in traditional classes. Year‐end achievement tests of listening and written language competency were administered to students in both the distance and face‐to‐face courses. Results in the first two years showed that test scores of students in the distance learning course were higher than those of students in the face‐to‐face classes; however, possible group differences in motivation, general ability, and experience as language learners could not be ruled out as explanations for the difference. Therefore, achievement measures were supplemented in the third year with data on students’ perceived efficacy as Japanese language users, their grades, and their previous foreign language learning experience. The achievement data again showed differences favoring the distance learning group; trends were consistent for students with differing levels of school success and amount of prior language learning experience. Factors that could account for these results are hypothesized and suggestions for future research are proposed.     

Cognitive and motivational profile shape predicts mathematical skills over and above profile level

The interpretation of subtest profiles from intelligence testing remains popular among many practitioners who use subtest performance to draw diagnostic conclusions, in spite of criticism by some researchers, who point to the low reliability and predictive validity of subtest scores in predicting achievement outcomes. Prior research outlines two approaches to the study of subtest variation: the examination of interindividual variation in specific cognitive domains or subtests as compared to a standard sample, and the examination of intraindividual strengths and weaknesses, regardless of overall level. The present study seeks to add to knowledge in this field with data from 567 children ages 5 to 10 years who exhibit meaningful subtest variation on a new test of intellectual abilities. Results from the present sample point to statistically significant utility, with small to medium effects, of intraindividual cognitive and motivational profile shape over and above profile level in predicting mathematical skills. We discuss implications for school psychological and educational assessment research.     

Age of Entry to Kindergarten and Children's Academic Achievement and Socioemotional Development

Research Findings: Data on more than 900 children participating in the National Institute of Child Health and Human Development Study of Early Child Care were analyzed to examine the effect of age of entry to kindergarten on children's functioning in early elementary school. Children's academic achievement and socioemotional development were measured repeatedly from the age of 54 months through 3rd grade. With family background factors and experience in child care in the first 54 months of life controlled, hierarchical linear modeling (growth curve) analysis revealed that children who entered kindergarten at younger ages had higher (estimated) scores in kindergarten on the Woodcock—Johnson (W-J) Letter-Word Recognition subtest but received lower ratings from kindergarten teachers on Language and Literacy and Mathematical Thinking scales. Furthermore, children who entered kindergarten at older ages evinced greater increases over time on 4 W-J subtests (i.e., Letter-Word Recognition, Applied Problems, Memory for Sentences, Picture Vocabulary) and outperformed children who started kindergarten at younger ages on 2 W-J subtests in 3rd grade (i.e., Applied Problems, Picture Vocabulary). Age of entry proved unrelated to socioemotional functioning.

Practice: The fact that age-of-entry effects were small in magnitude and dwarfed by other aspects of children's family and child care experiences suggests that age at starting school should not be regarded as a major determinant of children's school achievement, but that it may merit consideration in context with other probably more important factors (e.g., child's behavior and abilities).     

Exploring the Influence of Efficacy Beliefs and Homework Help in Predicting Reading Achievement Among Underserved Children in an Afterschool Program

The purpose of this study was to determine the effectiveness of a local afterschool program in helping underserved elementary school students improve their reading achievement. The study followed a cohort of students with 28 participants who were low-income, ethnic minority children in the 1st–6th grades between the ages of 6 and 12. Data on students’ developmental assets and school progress were collected at two different time points. Overall, students showed increased perceptions of efficacy about having the ability and skills to do well on a task and getting good grades in school, as well as improvements in reading achievement over time. While changes in homework completion predicted changes in reading achievement, changes in efficacy beliefs and program exposure did not. Results suggest that teacher perceptions of homework completion may be an important pathway through which afterschool programs can help narrow the reading achievement gap experienced by ethnic minority students from disadvantaged backgrounds.     

Age of Entry to Kindergarten and Children's Academic Achievement and Socioemotional Development

Research Findings: Data on more than 900 children participating in the National Institute of Child Health and Human Development Study of Early Child Care were analyzed to examine the effect of age of entry to kindergarten on children's functioning in early elementary school. Children's academic achievement and socioemotional development were measured repeatedly from the age of 54 months through 3rd grade. With family background factors and experience in child care in the first 54 months of life controlled, hierarchical linear modeling (growth curve) analysis revealed that children who entered kindergarten at younger ages had higher (estimated) scores in kindergarten on the Woodcock—Johnson (W-J) Letter-Word Recognition subtest but received lower ratings from kindergarten teachers on Language and Literacy and Mathematical Thinking scales. Furthermore, children who entered kindergarten at older ages evinced greater increases over time on 4 W-J subtests (i.e., Letter-Word Recognition, Applied Problems, Memory for Sentences, Picture Vocabulary) and outperformed children who started kindergarten at younger ages on 2 W-J subtests in 3rd grade (i.e., Applied Problems, Picture Vocabulary). Age of entry proved unrelated to socioemotional functioning.

Practice: The fact that age-of-entry effects were small in magnitude and dwarfed by other aspects of children's family and child care experiences suggests that age at starting school should not be regarded as a major determinant of children's school achievement, but that it may merit consideration in context with other probably more important factors (e.g., child's behavior and abilities).     

“How do you feel about math?”: relationships between competence and value appraisals,achievement emotions and academic achievement

This study analyzes the relationships between cognitive appraisals, classroom and test emotions, and math achievement in a sample of 1219 Portuguese students from the 6th and 8th grades. Participants completed measures of perceived value, perceived competence, and seven math achievement emotions (boredom, hopelessness, anger, anxiety, enjoyment, pride, and relief) experienced in two different settings: classroom and tests. Math achievement was obtained from school records. Results showed significant associations between student competence and value appraisals, their emotional experiences in test and classroom situations, and their math achievement. However, when emotions were considered simultaneously in structural equation modeling, only anger in test situations and hopelessness were significant negative predictors of students’ math achievement. Hopelessness appears to play a particular role in the interplay between cognitive appraisals, emotions, and academic achievement as it is the only emotion that relates to math achievement both in test and classroom situations. Furthermore, findings also support the existence of differences in the relationships between cognitive appraisals and the achievement emotions students experience in these two settings.