The association of precollege use of calculators with student performance in college calculus

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about students’ demographics, standardized test scores, and high school mathematics course enrollment and performance. Factor analysis reduced ten items describing high school calculator usage to two composites: how extensively calculators were employed and teacher-imposed restrictions on their use. Hierarchical linear models predicted students’ college calculus grades, reported by their professor, while controlling for differences between colleges and student backgrounds. The more extensively students had used calculators in high school, the lower their grade in college calculus. However, students earned higher college calculus grades to the extent that their high school teachers had limited calculator use on quizzes and exams and had restricted calculator use until paper-and-pencil methods had been mastered, which offset the negative association of extensive calculator use with grades. The effect sizes of both calculator composites were very small. Overall, the findings raise doubts about any substantial long-term effects on college mathematics performance of calculator use in high school.     

Analysis of Student Performance in Large-Enrollment Life Science Courses

This study examined the historical performance of students at Michigan State University in 12 life sciences courses over 13 yr to find variables impacting student success. Hierarchical linear modeling predicted 25.0–62.8% of the variance in students’ grades in the courses analyzed. The primary predictor of a student''s course grade was his or her entering grade point average; except for the second course in a series (i.e., Biochemistry II), in which the grade for the first course in the series (i.e., Biochemistry I) was often the best predictor, as judged by β values. Student gender and major were also statistically significant for a majority of the courses studied. Female students averaged grades 0.067–0.303 lower than their equivalent male counterparts, and majors averaged grades were 0.088–0.397 higher than nonmajors. Grades earned in prerequisite courses provided minimal predictive ability. Ethnicity and involvements in honors college or science residential college were generally insignificant.     

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.     

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.     

Gender Bias in the Prediction of College Course Performance

Is the relationship of college grades to the traditional predictors of aptitude test scores and high school grades different for men and women? The usual gender bias of underpredicting the grade point averages of women may result from gender-related course selection effects. This study controlled course selection effects by predicting single course grades rather than a composite grade from several courses. In most of the large introductory courses studied, no gender bias was found that would hold up on cross-validation in a subsequent semester. Usually, it was counterproductive to adjust grade predictions according to gender. Grade point average was predicted more accurately than single course grades     

Examination of Indices of High School Performance Based on the Graded Response Model

We examined summary indices of high school performance (coursework, grades, and test scores) based on the graded response model (GRM). The indices varied by inclusion of ACT test scores and whether high school courses were constrained to have the same difficulty and discrimination across groups of schools. The indices were examined with respect to skewness, incremental prediction of college degree attainment, and differences across racial/ethnic and socioeconomic subgroups. The most difficult high school courses to earn an “A” grade included calculus, chemistry, trigonometry, other advanced math, physics, algebra 2, and geometry. The GRM‐based indices were less skewed than simple high school grade point average (HSGPA) and had higher correlations with ACT Composite score. The index that included ACT test scores and allowed item parameters to vary by school group was most predictive of college degree attainment, but had larger subgroup differences. Implications for implementing multiple measure models for college readiness are discussed.     

The Role of Socioeconomic Status in SAT–Freshman Grade Relationships Across Gender and Racial Subgroups

Recent research has shown that admissions tests retain the vast majority of their predictive power after controlling for socioeconomic status (SES), and that SES provides only a slight increment over SAT and high school grades (high school grade point average [HSGPA]) in predicting academic performance. To address the possibility that these overall analyses obscure differences by race/ethnicity or gender, we examine the role of SES in the test‒grade relationship for men and women as well as for various racial/ethnic subgroups within the United States. For each subgroup, the test‒grade relationship is only slightly diminished when controlling for SES. Further, SES is a substantially less powerful predictor of academic performance than both SAT and HSGPA. Among the indicators of SES (i.e., father's education, mother's education, and parental income), father's education appears to be strongest predictor of freshman grades across subgroups, with the exception of the Asian subgroup. In general, SES appears to behave similarly across subgroups in the prediction of freshman grades with SAT scores and HSGPA.     

Sensitivity to orthotactic rules in visual word recognition by below average readers

The study reports 2 lexical decision experiments on below average readers' sensitivity to Basic Orthographic Syllabic Structure (BOSS) of Taft in visual word recognition. In Experiment 1, 20 words and 20 pseudo words with BOSS and non-BOSS conditions (e.g., tractOR, tracTOR; BLUNDin, BLUNdin) were presented on a microcomputer screen to 75 grades 4, 5, and 6 poor readers divided into poor reading/spelling subgroups. ANOVA of the correct reaction time scores shows significant main effects for grade, reading/spelling subgroup and lexicality with both word and pseudo word BOSS condition being the most discriminating. Experiment 2 provides a stronger test for the BOSS parsing principle with 48 items of correctly affixed real words (e.g., reTURN), pseudo-affixed words (e.g., ENTer), and incorrectly affixed pseudo words (e.g., AVOIDer) presented on the microcomputer screen for lexical decision. The target subjects were 20 grade 6 and 22 grade 7 below average readers compared with 23 above average chronological age control readers in each of the same grades 6 and 7. ANOVA results of the correct RT scores show significant main effects for reding level and affixation condition with the correctly affixed BOSS condition being the most discriminating. Taken together, the 2 experiments suggest that children are sensitive to the BOSS parsing principle and this could be used in promoting word knowledge.     

College Course Grades for Dual Enrollment Students

This study compared college course grade outcomes, both during and after high school, of dual-enrollment students to those of traditional students. The study was based on a large, multiyear sample of Iowa high school and community college students. The results showed that while in high school, dual-enrollment students consistently outperformed traditional students in community college courses. However, much of the difference might be due to underlying differences in the two groups associated with the type of college the students chose to attend after high school (i.e., four-year vs. two-year). Dual enrollment students tended to perform about the same as traditional students in terms of post-high-school community college course grades. For students who enrolled in four-year institutions after high school, analyses of college course grade data suggested a small positive effect of dual enrollment on first-year college grade point average (GPA).     

THE ASSOCIATION AMONG STUDENT SUCCESS IN COURSES,PLACEMENT TEST SCORES,STUDENT BACKGROUND DATA,AND INSTRUCTOR GRADING PRACTICES

Growth in the use of testing to determine student eligibility for community college courses has prompted debate and litigation regarding over the equity, access, and legal implications of these practices. In California, this has resulted in state regulations requiring that community colleges provide predictive validity evidence of test-score?based inferences and course prerequisites. In addition, companion measures that supplement placement test scores must be used for placement purposes. However, for both theoretical and technical reasons the predictive validity coefficients between placement test scores and final grades or retention in a course generally demonstrate a weak relationship. The study discussed in this article examined the predictive validity of placement test scores with course grade and retention in English and mathematics courses. The investigation produced a model to explain variance in course outcomes using test scores, student background data, and instructor differences in grading practices. The model produced suggests that student dispositional characteristics explain the high proportion of variance in the dependent variables. Including instructor grading practices in the model adds significantly to the explanatory power and suggests that grading variations make accurate placement more problematic. This investigation underscores the importance of academic standards as something imposed on students by an institution and not something determined by the entering abilities of students.     

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.     

Selected factors associated with achievement of biology preparatory students and their follow-up to higher level biology courses

This study was undertaken to determine whether a biology preparatory course given at an urban community college was helping students to develop the proper skills and background necessary for them to successfully complete follow-up courses in biology. A group of students who enrolled in a biology preparatory course, and subsequently, a follow-up anatomy and physiology or general biology course (experimental group) was compared to a group of students who should have registered for the preparatory course, but who enrolled directly into the anatomy and physiology or general biology course (control group). It was shown that there was no significant difference in their anatomy and physiology or general biology grades. Furthermore, only 16% of the initial group of preparatory students enrolled in and passed a follow-up biology course. Examination of the preparatory group using discriminant analysis ascertained that mathematics score was the principle discriminator between pass/fail groups. A stepwise multiple regression analysis of the variables explaining the preparatory grade showed that mathematics score, reading score, and type of high school degree explained 33% of the variance. Of the students who did pass the preparatory course and enrolled in a follow-up biology class, their preparatory grade was a good predictor of their achievement (measured by follow-up course grade), as determined by multiple regression.     

浅谈微积分在初等数学中的应用

本文通过对微分在解决一些初等函数单调性、求曲线的切线以及几个初等数学命题的积分证明等问题的讨论,为我们解决一些初等数学问题提供了一些新的思想,使微积分对初等数学的指导作用得到具体体现。     

Academic Performance,Age, Gender,and Ethnicity in Online Courses Delivered by Two-Year Colleges

This study investigated the effects the demographic variables age, gender, and ethnicity and their interactions had on academic performance in online courses delivered by public two-year colleges in Kentucky. The study controlled for previous academic performance measured by cumulative grade point average (GPA). The study used a random sample (N = 320) of all students who had enrolled in at least one online course delivered by the institutions of the Kentucky Community and Technical College System in the spring 2008 semester. A linear hierarchical multiple regression acting as ANCOVA served as the main analysis, with the order entry as follows: cumulative GPA; independent variables (age, gender, ethnicity); interaction vectors; and product vectors. Final course grade served as the dependent variable. The results of the analysis indicated that only cumulative GPA was a significant predictor, explaining approximately 40% of the variance of the final grade. Although differences in final grades were present among the variables age and ethnicity, these differences disappeared when controlling for cumulative GPA. Significance of the results and recommendations for future research are discussed.     

Predicting Student Success in a Major’s Introductory Biology Course via Logistic Regression Analysis of Scientific Reasoning Ability and Mathematics Scores

Studies over the last 30 years have considered various factors related to student success in introductory biology courses. While much of the available literature suggests that the best predictors of success in a college course are prior college grade point average (GPA) and class attendance, faculty often require a valuable predictor of success in those courses wherein the majority of students are in the first semester and have no previous record of college GPA or attendance. In this study, we evaluated the efficacy of the ACT Mathematics subject exam and Lawson’s Classroom Test of Scientific Reasoning in predicting success in a major’s introductory biology course. A logistic regression was utilized to determine the effectiveness of a combination of scientific reasoning (SR) scores and ACT math (ACT-M) scores to predict student success. In summary, we found that the model—with both SR and ACT-M as significant predictors—could be an effective predictor of student success and thus could potentially be useful in practical decision making for the course, such as directing students to support services at an early point in the semester.     

It's not which school but which set you're in that matters: the influence of ability grouping practices on student progress in mathematics

The mathematics achievement of a cohort of 955 students in 42 classes in six schools in London was followed over a 4‐year period, until they took their General Certificate of Secondary Education examinations (GCSEs) in the summer of 2000. All six schools were regarded by the Office for Standards in Education (Ofsted) as providing a good standard of education, and all were involved in teacher training partnerships with universities. Matched data on Key Stage 3 test scores and GCSE grades were available for 709 students, and these data were analysed in terms of the progress from Key Stage 3 test scores to GCSE grades. Although there were wide differences between schools in terms of overall GCSE grades, the average progress made by students was similar in all six schools. However, within each school, the progress made during Key Stage 4 varied greatly from set to set. Comparing students with the same Key Stage 3 scores, students placed in top sets averaged nearly half a GCSE grade higher than those in the other upper sets, who in turn averaged a third of a grade higher than those in lower sets, who in turn averaged around a third of a grade higher than those students placed in bottom sets. In the four schools that used formal whole‐class teaching, the difference in GCSE grades between top and bottom sets, taking Key Stage 3 scores into account, ranged from just over one grade at GCSE to nearly three grades. At the schools using small‐group and individualized teaching, the differences in value‐added between sets were not significant. In two of the schools, a significant proportion of working‐class students were placed into lower sets than would be indicated by their Key Stage 3 test scores.     

Announced Repetitive Tests as a Basis for Self-Directed Study and Evaluation

College students voluntarily took all their courses or one course on a pass-fail basis. The mean grade point average (GPA) before conversion to pass-fail for freshmen taking all their courses on a pass-fail basis was 1.67 (C-), which is significantly lower than the 2.26 (C+) for controls who wanted but were denied pass-fail grading. Even after returning to conventional grading the former pass-fail students continued to get significantly lower grades than controls. Juniors taking one course on a pass-fail basis received significantly lower grades, before conversion, in their pass-fail course (mean 2.07) than did controls who wanted but were denied pass-fail grading (mean 2.40). There was no compensatory improvement in the grades received in non-pass-fail courses.     

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.     

Monitoring Student Achievement for Accountability: The Demonstration of a Model

Abstract

This study demonstrated a procedural model that can be applied by any school to assess, guide, and account for the progress of its students as well as to analyze its own effectiveness. The model uses equivalent achievement tests to monitor student achievement in subject areas at grade levels, between grade levels, and across subgroups of students. Multiple regression analyses of test scores between grades identify factors associated with achievement Using sixth and eighth grade Comprehensive Tests of Basic Skills scores in a matched longitudinal sample of 208 students, the study found small differences in average achievement between boys and girls. Differences between corresponding sixth and eighth grade test means were higher in mathematics than in language. From the sixth grade to the eighth, there was a widening gap in average achievement between high and low I.Q. groups. In multiple regressions of eighth grade test scores on sixth grade measures, I.Q., study skills, and reading were prevalent in the regression equations, but clusters of measures associated with achievement differed between high and low’ LQ. groups. The results of the study have implications for developing and evaluating the achievement of students with varying mental abilities.