The Effects of Within-Class Ability Grouping on Academic Achievement in Early Elementary Years

Abstract

By incorporating two theoretical frameworks this study examines how school characteristics shape first-grade reading ability-grouping practices, and how this, in turn, affects students’ reading achievement. The author uses the data from the Early Childhood Longitudinal Study and applies the propensity-score method to examine whether first-grade ability grouping improves student achievement, whether ability grouping increases achievement inequalities, and whether its effects vary by student initial abilities and/or school contexts. Findings support an argument that ability grouping is an organizational response to problems of diversity in the student body. Schools that use ability grouping are likely to have heterogeneous ability compositions. They are also public, low-performing, low socioeconomic status, and high-minority schools. In these schools, ability grouping has no effects or negative effects, particularly for low-ability students. In contrast, ability grouping may improve achievement for all students in schools with advantageous characteristics, mostly private schools, and may reduce achievement inequalities, because low-ability students benefit the most from this practice.     

Achievement and Attitudinal Differences among Students in Regular,Remedial, and Advanced Classes

The collection of data by the National Center for Educational Statistics for the High School and Beyond study offered an opportunity to examine differences in achievement and attitudinal measures among students in regular, remedial, and advanced classes. Groups of low achieving and high achieving sophomores and seniors were identified on the basis of overall grades. Comparisons were made between students in regular and ability-grouped English and mathematics classes. The data were consistent with views that grouping leads to improved achievement and attitude toward subject matter for students in regular and remedial classes. The data were not consistent with a view that remedial group placement leads to poor self-concept or attitude toward school.     

Academic Outcomes of Ability Grouping Among Junior High School Students in Hong Kong

Abstract

Ability grouping is supposedly undesirable because it leads to deficits in academic self-concept and academic achievement. However, it appears to be justifiable for its improvement of teaching and learning in schools, perhaps more so in a collectivist culture. In view of the paucity of data examining the controversy in Hong Kong, the authors collected data from 2,720 junior high school students with a random sampling procedure and obtained teachers' reports about the students' subsequent academic achievement, ability grouping, and the ability level of the class. The authors maintained students' past academic achievement as a control variable in predicting their subsequent academic achievement and self-concepts. Results revealed no significant detrimental effect caused by the ability-grouped class and the ability level of the ability-grouped class. Rather, students in classes that were more homogeneous according to past academic achievement tended to have significantly higher subsequent academic achievement and self-esteem. Results revealed no variation attributable to each student's gender and IQ in the effects of ability grouping.     

An Education Action Zone at work: primary teacher perceptions of the efficacy of a creative learning and collaborative leadership project

This article reports on the grouping practices used by a cohort of 10 newly qualified primary teachers for teaching mathematics in different English primary schools. It examines the factors that influence why these teachers group as they do. All the teachers grouped their pupils on the basis of achievement or perceived ability for mathematics. It was found that the factors that influenced the grouping arrangements were complex and not always consistent with the teachers' aims and beliefs.     

Grouping Students for Elementary School Mathematics: A Survey of Principals in 12 States

ABSTRACT

In this study I explored how elementary school students are initially assigned to homeroom classrooms (criteria used and heterogeneous vs. homogeneous grouping), subsequently assigned to mathematics classes (e.g., self‐contained, regrouped, departmentalized), and grouped for mathematics instruction within classes (e.g., whole‐class, two groups, individualized). This three‐dimensional typology of school and classroom organization was used to survey 571 elementary school principals from 12 states. Results showed that students were generally assigned to heterogeneous self‐contained homeroom classes, that they remained in these same classes for mathematics, and that mathematics was usually taught to entire classes (whole class). Within‐class ability grouping, within‐grade regrouping, and departmentalized plans were used increasingly for mathematics at the intermediate grades, but across‐grade or Joplin Plan programs were infrequent.     

Testing the Immediate and Long-Term Efficacy of a Tier 2 Kindergarten Mathematics Intervention

ABSTRACT

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly assigned to treatment or control conditions. Measures of mathematics achievement were collected in the fall (pretest) and spring (posttest) in kindergarten and in the winter of first grade (delayed posttest). Significant differences between conditions favoring treatment students were found on four of six measures at posttest. Treatment students reduced the achievement gap with their not-at-risk peers. No effect was found on follow-up first-grade achievement scores. Implications for Tier 2 mathematics instruction in a Response to Intervention model are discussed.     

Improving quality and equity in schools in socially disadvantaged areas

Background: Recent effectiveness studies have investigated the relationship between two dimensions of effectiveness – namely, quality and equity. Specifically, the question of whether effective schools can also reduce the initial differences in student outcomes attributed to student background factors has been examined. In this context, the Dynamic Approach to School Improvement (DASI) makes use of theory and the research findings of effectiveness studies to try to improve school effectiveness in terms of quality and equity.

Purpose: This study aimed to examine whether the implementation of DASI in primary schools in socially disadvantaged areas in four European countries (Cyprus, England, Greece and Ireland) was able to promote student learning outcomes in mathematics and to reduce the impact of student background factors on student achievement in mathematics.

Design and methods: A sample of 72 primary schools across the four countries was randomly split into experimental and control groups. At the beginning and at the end of the school year, mathematics tests were administered to all students of Grades 4–6 (n = 5560; student ages 9–12 years). The experimental group made use of DASI. Within-country multilevel regression analyses were conducted to evaluate the impact of the intervention and search for interaction effects between the use of DASI and student background factors on final achievement.

Results: In each country, the experimental group achieved better results in mathematics than the control group. At the beginning of the intervention, the achievement gap based on socio-economic status (SES) was equally large in the experimental and the control groups. Only in the experimental group did the achievement gap based on SES become smaller. However, DASI was not found to have an effect on equity when the equity dimension was examined by focusing on the achievement gap based on either gender or ethnicity.

Conclusions: Implications of findings are drawn and the importance of measuring equity in terms of student achievement gaps based on different background factors, rather than only on SES, is emphasised. We propose the evaluation of the impact of interventions on promoting equity by the use of various criteria.     

Institutional and Student Factors and Their Influence on Advanced Mathematics Achievement

Abstract

The author examined advanced mathematics achievement with 1,839 students from 162 schools. The data were obtained from the Third International Mathematics and Science Study Population 3 cohort; the author used hierarchical (multilevel) linear modeling to examine student- and school-level factors. Even within the advanced mathematics cohort, gender and economic disparities existed, but the magnitude of these disparities varied from school to school. Average parent education was observed to be associated with the magnitude of the coefficient for attitude toward mathematics on achievement. The more a student believed that success in mathematics was caused by natural ability, the higher the score on the test. Finally, resources, school size, and average parent education were significantly associated with school mean achievement in advanced mathematics.     

Extroversion as a Factor Conditioning AchieveMent in the Fifth and Sixth Grades of the Elementary School

Abstract

One-hundred-eighty-five hig-school junior and senior students were classified as underachievers, overachievers, and achievers, by percent lie rank positions on CEE11 scores and achievement tests In mathematics. An examination was made of the relationship of facilitating: and debilitating anxiety and four teacher motivation cues to the three levels of scholastic achievement. Girls were more sensitive than the hoys to the motive-arousing: cues provided by their teachers, yet differential sex and group reactions were reported In the perception of teacher cues. Facilitating as well as debilitating anxiety was a determining variable for both sexes on all three achieving groups.     

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the “Groupitizing” ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.     

The Present Status and Significance of Manuscript Writing

Abstract

Teachers’ expectations as they relate to student achievement outcomes have received much research attention. Student expectations for their own achievement have not. Noninduced student expectations for their individual achievement, and for male and female differential achievement, in mathematics classes were assessed for 698 eighth grade students. Expectations were measured early in the school year via written self-report. Student ability level was also ascertained and controlled. Individual achievement expectations were found to relate to students’ subsequent achievement across criterion variables and times of the year.     

Effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers

An experiment was conducted to examine the effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers at a middle school in the North‐West Province of South Africa. Forty standard (std) 7 pupils were identified whose non‐verbal general ability and previous mathematics achievements were significantly lower than those of other std 7 pupils. These subjects were randomly assigned to an experimental group and a control group. Metacognitive strategies in solving mathematical problems related to four mathematics topics were individually taught to the members of the experimental group, while the pupils in the control group were taught the four mathematics topics through the conventional method of teaching mathematics. The comparisons of pretest and posttest measures of general ability, metacognitive awareness, attitude towards mathematics, and mathematics achievement revealed that the posttest scores of all the four variables for the experimental group were significantly higher than those for the control group.     

A Longitudinal Assessment of Antecedent Course Work in Mathematics and Subsequent Mathematical Attainment

Abstract

Using six waves of data (Grades 7–12) from the Longitudinal Study of American Youth, the author examined the effects of different mathematics course work (pre-algebra, geometry, calculus) on subsequent achievement in, and attitude toward, mathematics, with partial adjustment for student background characteristics. Results showed that in the early grades of high school, algebra courses significantly affected mathematics achievement. Mathematics course work, however, did not play a significant role in mathematics achievement in the middle grades of high schools. There was a “harvest” of significant course-work indicators in the later grades of high school; every advanced mathematics course affected mathematics achievement. Many course-work effects were substantial even after accounting for variables such as prior mathematics achievement and socioeconomic status.     

Relationship between affect and achievement in science and mathematics in Malaysia and Singapore

Background : The Trends in International Mathematics and Science Study (TIMSS) assesses the quality of the teaching and learning of science and mathematics among Grades 4 and 8 students across participating countries.

Purpose : This study explored the relationship between positive affect towards science and mathematics and achievement in science and mathematics among Malaysian and Singaporean Grade 8 students.

Sample : In total, 4466 Malaysia students and 4599 Singaporean students from Grade 8 who participated in TIMSS 2007 were involved in this study.

Design and method : Students’ achievement scores on eight items in the survey instrument that were reported in TIMSS 2007 were used as the dependent variable in the analysis. Students’ scores on four items in the TIMSS 2007 survey instrument pertaining to students’ affect towards science and mathematics together with students’ gender, language spoken at home and parental education were used as the independent variables.

Results : Positive affect towards science and mathematics indicated statistically significant predictive effects on achievement in the two subjects for both Malaysian and Singaporean Grade 8 students. There were statistically significant predictive effects on mathematics achievement for the students’ gender, language spoken at home and parental education for both Malaysian and Singaporean students, with R ² = 0.18 and 0.21, respectively. However, only parental education showed statistically significant predictive effects on science achievement for both countries. For Singapore, language spoken at home also demonstrated statistically significant predictive effects on science achievement, whereas gender did not. For Malaysia, neither gender nor language spoken at home had statistically significant predictive effects on science achievement.

Conclusions : It is important for educators to consider implementing self-concept enhancement intervention programmes by incorporating ‘affect’ components of academic self-concept in order to develop students’ talents and promote academic excellence in science and mathematics.     

A Beginning Reading Vocabulary

Abstract

Two ability tests (verbal and nonverbal), six achievement tests, and seven scales of the Self Observation Scales (a measure of self- concept) were completed by 225 sixth graders in two West Virginia rural counties. Self concept (measured by the SOS) was shown to add significantly to the prediction equation for achievement over and above the contribution of nonverbal intelligence. The SOS accounted for 22 percent of the variance in reading achievement, and combined with nonverbal intelligence to account for 34 percent of the variance in reading achievement.     

Effects of Classroom Structure on Student Achievement Goal Orientation

Abstract

The authors assessed how classroom structure influenced student achievement goal orientation for mathematics. Three elementary school classes were assigned randomly to 1 classroom structure condition: token economy, contingency contract, or control. Students in each condition were required to set individual achievement goals on a weekly basis. The authors assessed differences in goal orientation by comparing the number of learning vs. performance goals that students set within and across classroom structure conditions. Results indicated that students in the contingency-contract condition set significantly more learning goals than did students in other classroom structure conditions. No significant differences were found for performance goals across classroom structure conditions. Within classroom structure conditions, students in the contingency-contract group set significantly more learning goals than performance goals, whereas students in the token-economy condition set significantly more performance goals than learning goals.     

Curriculum: Broad brushstrokes or paint‐by‐the‐numbers?

Abstract

A renewed emphasis on standardized achievement tests has left teachers bewildered about what to teach and how to teach it. This article attempts to address that issue. Modified or enhanced mathematics instruction was the focus of this study based on two factors: national concerns over students’ achievement in mathematics and technology and the existence of an identified, national set of standards for mathematics instruction. Qualitative methodology was used to address research questions. Teachers involved in the study were trained in the different elements of curriculum modification practices and had one additional hour of orientation to the mathematics unit used in the study. Results of this study suggested that a modified or enhanced curriculum unit alone, with appropriate, escalated learning goals (Schunk, 1996) and authentic resources and products (Renzulli, 1977) can create substantial interest, motivation, and a perceived value in learning for students of all ability levels.     

Performance in solving arithmetic problems: a comparison of children with different levels of achievement in mathematics and reading

The aim of the present study was to investigate the performance in arithmetic related to achievement levels in reading and mathematics. Basic arithmetical facts and multi‐step calculations were examined. The participants were 941 pupils aged 8 (N = 415), 10 (N = 274) and 13 (N = 252) years. The pupils were divided into four groups by standardized achievement tests. One group showed low achievement in both mathematics and reading (MLRL), a second group showed low achievement in mathematics only (ML‐only), a third group in reading only (RL‐only) and a fourth group showed normal achievement in both mathematics and reading (NA). The ML‐only and the MLRL groups did not differ significantly in basic arithmetical facts at any age level, but both groups performed below the RL‐only and NA groups. The two latter groups also performed similarly at all year levels. In multi‐step calculation all groups differed significantly at the lowest age level, with the NA as the group with the best achievement, followed by RL‐only, ML‐only and the MLRL group. At the two highest age levels the relations between the groups, in multi‐step calculation, were in accordance with the results regarding basic facts. The findings indicate, for both normal and low general mathematical ability, that low achievement in reading to a small extent interferes with the pupils’ development of arithmetic performance     

Recency of Secondary School Mathematical Preparation as an Influence on First-Year College Mathematics Achievement

Abstract

A random sample of four hundred college freshman mathematics students with comparable high school mathematical preparation was selected from 1,435 students. The test group included 126 members who had not attempted a mathematics course during their last year in high school, designated as Group N, and 263 members who had received mathematical credit during their last year, designated as Group Y. Statistical treatment of data for each group indicated that the SAT mathematical aptitude scores, CEEB (Level I) mathematical achievement scores, and achievement in first-year college mathematics courses was greater for Group Y at the .01 level of confidence. The achievement comparison was based on an analysis of covariance procedure with SAT Mathematical scores, CEEB Mathematical scores, and sex of student used as adjusting variables.     

A Comparison and Evaluation of Two Methods of Organization for the Teaching of Reading

Abstract

In order to test the hypothesis that field independence would interact with level of guidance, students in five mathematics classes were randomly assigned to either a low guidance or a high guidance treatment group for a week of instruction. Both treatments used an inductive sequence of instruction on the topic of networks. Students were assessed on two aptitudes, field independence and general reasoning. Achievement was significantly better (p > .05) in the high guidance group than the low guidance group on both the posttest and the retention test. No significant interactions with the aptitude variables were found.